Mathematical Engineering

To present mathematical models and advanced techniques in the theory of partial differential equations, of frequent use in the applied sciences.

At the end of the course the student is expected:
1. To know the basic theory of Hilbertian Sobolev spaces: density and approximation by smooth functions, traces, compactness, embeddings, Bochner integral. The theory of the Faedo-Galerkin method and its applications. The basic theory of the fundamental differential equations in mathematical physics.
2. To be able to derive the variational formulation of the most common boundary and initial boundary value problems for stationary and evolution PDEs and analyze their well-posedness. Knowledge of some nonlinear equations such as the Navier-Stokes system, semilinear elliptic equations, conservation laws, Korteweg-de Vries equations. To be able to analyze a physical model and to set up the related partial differential equation.

1. Sobolev spaces. Definitions of the Hilbert-type spaces and their duals. Traces. Poincaré inequalities. Embedding theorems. Time dependent Sobolev spaces, the Bochner integral.
2. Elliptic equations. Variational formulation of some boundary value problems for equations in divergence form. Lax-Milgram Theorem and analysis of the well posedness. Eigenvalues and eigenfunctions. The Stokes system. Nonlinear equations: steady Navier-Stokes equations, semilinear elliptic equations, critical point theory.
3. Evolution equations. First order quasilinear equations: characteristic lines and shocks. Hilbert triples. Abstract second order evolution problems: existence, uniqueness, stability for abstract equations. Parabolic equations: weak formulation of the most common initial-boundary value problems. Weak maximum principles. Wave equation: weak formulation of the most common initial-boundary value problems.
4. Conservation laws. Models of traffic flows and fluids. Characteristics, shock waves and rarefaction waves, classical and weak solutions, existence and uniqueness. The Rankine-Hugoniot condition, entropy solutions. Solitary waves for evolution equations, basic examples. Conservation of mass, momentum, energy. The Korteweg-de Vries equations.

Prova scritta obbligatoria, senza prove in itinere
Written examination with 3 or 4 open questions exercises or applications of theoretical statements.
Optional oral examination, upon request by the teaches or by the students: possible only for those students who already reached average with the written exam. The total grade will be the average of the written and oral exam (if any). The written exam is evaluated up to 33, the students who deliver the exam and obtain a grade <12, will be "riprovato"; the students may withdraw until the very last minute before delivering. It is mandatory to sign up before the deadline, no exception will be made.

Filippo Gazzola, Advanced Partial Differential Equations for Mathematical Engineers (with exercises), Editore: Esculapio, Anno edizione: 2025, ISBN: 978-88-9385-467-2

This course provides the students with all the skills necessary to write efficient algorithms and large-scale software, so as to be able to solve complex and big data problems on parallel systems. The emphasis is on teaching concepts applicable across a wide variety of problem domains (including scientific modelling, statistics, machine learning, operations research, and quantitative finance), and transferable across a broad set of frameworks. The goal of the course is to enable students to master object-oriented and parallel programming methods that nowadays are necessary to produce software systems with industrial strength quality. The course covers Object Oriented Programming (OOP) principles, C++, and OpenMPI for parallel programming. Each topic is treated both theoretically and practically. Lab sessions allow students to acquire a good level of autonomy in learning new topics.

Knowledge and understanding (DD1):
Learn OOP principles and mechanisms through C++
Learn the core characteristics of parallel systems and MPI communication primitives
Applying knowledge and understanding (DD2):
Develop computational thinking skills to support the modelling, solution, and analysis of advanced mathematical models
Structure a problem solution through OOP methods
Develop and compare parallel algorithms
Analyze software code written by others, use software libraries
Implement advanced methods and solve or analyze mathematical models in a parallel programming framework
Develop and test code fulfilling problem requirements
Making judgements (DD3):
Identify and evaluate software architectural choices
Apply complexity methods to evaluate multiple algorithms or data structure implementations
Communication skills (DD4):
The laboratory will allow students to:
Organize code in packages and classes for readability and reuse
Compare and discuss their implementation with teammates during lab sessions
Learning skills (DD5):
Develop and structure software at large scale
Analyze and understand the goals, assumptions, and requirements associated with a problem in the scientific computing, statistics or quantitative finance domains

Description
Historically, parallel computing has been considered to be the high end of computing and has been used to model difficult problems in many areas of science and engineering. Today, commercial applications provide an equal or greater driving force in the development of faster programs. These applications require the processing of large amounts of data in sophisticated ways. Data-intensive applications such as data mining, recommender systems, financial modelling and multimedia processing have implications on the design of algorithms and provide a new challenge for the modern generation of computing platforms. Parallel processing is the only cost-effective method for the fast solution of these big data problems. The emergence of inexpensive parallel computers such as commodity desktop multiprocessors, graphic processors and clusters of entry level servers has made parallel methods generally applicable, as have software standards for portable parallel programming.
Content
T he course is structured in three parts.
The first part of the course covers modern OOP and introduces the fundamentals of the C++ programming language. C++ is used as the reference language throughout the rest of the course. Students will gain experience in designing simple but powerful object-oriented applications and in writing code using C++. Example problems cover both traditional computer science algorithms (sorting, searching, lists) as well as simple scientific computing algorithms (matrix computations, gradient descent). This initial part provides the principles for developing at-scale industry software.
The second part covers the main aspects of parallel computing: parallel architectures, programming paradigms, and parallel algorithms. Parallel architectures range from inexpensive commodity multicore desktops, to general purpose graphic processors, to clusters of computers, to massively parallel computers containing tens of thousands of processors. Students learn how to analyze and classify these architectures in terms of their components (processor architecture, memory organization, and interconnection network).
The third part of the course introduces MPI, one of the most widely used standards for writing portable parallel programs. This part includes a significant programming component in which students face concrete examples from big data and scientific domains, machine learning, and operations research.
During lab sessions, students are invited to discuss their code with teammates, tutors and the instructor and to identify pros and cons of their implementation with respect to the ones provided as solutio. The laboratory sessions will be supervised by the course instructors and by some tutors.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
Valutazione continua facoltativa (a scelta dello studente)
The assessment will be based on a written exam at the end of the course. The elements that will be considered in the assessment activities are the followings:
Written test - Exercises focusing on design aspects
Design of data structures and algorithms
Identification and evaluation of alternative algorithms to solve a given problem
Definition of the high-level architecture and main classes for a software system according to the OOP paradigm
Definition of code fragments in C++ and in OpenMPI for parallel programs
Students can also earn some additional points (up to 3) in the final evaluation by submitting their solutions to three challenging problems that will be assigned during the course.

Official web site https://webeep.polimi.it/
Stanley B. Lippman, Jos©e Lajoie e Barbara E. Moo, C++ Primer, Editore: Addison-Wesley, Anno edizione: 2012, ISBN: 9780321714114
Note: Used also within ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING course
Peter S. Pacheco, An Introduction to Parallel Programming http://www.amazon.it/Introduction-Parallel-Programming-Peter-Pacheco/dp/0123742609
Bjarne Stroustrup, Programming - Principles and Practice Using C++, Anno edizione: 2014, ISBN: 978-0321-992789

The course educates students to become professional data scientits by reviewing several statistical models, methods and algortihms aimed at the statistical analysis of mutivariate data. The aim is twofold: first, to provide future data scientists with the mathematical knowledge and understanding necessary for making proper judgments when selecting appropriate methods and algorithms, producing sensible interpretations of the results generated by their application and grasping their strenghts and weaknesses and, second, to enhace the students ability in applying the knowledge and understanding of the statistical approach to data analysis by emphasizing real life and engineering applications where statistical methods and modern computer packages permit to elicit information from multivariate data through complex statistical analyses.
The course is offered in two versions, for 8 CFU and 10 CFU respectively. Both versions are named Applied Statistics and are described in the present document. In the 8 CFU version, the course will cover classical topics of Multivariate Data Analysis (e.g.: dimension reduction, inference for regression, supervised and unsupervised classification) with overtures to the modern treatment of multiple inference (FDR) or to novel statistical learning methods and algorithms (e.g. support vector machines, ensemble leraning methods). To these contents, the 10 CFU version of the course adds three modules of Advances in Statistical Learning, leveraging on seminars offered by experts of the fields (e.g.: Linear Mixed Models, Functional Data Analysis, Spatial Statistics).
Through an extensive recourse to blendend learning and flipped classroom innovative teaching, both during the lectures and the lab sessions, the course will enahace the students ability in autonomous learning; this will also be accomplished by perusing new teaching media like the MOOC on Statistical Learning by Hastie and Tibshirani referenced in the Bibliography.
Particular emphasis is given to the devolopment of a responsible and efficient attitude toward work in a multidisciplinary environment where the data scientist collaborates on a peer-to-peer basis with other engineers and scientists for the modeling and understanding of complex phenomena of scientific or industrial interest. Hence, the course requires team work on real data statistical analyses, either in interaction with industrial partners of the statistical research group of the Department of Mathematics or in collaboration with scientists and engineers demanding a data-driven approach to the solution of their research problem. Work-in-progress of the teams will be periodically discussed in class, drawing attention not only on the appropriatness of the statistical methods and algorithms, but also on the communication skills of the teams when informing an audience of peers.
The course fits into the overall program curriculum pursuing some of the defined general learning goals. In particular, the course contributes to the development of the following capabilities:
Design models and utilize information from experimental data for inferential estimation, verification and adaptation of the models and for their heuristic developments;
Provide the statistical interpretation and simulation of scenarios for the treatment of data in situations of high complexity;
Use R for the analysis and treatment of complex data.

Both versions of the course have the following common learning goals:

• At the end of the course students are expected to be able to design - and run with R - data analyses aimed at: reducing the dimensionality of a dataset, solving a classification problem, both supervised or unsupervised, making multiple inference on multiple mean vectors or their components, choosing the most appropriate regression model and fitting it while making inference on its components, handling classical (OLS) or more modern approaches to model building and selection (ridge regression and lasso). Leveraging on their engineering forma mentis and on the skills in data analysis acquired in the course, students are expected to be able to evaluate the practical and statistical significance of the final result of their data analysis, to quantify its uncertainty analytically or through simulation, e.g. by cross-validation, and to diagnose its potential shortcomings, either when used to provide an empirical explanation of the industrial or scientific problem under study or when the main goal of the analysis is to formulate predictions.
• To prepare for responsible and efficient interactions in a working environment, every student is required to take part in a real data analysis project developed by an independently formed team of 3-5 members. The work in progress of the projects will be collectively discussed during general meetings scheduled along the course; final analyses and results will be presented in a workshop which will take place at the end of the course.
• Students are expected to be able to communicate and transfer the results and interpretations of their data analysis to a wider audience of experts, using effective graphical or analytical means, suitable for the problem under study, the findings of the analysis and, finally, the audience.
  Moreover, the students of the 10 CFU version of the course are expected to have a basic understanding of the more complex issues - and the methods and algorithms developed to solve them - characterizing the statistical analysis of data when heterogeneity and temporal or spatial dependence is of importance or when data do not belong to the finite dimensional Euclidean setting considered in the classical Multivariate Data Analysis framework, like in the case of functional data.

The topics covered by the 8 CFU version of the course are the following:
1) The essence of statistical learning. The regression function: local methods and the curse of dimensionality. Structured models. Test error, training error and expected test error. The bias variance tradeoff. Generalization error and Expected generalization error. Bias-variance tradeoff.
2) Exploring a multivariate dataset: descriptive statistics and graphical displays. The geometry of a multivariate sample. Generalized Variance. The metric induced by the covariance matrix.
3) Data representation and dimensional reduction: the analysis of the covariance structure, principal component analysis. Independent component analysis.
4) Inferences about a mean vector: Hotelling T^2 test. Confidence regions and simultaneous comparisons of component means. The Bonferroni method for multiple comparisons. Familywise Error Rate and False Discovery Rate. Comparisons of several multivariate means. ANOVA and MANOVA. Inference for Linear Models. Beyond Ordinary Least Squares: ridge regression, lasso, regularized least Squares. Cross-validation and model selection. Ensemble learning methods: random forests for regression and classification.
5) Discrimination, classification, clustering. Statistical classification: model, misclassification costs and prior probability. Bayesian supervised classification and the Fisher approach to discriminant analysis. Alternative approaches to classification: support vector machines and CARTs. Similarity measures. Unsupervised classification; hierarchical and nonhierarchical methods. Multidimensional scaling.
In the 10 CFU version of the course, the above topics are complemented with the following three modules of Advances in Statistical Learning:
6) Linear Mixed Models. Enriching the covariance structure of a linear model to take into account heteroschedasticity and dependence, random effects, hierarchical grouping structures, longitudinal data.
7) Functional Data Analysis. Data smoothing, dimensional reduction and representation. Functional principal component analysis. Data registration: phase and amplitude variability. Classification of functional data.
8) Spatial Statistics. Random fields, variogram models and variogram fitting. Spatial prediction and Kriging, Functional data with spatial dependence.
In both versions of the course, methods and algorithms will be illustrated in the lab sessions through applications to real data sets; analyses will be performed in R, an opensource package for the statistical analysis downloadable at www.r-project.org.
Through the course, students are required to work in team on a real data analysis project whose progress will be shown periodically to the class.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of two parts:
(a) A written exam. The written exam consists of questions (theory and practice) and of a few data analysis problems to be individually solved with R; two problems for the students following the 8 CFU versions of the course, three problems - with extra time - for those registered in the 10 CFU version. For the students taking the course for 10 CFU, the extra problem will be related to the three advanced topics treated in the modules characterizing their additional 2 CFU; working on this problem is mandatory to pass the exam of the 10 CFU version of the course. For all students, the use of a personal computer is allowed as well as that of books, personal notes etc.
In the written exam the student must show the ability to conduct a stylized data analysis, by selecting the appropriate methods and algorithms - among those introduced in the course - for solving the problems, by running the algorithms with R, by identifying the significant results and by reporting them with the precision and property of language which characterize the technical and scientific communication.
(b) Team project evaluation. Projects will be collectively evaluated by the teachers of the course and by the students participating to a final workshop at the end of the course.
During the presentation of their projects, teams must prove their ability to conduct and report a real life statistical data analysis, showing knowledge and understanding of the problem at hand and the nature of the data, proper judgment for the selection of the appropriate methods and algorithms, sensible interpretations of the generated results - grasping not only their strenghts but also their weaknesses - and, finally, communication skills when informing an audience of peers.
To pass the exam the student must pass each part of the exam with a score greater than or equal to 18/30; the final score is then obtained as the weighted average of the two scores, with weights respectively equal to 0.6 for the written exam and 0.4 for the project evaluation.

Galecki A., Burzykowski T., Linear Mixed-Effects Models using R, Editore: Springer, Anno edizione: 2013
Jhonson R.A., Wichern D.W., Applied Multivariate Statistical Analysis, Editore: Prentice Hall, Anno edizione: 2007
Ramsay, J.O. e Silverman, B.W., Functional Data Analysis (second edition), Editore: Springer, Anno edizione: 2005
Cressie, N., Statistics for Spatial Data (Revised Edition), Editore: Wiley, Anno edizione: 1993

From theory to practice in finance. The course presents with a case-study approach some significant examples where a financial engineer could provide a relevant contribution:
Credit Risk: single-name and multi-name products;
Quantitative Risk Management (RM): from RM measures to RM techniques;
Structured products: calibration, valuation and some hedging issues.
This teaching includes a version of 10 cfu, which is linked to a joint-course teaching by 8 cfu called FINANCIAL ENGINEERING (course 052505). This form defines objectives, programs and learning outcomes expected for both courses.

Both versions of the course have the following common learning goals:
1. to know and to understand

• fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);
• their limits of applicability;
• some risk management techniques;
• single name and multi-name credit problems and models;
• main structured product typologies.
  2. to apply this knowledge on some "Quantitative Case Studies" via the
• valuation of the relevant financial quantities (e.g. Net Present Value of some financial portfolios, risk measurement);
• calibration of underlying models;
• selection of an adequate risk management instrument/trading strategy.
  It is expected an understanding by the student not limited to the definitions, the main results and the solution of standard exercises, but a critical knowledge able to discriminate different financial situations and a conscious model selection, justifying the chosen approaches.
  Moreover the student should obtain correct solutions, explain adequately the codes, and expose properly the theory.

0. Basic derivatives’ concepts

• Forward & option: Exchange-traded Markets vs OTC markets, Forward vs Futures. Forward Price: deduction via a no-arbitrage argument. European Option (Call/Put): decomposition in Intrinsic Value & Time Value; Put Call Parity. CRR & Black Model and examples. Monte-Carlo technique.
• Main Greeks: Delta, Gamma, Vega e Theta. Volatility Smile.
• Basic Interest Rate (IR) instruments: Fundamental year-fractions in IR Derivatives. Depos, Forward Depos, FRA, STIR Futures, IR Swaps & Fwd Swap, Cap/Floor, Swaptions, “InterBank Floaters”.
• IR bootstrap. Sensitivities: BPV, DV01 and duration. For a linear portfolio, sensitivity analysis and hedging of IR risk with IRS.
  1. Credit Risk
• Introduction to credit risk.
• Basic FI instruments in presence of Credit Risk: Fixed Coupon Bond, Floater Coupon Bond, Asset Swap, CDS. SPOL, CDS, ASW relations. Bootstrap Credit Curve.
• Firm-value (Merton, KMV calibration, Black-Cox) & Intensity Based Models (Jarrow & Turnbull, inhomogeneous Poisson).
• Multiname products (ABS, MBS, CDO) and models for HP and LHP (Vasicek).
• O'Kane & Schloegl model, double t-Student, General Threshold Model.
• Copula approach and Li model with examples (Archimedean and Gaussian Copulas).
• Implied Correlation in CDO trances.
  2. Quantitative Risk Management
• Basel Accords, Risk Management Policy.
• VaR/ES: examples, Variance-Covariance method, Historical Simulation, Weighted Historical Simulation, Bootstrap, Full valuation Monte-Carlo, Delta-normal & Delta Gamma method, plausibility check, scaling rule.
• Coherent measures: assioms, VaR subadditivity (counterexample, elliptic case), ES coherence.
• Backtest VaR: Base approach, unconditional backtest, conditional backtest. [Only for 10 cfu version]
• Capital Allocation: Euler Principle & Contribution to VaR & ES.
  3. Structured products main typologies with examples
• Certificates, Equity and IR Structured bond: the general Monte-Carlo approach for pricing non-callable structured products. Callable & Autocallable products.
• Deal structuring and Issuer hedging.
• Digital Risk: Slope impact & Black Correction in Autocallable products, FFT technique. Lewis formula for option pricing and analytic strip via an example: Exponential Levy model (NIG & VG). Global calibration and pricing via a Monte-Carlo (NIG & VG). Sticky Strike & Sticky Delta. Parsimony and smile symmetry.
• IR products and models: plain vanilla and exotics. HJM models: Main equation under Risk Neutral measure. Equivalence with a ZC bond approach and Fundamental Lemmas. Main examples:
  o Market models: forward measure and application in the general derivative premium case. LMM and caplet solution. Calibration: Flat Vol vs Spot Vol in Cap/Floor markets.
  o Hull White model (Extended Vasicek): Cap/Floors solution, Bond Options & Swaptions exact solution. Calibration issues. Pricing: Trinomial Tree Construction.
  The 10 cfu version of the course (course 052500) uses some "Innovative teaching methods" designed and realized in collaboration with the financial industry (most of these methods are not included in the 8 cfu version, course 052505). Often this teaching methodology uses some "Quantitative Case Studies" that present some concrete problems for a financial institution, but simplified in order to be treated in a classroom. This approach requires the student to propose and realize quantitative solutions within a group (composed by 3 to 5 students) and with strict time constraints.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The are five possible examination appeal dates, established in the academic calendar (two in June/July, one in September, two in January/February). Each exam appeal is composed by a written part and an oral part.
In the written part, the student is required to write:

• Matlab codes that solve some financial engineering problems;
• a document describing the chosen methodology, numerical results and problems/criticalities (if present).
  The written and the oral part contribute to the final score with the same weight (15/30).
  The examination appeal for the 8 cfu version, called FINANCIAL ENGINEERING (course 052505), does not include arguments specific of the 10 cfu version (both in the written and oral part).
  The examination has the objective to verify whether the student has acquired the following skills:
  1. The knowledge of
• fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);
• their limits of applicability;
• some risk management and quantitative finance approaches;
• single name and multi-name credit problems and models.
  2. The ability in applying the acquired knowledge in the computational/mathematical approaches for the
• calibration of financial models from real datasets;
• valuation/risk measurement/risk management of portfolios of elementary/structured products in presence of market and credit risks.

A. J. McNeil, R. Frey & P. Embrects, Quantitative Risk Management: Concepts, Techniques and tools, Editore: Princeton University Press, Anno edizione: 2005, ISBN: 0691122555
Note: Risk Management
P.J. Schonbucher, Credit Derivatives Pricing Models, Editore: Wiley, Anno edizione: 2003, ISBN: 0470842911
Note: Credit Risk
J. Hull, Options, futures and other derivatives, Editore: Pearson Prentice Hall, Anno edizione: 2009, ISBN: 0136015867

The goal of the course is to introduce the language of groups and their representations. After discussing basic notions of group theory, we will treat Lie groups, Lie algebras, and their representations, focusing on several examples of classical groups, following the elementary "matrix approach".

The student is expected to master the fundamental topics of group theory and their representations, in particular:
groups, subgroups, group actions
classical examples of finite groups and matrix groups
Lie groups and Lie algebras
exponential and logarithm for matrices
representations, operations with representations, irreducible representations
The student is expected not only to learn definitions and results, but also to be able to apply the knowoledge in a critical way to solve exercises and problems.
Explicit overview of relevant Dublin Descriptors for this course:
DD1- Knowledge and understanding. The lessons and exercise sessions aim to allow the student to develop a deep understanding of the fundamentals of group theory and representation theory, and to understand the connections among the different concepts treated in the course. The student will also learn to give a coherent exposition of the theory.
DD2- Applying knowledge and understanding. The lessons and exercise sessions aim to allow the student to develop problem solving skills, allowing them to solve exercises and problems related to the topics of the course.

General group theory. Definition of group. Abelian groups. Examples. Symmetric groups. Subgroups. Generators. Cyclic groups. Homomorphisms. Direct product. Cayley’s theorem.
Lie groups. Matrix Lie groups. The classical Lie groups. Lie group homomorphisms. Connected and compact groups. Analysis of some Lie groups of small dimension.
Matrix exponential. Matrix exponential. Matrix logarithm. Lie product formula. One parameter subgroups.
Lie algebras. The Lie algebra of a Lie group. Lie algebras of the classical Lie groups. The Lie group - Lie algebra correspondence. Geometric interpretation. The exponential map for connected groups.
Representation theory. Group actions. Representations of groups and algebras. Representations in the Lie group - Lie algebra correspondence. Irreducible representations. Complete reducibility. Representation theory of SL(2; C). Schur’s Lemma. Discussion of SO(2), SU(2), SO(3).

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The final exam consists of a test in which the student is asked to answer questions in written form, and then discuss the answers orally with the instructor.

Brian Hall, Lie Groups, Lie Algebras, and Representations, Editore: Springer
Note: Freely available version on arXiv:
https://doi.org/10.48550/arXiv.math-ph/0005032
John Stillwell, Naive Lie Theory, Editore: Springer, ISBN: 978-0-387-78214-0
Note: Free online access provided by Politecnico di Milano
Peter Woit, Quantum Theory, Groups and Representations, Editore: Springer
Note: Freely available version on author's personal webapge:
https://www.math.columbia.edu/woit/QM/qmbook.pdf

LASER AD ALTA INTENSITA' PER APPLICAZIONI NUCLEARI E FISICHE I L'insegnamento si propone di fornire innanzitutto una solida conoscenza sui laser e sulle proprietà dei fasci laser, con particolare attenzione agli aspetti legati al regime ad alta intensità. Argomenti (in sintesi): richiami di elettromagnetismo; risonatori e fasci gaussiani; assorbimento, decadimento spontaneo, emissione stimolata della luce; regime continuo e impulsato dei laser; materiali attivi per alte energie.

The aim of the course is twofold.
In the Insurance module, students are introduced to actuarial mathematics and learn models and methods used to price insurance contracts and analyse insurance portfolios, both in the life and non-life insurance cases.
In the Econometrics module, students are equipped with the skills needed to thoroughly and appropriately model, analyse, and forecast financial time series.

Lectures and computer laboratory sessions allow students to acquire the following competences.

• Knowledge and understanding.
  Students know the main models and methods used in actuarial mathematics, both in the life and in the non-life insurance cases.
  Students understand the main concepts of statistics and econometrics used to analyse and forecast financial time series.
• Ability to apply knowledge and understanding.
  Students can apply the models and methods of actuarial mathematics to price life insurance benefits, and to model and analyse insurance portfolios to guarantee profitability and solvability of insurance companies.
  Students can analyse in a proper way a financial time series.
• Making judgements.
  Students can judge the main risks in insurance contracts and quantify their impact on insurance portfolios.
  Students can find proper modelling assumptions to analyse and forecast financial time series.
• Communication skills.
  Students are able to express mathematical and financial concepts in a clear and rigorous way.

Actuarial mathematics.
Life insurance: survival models, life tables, pricing of insurance benefits and annuities, reserves, modelling life insurance portfolios, Solvency II regulation.
Non-life insurance: collective risk models for general insurance portfolios, premium calculation principles, the Cramér-Lundberg model.
Econometrics.
Financial time series; stationary processes and selection, estimation, and forecasting of ARMA models; unit root processes, vector autoregressive (VAR) models, and key concepts such as Granger causality and cointegration (Engle and Granger theorem); discrete-time models for heteroskedasticity, including ARCH and GARCH.
Throughout the course, numerous applications to financial market time series are discussed, including volatility estimation and topics in green finance.
Computer laboratory sessions are an integral part of the course. Two group project works, one for each module, are assigned during the semester and evaluated at the end of the course.

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The evaluation consists in two project works, one for the Insurance module and the other one for the Econometrics module, and an oral exam.
Project works need to be carried out in groups. Students are expected to apply the models and methods taught in class to actual case studies and real-world data, and to develop teamworking skills.
Project works are assigned during the semester and specific deadlines for submission are communicated in due time, for each of them.
Project works are evaluated at the end of the course, each on a scale 0-12, based on the submitted documents (report, MATLAB or R code, etc.). Students are required to show:
Knowledge and understanding of actuarial mathematics models and methods and the Solvency II regulation;
The ability to price insurance contracts and to analyse the profitability of an insurance company;
The ability to discern and analyse the main sources of risk of insurance portfolios;
Knowledge and understanding of econometrics models and methods, time series volatility modelling and cointegration, and multivariate time series models;
The ability to properly analyse and forecast financial time series;
The ability to express mathematical and financial concepts in a clear and rigorous way.
The oral exam is individual, distinct for the Insurance and the Econometrics modules, each evaluated on a scale 0-20. The oral exam can be taken only during official exam sessions; a midterm oral exam will also be scheduled.
The oral exam consists of three questions for each module on the whole program of the course. To pass the oral exam, students must correctly answer to two questions for each module.
Students are expected to show:
Knowledge and understanding of the models and methods taught in class;
The ability to prove in a rigorous way the results discussed during lectures;
The ability to interpret the concepts from an actuarial and/or financial perspective;
The ability to apply the acquired knowledge to examples and case studies;
The ability to express mathematical and financial concepts in a clear and rigorous way.
The final grade of each module, on a scale 0-32, is given by:
Insurance module: sum of project work (0-12) and oral exam (0-20);
Econometrics module: sum of project work (0-12) and oral exam (0-20).
The exam is passed if and only if the grade of each module is 16 or higher and their arithmetic average, denoted by AVG, is 18 or higher. In this case, the final grade of the exam is:
AVG/30, if AVG is between 18 and 30;
30/30, if AVG is higher than 30; in this case, the teachers may award the grade 30/30 cum laude, at their own discretion.
The grades of the project works and of the midterm exam are valid up to the last exam session for this edition of the course (January-February 2027); they are erased afterwards.
If during an exam session only one of the grades of each module is 16 or higher, then the student may retain that grade for the next exam sessions, up to the last one for this edition of the course (January-February 2027); it is erased afterwards.

D. Dickson, M. Hardy and H. Waters, Actuarial Mathematics for Life Contingent Risks, Editore: Cambridge University Press, Anno edizione: 2020, ISBN: 978-11-08-47808-3 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma99632799908776
H. Schmidli, Risk Theory, Editore: Springer, Anno edizione: 2017, ISBN: 3-319-72005-8 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma99590686508776
A. Olivieri and E. Pitacco, Introduction to Insurance Mathametics, Editore: Springer, Anno edizione: 2015, ISBN: 9783319213774 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/fpq6t9/cdi_askewsholts_vlebooks_9783319213774
H. Schmidli, Stochastic control in insurance, Editore: Springer, Anno edizione: 2008, ISBN: 1-281-13740-5 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma9948777108776
Brooks, Chris., Introductory econometrics for finance., Editore: Cambridge university press, Anno edizione: 2019, ISBN: 978-0-13-348686-2
R. Tsay, Financial Time Series, Editore: Wiley Finance

The aim of the course is to present the methodological foundations of arbitrage theory in continuous time and to provide students with the main mathematical models and methods used in modern quantitative finance. These will be applied to describe financial markets from a mathematical point of view, to tackle the problem of pricing financial derivatives, and to construct hedging strategies.

Students are expected to acquire the following competences.
Knowledge and understanding.
Students know the main models and methods used in modern mathematical finance.
Students understand the main techniques used to price financial derivatives and construct hedging strategies.
Students understand the assumptions of arbitrage theory in continuous time, the advantages and drawbacks of each model, and the differences between them.
Ability in applying knowledge and understanding.
Students are able to apply the models and methods used in modern mathematical finance to correctly price financial derivatives and to construct hedging strategies.
Students are able to select the most appropriate model to solve a financial problem.
Students are able to apply the general theory to derive analytical results starting from a given model.
Students are able to correctly interpret the results obtained in the solution of a problem, from the theoretical, numerical, and financial points of view.
Making judgements.
Students can judge which model and/or method is more suited to solve a financial problem.
Students can judge the main advantages and limitations of the studied models, both from a mathematical and a financial point of view.
Communication skills.
Students are able to express mathematical and financial concepts in a clear and rigorous way, both in written and in oral form.

• Introduction. Financial markets and financial derivatives. Review of basic financial principles.
• Discrete-time models. Portfolios and arbitrage opportunities. First and second fundamental theorems of asset pricing. Risk-neutral valuation of financial derivatives and hedging strategies. No-arbitrage option inequalities. Put-call parity.
• Portfolio dynamics in continuous-time. The classical Black & Scholes model. Derivation of the Black & Scholes equation via no-arbitrage arguments. Probabilistic representation via the risk-neutral measure. Valuation formulae for simple contingent claims, European options, forward and futures contracts, options on futures. Dynamic hedging of simple contingent claims. Volatility estimation. Greeks. Buy-and-hold strategies.
• The multidimensional Black & Scholes model. Derivation of the Black & Scholes equation via no-arbitrage arguments. The market price of risk vector. Probabilistic representation via the risk-neutral measure. Valuation formulae for simple contingent claims. Dynamic hedging of simple contingent claims.
• The Black & Scholes model for dividend-paying assets.
• Currency derivatives and quanto products. The Garman-Kohlhagen model.
• Valuation of exotic derivatives in the Black & Scholes model.
• The optimal stopping problem. Discrete-time formulation, the backward recursion algorithm, characterization of the value function via the Snell envelope. Continuous-time formulation, the variational inequality and the free boundary problem. Valuation of American options.
• The martingale approach to arbitrage theory. A general market model. Equivalent martingale measures. The first and second fundamental theorem of asset pricing. Absence of arbitrage and completeness of the Black & Scholes model. Change of numéraire.
• Incomplete markets. Calibration to market data.
• (Only for 10 ECTS exam) Interest rate models. General facts on interest rates and valuation of fixed-income derivatives. Short-rate models, affine models and affine term structures. The Vasicek, Ho-lee, Cox-Ingersoll-Ross, Hull and White Models. The Heath-Jarrow-Morton framework to model forward rates. The LIBOR market model. Valuation of Caps, Floors and Swaptions.
  Exercise sessions will be devoted to the application to the valuation of financial derivatives and hedging problems of the models and methods discussed in class, both from a theoretical and algorithmic point of view.
  In laboratory sessions students will discuss and implement in MATLAB, with a hands-on approach, the numerical valuation of derivatives in the Black & Scholes model, the bootstrap method and the numerical valuation of interest rates derivatives.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
The exam includes two assignments, a written and an oral exam.
Assignments.
The two assignments are small group works based on computer laboratory sessions, which will be devoted to the valuation of plain vanilla derivatives and to interest rate models. They are mandatory only for the 10 ECTS exam. Deadlines are communicated during the course. The overall grade for assignments is on a scale 0-3.
Written exam.
The written exam is based on exercises and applications of mathematical finance, with some aspects of the general theory. It is evaluated on a scale 0-30. Students are expected to show knowledge and understanding of the concepts taught during the course, the ability to rigorously apply stochastic calculus in the context of mathematical finance, to perform an appropriate valuation of financial derivatives, to correctly apply models and methods of mathematical finance to solve problems, to adequately intepret the results obtained.
Oral exam.
The oral exam is based on the whole program of the course. The oral exam can be taken only if the sum of the assignments and the written exam grades is 18 or higher. The oral exam is evaluated on a scale 0-33, with grades in the interval 31-33 assigned only in case of exceptionally brilliant exams.
Students are expected to show knowledge and understanding of the concepts taught during the course, the ability to rigorously prove mathematical statements, to provide the correct financial interpretation of the results, and to present adequate examples to illustrate the concepts.
Final grade.
The exam is passed if and only if the arithmetic average, denoted by AVG, between the sum of the assignments and the written exam grades, and the oral exam grade, is 18 or higher. In this case, the final exam grade is:

• AVG/30, if AVG is between 18 and 30;
• 30/30, if AVG is higher than 30; in this case, the teacher may assign the grade 30/30 cum laude, at his own discretion.

T.Bjork,, Arbitrage theory in continuous time, Editore: Oxford University Press, Anno edizione: 2009 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
E. Rosazza Gianin, C. Sgarra, Mathematical finance: theory review and exercises, Editore: Springer, Anno edizione: 2013 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
M. Musiela, M. Rutkowski, Martingale methods in financial modelling, Editore: Springer, Anno edizione: 2005 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
S. E. Shreve, Stochastic Calculus for Finance I. The Binomial Asset Pricing Model, Editore: Springer, Anno edizione: 2004 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99902417508776
S. E. Shreve, Stochastic Calculus for Finance II. Continuous-Time Models, Editore: Springer, Anno edizione: 2004 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99915720808776
J. Hull, Options, futures, and other derivatives, Editore: Pearson, Anno edizione: 2022 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99915720808776
D. Filipovic, Term-structure models, Editore: Springer, Anno edizione: 2009 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99926232908776

Aims and scope
The course aims to derive the macroscopic properties of gaseous systems starting from
their microscopic (molecular dynamics) analysis.
In this perspective, analytical and numerical methods for the solution of kinetic equations
are presented.

Knowledge and understanding
At the end of the course the students are expected to:
-know the basic mathematical properties of the Boltzmann and related kinetic equations
-be able to solve kinetic equations both analytically and numerically
-be able to model various problems in science

Program
1-Introduction to Statistical Mechanics

• The postulate of classical statistical mechanics.
  -Microcanonical Ensemble.
  -Canonical Ensemble.
  -Grand Canonical Ensemble.
  2-The Boltzmann equation
• Derivation (Lanford Theorem). Existence of solutions (Diperna-Lions Theorem).
  -The BBGKY Hierarchy.
  -Elementary properties of the collision operator.
  -Boundary conditions and the gas-surface interaction.
  -The H-Theorem and the problem of irreversibility.
  -Kinetic Models.
  3-Methods of solution of the Boltzmann equation
• Variational Methods.
  -Transformation into Integral Equations.
  -Numerical methods.
  4-Quantum kinetic equations
  -The Boltzmann-Nordheim equation.
  -Equilibrium states and the H-Theorem.
  -Quantum BBGKY-like Hierarchies.
  -Kinetic theory of Bose-Einstein condensation.
  5-Application of the Boltzmann equation to Microfluidics
• Analytical and numerical investigation of microchannel flows (Poiseuille, Couette and
  Thermal-Creep problems; sound waves propagation).
  -Slip boundary conditions for the Navier-Stokes equations.
  -Kinetic modeling of gas mixtures.
  6-Mathematical Models and Methods in Micro-Nano-Technologies
  -Characterization of Micro-Electro-Mechanical Systems (MEMS) devices.
  -Analysis of damping forces in low-frequency and radio-frequency MEMS devices.
  7-Kinetic equations for Biomedical applications
  -The Smoluchowski equation.
  -Two-scale homogenization.
  -Mathematical models of neurodegenerative diseases.

Prova scritta facoltativa (a scelta dello studente), senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Examination
The final exam consists either in an oral discussion on the whole program,
or in a written project in which one of the topics, dealt with during the course,
is investigated thoroughly.

Kerson Huang, Statistical Mechanics, Editore: John Wiley & Sons, Anno edizione: 1987, ISBN: 978-0-471-81518-1
Carlo Cercignani, The Boltzmann Equation and Its Applications, Editore: Springer-Verlag, Anno edizione: 1988, ISBN: 3-540-96637-4
Carlo Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations, Editore: Cambridge University Press, Anno edizione: 2000, ISBN: 0-521-65992-2

The goal of the course is to enable students to extract (“learn”) from measured data useful information. The course covers advanced topics of data-driven black-box system identification and virtual sensing, with focus on dynamical systems. Examples of AI-based variable estimation are presented.

Through theoretical lectures and numerical-exercises sessions, the students are expected to:
Understand the fundamental problems that can be encountered while extracting information from a finite set of observations taken from an unknown system [Dublin Descriptor 1]
Learn the main tools of system identification and virtual sensing. [DD1, DD2]
Be able to formulate identification problems corresponding to different applications. [DD3, DD5]
Understand a range of algorithms along with their strengths and weaknesses. [DD1, DD3]
Be able to apply suitable algorithms to solve application problems. [DD2, DD3]
Be able to read current research papers and understand the issues raised by current research in the field. [DD5]

The program of the course is as follows.
Non-parametric system identification: the subspace-based state-space approach
Frequency domain parametric identification of models from data
Kalman Filter: prediction, virtual-sensing and gray-box system identification
Analysis and design of closed-loop systems using the minimum-variance approach
Non-linear system-identification and SW-sensing: parametric nonlinear fitting; N-ARMAX models; Examples of AI-based variable estimation are presented.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i condizionato (a scelta del docente), di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The exam will be a written test in one of the official available dates. The exam will consist of both theoretical questions and simple (i.e., no computer-aided) exercises. The final marks will be awarded based on correctness of the answers, appropriateness of technical terminology, and clarity of exposition.
The written exam is designed to assess the achievement of the following Dublin Descriptors:
DD1 – Knowledge and understanding: students will be required to demonstrate a solid understanding of the theoretical foundations of system identification and data-driven modeling, including stochastic modeling, parametric and non-parametric identification methods, and the main issues arising when extracting information from finite data sets, together with the corresponding countermeasures.
DD2 – Applying knowledge and understanding: students will be asked to apply suitable identification, estimation, and analysis methods to solve system-identification problems of moderate complexity, through analytical reasoning and simplified exercises, and to correctly interpret the obtained results.
DD3 – Making judgements: students will be evaluated on their ability to critically analyze an identification problem, to select and justify the most appropriate modeling and identification tools for a given application, and to discuss the strengths and limitations of alternative approaches.
DD5 – Lifelong learning skills: through questions requiring synthesis and critical interpretation, students will demonstrate their ability to reason on advanced methodologies and to frame specific problems within a broader system-identification context, showing the conceptual tools needed to approach new methods and current research literature.

Sergio.M. Savaresi, Lecture notes
Sergio Bittanti, Model Identification and Data Analysis, Editore: Wiley, Anno edizione: 2019
P. van Overschee, B.L. de Moor, Subspace Identification for Linear Systems: Theory, Implementation, Applications, Editore: Kluwer Academic Publishers, Anno edizione: 1996 ftp://ftp.esat.kuleuven.be/pub/SISTA/ida/reports/96-26a.pdf
Note: Freely available online.
L. Ljung, System Identification: theory for the user (II ed.), Editore: Prentice-Hall, Anno edizione: 1999
T.S. Soderstrom, P.G. Stoica, System Identification, Editore: Prentice-Hall, Anno edizione: 1989

Main Objectives: The aim of this course is twofold: firstly, to comprehensively address multidimensional finite element analysis for Partial Differential Equations (PDEs) stemming from a wide range of applications in Science and Engineering; secondly, to sustain the theoretical analysis with computer laboratory sessions. The course includes substantial hands-on involvement in a course project drawn from Engineering and Applied Science applications.
Complementary Objectives: The complementary objective of the course is to train students in the ability

• to employ advanced simulation techniques for the numerical approximation of a broad spectrum of PDE models;
• to employ a widely-used programming language, such as MATLAB, for algorithm development and numerical computations.
  Blended learning and flipped-class innovative teaching methods will be employed to enable students to develop a good level of autonomy in learning new topics and to improve specific communication and soft skills, such as problem-solving and teamwork.
  Throughout the course, students are stimulated to:
• develop specialised knowledge on numerical methods for the approximate solution of Partial Differential Equations stemming from a wide range of Science and Engineering applications (Dublin Descriptor 1);
• analyse, implement, and apply numerical algorithms for PDEs and critically interpret the results (Dublin Descriptor 1, Dublin Descriptor 2);
• select the most appropriate technique and critically use advanced simulation tools by motivating the choices made (Dublin Descriptor 3, Dublin Descriptor 4, Dublin Descriptor 5).

According to the Dublin Descriptors (DD), the expected learning outcomes are the following.
Lectures and computer labs will allow students to:

• develop a broad and deep knowledge of numerical methods for Partial Differential Equations (DD1);
• understanding and mastering the theoretical properties of numerical methods and algorithms for solving various mathematical problems arising in Science and Engineering (DD1);
• critically apply advanced numerical models to mathematical problems stemming from real-world engineering applications independently of their own field of specialization (DD2);
• motivate the choice of the adopted methods and tools (DD2, DD3);
• critical interpretation of the results obtained in the light of the theory through the implementation of the algorithms using the Matlab software (DD2, DD3);
  The course project will allow students to:
• improve and integrate higher-order thinking skills: critical thinking, problem-solving, communicative and working group skills (DD3, DD4, DD5);
• analyze critically the obtained numerical results (DD3);
• summarize and present the results achieved during the project activities (DD4);
• write a scientific document (DD4).

Lectures. The lectures will cover the following topics:

• Multidimensional diffusion problems: the multidimensional Poisson problem and general elliptic problems; the Lax-Milgram lemma; Galerkin approximation; Galerkin orthogonality; abstract stability and convergence analysis; the Finite Element Method (FEM): formulation, stability, error estimates, and implementation details. The discontinuous Galerkin (DG) method: formulation, stability, error estimates, and implementation details. Spectral and Spectral Element Methods (SEM): formulation, stability, error estimates, and implementation details. Spectral and Spectral Element Methods with numerical integration (SEM-NI): formulations, stability, error estimates, and implementation details.
• Multidimensional advection-diffusion problems: limits of the Galerkin method for convection-dominated problems; stabilized finite element schemes; the generalized Galerkin formulation; the artificial diffusion and the upwind schemes; strongly consistent stabilized methods; stability and convergence analysis for the GLS scheme; stabilization based on bubble functions (hints).
• Multidimensional heat equation: the semi-discrete formulation; the theta-method; a priori estimates; convergence analysis for the semi-discrete form; stability analysis for the fully discrete formulation; convergence result for the fully discrete problem.
• Stokes equations: weak formulation; well-posedness of saddle-point problems; Galerkin approximation of saddle-point problems; stability and convergence analysis; inf-sup stable finite element spaces; algebraic formulation.
• Linear elasticity: weak formulation, the locking phenomenon, compatible finite element discretizations. Hints of the theoretical analysis.
• Wave propagation problems: weak formulation of the scalar wave equation, Galerkin approximation, Finite Element, Spectral Element, DG methods for the space discretization of the scalar wave equation, main theoretical results. Time integration scheme and theoretical results for the fully-discrete formulation. The elastodynamics equation (hints): semi-discrete and fully-discrete formulations,
• Domain Decomposition methods: Schwarz and Schur paradigms. Parallel preconditioners. Theoretical results. Optimality and scalability for parallel computing.
  Computer lab and exercise sessions. The methods presented during the lectures will be numerically investigated during the laboratory sessions based on employing the software Matlab.
  Course project. The project is an integral part of the course. Projects will be assigned at the begin of the semester. Students work in small groups. The projects deal with an applicative or advanced problem, not necessarily dealt with during the course. The goal is to help students developing high-order thinking skills such as critical thinking, problem-solving attitude, communicative and working group skills.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of a written test and of a course project.
Written test. The written exam takes place in the computer room. The exam covers all the theoretical and practical arguments considered at the lectures and lab sessions. Part of the questions and problems are solved numerically using MATLAB; the exam includes implementing and programming numerical algorithms. The problems mainly focus on definitions, application of important lemmas and theorems, and important examples. Light calculations may be needed. It is not allowed to use any course materials.
Course project. Students work in small groups on a project. Projects can focus on an applicative or advanced theoretical problem, not necessarily dealt with during the course. The assessment of the project will be based on subject knowledge matters, oral delivery, quality of the work, demonstration of teamwork and individual contributions, and quality of the written report. At the conclusion of the course, students will showcase the initial progress of their assigned project as part of a course challenge. Students may choose either a Type-B project (extended option) or a Type-A project (regular option). The Type-B project is available only to students enrolled in the 10-CFU course.
The final grade is determined as follows:
Written test (60% of the final grade) + Type-B project (40% of the final grade) - available only for the 10 CFU course
Written test (80% of the final grade) + Type-A project (20% of the final grade)
The instructor reserves the right to require an oral examination after the written examination to assess and verify students' knowledge and competencies.
Intended learning outcomes. Students are expected to

• know and understand numerical methods for differential problems, as well as evaluate their properties;
• write and interpret algorithms;
• choose the most appropriate numerical scheme for solving a given differential problem;
• solve mathematical problems with the computer via MATLAB;
• implement algorithms and use them appropriately;
• critically reason and interpret the results obtained in the light of the theory;
• model and numerically simulate Engineering problems.
  Assessment. The assessment covers:
• The student's ability to apply the subject-specific knowledge and techniques acquired during the course (Dublin Descriptors 1 and 2).
• The student's ability to choose the most appropriate numerical algorithms and critically interpret the results (Dublin Descriptors 2 and 3).
• The students' ability to integrate knowledge for problem-solving, collaborate effectively in teams, and communicate results (Dublin Descriptors 3, 4, and 5).

Quarteroni, Alfio, Numerical Models for Differential Problems, 3rd Edition, Editore: Springer, Series: MS&A, Vol 16, Anno edizione: 2017, ISBN: 978-88-470-5522-3

Objectives
The goal of the course is to provide students with important mathematical tools widely used in other courses in mathematical analysis and in mathematical physics. The course also provides the rigorous mathematical foundations necessary for the critical use of the tools. We will also explore applications of spectral theory to quantum mechanics. Specifically, we will apply spectral theory to various quantum systems, such as the quantum harmonic oscillator and the hydrogen atom.

Expected Learning Outcomes
At the end of the course and after passing the exam, students will be familiar with the concepts of operator theory.
More specifically:

• Knowledge and understanding – DD1
  Students will acquire the knowledge and understanding of the main definitions, of the main concepts in operator theory introduced in the course, the reasons they were introduced as well as some applications of the theory mathematical physics.
• Applying knowledge and understanding – DD2, DD3
  Students will acquire knowledge and understanding of the statements of the theorems and their proofs; they will have the ability to produce examples and counterexamples that illustrate the validity or invalidity of implications between certain properties in operator theory. Additionally, students will be able to solve exercises on the topics of the course.
• Communication skills – DD4
  Students will be proficient in the correct and precise use of mathematical language and symbolism in operator theory.

Programme
Part (I) Linear Operators in Hilbert Spaces
Hilbert spaces, basis and orthonormal complete sets;
bounded operators, the holomorphic functional calculus for bounded operators,
Fredholm operators, closed operators, invertible operators, adjoint;
symmetric and self-adjoint operators;
isometries and unitary operators, projectors;
finite-rank, compact, Hilbert-Schmidt and trace-class operators;
spectrum: pure point, continuous and residual spectrum;
resolvent: first and second resolvent identities and Weyl theorem.
Part (II) Self-adjoint Operators and Spectral Theorem
Criterion of self-adjointness;
perturbation theory and Kato-smallness (Kato-Rellich theorem);
quadratic forms and self-adjointness (KLMN theorem);
deficiency spaces and Von Neumann theory of self-adjoint extensions;
spectral theorem for bounded and unbounded self-adjoint operators (multiplication operator version);
spectral theorem (functional calculus);
spectral theorem (spectral resolution and spectral measure);
discrete and essential spectrum and Weyl criterion;
Stone theorem.
Part (III) This part is devoted to modern aspects in operator theory, according to the students' interests. This portion of the program is intended to be informative and will not be among the topics required for the exam.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
Assessment Methods
The exam consists of a written test, which includes both exercises on the program topics and theoretical questions on definitions, theorem statements and their proofs, presentation of examples and counterexamples on the program topics.
When answering questions on the exam program, the student must demonstrate knowledge and understanding of the definitions and of the concepts introduced in the course (Dublin Descriptor 1) and the reasons they were introduced; knowledge and understanding of the statements of the theorems and their proofs; the ability to produce examples and counterexamples that illustrate the validity or invalidity of implications between certain properties (Dublin Descriptor 2 and 3); proficiency in the correct and precise use of mathematical language and symbolism (Dublin Descriptor 4).
Additionally, the student must demonstrate the ability to solve exercises on the course topics.
The exam dates are set according to the School’s regulations, and there are no midterm exams.

K. Schmüdgen, Unbounded Self-adjoint Operators on Hilbert Space, Editore: Springer, Anno edizione: 2012
M. Reed, B. Simon, Methods of Modern Mathematical Physics, Editore: Academic Press, Anno edizione: 1981
E.H. Lieb, M. Loss, Analysis, Editore: AMS, Anno edizione: 2001

This course aims to provide students with the knowledge of some basic topics of Mathematical Analysis. Such topics play an essential role, for instance, in Probability and Statistics (measure theory and integration) as well as in the modern approach to partial differential equations (Banach and Hilbert spaces, linear operators). The goal is to get students familiar not only with the results and their applications, but also with the technicalities of the proofs and the rigorous check of the hypotheses through examples and counterexamples.

Lectures and exercise sessions will allow students to acquire the following abilities:
Knowledge and understanding
know some basic concepts of mathematical analysis which are helpful in several applications
know the proofs of some fundamental theorems in measure and integration theory and in linear functional analysis
understand the range of applicability of various results through counterexamples
Ability in applying knowledge and understanding
state rigorous definitions of the presented notions
state and prove the most relevant theorems
solve theoretical problems related to the presented theory
Making judgements
find simple counterexamples
Communication skills
write and speak mathematical concepts in a clear and rigorous way

1. Real Analysis. Measurable space, measure, outer measure. Generation of an outer measure. Carathéodory's condition, measure induced by an outer measure. Lebesgue's measure on R ^n. Measurable functions. The Lebesgue integral. Abstract integration. Monotone convergence theorem, Fatou's Lemma, Lebesgue's dominated convergence theorem. Comparison between the Lebesgue and Riemann integrals. Different types of convergence. Derivative of a measure and the Radon-Nikodym theorem. Product measures and the Fubini-Tonelli theorem. Absolutely continuous functions and weak derivatives.
2. Functional Analysis. Metric spaces, completeness, separability, compactness. Normed spaces and Banach spaces. Spaces of integrable functions. Linear operators. Uniform boundedness theorem, open mapping theorem, closed graph theorem. Dual spaces and the Hahn-Banach theorem. Reflexivity. Weak and weak* convergences. Banach-Alaoglu theorem. Compact operators. Hilbert spaces. Projection theorem, Riesz representation theorem. Orthonormal basis, abstract Fourier series. Spectral theorem for compact symmetric operators. Fredholm alternative.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The exam consists of a written test, divided into two parts. The first one contains theoretical questions on topics covered in the course, concerning definitions, theorems, proofs, examples and counterxamples. The second part contains exercises. To pass the exam, it is required a positive assessment both in the first part and in the second one. In some cases, if it is requested by the professor, the written examination could be followed by an oral one. No mid-term test is planned.
The exam has the goal of checking whether the student has acquired the following skills:
knowledge of some basic concepts of mathematical analysis which are helpful in several applications
knowledge of the proofs of some fundamental theorems in measure and integration theory and in linear functional analysis
understanding of the range of applicability of various results through counterexamples
ability to state rigorous definitions of the presented notions
ability to prove some of the presented theorems
ability to apply the presented theory to solve given problems
finding simple counterexamples
communicating mathematical concepts in a clear and rigorous way
Referring to the Dublin Descriptors, the exam is aimed at evaluating acquired skills, understanding of mathematical tools and the ability to apply knowledge (DD1, DD2, DD3, DD4).

H. Brézis, Functional Analysis. Sobolev Spaces and Partial Differential Equations, Editore: Springer, Anno edizione: 2010
G. B. Folland, Real Analysis, Editore: Wiley and Sons, Anno edizione: 1999
Note: (second edition)
M. Muratori, F. Punzo, N. Soave, Esercizi Svolti di Analisi Reale e Funzionale, Editore: Esculapio, Anno edizione: 2021
Note: Eserciziario
H.L. Royden, P. Fitzpatrick, Real Analysis, Editore: Pearson, Anno edizione: 2010
W. Rudin, Real and Complex Analysis, Editore: McGraw-Hill, Anno edizione: 2007
Note: (third edition)
W. Rudin, Functional Analysis, Editore: McGraw-Hill, Anno edizione: 1991
Note: (second edition)

The major goal of this course is to give the students the basic notions necessary in order to understand the physical properties of condensed matter. Since the topic is extremely vast, the course focuses on a particular aspect, i.e. the periodic structures and the physical consequences of the translational symmetry, starting from the Bloch theorem down to its various implications. These concepts are applied to the electronic states in a periodic potential and to the vibrational properties of periodic lattices. A brief introduction to the description of solids in terms of elementary excitations will also be given. Part of the course is dedicated to the methods of statistical physics that lie at the basis of the thermodinamical description of the properties of solids. The final part of the course is devoted to superconductivity: we will present the phenomenological aspects are discuss the occurrence of superconductivity in terms of the transition phase theory of Landau.

• Knowledge and understanding (DD1) The students will learn the fundamental physical laws, based on quantum mechanics and statistical physics, which regulate condensed matter phenomena. Due to the universal character of these laws the students will be exposed to their use also in other fields of physics such as quantum field theory and its applications to the investigation of fundamental particles.
• Apply knowledge and understanding (DD2) The students will acquire the correct perspective concerning the experimental techniques and the theoretical methods nowaday employed in the field of condensed matter physics. Since solid state physics is at the heart of the modern technological revolution the students will be made aware of the possible applications of the topics of the course and of their consequences on human life.
• Making Judgements (DD3) The students will develop a correct perception of the orders of magnitude of the physical quantities involved in the processes taking place in condensed matter. The students will be stimulated to learn how to implement a true research project starting from the basic physical ideas and making the proper strategic choices, with a particular emphasis on aspects such as the feasibility of the project as far as the human and economical resources are concerned.
• Lifelong learning skills (DD5) Students will acquire the capability to focus on the relevant aspects of a particular phenomenon and forecast the necessary steps, both on the experimental and on the theoretical ground, for understanding and exploiting it. All this in the perspective of a team work where the activity is split between team components but each of them will maintains an integrated vision of its specific duty.

The course focuses on the fundamental concepts of condensed matter physics and is mainly devoted to the study of periodic structures and their properties.
The topics covered are:

• Periodic structures and their description in real space
• Elements of the theory of symmetry
• Reciprocal space
• Electronic states in a periodic potential: the Bloch theorem
• Models with quasi-free electrons and strong bond
• Bands of insulators, metals and semiconductors
• Semiclassical dynamics of electrons in a solid
• Interaction between electrons
• Diffraction
• Classical theory of lattice vibrations: dispersion relations
• Quantum theory of lattice vibrations: the concept of phonon
• Elements of statistical physics
• Superconductivity
  The topics, many of them of considerable complexity, will be presented seeking to highlight their physical meaning and making sure to avoid it being overshadowed by the mathematical formalism. Although this is a course on the theoretical foundations of the theory of solids, the concepts will be exemplified from time to time by reference to experimental techniques actually used in the field of condensed matter.
  The course will consist of lectures and exercises during which the topics of the lectures will be discussed at a deeper level and in relation to their experimental implications.

Prova scritta obbligatoria, senza prove in itinere
The final exam will be in written form and will consist of a series of questions on a series of specific topics covered during the course. Each question will not simply involve the exposition of a specific topic but will be conceived in order to be multidisciplinary and aimed at verifying the knowledge acquired by the student on individual topics and also the comprehension of the discipline as a whole and the ability to cross correlate the various topics covered during the course.

Neil W. Ashcroft - N. David Mermin, Solid State Physics
H. Ibach - H. Lüth, Solid-State Physics, Editore: Springer
Ezio Puppin, Fisica dei solidi, Editore: Lecture notes on Solid State Physics

1. Introducing Stochastic Calculus and its rules.
2. Introducing Stochastic Differential Equations.
3. Showing their utility in modelling evolutions with noise in different contexts such as Finance, Engineering, Chemistry, Physics.

Knowledge and understanding
Lectures and exercise sessions will allow students to

• know the fundamental elements of stochastic processes (Brownian motion, martingales and Markov processes), stochastic calculus and stochastic differential equations;
• understand the applications: there are very many situations (in finance, telecommunications, control,...) where stochastic processes, and in particular diffusions, are a natural model;
• understand the connections with other branches of pure mathematics, in particular with partial differential equations.
  Ability in applying knowledge and understanding
  Lectures and exercise sessions will allow students to
• manipulate the basic notions of stochastic calculus acquiring elements of the theory and ability to work with them;
• have an adequate knowledge of the techniques to formalize and to model evolutions with noise in different contexts of science and technology;
• learn the constructive mathematical proofs of some key result of the theory;
• acquire the ability to present in a clear and precise way the models and the results of the theory.

1. Elements of Probability. Probability spaces, random variables. Variance, covariance, probability distribution, density. Independence. Random vectors. Convergence of random variables. Characteristic functions. Gaussian laws. Measurability theorems.
2. Stochastic processes. Filtrations. Trajectories. Equivalent processes, modifications, indistinguishable processes. Finite-dimensional laws and Existence Kolmogorov’s theorem. Kolmogorov’s continuity theorem. Stopping times.
3. Brownian motion. Definition and basic properties. Finite-dimensional distributions. The White Noise.
4. Conditional probability. Conditional expectations. The augmented Brownian filtration.
5. Martingales. Definitions and basic properties of continuous time Martingales.
6. The stochastic integral. Elementary processes. The stochastic integral. Ito Isometry. The stochastic integral as a process. Stopping theorems. Local martingales.
7. Stochastic calculus. Stochastic differential of an Ito process. Ito's Lemma. Girsanov’s Theorem. The martingales of the Brownian filtration.
8. Stochastic Differential Equations. A class of SDE. Definition of solutions. Existence and Uniqueness theorems for the solution. SDE and Markov processes. Connections between SDE and PDE. Feynman-Kac formula.

Prova scritta obbligatoria, senza prove in itinere
The exam consists of a written test, divided into two parts denoted, respectively, A and B. Part A contains theoretical questions in order to ascertain the understanding of the basic notions (definitions, theorems, proofs, counterexamples) of stochastic processes, stochastic calculus and stochastic differential equations.
Part B contains 2 exercises, each one containing 7 – 10 questions, on

• stochastic processes, and in particular Brownian Motion, and their properties;
• conditioning, martingales and their applications in the investigation of stochastic processes;
• stochastic calculus: stochastic integral and Ito’s formula;
• stochastic differential equations: existence and uniqueness of the solution and its properties.
  During the written test it is not allowed neither to consult documents or archives nor to communicate with other people. In particular it is not allowed to keep on the mobile phone or some other device allowing to communicate, or to use internet, to consult documents.
  The candidate will be asked to solve problems with computations and to justify rigorously all passages. He/she will be required to possess the elements of the theory and to be able to manipulate the theoretical notions.
  The evaluation of the written test will take into account the clarity in the exposition of the used procedures, the skill to motivate them, the accuracy in the computations, the familiarity with mathematical language.
  To pass the exam, it is required a positive assessment both in the part A and in the part B. The maximum grade of A+B is 30/30. In order to pass the exam, the student must get at least 18/30. In some cases, if it is requested by the professor, the written examination could be followed by an oral one. To get the laude the oral exam is mandatory.
  No mid-term test is planned.
  THE EXAM STRUCTURE COULD BE MODIFIED IN CASE OF EMERGENCY.
  The exam has the goal of checking whether the student has acquired the following skills:
  knowledge of some basic concepts of stochastic analysis which are helpful in several applications
  knowledge of the proofs of some fundamental theorems in stochastic integration theory, stochastic calsulus and stochastic differential equations
  understanding of the range of applicability of various results through counterexamples
  ability to state rigorous definitions of the presented notions
  ability to prove some of the presented theorems
  ability to apply the presented theory to solve given problems
  finding simple counterexamples
  communicating mathematical concepts in a clear and rigorous way

P. Baldi, Stochastic Calculus, Editore: Springer, Anno edizione: 2017, ISBN: 978-3-319-62225-5
P. Baldi, Equazioni differenziali stocastiche e applicazioni, Editore: Pitagora Editrice, Bologna, Anno edizione: 2000, ISBN: 88-371-1211-4
F. Caravenna, Moto Browniano e Analisi Stocastica, Anno edizione: 2011 http://www.matapp.unimib.it/~fcaraven/download/other/dispense-3.3.pdf
B. Oksendal, Stochastic Differential Equations, Editore: Springer, Anno edizione: 2000, ISBN: 3540637206
S.E. Shreve, Stochastic calculus for finance - Continuous-time models (Vol 2), Editore: Springer, Collana Springer finance, Anno edizione: 2004, ISBN: 0387401016

The aim of this course is to provide a simple and accessible introduction to discrete and time-continuous Markov chains, the simplest mathematical model for random phenomena evolving in time, with applications to queueing models, biological models, Markov chain Monte Carlo, reliability. Moreover, a wide variety of models will be illustrated to provide the student with useful tools to apply the methods in new situations. A brief introduction to martingale theory and methods with applications to Markov chains will also be given.
Lectures and exercise sessions will allow students to:

• Analyze and understand the goals, assumptions and requirements associated with Markovian models in discrete and continuous time
• Identify situations in which the Markov property may hold or not
• Learn the most relevant models (random walks, birth and death processes, random queues)
• Learn methods for computing the relevant probabilities and mean times
• Study the behaviour of the random evolution

Learn the fundamental mathematical models with discrete and continuous time Markov chains and martingale methods. Learn the constructive mathematical proofs of some key result of the theory. Understand the key structures underlying Markov chain models.
Analyze random phenomena discriminating those that can be described by Markov chains and design the corresponding models with a correct scientific approach. Develop new ideas and solutions to find quantitative rigorous solutions in new situations creating new models.
Acquire the ability to present in a clear and precise way the models and results of the theory.

1. DISCRETE TIME MARKOV CHAINS. Transition kernels. Markov chains, classes of states and their structure, irreducibility, periodicity, transience and recurrence. Random walks, recurrence and transience of random walks, binary communication channels. Invariant distributions (discrete and continuous state space). Recurrence and transience. Harris recurrence. Stopping times and strong Markov property. Hitting times and absorption probabilities. Mean absorption times. Application to ruin problems (ruin probability and mean ruin time). Empirical means and ergodic theorem. Reversibility. Applications to queueing models and population models. Lyapunov functions and Foster criteria. Exponential convergence to invariant distributions and Doeblin condition. Monte Carlo methods, Metropolis algorithm, binomial model.
2. CONTINUOUS TIME MARKOV CHAINS. Consistent families of probability distributions, Kolmogorov’s theorem, canonical processes. Trajectories and modifications. Transition rates, Chapman-Kolmogorov equation and transition semigroup, forward and backward Kolmogorov equations. Transition rate matrices and their exponentials. Markov property and exponential sojourn times, jump chain and holding times of a continuous time Markov chain. Invariant distributions, ergodic theorem and convergence to invariant distributions. Poisson process, independence of increments. Birth and death processes. Non-minimal chains and explosion in finite time. M/M/1 and M/M/k queues and performance indices. Epidemic models.
Renewal processes: law of large numbers and central limit theorem. Hidden Markov Models.
3. MARTINGALES. Martingales, supermartingales and submartingales. Modelling a player’s fortune. Filtrations and information. Stopping theorem. Maximal inequality and Doob inequality. Martingales of a Markov chain, Lyapunov functions and submartingales.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The exam consists of a written test (compulsory) and an oral examination. The written test consists of two parts denoted, respectively, A and B. Part A contains theoretical 2-3 questions in order to ascertain the understanding of the basic notions (definitions, theorems, proofs, counterexamples) of stochastic processes, Markov chains, applications and models. Part B contains 2 exercises with 5-6 questions (sometimes three shorter exercises) whose solutions require the theoretical, Markov chain (both discrete and continuous time), martingale and modelling tools developed through the course.
During the written test it is not allowed to keep the mobile phone or some other device allowing to communicate, or to use internet, to consult documents, except the course lecture notes (teacher’s notes or your own personal notes).
The candidate will be usually asked to construct the mathematical model that he will analyze to obtain quantitative information (probabilities, mean times …), to solve problems with computations and to rigorously justify all steps. He/she will be required to possess the elements of the theory and to be able to manipulate the theoretical notions and apply them rigorously and correctly in the construction and quantitative analysis of models.
The evaluation of the written test will take into account the clarity in the exposition of the used procedures, the skill to motivate them, the accuracy in the computations, the familiarity with mathematical language.
The maximum grade of A+B is 30/30. In order to pass the exam, the student must get at least 18/30. The teacher may require an oral exam in addition to the written one. As a general rule, this will apply to students who achieved a score of 26 or higher on the written test. Any oral examination will serve to confirm the assessment of the level of learning resulting from the written exam. (Additional note: it is not to be considered an additional test to "improve the result," as no such provision exists).To get the laude the oral exam is mandatory. No mid-term test is planned.
The exam has the goal of checking whether the student has acquired the following skills:
Knowledge of some basic concepts of stochastic processes, especially Markov processes and martingales, which are helpful in several applications
Knowledge of the proofs of some fundamental theorems in the theory of discrete and continuous Markov chains and martingales,
Ability to construct Markov models in concrete applications,
Understanding of the range of applicability of various results through counterexamples
Ability to state rigorous definitions of the presented notions
Ability to prove some of the presented theorems
Ability to apply the presented theory to solve given problems
Finding simple counterexamples
Communicating mathematical concepts in a clear and rigorous way

J.R. Norris, Markov Chains, Editore: Cambridge University Press, Anno edizione: 2012, ISBN: 9780511810633
Lecture Notes
Note: available on WeBeep

The goal of the course is to enable students to understand and be familiar with model-based and simulation-based approaches to statistics. In particular, the course focuses on Bayesian learning, its tools and main classes of models. This will enhance students’ abilities to address the statistical analysis of complex systems for which transversal and multidisciplinary skills are required. The Bayesian approach tells us how to update prior beliefs about parameters and hypotheses of a probabilistic model in the light of data, to yield posterior beliefs. In particular, Bayes' Theorem quantifies the problem of how to learn from data. Bayesian learning hinges on simulation methods, typically MCMC algorithms, to compute the posterior distribution.
The course adopts innovative teaching methods:
a data analysis project, as a part of the student assessment, to enhance specific soft skills such as Making judgements, Communication skills and Ability in learning ( 3 rd, 4 th and 5 th elements of the so-called European “Dublin Descriptors” – DD )
collaborative activities among students, some in small groups, and with continuous assessment of learning. This type of activity is in presence.
This is a 10 ECTS course, course code # 052499. However, there is a version of it (code # 052502, Bayesian Statistics, 8 ECTS). The only difference between the two courses is that the topics of the 8-credits course do not include neither topic 6 nor models for areal and point-referenced data in topic 7 (see the list of topics below).
For the LM program in Mechanical Engineering, there is a 5 ECTS course in Bayesian Statistics. In this case, the topics are only 1-4 from the list below.

On successful completion of the course, students will be able to:
understand the fundamental principles, tools and models of Bayesian Statistics (DD 1 - knowledge and understanding )
model simple engineering problems in terms of statistical problems using the Bayesian approach to update prior belief in the light of new data (DD 2 - Ability in applying knowledge and understanding )
select appropriate Bayesian tools to give statistical answers and use appropriate software ( R packages, JAGS, Stan, Python) for the computation of posterior inference, or to build this software by themselves (DD 2)
operate and communicate the choices made, making independent judgments, when using Bayesian tools for dealing with statistical problems from the real world (DD 3, 4 and 5)
work effectively as part of a team.

The first part of the course (topic 1) will enable students to understand foundational aspects of Bayesian Statistics (the choice of the prior, for instance), while in the second part (topics 2-7), after the introduction of Markov Chain Monte Carlo techniques for simulation from the posterior, students will be able to use specific statistical models for estimation, prediction or clustering.
1. Basics of Bayesian inference. Likelihood principle, prior and posterior distribution. Bayes' Theorem for dominated models. Posterior summary values. Interpretation of scientific inference via the Bayesian approach. Simple univariate Bayesian models. The three main inferential problem: point estimation, hypothesis testing, interval estimation: comparison between the frequentist and the Bayesian approach. Prior distributions. The choice of a prior distribution, noninformative priors, conjugate priors and their mixtures, semi-conjugate priors. Robustness. Exchangeability and de Finetti's representation theorem for exchangeable sequences. Implications of de Finetti's theorem on the Bayesian approach. Predictive inference. Asymptotic results on the posterior distribution.
2. Simulation methods for Bayesian Statistics. A quick recap on the theory on general state space Markov chains. Markov chain Monte Carlo methods. Gibbs sampler and Metropolis-Hastings algorithms for computing posterior inference. Implementing Markov chain Monte Carlo: software for Markov chain Monte Carlo (BUGS/JAGS from R), assessing convergence and run-length.
3. Goodness-of-fit and model choice. AIC, BIC, DIC, Predictive Bayesian tail probabilities, log-pseudo marginal likelihood (LPML), WAIC; prior and posterior distributions for the model index, maximum a posteriori (MAP) model selection.
4. Bayesian linear models and generalized linear models. Hierarchical linear models with random effects. Parameter estimation and covariate selection.
5. Bayesian survival analysis / reliability with censored data. Regression models: accelerated failure time and proportional hazards models.
6. Bayesian nonparametric models. The Dirichlet process and generalizations. Bayesian nonparametric mixture models, with application to density estimation and clustering.
7. Introduction to models for longitudinal data, time series, spatial data (point-referenced and areal data).
Within the Innovative teaching activity, we include 2 classes (4h + 4 h) in presence, during which students will be required to do exercises for designing and implementing (using Python or R software) algorithms for simulation, supervised by tutors and the teaching assistant. This type of active learning will include continuous assessment of learning.
The oral exam consists in the presentation of the project (in groups), focusing on a statistical problem with data, using Bayesian models, to enhance students’ soft skills such as Making judgements, Communication skills and Ability in learning. There will be intermediate revisions of the projects (this is a group activity), where the groups will discuss with tutors, TA and instructors, in presence. This type of active learning will include continuous assessment of learning.
The list of topics for the course with code # 052502, 8 ECTS, do not include topic 6 nor models for areal and point-referenced data in topic 7.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of two parts: a written exam and a project work (with a final oral presentation). It is compulsory to register for the written exam, which is scheduled twice in January-February, twice in June-July, and one in September.
The final project assessment is the presentation of the work on project, i.e. analyzing a statistical problem with data, using Bayesian tools and models. The projects will be developed in teams. The evaluation of the projects will be based on the revisions (activity in presence - at most two) the teams will undergo during the course and a conclusive presentation. During the conclusive presentation, each students’ team must hand over a project report (10-20 pages).
Participation in presence to the revisions and the final presentation is compulsory for all team members, but for Erasmus students.
If, at the beginning of the semester, the student understands he will not be able to actively participate in the group project during the semester for any reason, the student is allowed to discuss an individual project after passing the written test, instead of the group project. Because the student will not be tested on all the Expected Learning Outcomes (Risultati di apprendimento attesi), the final grading of the individual project cannot be larger than 26/30.
To obtain a positive final mark, the student should pass with a grade greater or equal than 18/30 for both parts of the exam.
Final grading: 40% written exam, 60% project work.
After the exam:
the student will know the fundamental principles, tools and models of Bayesian Statistics (DD1),
he/she will be able to apply the acquired knowledge to statistical problems from the real world (DD2),
making independent judgments, the student will operate and communicate the choices made, when using Bayesian tools to solve statistical problems from the real world (DD3,DD4,DD5).

Rosner, G. L., Laud, P. W., Johnson, W. O., Bayesian Thinking in Biostatistics, Editore: Chapman and Hall/CRC, Anno edizione: 2021
Guglielmi, Lecture Notes
Jackman, S., Bayesian analysis for the Social Sciences, Editore: Wiley, Anno edizione: 2009, ISBN: 978-0-470-01154-6
Andrew Gelman et al., Bayesian Workflow, Editore: Taylor and Francis
Lunn D., Jackson C., Best N., Thomas A., Spiegelhalter D., The BUGS book, Editore: CRC Press, Anno edizione: 2013, ISBN: 978-1-58488-849-9
Hoff, P., A first course in Bayesian Statistical Methods, Editore: Springer, Anno edizione: 2009, ISBN: 978-0-387-92299-7
Mueller, P., Quintana, F., Jara, A., Hanson, T., Bayesian Nonparametric Data Analysis, Editore: Springer, Anno edizione: 2015
Christensen, R., Johnson, W., Branscum, A., Hanson, T.E., Bayesian Ideas and Data Analysis, Editore: CRC Press, Anno edizione: 2011, ISBN: 978-1-4398-0354-7

The aim of the course is to make students familiar with the advanced quantitative methods adopted in describing the dynamics of financial markets, in valuating and hedging financial derivatives, and in optimal investments problems. An implementation of all models and methods in Matlab is an essential part of the program. The goal is to provide students with all the instruments necessary to be able to solve a financial problem, like pricing derivatives, choosing the best model and coding to obtain a numerical solution. A part of the course is also devoted to Fintech applications.
This course is connected to the joint-course 097667 - COMPUTATIONAL FINANCE (8 cfu). This sheet defines objectives, programs and learning outcomes expected for both courses.

Lectures and coding sessions will allow students to acquire the following competences:

• Knowledge and understanding
  know some advanced concept of stochastic calculus, which are essential in quantitative finance;
  know how to choose modeling assumptions to solve a financial problem properly.
• Ability in applying knowledge and understanding
  know how to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledgements.
• Making judgements
  find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
  be able to judge the possible financial risks raising from using wrong modeling assumption (like misprice of financial products).
• Communication skills
  to be able to express mathematical and financial concepts in a clear and rigorous way.

Advanced Models for Financial Markets and Asset Allocation
Lévy processes: stochastic calculus for jump processes; fundamental properties of Lévy processes and reason why they overcome the Black&Scholes limits; Lévy-Kintchine formula; simulating Lévy processes; approximate small jumps with a Wiener process; construction of Lévy processes by subordination; Lévy-Ito formula; Extension to additive processes; example of additive processes
Stochastic Volatility models: Heston, Hull-White, Stein & Stein models.
Stochastic volatility models with jumps: Bates, BNS, time change Lévy
Numerical Methods for Finance
Monte Carlo Simulations: sampling from uniform and other distributions; simulating continuous processes; simulating jump diffusion processes; variance reduction techniques; pricing European and exotic options; pricing American derivatives: the Longstaff & Schwarz algorithm.
PDE: Finite Differences discretizations: evaluating barrier and European options via Finite Differences; pricing American derivatives: the PSOR algorithm.
FFT: Carr-Madan method for European derivatives. The Convolution method
Energy Finance
Energy commodities; Jump processes for commodities; Valuation of a Swing option on Gas
Asset Allocation
Black&Litterman approach; asset allocation and efficient portfolio frontier
For the 8 cfu version: you can choose between the Energy Finance and Asset Allocation
For the 10 cfu version: all parts are mandatory

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, senza presentazione/discussione finale
Exam Structure and Evaluation The exam consists of three components: a) Projects focusing on energy finance, asset allocation, and hedging topics. b) A theoretical and coding exam. c) A mandatory oral exam.
Project Guidelines The objective of the projects is to foster collaborative group work, allowing students to apply the approaches and principles taught in class. Projects will be assigned throughout the semester, with specific submission deadlines announced at the time of assignment. Evaluation will be based on the submitted artifacts (e.g., documentation and code). The maximum score for the projects is 12/30 (4 points per project). The hedging project will be graded with two points for document and code and two points based on the group score (2 points for the first two groups and 1 point for third and fourth positions).
Written Exam and Admission to Oral Exam: the theoretical and coding exam accounts for a maximum of 18/30 points (14 points for coding and 4 points for theory). To be admitted to the oral exam, the combined score of the projects and the written exam must be at least 14/30 and the mark on the theoretical part should be at least 2/4.
Oral Exam The oral exam is mandatory. It can increase the final grade by a maximum of 4/30 points, but it may also result in a negative adjustment with no lower limit.
097667 - COMPUTATIONAL FINANCE (8 CFU) Students enrolled in the 8 CFU version of the course may opt to skip either the portfolio project or the energy project. For these students, for these students the portfolio and the hedging project mark are rescaled accordingly.
The exam has the goal of checking whether the student has acquired the following skills:

• knowledge of advanced concepts of stochastic calculus, which are essential in quantitative finance;
• knowledge of how to choose modeling assumptions to solve a financial problem properly;
• ability to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledge;
• ability to find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
• ability to express mathematical and financial concepts in a clear and rigorous way.

R. Cont, P. Tankov, Financial Modelling with Jump Processes, Editore: CRC/CHAPMAN-HALL, Anno edizione: 2004
R. Seydel, Tool for Computational Finance, Editore: Springer-Verlag, Anno edizione: 2012

This course is part of the Computational Science and Computational Learning track in the Master Program in Mathematical Engineering. The aim is to provide students with the fundamentals of mathematical models and numerical methods for partial differential equations that describe the motion of fluids in both laminar and turbulent regimes. This is a very dynamic area of study full of new contributions. Therefore the course, in addition to the basic aspects, aims to encourage the study of the latest methodological approaches. In this part of the integrated course the focus will be on the statistical description of turbulence and on its modelling.
This course is also offered in a reduced 3 CFU version 052029 - COMPUTATIONAL FLUID DYNAMICS [2] which together with the course on 052028 - COMPUTATIONAL FLUID DYNAMICS [1] (5 CFU) defines the integrated course on 052030 - COMPUTATIONAL FLUID DYNAMICS [C.I.] (8 CFU). The present sheet defines the objectives, programs and learning outcomes for both courses.

The student will be able to know and understand:

• the statistical quantities that are useful to describe the main features of a turbulent flow;
• the Kolmogorov theory for statistically homogeneous, stationary and incompressible turbulence;
• the limitations of the Kolmogorov theory
• the main families of turbulent models: Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES)
• the properties and limits of the different turbulent models
  The student will be able to apply the knowledge and comprehension to:
• (*) characterize the main transport and diffusion properties of a passive scalar in a turbulent flow.
• (*) characterize the features of two-dimensional turbulence and the main differences with respect to three-dimensional turbulence.
• (*) characterize the features of the turbulent boundary layers.
• the implementation of wall laws in the framework of RANS turbulence models.
• calibrate the model parameters of RANS turbulence models.
• the implementation of simple turbulence models in finite element solvers.
  (*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

• Statistical description of turbulence. Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows. Limitations of Kolmogorov's theory.
• (*) Transport and diffusion of a passive scalar in a turbulent flow.
• (*) Two-dimensional turbulence.
• (*) Turbulent boundary layer.
• Turbulence models for Reynolds Averaged Navier Stokes (RANS) equation; turbulent viscosity models, mixing length,
  two equation models: k-epsilon model, k-omega model.
• Large Eddy Simulation (LES) turbulence models: filtering technique, Smagorinsky turbulent viscosity model,
  similarity scale models, dynamic models, dynamic mixed models, anisotropic models.
  (*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The student will attend a written test including theory and programming exercises and oral examinations with the two teachers of the course. The exam is passed if the student reaches a sufficient mark (>=18) in each of the three parts (written exam and two oral exams) and the final mark is the average of the three marks.
The student must prove to know the main definitions and concepts inherent in turbulent flows.
He must be able to critically discuss the different theoretical aspects of turbulent phenomena: the characteristics of the relevant statistical descriptors; the Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows and subsequent developments; (*) the transport and diffusion of a passive scalar in a turbulent flow; (*) two-dimensional turbulence; (*) the turbulent boundary layer; the turbulence models both in the framework of Reynolds Averaged Navier Stokes and of Large Eddy Simulation.
He must be able to propose the most adequate analytic and modelling approach that guarantees the best compromize in terms of accuracy and computational efficiency for a given turbulent flow.
In particular during the oral part the student should be able to present complex arguments in a rigorous, clear and concise way.
(*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

Lecture Notes available on beep channel
J. Ferziger, M. Peric, Computational Methods for Fluid Dynamics (4th edn), Editore: Springer-Verlag, Anno edizione: 2020, ISBN: 9783319996912
P.A. Davidson, Turbulence - An Introduction for Scientists and Engineers (2nd edn), Editore: Oxford University Press, Anno edizione: 2015, ISBN: 9780198722588
U. Frisch, Turbulence, Editore: Cambridge University Press, Anno edizione: 1995, ISBN: 9780521457132

The course aims at training master students in the analysis of fluid dynamic processes from different perspectives. Students learn to handle a variety of techniques in order to capture and model the complexity of fluid dynamic phenomena: theoretical approaches, numerical modelling, experimental testing. Students are asked to combine information with different nature (theoretical vs. heuristic) and origin (numerical/theoretical vs. experimental), with the aim of understanding the physics of fluid flow processes and its engineering handling.

Knowledge and ability in understanding:
recognize and describe basic features of internal and external flows, for both laminar and turbulent regimes
know a variety of theoretical and heuristic models in fluid dynamics
understand the role of closure models
Ability in applying knowledge and understanding:
make use of statistical tools in data analysis
make use of numerical tools for solving differential models in fluid mechanics
apply a variety of models for the investigation of simple yet engineering-relevant fluid dynamics processes
carry out a phenomenological analysis of relevant processes in fluid dynamics
Making judgments:
choose adequate models for the engineering description of fluid dynamic processes
evaluate uncertainties in experimental results
evaluate the physical consistency of the numerical solution
evaluate uncertainties in numerical modelling

The course comprises theoretical, numerical and experimental analyses of a variety of fluid flows.
The THEORETICAL BACKGROUND is offered through the following modules:
1) equations governing flow flows
basic concepts of continuum mechanics
physical properties of fluids: density; vapor tension and cavitation; coefficients of compressibility; viscosity and rheology; surface tension
fluid statics
kinematics: Eulerian and Lagrangian frameworks; material derivative; streamlines and pathlines; rate of strain tensor and rigid rotation tensor
mass and momentum conservation equations
inviscid flows: the Euler equations; the Bernoulli equation; irrotational flows and potential flows
the Navier-Stokes equations for viscous, Newtonian flows in differential, integral, and dimensionless formulations
2) modelling of turbulent flows
basic elements of turbulence
brief overview of the basic approaches in turbulence modelling: DNS, LES, (U)-RANS
(U)-RANS-based modelling of turbulence: the eddy-viscosity assumption and the k-epsilon standard turbulence model. Brief outline of other eddy-viscosity based models and Reynolds stresses models.
3) internal flows
developing and fully-developed flow in pressurized pipes
fully-developed laminar flow in pressurized pipes: plane and cylindrical Poiseuille flow
fully-developed turbulent flow in pressurized pipes: frictional losses, viscous and Reynolds stresses, Reynolds-averaged velocity profile, Prandtl's assumption of inner layer and universal law of the wall
4) external flows
concepts of boundary layer and wake
boundary layer formulation of the Navier-Stokes and RANS equations
development of the boundary layer along a flat plate (includes some interacting teaching)
flow around a circular cylinder; separation of the boundary layer, unsteady effects and Strouhal number
concepts of drag and lift force
functional relations for the drag and lift coefficients: flat plate and cylinder/sphere.
Goal of NUMERICAL LABORATORIES is to introduce the students to the correct use of Computational Fluid Dynamics (CFD) codes for engineering applications. In this perspective, the focus is not so much on solution algorithms and implementation-related issues but, rather, on the best practices and guidelines which must be followed to obtain reliable CFD predictions. Particular attention will be given to the concepts of benchmarking, calibration, and validation, as well as to convergence assessment, grid independence, and critical evaluation of the physical consistency of the simulation output. A deep discussion is made around the sources of uncertainty of the CFD solution, especially in relation to the modelling of turbulence in the RANS framework. CFD simulations of two benchmark yet engineering-relevant configurations are performed and post-processed by the students as single or in small groups under the step-by-step guidance of the teachers. Specifically, the two CFD cases are the laminar oil transport and the turbulent water transport in pipelines.
In the EXPERIMENTAL LABORATORIES, the fluid mechanics processes are analyzed on laboratory measurements. An introduction to commonly used instrumentation in experimental fluid mechanics is provided, including a detailed discussion around the process of calibration and a few notes on basic concepts on data acquisition and processing. Videos of laboratory experiments will be shown, and the experimental data will be provided to the students, who will analyze and process them as single or in small groups under the step-by-step guidance of the teachers. Specifically, the three experimental cases relate with the calibration of a load cell and the analysis of the velocity field and the hydrodynamic forces on circular cylinder in a water channel.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The exam consists of a written test, mainly focused on the theoretical part of the course. By answering the written questions, which might also include simple exercises, the students demonstrate knowledge of the theoretical contents, competence on fluid mechanics processes as well as critical reasoning skills by discussing various fluid mechanics phenomena. Upon positive evaluation of the written test, an oral colloquium will take place, which will be mostly focused on the laboratory activities. Each student is requested to bring to the oral exam the results of the numerical and experimental laboratories, which can be obtained either individually or in small groups of 2-3 people maximum. Upon request of the teacher, the students should be able to produce also the simulation files and the scripts developed to process the numerical and experimental data.

B.R. Munson, T.H. Ohiishi, W.W. Huebsch, A.P. Rothmayer, Fundamentals of Fluid Mechanics (7th Edition), Editore: John Wiley and Sons, Anno edizione: 2013, ISBN: 9781118318676
Y.A. Cengel, J.M. Cimbala, Fluid Mechanics, Editore: McGraw-Hill, Anno edizione: 2005, ISBN: 9780071249348
H. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Editore: Pearson Prentice Hall, Anno edizione: 2007, ISBN: 9780131274983
S.B. Pope, Turbulent flows, Editore: Cambridge University Press, Anno edizione: 2000, ISBN: 9780521598866

The key goal of the course is to provide a very successful example of a mathematical rigorous formulation of a physics theory - quantum mechanics -, starting from first principles (postulates) down to the discussion of concrete phenomena in atomic physics. In this respect, the course is meant to illustrate some typical features of modern mathematical physics and some insights on contemporary research lines in the field.
A self-contained presentation of quantum mechanics and its mathematics, suited in particular for students with mathematical background, is given. It is shown that a fully rigorous mathematical construction can lead to non-trivial physics results, so testifying that mathematical physics can in fact shed light on physics phenomena. Indeed, all the most intriguing and counter-intuitive phenomena of quantum mechanics (uncertainty, probabilistic behavior, interference etc.) as well as their mathematical formulation are discussed. On the other hand, several mathematical tools on functional analysis, operator theory, functional inequalities, etc., are introduced and discussed in details so that the mathematical content of the course is valuable as well for students more oriented towards abstract mathematics.
We denote by (*) the topics covered by the 5 CFU version of the course.

From the physics point of view, we expect that students without any previous knowledge of quantum mechanics acquire a basic understanding of the main features of the theory, while those who have already attended physics courses on the topic discover a more mathematically sounded presentation of quantum mechanics.
In addition, we expect that the students at the end of course

• know the first principles of quantum mechanics and are able to translate them in the mathematical language (*);
• are able to describe how the core physical aspects of quantum mechanics (uncertainty, probabilistic behavior, dispersion, interference, etc.) follow from the postulates of the theory (*);
• know the rigorous mathematical modelling of simple quantum systems as the free particle, the harmonic oscillator and the hydrogen atom (*);
• know the key features of the quantum description of atomic matter and many-body systems;
• understand the mathematical framework of non-relativistic scattering theory;
• know the basics of second quantization and quantum field theory;
• get an introduction to some research lines about the mathematical features of quantum mechanics.

1. Postulates of Quantum Mechanics (*)
2. Observables and States (*)
Brief recap of operator theory; Heisenberg uncertainty relation; self-adjointness criterion and self-adjoint extensions; spectral theorem and probabilistic interpretation of quantum mechanics; spectral decomposition; mixed states and density matrices; Stone theorem and existence of the dynamics.
4. Free Particle and Harmonic Oscillator (*)
Free particle: time evolution of wave packets, dispersion and interference, semiclassical limit; harmonic oscillator: spectrum, creation and annihilation operators, coherent states.
5. Hydrogen Atom (*)
Self-adjointness and stability; spectrum; angular momentum; eigenfuctions.
6. Perturbation Theory (*)
Perturbation theory in finite dimensions; analytic perturbation theory; perturbation of spectral projectors; variational methods: min-max principle; physical applications: Zeeman effect, anharmonic oscillator.
7. Many-body Quantum Mechanics & Atomic Matter
Spin and identical particles: bosons and fermions; reduced density matrices; non-interacting many-particle systems; atomic Hamiltonians and stability of matter of the first kind; Lieb-Thirring inequalities; stability of matter of the second kind; Bose-Einstein condensation, superfluidity and superconductivity; nonlinear models for condensed matter physics.
8. Scattering
Scattering by a potential; time-dependent scattering theory; asymptotic completeness; Lippman-Schwinger equation and generalized eigenfunctions.
9. Quantum Field Theory
Fock spaces: the mathematics of second quantization; annihilation and creation operators; Fock space calculus; free and regular field theories: time-zero and spacetime fields, spin-boson and Nelson models; interacting field theories and renormalization.

Prova orale obbligatoria
Valutazione continua facoltativa (a scelta dello studente)
The exam consists of two components: a final oral exam (worth up to 27 points) and ongoing assessments (optional, worth up to 6 additional points).
The two assessment sessions (up to 3 points each), held halfway through the course and at its end, are optional and consist of exercises completed during the exercise classes. They may be replaced by a question session covering the entire syllabus during the final exam.
The final oral exam may take the form of a presentation on a topic chosen from a list provided by the instructor, followed by questions on that topic, or a traditional oral examination covering all the material discussed during the course.
The exam for the 5 CFU version of the course consists in a traditional oral examination.

lecture notes on WeBeep
Note: (handwritten)
lecture notes on WeBeep
Note: (in italian)
Alessandro Teta, A Mathematical Primer in Quantum Mechanics, Editore: Springer, Anno edizione: 2018, ISBN: 9783319778938
Alberto Galindo, Pedro Pascual, Quantum Mechanics I, Editore: Springer, Anno edizione: 1990, ISBN: 978-3-642-83854-5
Alberto Galindo, Pedro Pascual, Quantum Mechanics II, Editore: Springer, Anno edizione: 1991, ISBN: 978-3-642-84129-3
J. Blank, P. Exner, M. Havlícek, Hilbert Space Operators in Quantum Mechanics, Editore: Springer, Anno edizione: 2010, ISBN: 9789048180127
E.H. Lieb, R. Seiringer, The Stability of Matter in Quantum Mechanics, Editore: Cambridge University Press, Anno edizione: 2009, ISBN: 9780511819681
M. Lewin, Spectral Theory and Quantum Mechanics, Editore: Springer Cham, Anno edizione: 2024, ISBN: 9783031668777
A. Arai, Analysis on Fock Spaces and Mathematical Theory of Quantum Fields, Editore: World Scientific Publisher, Anno edizione: 2018, ISBN: 9789811288425
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 1 - Functional Analysis, Editore: Academic Press, Anno edizione: 1981, ISBN: 9780125850506
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 2 - Fourier Analysis, Self-adjointness, Editore: Academic Press, Anno edizione: 1975, ISBN: 9780125850025
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 3 - Scattering Theory, Editore: Academic Press, Anno edizione: 2012, ISBN: 9780123958273
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 4 - Analysis of Operators, Editore: Academic Press, Anno edizione: 2012, ISBN: 9780123958280

The course covers advanced topics in computational mechanics and provides an introduction to modern machine learning techniques for civil engineering applications. These methodologies have become essential tools for the modern engineer, enabling the analysis of complex problems, the development of predictive models, and the design of innovative data-driven engineering solutions. The course combines theoretical foundations with practical implementation, equipping students with the computational skills required to address contemporary challenges in civil engineering.

Upon successful completion of the course, students will be able to:
Understand the theoretical foundations of advanced computational mechanics methods and their application to complex engineering problems.
Formulate and implement numerical models for the analysis of nonlinear and multiphysics problems relevant to civil engineering.
Critically assess the accuracy, efficiency, and limitations of computational methods, and interpret numerical results.
Understand the principles of data-driven modeling, distinguish between the main supervised and unsupervised learning paradigms, and grasp the formulation of fundamental machine learning algorithms.
Apply machine learning techniques to engineering datasets for regression, classification, dimensionality reduction, anomaly detection, surrogate modeling, and data assimilation for parameter estimation.
Integrate computational mechanics and machine learning methodologies to address challenging engineering problems, recognizing their potential and limitations.
Select and use appropriate computational tools to solve real-world engineering problems, developing the skills expected of modern civil engineers.
Design, implement, document, and present a numerical project, demonstrating the ability to work independently and to communicate technical results effectively through appropriate graphical, numerical, and analytical representations.

The course consists of lectures complemented by practical laboratory sessions. Lectures provide the theoretical foundations of the methodologies, while laboratory sessions focus on the implementation of algorithms and their application to representative civil engineering problems using Python.
Computational Mechanics: Finite Elements for Dynamics and Nonlinear Problems
Review of the finite element method for linear elasticity: weak formulation, finite element discretization, and numerical implementation.
Structural dynamics: semi-discrete equations of motion, modal analysis, and implicit time integration schemes.
Geometric nonlinear finite element analysis: nonlinear equilibrium equations, Newton-Raphson solution procedures, and tangent stiffness formulation.
Applications to nonlinear structural problems: buckling, contact mechanics, and coupled multiphysics examples.
Development of finite element codes in Python for dynamic and nonlinear structural analysis.
Machine Learning – Part I: Supervised and Unsupervised Learning
Review of probability theory: probability distributions, random sampling, Monte Carlo methods, sampling techniques, and Bayes’ theorem.
Regression and classification perspectives for direct and inverse engineering problems.
Regression methods: linear regression, multivariate regression, polynomial regression, and regularization techniques.
Classification methods: linear discriminant analysis, logistic regression, support vector machines, and decision Trees.
Dimensionality reduction: principal component analysis and singular value decomposition.
Clustering and anomaly detection.
Applications of supervised and unsupervised learning techniques to civil engineering problems.
Machine Learning – Part II: Neural Networks and Deep Learning
Fundamentals of artificial neural networks.
Regression and classification using neural networks.
Network architectures and optimization algorithms.
Convolutional neural networks.
Transfer learning and pre-trained models.
Engineering applications scientific machine learning and deep learning.
Machine Learning – Part III: Data Assimilation and Inverse Problems
Bayesian formulation of parameter estimation.
Gaussian filtering methods: Kalman filter and extensions.
Application to structural identification and engineering monitoring problems.
Teaching approach
The course combines theoretical lectures with extensive hands-on programming sessions. Strong emphasis is placed on the practical implementation of numerical methods and machine learning models applied to representative civil engineering problems. In addition to the core topics listed above, invited seminars will cover advanced and emerging topics in computational mechanics, scientific machine learning, and data-driven engineering.

Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The assessment consists of the development and presentation of a numerical project on a topic covered in the course, to be agreed upon with the instructors.

Dispense del corso
Course material, source code, and notebooks are available from the course GitHub repository: https://github.com/MatteoTorzy/acm.git
Goulet J.-A., Probabilistic Machine Learning for Civil Engineers, Editore: MIT Press, Anno edizione: 2020
Stevens E., Antiga L., Viehmann T., Deep Learning with PyTorch, Editore: Manning, Anno edizione: 2020
Blitzstein J.K., Hwang J., Introduction to probability, Editore: Chapman and Hall/CRC, Anno edizione: 2019
James G., Witten D., Hastie T., Tibshirani R, An introduction to statistical learning: with applications in R, Editore: Springer, Anno edizione: 2013

The course is thought for students attending an MSc in Engineering who want to deepen the numerical treatment of coupled problems arising in different engineering applications. The course is divided into two parts: in the first one (5 CFU), numerical methods to address general coupled problems arising in practical scenarios will be introduced and analyzed; in the second part (3 CFU), the general methods introduced in the first part will be applied to a specific context, namely the numerical modeling of the cardiovascular system, which is characterized by several coupling of different nature. This will allow to introduce the students towards projects inspired by the clinical needs. Thus, this course presents a modular structure, so that an MSc could possibly introduce only one of these two moduli among its courses.
The students will be addressed during the course towards new and advanced numerical strategies to handle complex coupled problems that could arise in different engineering contexts.
In order to have practical answers of the new numerical strategies introduced in this course, several laboratories with the computer will be considered, where the students will utilize some of the new numerical technique in a Finite Elements library.
The learning process will involve lectures on the theory and computer laboratories about the application of examples of
numerical methods.
The course could be performed also in a short version by 5 CFU called "053464 - ADVANCED NUMERICAL METHODS FOR COUPLED PROBLEMS". The present description accounts for both the courses (the extended and the short one).

For both the version of the course (extended and short), the lectures and the laboratories will provide students with the knowledge and understanding of

• Numerical techniques for homogeneous and heterogeneous problems based on domain decomposition;
• Numerical approximation of the coupling between a fluid and a structure;
  Limited to the extended version of the course, the lectures and the laboratories will provide students also with the knowledge and understanding of
• Numerical treatment of the coupling between geometrically heterogeneous models;
• The electro-mechanical coupled problem in the heart
• Fluid-structure interaction with immersed structures
  Moreover, both for the extended and the short courses, the ability to apply the previous knowledge to some examples on the calculator will be stimulated. In particular the student is required to
• be able to run executables introduced during laboratories;
• critically discuss the results of the numerical experiments above in prespective of the theory;
  The instructor expects a broad comprehension of the subjects which should not be limited to the statement of theoretical results.
  Instead, the acquired knowledge should enable students to express critical judgment.
  The students are expected to express their answers in a mathematically rigorous and clear way.

In what follow, the topics of the courses will be presented. Part I is common (extended and short version of the course), whereas part II refers only to the extended course
PART I (5 CFU) (Extended and short course)
I Numerical techniques for heterogeneous problems based on domain decomposition
I.1 Domain Decomposition methods and formulation of the problem
I.2 Interface equation
I.3 Weak formulations and Finite Elements approximations
I.4 Extensions to the Hooke and Stokes equations
I.5 Heterogeneous Domain Decomposition: examples
II Numerical approximation of the coupling between a fluid and a structure
II.1 Introduction to the cardiovascular system and examples of applications
II.2 Preprocessing: Image reconstruction and mesh generation
II.3 A brief review of the numerical approximation of the elasto-dynamics and Navier-Stokes equations
II.4 Position of the coupled problem
II.5 Arbitrary Lagrangian-Eulerian formulation
II.6 The treatment of the geometric coupling
II.7 Numerical algorithm based on partitioned schemes. Added mass effect
II.8 Monolithic strategies and preconditioning
PART 2 (3 CFU) (Extended course)
III Numerical treatment of the coupling between geometrically heterogeneous models
III.1 Numerical treatment of defective boundary conditions
III.2 The 1D model for blood dynamics
III.3 OD models and outflow conditions
III.4 Geometric multiscale models: 3D-1D and 3D-0D coupling
IV Application to the heart function
IV.1 Brief introduction to cardiac physiology
IV.2 The electrical propagation and the Bidomain equations
IV.3 Numerical strategies for electro-physiology
IV.4 The mechanical contraction and electro-mechanical coupled problem
IV.5 Electro-mechanical coupling models
IV.6 Numerical strategies for the Electro-mechanical coupling
IV.7 Valve modeling
IV.8 Towards an integrated heart functioning modeling

Prova orale obbligatoria
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), individuale, senza revisioni periodiche, con presentazione/discussione finale
The exam consists only in an oral discussion and is designed to test the student on the knowledge and understanding of the numerical techniques introduced to address the presented problems and of the examples provided.
The instructor expects a broad comprehension of the subjects which should not be limited to the statement of theoretical results.
Instead, the acquired knowledge should enable students to express critical judgment.
The students are expected to express their answers in a mathematically rigorous and clear way.
It is also possible to undertake an optional project, agreed upon with the instructor, on topics relevant to the course, for a maximum of 3 points.

Alfio Quarteroni and Alberto Valli, Domain Decomposition Methods for Partial Differential Equations, Editore: Oxford University Press, Anno edizione: 1999
Quarteroni A., Veneziani A., Vergara C., Geometric multiscale modeling of the cardiovascular system, between theory and practice/Computer Methods in Applied Mechanics and Engineering, Editore: Elsevier, Anno edizione: 2016, Fascicolo: 302
Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications/Acta Numerica, Anno edizione: 2017, Fascicolo: 26

The course aims to provide concepts of scientific computing and C++ programming. It addresses procedural, object-oriented, and generic programming techniques; parallel computing with message passing (MPI) and shared memory (OpenMP) paradigms; compiling, debugging, testing, and profiling computer code; program organization; data structures; design patterns; and numerical algorithms.
The student will also acquire knowledge of tools for code development (git, makefiles) and for interfacing C++ with other programming languages (python, R) largely used in the scientific computing and machine learning community. Students are also provided with an extensive set of examples, freely downloadable from a git repository, that they can use and modify to autonomously test their acquired capabilities.
The course is offered in a 10-credit version and in an 8 CFU version. The present detailed program defines the aims, educational outcomes, and syllabi for both versions. The main difference between the two versions is in the evaluation procedure, where the 10-credit course necessarily implies the development of a project.
The course is organized in lectures given in lecture rooms, which also include the description of practical examples, exercise sessions carried out using the computer, where the students have to implement and test autonomously, but with the aid of a teaching assistant, small programs where they can apply the techniques introduced at the lectures, and auto evaluation activities consisting of developing autonomously some simple computer codes for scientific computing problems and discussing them with the lecturers. This latter activity is evaluated and can contribute to the final evaluation

The expected learning outcomes are:
Knowledge and understanding:
Learn and understand the main programming techniques and design patterns instrumental to the development of scientific codes;
Learn and understand the practical implementation of some numerical techniques adopted in scientific computing;
Learn and understand how to develop scientific code in a scalar and in a parallel environment;
Learn tools for program development, like git and makefiles, which are common in computer programming practices.
Learn and understand how to write efficient scientific code and the main techniques for debugging and profiling.
Applying knowledge and understanding:
Apply the acquired techniques to practical contexts;
Motivate the choice of the adopted methods and tools;
Making judgment:
Choose the appropriate code design for a specific objective
Develop autonomous thinking by choosing the structure and design of the developed code with great autonomy;
Communication skills:
Organize code for readability and comment it using de facto standard tools to produce a reference manual automatically;
Strengthen written and oral communication skills through the writing of the project report and the presentation of the results.
Ability in learning:
The students have to elaborate on the material provided during lectures and laboratory sessions in order to choose the appropriate software design, programming paradigms, and implementation techniques. Will also learn how to interface his/her code with existing libraries. This activity will strengthen his/her capability of autonomous learning.

1) Advanced C++ programming. This part aims to complete the student's knowledge of computer languages by providing an exhaustive illustration of the advanced features of C++, including those added in the newest standards, with an emphasis on scientific computing applications. We will also cover elements of numerical linear algebra, such as iterative solutions of large linear systems, and solutions of nonlinear systems of equations.
2) Code design and organization. In this part of the course, we cover the main design patterns, exception handling, static and dynamic libraries, computer code debugging and profiling, and code versioning systems.
3) Application of Parallel programming. In this part of the course, we address practical issues of parallel programming in the context of numerical algorithms.

Prova scritta condizionata (a scelta del docente), senza prove in itinere
Progetto/i - Elaborato/i condizionato (a scelta del docente), di gruppo, senza revisioni periodiche, con presentazione/discussione finale
Valutazione continua facoltativa (a scelta dello studente)
Altro
For the 10-credits version, the final assessment is a project in which a mathematical problem or an engineering application is solved by developing a computer program. Students should prepare a short report and present the project with an oral presentation, followed by teacher questions. Projects may be carried out in groups of up to three students. In exceptional cases (more complex projects), the group may be formed by more students.
For the 8-credit version, the student takes a written exam with questions concerning the techniques presented during the course and a simple program to develop and test. The teacher may require an oral assessment if needed to clarify student responses. Alternatively, the student may choose to carry out a project, similarly to the 10-credit version.
The possibility of carrying out the written examination is also given to the 10-credit students, with a mark limit of 25.
During the course, the student may engage in activities (called challenges), which consist of developing some simple computer codes for scientific computing problems autonomously. These activities are evaluated and contribute to the final mark.
In the evaluation, we assess:
1) The quality of the report and the oral presentation, both in terms of clarity and completeness. (Descriptors 3 and 4)
2) The originality of the software design, its usability, extendability, and efficacy for the target problem (Descriptors 2 and 3)
3) The capability of the student to apply the knowledge and techniques acquired during the course (Descriptors 1 and 2)
4) The autonomy in choosing tools, programming paradigms, and external libraries (Descriptor 5)

O Klein, Modern C++ Programming Techniques for Scientific Computing,, Anno edizione: 2021 https://conan.iwr.uni-heidelberg.de/data/people/oklein/pdf/klein_modern_cpp.pdf
Note: A freely downloadable text on modern C++. It also covers C++20
B. Stroustrup, A tour of C++, ISBN: 0-13-681648-7 https://www.stroustrup.com/tour3.html
Note: The tour'' is tutorial overview of all of standard C++ (language and standard library) at a moderately high level for people who already know C++ or at least are experienced programmers.

The course aims to provide concepts of scientific computing and C++ programming. It addresses procedural, object-oriented, and generic programming techniques; parallel computing with message passing (MPI) and shared memory (OpenMP) paradigms; compiling, debugging, testing, and profiling computer code; program organization; data structures; design patterns; and numerical algorithms.
The student will also acquire knowledge of tools for code development (git, makefiles) and for interfacing C++ with other programming languages (python, R) largely used in the scientific computing and machine learning community. Students are also provided with an extensive set of examples, freely downloadable from a git repository, that they can use and modify to autonomously test their acquired capabilities.
The course is offered in a 10-credit version and in an 8 CFU version. The present detailed program defines the aims, educational outcomes, and syllabi for both versions. The main difference between the two versions is in the evaluation procedure, where the 10-credit course necessarily implies the development of a project.
The course is organized in lectures given in lecture rooms, which also include the description of practical examples, exercise sessions carried out using the computer, where the students have to implement and test autonomously, but with the aid of a teaching assistant, small programs where they can apply the techniques introduced at the lectures, and auto evaluation activities consisting of developing autonomously some simple computer codes for scientific computing problems and discussing them with the lecturers. This latter activity is evaluated and can contribute to the final evaluation

The expected learning outcomes are:
Knowledge and understanding:
Learn and understand the main programming techniques and design patterns instrumental to the development of scientific codes;
Learn and understand the practical implementation of some numerical techniques adopted in scientific computing;
Learn and understand how to develop scientific code in a scalar and in a parallel environment;
Learn tools for program development, like git and makefiles, which are common in computer programming practices.
Learn and understand how to write efficient scientific code and the main techniques for debugging and profiling.
Applying knowledge and understanding:
Apply the acquired techniques to practical contexts;
Motivate the choice of the adopted methods and tools;
Making judgment:
Choose the appropriate code design for a specific objective
Develop autonomous thinking by choosing the structure and design of the developed code with great autonomy;
Communication skills:
Organize code for readability and comment it using de facto standard tools to produce a reference manual automatically;
Strengthen written and oral communication skills through the writing of the project report and the presentation of the results.
Ability in learning:
The students have to elaborate on the material provided during lectures and laboratory sessions in order to choose the appropriate software design, programming paradigms, and implementation techniques. Will also learn how to interface his/her code with existing libraries. This activity will strengthen his/her capability of autonomous learning.

1) Advanced C++ programming. This part aims to complete the student's knowledge of computer languages by providing an exhaustive illustration of the advanced features of C++, including those added in the newest standards, with an emphasis on scientific computing applications. We will also cover elements of numerical linear algebra, such as iterative solutions of large linear systems, and solutions of nonlinear systems of equations.
2) Code design and organization. In this part of the course, we cover the main design patterns, exception handling, static and dynamic libraries, computer code debugging and profiling, and code versioning systems.
3) Application of Parallel programming. In this part of the course, we address practical issues of parallel programming in the context of numerical algorithms.

Prova scritta condizionata (a scelta del docente), senza prove in itinere
Progetto/i - Elaborato/i condizionato (a scelta del docente), di gruppo, senza revisioni periodiche, con presentazione/discussione finale
Valutazione continua facoltativa (a scelta dello studente)
Altro
For the 10-credits version, the final assessment is a project in which a mathematical problem or an engineering application is solved by developing a computer program. Students should prepare a short report and present the project with an oral presentation, followed by teacher questions. Projects may be carried out in groups of up to three students. In exceptional cases (more complex projects), the group may be formed by more students.
For the 8-credit version, the student takes a written exam with questions concerning the techniques presented during the course and a simple program to develop and test. The teacher may require an oral assessment if needed to clarify student responses. Alternatively, the student may choose to carry out a project, similarly to the 10-credit version.
The possibility of carrying out the written examination is also given to the 10-credit students, with a mark limit of 25.
During the course, the student may engage in activities (called challenges), which consist of developing some simple computer codes for scientific computing problems autonomously. These activities are evaluated and contribute to the final mark.
In the evaluation, we assess:
1) The quality of the report and the oral presentation, both in terms of clarity and completeness. (Descriptors 3 and 4)
2) The originality of the software design, its usability, extendability, and efficacy for the target problem (Descriptors 2 and 3)
3) The capability of the student to apply the knowledge and techniques acquired during the course (Descriptors 1 and 2)
4) The autonomy in choosing tools, programming paradigms, and external libraries (Descriptor 5)

O Klein, Modern C++ Programming Techniques for Scientific Computing,, Anno edizione: 2021 https://conan.iwr.uni-heidelberg.de/data/people/oklein/pdf/klein_modern_cpp.pdf
Note: A freely downloadable text on modern C++. It also covers C++20
B. Stroustrup, A tour of C++, ISBN: 0-13-681648-7 https://www.stroustrup.com/tour3.html
Note: The tour'' is tutorial overview of all of standard C++ (language and standard library) at a moderately high level for people who already know C++ or at least are experienced programmers.

The course aims at providing students with the critical and conceptual tools to reflect upon
some of the main ethical and social issues raised by the development of Artificial Intelligence
(AI). The course will be articulated in three modules, deeply interconnected to provide students
with a coherent narrative. The course will start with the analysis of the problems related to the
definition of "AI", starting from the first characterizations of AI dating back to the 1950s and
comparing them with the way AI is typically discussed nowadays. In the second module, the
topic of AI-related risk will be expanded so as to include aspects of uncertainty. In the last
module, the ethical framework of Trustworthy AI will be presented as a way to deal with AIrelated uncertainty. After a general presentation of the Trustworthy AI framework, specific
issues in AI ethics will be discussed, also depending on the students' interests.

This course is of 6 CFU and is associated with a version of 5 CFU named 097688 - ECONOMICS AND COMPUTATION (5 CFU). The current form specifies goals, program and expected learning results for both courses.
For both versions of the course (6 CFU and 5 CFU), the goal of the course is to provide the groundings of algorithmic microeconomics. More precisely, the course explores mathematical models, computational complexity, and algorithms for economic settings. The course focuses both on non-cooperative game theory, describing the models and the algorithms used in real-world applications in various settings (e.g., poker and security), and on mechanism design, describing economic mechanisms and algorithms used in auctioning settings (e.g., digital advertising and online auctions). The treatment of the topics will be both from a theoretical point of view, describing the models/algorithms and their properties, and from a practical point of view, discussing how the algorithms can be applied and applying them in practice during some laboratory sessions. Furthermore, the course aims at presenting some real-world applications of paramount importance. The difference between the two versions of the course (6 CFU and 5 CFU) is just in the depth with which some topics are discussed.

For both versions of the course (6 CFU and 5 CFU), we expect that the students learn:
how to model real-world applications by means of mathematical models from microeconomics,
how to identify the most suitable class of algorithms to solve a given problem,
how to use the tools already available to solve a given problem in practice,
how to design an algorithm to solve a given problem whenever no algorithm is known

We report the topics discussed in both versions of the course (6 CFU and 5 CFU). We use '(*)' for the topics that will not be discussed in the 5 CFU version.
PRELIMINARIES OF GAME THEORY
Definition of non-cooperative game
Representations of a game
ALGORITHMIC GAME THEORY
Solving maxmin/minmax problems
Computational complexity of finding a Nash equilibrium
Algorithms for finding a Nash equilibrium
Arrow-Debreu market model and equilibrium (*)
Algorithms for finding a Stackelberg equilibrium
Real-world application: security games
Congestion games
Price of Anarchy and Price of Stability
ECONOMIC MECHANISM DESIGN
Social choice function
Definition of economic mechanism
Gibbard-Satterthwaite theorem
Quasi-linear environment and linear environment
Implementation of a social choice function
Groves mechanisms
Green-Laffont characterization and Myerson characterization
Economic mechanisms for online advertising (real-world applications) (*)
ALGORITHMIC MECHANISM DESIGN
Non-scalability of Groves mechanisms (real-world examples: combinatorial auctions)
Developing computationally efficient mechanisms
Economic mechanisms for combinatorial auctions (real-world applications)
Economic mechanisms for double auctions (*)
Economic mechanisms for knapsack auctions
Automated mechanism design (*)

Prova scritta obbligatoria, con prove in itinere
Valutazione continua facoltativa (a scelta dello studente)
The exam is the same for both versions of the course (6 CFU and 5 CFU), except for the questions that, in the case of the 5 CFU version, may be different. More precisely, the exam can be of two forms:
standard: written exam (2.5 hours)
3 exercises (the first exercise is on noncooperative game theory models and on the adoption of operations research tools to solve a game, the second exercise is on algorithmic game theory or economic mechanism design, the third exercise is on economic mechanism design or algorithmic mechanism design) (max 27 points), --- here the students are required to solve exercises similar to those studied during the course or to answer some theoretical questions about topics discussed during the course; the capabilities the students must show are: modeling real-world applications by means of mathematical models from microeconomics, indentifying the most suitable class of algorithms to solve a given problem, using the tools already available to solve a given problem in practice ---;
1 question on advanced topics (on all the topics of the course) (max 5 points) --- here the students are required to answer a question that is beyond the topics discussed during the course; the capabilities the students must show are: generalizing the skills learned during the course to design an algorithm for a given problem that has not discussed during the course;
engaged: the course is divided into four parts (Part 1: noncooperative game theory models; Part 2: Maxmin and Nash equilibrium; Part 3: Stackelberg, Congestion games, social choice functions; Part 4: mechanism design and algorithm mechanism design), at the fourth week of each part of the course, students take part in a midterm exam (2.5 hours), composed as:
exercise/theory (1 exercise and 2 theory questions) (max 27 points) --- here the students are required to solve exercises similar to those studied during the course or to answer some theoretical questions about topics discussed during the course; the capabilities the students must show are: modeling real-world applications by means of mathematical models from microeconomics, identifying the most suitable class of algorithms to solve a given problem, using the tools already available to solve a given problem in practice ---;
challenge on scientific research problems (max 8 points); the challenge is carried on by teams, each of 2-3 students --- here the students are required to answer some questions that are beyond the topics discussed during the course; the capabilities the students must show are: generalizing the skills learned during the course to design an algorithm for a given problem that has not discussed during the course.
Each student can choose the form of the exam she/he prefers. If a student opts for the engaged form and she/he is not satisfied with the achieved grade, she/he can repeat the exam in the standard form.

Noam Nisan, Tim Roughgarden, Eva Tardos, V. Vazirani, Algorithmic Game Theory, Editore: Cambridge University Press
Kevin Leyton-Brown, Yoav Shoham, Essentials of Game Theory, Editore: Cambridge University Press

Il corso descrive le applicazioni dei tool di intelligenza artificiale (AI) all'analisi di segnali, immagini e dati biomedici, con particolare enfasi sulle esigenze peculiari di queste applicazioni. Verrà descritta l'attuale pratica sanitaria che utilizza AI, in particolare questioni relative alla sicurezza, agli aspetti etici e legali. Saranno trattati gli attuali sviluppi dell'AI in diverse aree: medicina di precisione, elaborazione diagnostica delle immagini e radiomica, classificazioni dei biosegnali, stadiazione e stratificazione del rischio del paziente, pianificazione chirurgica, selezione della strategia di trattamento per i pazienti oncologici.

The course educates students to become professional data scientits by reviewing several statistical models, methods and algortihms aimed at the statistical analysis of mutivariate data. The aim is twofold: first, to provide future data scientists with the mathematical knowledge and understanding necessary for making proper judgments when selecting appropriate methods and algorithms, producing sensible interpretations of the results generated by their application and grasping their strenghts and weaknesses and, second, to enhace the students ability in applying the knowledge and understanding of the statistical approach to data analysis by emphasizing real life and engineering applications where statistical methods and modern computer packages permit to elicit information from multivariate data through complex statistical analyses.
The course is offered in two versions, for 8 CFU and 10 CFU respectively. Both versions are named Applied Statistics and are described in the present document. In the 8 CFU version, the course will cover classical topics of Multivariate Data Analysis (e.g.: dimension reduction, inference for regression, supervised and unsupervised classification) with overtures to the modern treatment of multiple inference (FDR) or to novel statistical learning methods and algorithms (e.g. support vector machines, ensemble leraning methods). To these contents, the 10 CFU version of the course adds three modules of Advances in Statistical Learning, leveraging on seminars offered by experts of the fields (e.g.: Linear Mixed Models, Functional Data Analysis, Spatial Statistics).
Through an extensive recourse to blendend learning and flipped classroom innovative teaching, both during the lectures and the lab sessions, the course will enahace the students ability in autonomous learning; this will also be accomplished by perusing new teaching media like the MOOC on Statistical Learning by Hastie and Tibshirani referenced in the Bibliography.
Particular emphasis is given to the devolopment of a responsible and efficient attitude toward work in a multidisciplinary environment where the data scientist collaborates on a peer-to-peer basis with other engineers and scientists for the modeling and understanding of complex phenomena of scientific or industrial interest. Hence, the course requires team work on real data statistical analyses, either in interaction with industrial partners of the statistical research group of the Department of Mathematics or in collaboration with scientists and engineers demanding a data-driven approach to the solution of their research problem. Work-in-progress of the teams will be periodically discussed in class, drawing attention not only on the appropriatness of the statistical methods and algorithms, but also on the communication skills of the teams when informing an audience of peers.
The course fits into the overall program curriculum pursuing some of the defined general learning goals. In particular, the course contributes to the development of the following capabilities:
Design models and utilize information from experimental data for inferential estimation, verification and adaptation of the models and for their heuristic developments;
Provide the statistical interpretation and simulation of scenarios for the treatment of data in situations of high complexity;
Use R for the analysis and treatment of complex data.

Both versions of the course have the following common learning goals:

• At the end of the course students are expected to be able to design - and run with R - data analyses aimed at: reducing the dimensionality of a dataset, solving a classification problem, both supervised or unsupervised, making multiple inference on multiple mean vectors or their components, choosing the most appropriate regression model and fitting it while making inference on its components, handling classical (OLS) or more modern approaches to model building and selection (ridge regression and lasso). Leveraging on their engineering forma mentis and on the skills in data analysis acquired in the course, students are expected to be able to evaluate the practical and statistical significance of the final result of their data analysis, to quantify its uncertainty analytically or through simulation, e.g. by cross-validation, and to diagnose its potential shortcomings, either when used to provide an empirical explanation of the industrial or scientific problem under study or when the main goal of the analysis is to formulate predictions.
• To prepare for responsible and efficient interactions in a working environment, every student is required to take part in a real data analysis project developed by an independently formed team of 3-5 members. The work in progress of the projects will be collectively discussed during general meetings scheduled along the course; final analyses and results will be presented in a workshop which will take place at the end of the course.
• Students are expected to be able to communicate and transfer the results and interpretations of their data analysis to a wider audience of experts, using effective graphical or analytical means, suitable for the problem under study, the findings of the analysis and, finally, the audience.
  Moreover, the students of the 10 CFU version of the course are expected to have a basic understanding of the more complex issues - and the methods and algorithms developed to solve them - characterizing the statistical analysis of data when heterogeneity and temporal or spatial dependence is of importance or when data do not belong to the finite dimensional Euclidean setting considered in the classical Multivariate Data Analysis framework, like in the case of functional data.

The topics covered by the 8 CFU version of the course are the following:
1) The essence of statistical learning. The regression function: local methods and the curse of dimensionality. Structured models. Test error, training error and expected test error. The bias variance tradeoff. Generalization error and Expected generalization error. Bias-variance tradeoff.
2) Exploring a multivariate dataset: descriptive statistics and graphical displays. The geometry of a multivariate sample. Generalized Variance. The metric induced by the covariance matrix.
3) Data representation and dimensional reduction: the analysis of the covariance structure, principal component analysis. Independent component analysis.
4) Inferences about a mean vector: Hotelling T^2 test. Confidence regions and simultaneous comparisons of component means. The Bonferroni method for multiple comparisons. Familywise Error Rate and False Discovery Rate. Comparisons of several multivariate means. ANOVA and MANOVA. Inference for Linear Models. Beyond Ordinary Least Squares: ridge regression, lasso, regularized least Squares. Cross-validation and model selection. Ensemble learning methods: random forests for regression and classification.
5) Discrimination, classification, clustering. Statistical classification: model, misclassification costs and prior probability. Bayesian supervised classification and the Fisher approach to discriminant analysis. Alternative approaches to classification: support vector machines and CARTs. Similarity measures. Unsupervised classification; hierarchical and nonhierarchical methods. Multidimensional scaling.
In the 10 CFU version of the course, the above topics are complemented with the following three modules of Advances in Statistical Learning:
6) Linear Mixed Models. Enriching the covariance structure of a linear model to take into account heteroschedasticity and dependence, random effects, hierarchical grouping structures, longitudinal data.
7) Functional Data Analysis. Data smoothing, dimensional reduction and representation. Functional principal component analysis. Data registration: phase and amplitude variability. Classification of functional data.
8) Spatial Statistics. Random fields, variogram models and variogram fitting. Spatial prediction and Kriging, Functional data with spatial dependence.
In both versions of the course, methods and algorithms will be illustrated in the lab sessions through applications to real data sets; analyses will be performed in R, an opensource package for the statistical analysis downloadable at www.r-project.org.
Through the course, students are required to work in team on a real data analysis project whose progress will be shown periodically to the class.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of two parts:
(a) A written exam. The written exam consists of questions (theory and practice) and of a few data analysis problems to be individually solved with R; two problems for the students following the 8 CFU versions of the course, three problems - with extra time - for those registered in the 10 CFU version. For the students taking the course for 10 CFU, the extra problem will be related to the three advanced topics treated in the modules characterizing their additional 2 CFU; working on this problem is mandatory to pass the exam of the 10 CFU version of the course. For all students, the use of a personal computer is allowed as well as that of books, personal notes etc.
In the written exam the student must show the ability to conduct a stylized data analysis, by selecting the appropriate methods and algorithms - among those introduced in the course - for solving the problems, by running the algorithms with R, by identifying the significant results and by reporting them with the precision and property of language which characterize the technical and scientific communication.
(b) Team project evaluation. Projects will be collectively evaluated by the teachers of the course and by the students participating to a final workshop at the end of the course.
During the presentation of their projects, teams must prove their ability to conduct and report a real life statistical data analysis, showing knowledge and understanding of the problem at hand and the nature of the data, proper judgment for the selection of the appropriate methods and algorithms, sensible interpretations of the generated results - grasping not only their strenghts but also their weaknesses - and, finally, communication skills when informing an audience of peers.
To pass the exam the student must pass each part of the exam with a score greater than or equal to 18/30; the final score is then obtained as the weighted average of the two scores, with weights respectively equal to 0.6 for the written exam and 0.4 for the project evaluation.

Galecki A., Burzykowski T., Linear Mixed-Effects Models using R, Editore: Springer, Anno edizione: 2013
Jhonson R.A., Wichern D.W., Applied Multivariate Statistical Analysis, Editore: Prentice Hall, Anno edizione: 2007
Ramsay, J.O. e Silverman, B.W., Functional Data Analysis (second edition), Editore: Springer, Anno edizione: 2005
Cressie, N., Statistics for Spatial Data (Revised Edition), Editore: Wiley, Anno edizione: 1993

Il corso ha lo scopo di introdurre alla scienza che studia gli allineamenti astronomici degli edifici ed il loro significato, l'Archeoastronomia. Si tratta di una disciplina ormai ben assestata la cui importanza è andata via via crescendo quando ci si è resi conto che essa fornisce una chiave di lettura spesso nuova e inaspettata di molti monumenti.
Dopo una parte propedeutica di introduzione alla astronomia ad occhio nudo, che include il movimento apparente del sole e delle stelle e il concetto chiave di precessione, durante il corso vengono svolti i seguenti argomenti: Architettura megalitica nel Mediterraneo; Rapporti tra il paesaggio costruito e l'astronomia nell'America Pre-colombiana, L'orientazione astronomica nelle città etrusche e romane; I templi greci e della Magna Grecia, Architettura e astronomia nell'antico Egitto. Il corso comprende una parte pratica di introduzione all'utilizzo di software di simulazione astronomica e loro implementazione in Google Earth.

Nowadays, deep neural networks can outperform traditional hand-crafted algorithms, achieving human-level performance on many complex tasks, such as natural language processing, text modeling, gene expression modeling, and image recognition. The course provides a broad introduction to neural networks (NNs), ranging from traditional feedforward (FFNNs) and recurrent (RNNs) to the most successful deep learning models, such as convolutional neural networks (CNNs) and long short-term memory (LSTM).
The course's primary goal is to provide students with the theoretical background and practical skills to understand and use NN, and to become familiar with Deep Learning for solving complex engineering problems.
This goal is pursued in the course by
Presenting major theoretical results underpinning NN (e.g., universal approximation, vanishing/exploding gradient, etc.)
Describing the most important algorithms for NN training (e.g., backpropagation, adaptive gradient algorithms, etc.)
Illustrating the best practices on how to successfully train and use these models (e.g., dropout, data augmentation, etc.)
Providing an overview of the most successful Deep Learning architectures (e.g., convolutional networks, autoencoders for embedding, long-short term memories for sequence-to-sequence learning, etc.)
Providing an overview of the most successful applications with particular emphasis on models for solving visual recognition tasks.

Dublin Descriptors
Expected learning outcomes
Knowledge and understanding
Students will learn:
· What are neural networks and the fundamental methods and techniques used for neural networks training
· What are the fundamental architectures used in deep learning, such as convolutional neural networks and long-short term memories, and when to use them
· What are the neural network architectures used in the different visual recognition tasks
· What are the main differences between machine learning and deep learning
Applying knowledge and understanding
Given a specific data analysis problem, the student will be able to:
· Identify which paradigm better describes a given problem
· Identify which technique to start from with the analysis, apply it to model the data and evaluate its outcome
· Implement fundamental deep learning algorithms for image and text analysis autonomously
Making judgments
Given a complex data analysis problem, students will be able to:
· Identify the most relevant model to be applied in the specific problem
· Identify the occurrence of overfitting by the model under analysis
· Iteratively refine the selected model in order to balance performance, computational complexity and overfitting
· Compare and select different models for the problem under analysis
Communication
The student will learn to:
· Discuss in written form the pros and cons of different machine learning techniques for a specific problem
Lifelong learning skills
The student will learn to:
· Face a real-life data analysis problem with a sound and complete methodological approach
· Understand complex machine learning techniques beyond the fundamental ones presented during lectures
· Develop new machine learning pipelines adapting to the specific problem at hand

Neural networks are mature, flexible, and powerful non-linear data-driven models that have successfully been applied to solve complex tasks in science and engineering. The advent of the deep learning paradigm, i.e., the use of (neural) network to simultaneously learn an optimal data representation and the corresponding model, has further boosted neural networks and the data-driven paradigm. These topics will be described in the course according to the following detailed program:
From the Perceptron to Neural Networks and the Feedforward architecture
Backpropagation and Neural Networks training algorithms, e.g., Adagrad, Adam, etc.
Best practices in neural network training: overfitting and cross-validation, stopping criteria, weight decay, dropout, data resampling, and augmentation.
Image Classification Problem and Neural Networks
Recurrent Neural Networks and other relevant architectures, such as (Sparse) Neural Autoencoders
Theoretical results: Neural Networks as universal approximation tools, vanishing and exploding gradients, etc.
Introduction to the Deep Learning paradigm and its main differences with respect to classical Machine Learning
Convolutional Neural Networks (CNN) architecture
The breakthrough of CNN and its interpretation
CNN training and data-augmentation
Structural learning, Long-Short Term Memories, and their applications to text and speech
Autoencoders and data embedding, word2vec, variational autoencoders
Transfer Learning for pre-trained Deep models
Extended models, including Fully Convolutional CNN, networks for image segmentation (U-net) and object detection (e.g., R-CNN, YOLO )

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
The course foresees a written exam and some homework assignments in the form of coding exercises/challenges. The written exam is aimed at verifying the acquisition of theoretical knowledge of the course subject, while the coding exercises aim at acquiring practical experience with the most widely used tools in the field.
The homework assignments contribute between 0 and 10 points to the final grade. The written exam is compulsory and will contribute between 0 and 22 points. The final grade is the sum of the grades for the homework assignments and the written exam.
Homework assignments need to be delivered during the course on fixed dates. The grade obtained on these assignments is valid for the entire academic year and can be combined with the written exam grade from any call in the same academic year.
Type of assessment
Description
Dublin descriptor
Written test
Solution of numerical problems
· Computation of simple backpropagation derivation
· Computation of simple sizing problems on CNN architectures
Answer to theoretical questions
· Formal derivation of learning techniques and models
· Comparison of models in terms of complexity, overfitting issues, and applicability in different cases of data analysis
1, 2
1, 2, 3, 4, 5
Assessment of practical homework
Execution of practical homework exercises
· Application of deep learning techniques to small dataset
· Application of model selection and validation techniques on simulated and real datasets
2, 3, 4, 5

Ian Goodfellow, Yoshua Bengio, and Aaron Courville, Deep Learning, Editore: MIT Press, ISBN: 978-0262035613 http://www.deeplearningbook.org/

This course explores some of the advanced technologies enabling development of modern quantum optics and physics. An introductory review of quantum theory provides the students with the necessary theoretical background. The following topics cover the tools and techniques that have been used for electromagnetic control of atomic motion and some relevant experimental applications.

Knowledge and understanding (DD1)
Attending the lectures and passing the exam will allow the student to:

• understand the physical basis of atom-light interactions at a quantum level;
• learn the fundamental tools and techniques for manipulation of atoms and molecules;
• discover the technology behind modern optical frequency standards;
  Applying knowledge and understanding (DD2)
  The student will be able to apply the basic knowledge described above to:
• explain the operating principles of some prototypal optical devices developed for quantum optics;
• design the basic layout of a laser cooling device and ions trap;
• transfer the physical concepts to applications requiring manipulation of atoms;
  Communication skills (DD4)
  The exam requests the students to communicate clearly what they have learnt, with rigorous argumentation.
  Lifelong learning skills (DD5)
  Students will be capable to autonomously follow with greater awareness the new trends in the high-tech market dealing with atom optics and quantum technologies (from quantum communications to quantum computing).

The course of "Atom Optics and Quantum Technologies" is the Part 2 of a larger integrated course called "Quantum Optics and Technologies"; Part 1 is called "Quantum Opics and Information". Lessons related to Part 1 and 2 are given in the first and second half of the semester, respectively. Hence, students registered only to the course of "Atom Optics and Quantum Technologies" will attend their lessons starting from the second half of the semester, just by the end of lessons related to Part 1. The following is the list of subjects covered by the course of "Atom Optics and Quantum Technologies".
Quantum theory of optical resonators and amplifiers
1. Linearized quantum noise description
2. Quantum equation of motion for the cavity mode
3. Optical amplifiers
4. Squeezed light generators
Quantum theory of atom-light interactions
5. Basic concepts and definitions
6. Optical Bloch equations
7. Force on two-level atoms
Optical cooling and trapping of atoms and molecules
8. General properties concerning laser cooling
9. Photon recoil and Doppler cooling
10. Optical molasses, sub-Doppler cooling
11. Cooling and trapping of ions
12. Molecular cooling: direct and indirect methods
Application
13. Atomic fountains clocks
14. Atom mirrors, atom laser
15. Optical tweezer
16. Zeeman slower
17. Magneto-optical trap (MOT)

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The exam is made of a test in written form. The test will will have a duration of 1.5 hours, and will typically consist of 3 open questions on different topics. An optional oral exam, requested by the student or by the teacher in specific cases, may complete the evaluation.
The aim of the exam is to ascertain:

• the understanding of the physical basis of quantum optics and information;
• the knowledge of the definitions, theorems and general concepts related to quantum optics and quantum information;
• the capability to discuss, both qualitatively and quantitatively, the quantum physical models and protocols relevant for the course.
• the comprehension of the experimental techniques for laser cooling and trapping of atoms and molecules
• the understanding of relevant applications of atom optics and quantum technologies
  Students can take the exam in the usual five dates along the year (two in summer session, one in autumn session and two in winter session). As the course of "Atom Optics and Quantum Technologies" is the Part 2 of a larger integrated course called "Quantum Optics and Technologies", each exam will provide students with the chance to give the test on Part 1 and/or Part 2, separately. To this end, each exam is scheduled with an overall duration of 3 hours and 15 minutes: it starts with 1.5 hours dedicated to Part 1, then 15 minutes resting, and finally 1.5 hours on Part 2. Students registered to the course of "Atom Optics and Quantum Technologies" can give their test in the second half of the exam after the resting.

Gilbert Grynberg, Alain Aspect, Claude Fabre, Introduction to Quantum Optics, Editore: Cambridge University Press
Hans-A. Bachor, Timothy C. Ralph, A guide to experiments in quantum optics, Editore: WileyVCH Verlag GmbH & Co. KGaA
Christopher J. Foot, Atomic Physics, Editore: Oxford Master Series in Physics
Wolfgang Demtröder, Laser Spectroscopy 1 - 2, Editore: Springer

The objective of the course is the development of a general and specific know-how on the estimation and control methods for the autonomous navigation of road vehicles. The course focuses on ground vehicles and, more specifically, on passenger cars and alike. The course deals with the fundamental problems of trajectory and speed-profile generation, trajectory-tracking, positioning and obstacle-detection, and provides an overview of the main sensing and SW-sensing technologies in autonomous cars.
The course aims to illustrate the basic sub-problems and technologies needed to develop a completely-autonomous road vehicle, with special attention on the estimation issues, and on the control strategies and algorithms.
The main focus will be on fully-autonomous vehicles (L4 and L5), but also conditional autonomy (L3) will be considered, with attention on human-factors (disengagement and re-engagement of human driver).
The course will present the classical sub-topics of autonomous vehicle design:

• Sensing and perception, estimation, localization
• Global planning
• Local planning
• Trajectory tracking
  These topics will be developed at different levels of detail, where the emphasis will be on estimation and control algorithms specific for road vehicles (passenger cars or alike). The case of extreme performance (driving at the very limit of the car), in a in-circuit environment will be also considered.

Dublin Descriptor
Expected Learning Result (Specific to the Course)
Knowledge and understanding
Understand the fundamental problems, methods, and technologies for autonomous vehicle navigation (L3-L5), with a specific focus on estimation issues and control strategies (e.g., trajectory generation, localization, obstacle detection).
Applying knowledge and understanding
Design and apply control and estimation algorithms to solve specific sub-problems in autonomous navigation, such as trajectory-tracking, local planning, and vehicle control at the limits of handling.
Making judgements
Critically analyze and evaluate trade-offs between different design solutions, control algorithms, and sensing technologies for autonomous passenger cars, including considerations for human-factor issues in L3 systems.
Communication skills
Communicate a complex control-design solution for a specific autonomous vehicle application (e.g., path following, speed profiling) in a synthetic and technically precise way.
Learning skills
Autonomously read, interpret, and understand specialized industrial technical documentation and research papers in the field of autonomous vehicle control and estimation.

The course will cover the main areas of estimation and control technologies for autonomous cars (sensing and localization, global and local planning, trajectory-tracking and HMI). More specifically, the course sub-topics are the following:
Overview of “ego” sensing technologies; basics of their signal-processing
Road-sensing and vehicle-states sensing for control design: estimation of road-tire available friction, lateral and longitudinal slips (used for local planning and trajectory tracking)
Map-based positioning using GNSS, IMU and road-markers
Trajectory tracking (lateral, longitudinal, and joint lateral-longitudinal).
Local planning: control-oriented generation of trajectories (obstacle-avoidance trajectories)
Global planning: control-oriented generation of trajectories (in-circuit optimal trajectories) and optimal speed-profile (for energy, comfort, speed optimization)
Partially/conditioned autonomy and human factors

Prova scritta facoltativa (a scelta dello studente), senza prove in itinere
Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The exam will be a written test in one of the official available dates or a project (group or single). The exam consists of questions on the topics presented during the course. The project requires the development of techniques starting from the one seen in class.
Grading will be on the following basis: either 100% final project (group presentations with discussion with instructor) or 100% written test on the course topics.
The instructor reserves the right to hold an oral examination in cases where the written test does is not definitive in assessing the student's knowledge.
Type of assessment
Description
Dublin descriptor
Final project
Students are required to:
show their understanding of the main problems (and the corresponding solutions) in the field of control-systems design in vehicles;
use the knowledge acquired in the course to solve problems that they have not be exposed to in class.
select and describe the most appropriate tools for a given application;
be able to communicate in a oral presentation the solution to a specific application problem (modelling or analysis or control problem).
implement the solution they propose.
1,2, 3, 4, 5
Written test
show their understanding of the main problems (and the corresponding solutions) in the field of control-systems design in vehicles;
use the knowledge acquired in the course to solve problems that they have not be exposed to in class.
select and describe the most appropriate tools for a given application;
be able to communicate in a mixed text, graphical and mathematical way the solution to a specific application problem (modelling or analysis or control problem).
1, 2, 3, 4, 5

Matteo Corno, Lecture notes

The goal of the course is to enable students to understand and be familiar with model-based and simulation-based approaches to statistics. In particular, the course focuses on Bayesian learning, its tools and main classes of models. This will enhance students’ abilities to address the statistical analysis of complex systems for which transversal and multidisciplinary skills are required. The Bayesian approach tells us how to update prior beliefs about parameters and hypotheses of a probabilistic model in the light of data, to yield posterior beliefs. In particular, Bayes' Theorem quantifies the problem of how to learn from data. Bayesian learning hinges on simulation methods, typically MCMC algorithms, to compute the posterior distribution.
The course adopts innovative teaching methods:
a data analysis project, as a part of the student assessment, to enhance specific soft skills such as Making judgements, Communication skills and Ability in learning ( 3 rd, 4 th and 5 th elements of the so-called European “Dublin Descriptors” – DD )
collaborative activities among students, some in small groups, and with continuous assessment of learning. This type of activity is in presence.
This is a 10 ECTS course, course code # 052499. However, there is a version of it (code # 052502, Bayesian Statistics, 8 ECTS). The only difference between the two courses is that the topics of the 8-credits course do not include neither topic 6 nor models for areal and point-referenced data in topic 7 (see the list of topics below).
For the LM program in Mechanical Engineering, there is a 5 ECTS course in Bayesian Statistics. In this case, the topics are only 1-4 from the list below.

On successful completion of the course, students will be able to:
understand the fundamental principles, tools and models of Bayesian Statistics (DD 1 - knowledge and understanding )
model simple engineering problems in terms of statistical problems using the Bayesian approach to update prior belief in the light of new data (DD 2 - Ability in applying knowledge and understanding )
select appropriate Bayesian tools to give statistical answers and use appropriate software ( R packages, JAGS, Stan, Python) for the computation of posterior inference, or to build this software by themselves (DD 2)
operate and communicate the choices made, making independent judgments, when using Bayesian tools for dealing with statistical problems from the real world (DD 3, 4 and 5)
work effectively as part of a team.

The first part of the course (topic 1) will enable students to understand foundational aspects of Bayesian Statistics (the choice of the prior, for instance), while in the second part (topics 2-7), after the introduction of Markov Chain Monte Carlo techniques for simulation from the posterior, students will be able to use specific statistical models for estimation, prediction or clustering.
1. Basics of Bayesian inference. Likelihood principle, prior and posterior distribution. Bayes' Theorem for dominated models. Posterior summary values. Interpretation of scientific inference via the Bayesian approach. Simple univariate Bayesian models. The three main inferential problem: point estimation, hypothesis testing, interval estimation: comparison between the frequentist and the Bayesian approach. Prior distributions. The choice of a prior distribution, noninformative priors, conjugate priors and their mixtures, semi-conjugate priors. Robustness. Exchangeability and de Finetti's representation theorem for exchangeable sequences. Implications of de Finetti's theorem on the Bayesian approach. Predictive inference. Asymptotic results on the posterior distribution.
2. Simulation methods for Bayesian Statistics. A quick recap on the theory on general state space Markov chains. Markov chain Monte Carlo methods. Gibbs sampler and Metropolis-Hastings algorithms for computing posterior inference. Implementing Markov chain Monte Carlo: software for Markov chain Monte Carlo (BUGS/JAGS from R), assessing convergence and run-length.
3. Goodness-of-fit and model choice. AIC, BIC, DIC, Predictive Bayesian tail probabilities, log-pseudo marginal likelihood (LPML), WAIC; prior and posterior distributions for the model index, maximum a posteriori (MAP) model selection.
4. Bayesian linear models and generalized linear models. Hierarchical linear models with random effects. Parameter estimation and covariate selection.
5. Bayesian survival analysis / reliability with censored data. Regression models: accelerated failure time and proportional hazards models.
6. Bayesian nonparametric models. The Dirichlet process and generalizations. Bayesian nonparametric mixture models, with application to density estimation and clustering.
7. Introduction to models for longitudinal data, time series, spatial data (point-referenced and areal data).
Within the Innovative teaching activity, we include 2 classes (4h + 4 h) in presence, during which students will be required to do exercises for designing and implementing (using Python or R software) algorithms for simulation, supervised by tutors and the teaching assistant. This type of active learning will include continuous assessment of learning.
The oral exam consists in the presentation of the project (in groups), focusing on a statistical problem with data, using Bayesian models, to enhance students’ soft skills such as Making judgements, Communication skills and Ability in learning. There will be intermediate revisions of the projects (this is a group activity), where the groups will discuss with tutors, TA and instructors, in presence. This type of active learning will include continuous assessment of learning.
The list of topics for the course with code # 052502, 8 ECTS, do not include topic 6 nor models for areal and point-referenced data in topic 7.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of two parts: a written exam and a project work (with a final oral presentation). It is compulsory to register for the written exam, which is scheduled twice in January-February, twice in June-July, and one in September.
The final project assessment is the presentation of the work on project, i.e. analyzing a statistical problem with data, using Bayesian tools and models. The projects will be developed in teams. The evaluation of the projects will be based on the revisions (activity in presence - at most two) the teams will undergo during the course and a conclusive presentation. During the conclusive presentation, each students’ team must hand over a project report (10-20 pages).
Participation in presence to the revisions and the final presentation is compulsory for all team members, but for Erasmus students.
If, at the beginning of the semester, the student understands he will not be able to actively participate in the group project during the semester for any reason, the student is allowed to discuss an individual project after passing the written test, instead of the group project. Because the student will not be tested on all the Expected Learning Outcomes (Risultati di apprendimento attesi), the final grading of the individual project cannot be larger than 26/30.
To obtain a positive final mark, the student should pass with a grade greater or equal than 18/30 for both parts of the exam.
Final grading: 40% written exam, 60% project work.
After the exam:
the student will know the fundamental principles, tools and models of Bayesian Statistics (DD1),
he/she will be able to apply the acquired knowledge to statistical problems from the real world (DD2),
making independent judgments, the student will operate and communicate the choices made, when using Bayesian tools to solve statistical problems from the real world (DD3,DD4,DD5).

Rosner, G. L., Laud, P. W., Johnson, W. O., Bayesian Thinking in Biostatistics, Editore: Chapman and Hall/CRC, Anno edizione: 2021
Guglielmi, Lecture Notes
Jackman, S., Bayesian analysis for the Social Sciences, Editore: Wiley, Anno edizione: 2009, ISBN: 978-0-470-01154-6
Andrew Gelman et al., Bayesian Workflow, Editore: Taylor and Francis
Lunn D., Jackson C., Best N., Thomas A., Spiegelhalter D., The BUGS book, Editore: CRC Press, Anno edizione: 2013, ISBN: 978-1-58488-849-9
Hoff, P., A first course in Bayesian Statistical Methods, Editore: Springer, Anno edizione: 2009, ISBN: 978-0-387-92299-7
Mueller, P., Quintana, F., Jara, A., Hanson, T., Bayesian Nonparametric Data Analysis, Editore: Springer, Anno edizione: 2015
Christensen, R., Johnson, W., Branscum, A., Hanson, T.E., Bayesian Ideas and Data Analysis, Editore: CRC Press, Anno edizione: 2011, ISBN: 978-1-4398-0354-7

Goals
The objective of the course is to present to the students, approaching the end of their M.Sc. educational carrier, an overview of the field of biochips and analytical lab-on-chip microsystems (whose recent advances are relevant both from the scientific and industrial point of view) with specific insights on the technological aspects of the interface between (micro)electronics and electrochemistry and biology, both at cellular and molecular levels. The content of the course reflects the multidisciplinarity of the nano-bio-tech field and is mainly focused on the different manipulation and detection approaches of biochemical target analytes on chip. The main goal is to provide the students with the fundamental theoretical tools for the design of active microfluidic systems (basics of fluid dynamics at the microscale), and of the engineering of the detection systems (optical and electrochemical transducers). At the same time, several practical examples are discussed in order to illustrate design choices and trade-offs. Starting from 2020, a part of the course will be taught by means of innovative learning techniques. The topics of microfabrication (hard and soft-lithography) will be addressed by means of MOOC videos recorded in actual clean-rooms and fabrication facilities. Finally, a "blended" and "flipped-classroom" approach will be adopted in the last part of the course including a project-based and a laboratory activities where student will fabricate real devices and boards: at first they will be grouped into small teams (3-4 persons max.), will design at home the layout of the microchannels and electrodes on a PCB including a transimpedance amplifiers, according to some design challenges posed by the teacher, and then will fabricate them in the lab with 3D printing and soft-lithography (PDMS elastomer by means of replica molding). A characterization with fluids, electrolytes. digital microscopes, pumps and virtual instrumentation (oscilloscope, network analyzer used for impedance measurements) will conclude this experimental activity. Prior to fabrication of the PCB, each team will present their design in the class and feedback from a general discussion will be collected.

Expected Learning Outcomes
Knowledge and understanding (Dublin Descriptor #1)
At the end of the course the students are expected to:
· possess a good understanding of lab-on-chip systems (needs, applications, advantages and limits) and bio-electronics convergence
· possess a basic knowledge of hard and soft lithographic microfabrication approaches
· possess a basic knowledge of the laws describing the flow of liquid in microchannels and the forces to actuate particles in liquid
· presses a good knowledge of the electrochemical interface and instrumentation for biosensing
· possess a good knowledge of the DNA macromolecule and the instrumentation for its analysis
· understand the potentials and challenges of CMOS/biochips integration
Applying knowledge and understanding (Dublin Descriptor #2)
At the end of the course the students are expected to:
· be able to analyze and design a microfluidic system in laminar regime (fluidic sizing, choice of components such as pumps/valves), starting from the sample preparation and manipulation
· be able to design an analytical assay (for instance for molecular recognition or DNA analysis)
· be able to design integrated detectors (both optical and electrochemical)
· be able to design current and impedance sensing circuits for biochips
Making judgements (Dublin Descriptor #3)
Students will be able to:
· evaluate the most appropriate approach (materials, fabrication) to address an analytical need
· apply the knowledge to different application areas
· apply the knowledge to design a novel micro-device
Communication (Dublin Descriptor #4)
During the work in teams for the experimental laboratory, students will be able to communicate among each other (in the first phase at home, when the microfluidic channels are designed upon technological specifications set in the classroom). Then, during the lab. and the oral exam their communication skills are deployed to motivate their design choices and comment the experimental results.

Topics
The course is articulated in theoretical lessons, combined with quantitative exercises and with case studies oriented to the analysis and design of microsystems. An experimental laboratory consisting of: a design phase at home in teams with a propor design software and two days of experimental activity in the lab. (fabrication and characterization of a PDMS microfluidic device). Experts in the biochip field are also invited during the course to lecture seminars on specific topics, such as micromagnetism and DNA analysis, or to present the point of view of companies carrying on R&D in the biochip field (STMicroelectronics, Flextronics, Dianax etc…). A visit to the renewed clean-room and microfabrication facility of Politecnico di Milano (PoliFab) concludes the course.
1. Introduction to biochips: architecture of lab-a-chip micro-analytical systems, motivations and impact, design paradigms, market projections, basic biological macromolecules used for as receptors in affinity biosensors.
2. Introduction to microfluidics: fluid dynamics, Reynolds number, electrical equivalent of hydraulic circuits (fluidic capacitance) and electro-osmotic flow. Actuation forces for particle manipulation within biochips: diffusion, electrophoresis, dielectrophoresis, electrowetting and droplet-based digital microfluidics. Active and passive microfluidic components: valves, mixers and pumps.
3. Introduction to microfabrication: review of Silicon CMOS-MEMS processes, lithography, thin film deposition and patterning, as compared to elastomer (PDMS) and plastic based soft lithography (replica molding).
4. Optical detection: fluorescence (strengths and limitations, Atomic Force Microscopy ), source-filter-detector architectures, integrated photonics for biosensing based on evanescent field (waveguides, Mach-Zehnder interferometers, ring resonators and contactless light monitors). Electrochemical detection: the electrochemical interface with physiological ionic solutions (charge transfer and induction).
5. Electrochemical instrumentation: analytical techniques (cyclic voltammetry, amperometry and impedance spectroscopy) and the potentiostatic workstations. Micro and nano-scale electrochemistry: effects of electrode scaling.
6. Low-noise current measurements: review of noise in electronic devices, the transimpedance amplifier (working principle, properties and limitations) and advanced circuit topologies (integrator-differentiator schemes with different CMOS-compatible bias resetting solutions).
7. Impedance measurements and instrumentation, comparison of sensing configurations: bridge, ratiometric, current sensing, lock-in detection, resonant circuits, FFT-based and time-domain approaches.
8. Detection of DNA: structure and properties, microarrays (spotting and probe synthesis), electrophoresis, amplification with Polymerase Chain Reaction and quantitative detection with real-time PCR and approaches for sequencing.
9. Biochips for molecular detection: resonating cantilevers for molecular weighing, amperometric detection of neurotransmitters, redox cycling, glucose sensors based on enzymatic mediators, and nanopores. Biochips for cellular detection: interface with electrogenic cells, equivalent model of passive cells, label-free impedance monitoring a cell colony dynamics and single cell counting and sizing with microfluidic impedance flow cytometry (design case study).
10. Sample preparation (cell lysis, sample mixing, concentration and purification). Microelectronics CMOS biochips: state of the art performance in CMOS detection, design criteria, advantages and limits, the critical role of the substrate, packaging and interfacing issues.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente) o condizionata (a scelta del docente)
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
Assessment
Exams are held at the end of the course (no intermediate tests). The exam consists of a written test (of a duration of 2 hours) followed by an oral exam. The written test (assessing Dublin Descriptors 1 and 2) encompasses the solution of numerical exercises focusing on 2 types. The first type concerns the microfabrication and the fluidics (and components) of micro-channels and devices. The second type mostly focuses on electrochemical detection. The students will be asked to analyze circuits and systems, as well as to design them. The maximum evaluation of the written test is 30. Two bonus points are added for those who attended the laboratory activity.
The outcome of the written tests is communicated to the students by email. Then, a meeting in the classroom is scheduled for the students to vision and discuss the correction of the written test. They can accept or refuse the evaluation, either by email or in-person communication. They can undertake the oral test in the following days, by agreeing a calendar with the teacher.
The oral discussion (assessing Dublin Descriptors 1,2,3,4) is mandatory for students achieving top marks in the ranking (> 27/30) in the written test and it is optional and open for all students with a mark above 17/30 in the written test. In the oral test (lasting 15 to 40 minutes) students will be asked discuss the ultimate limits of the different technologies, pros and cons, compare them, and to design complete systems to address novel design cases proposed during the oral exam. The maximum evaluation is 30 cum laude.

Patrick Tabeling, Introduction to Microfluidics, Editore: Oxford University Press, Anno edizione: 2010, ISBN: 9780199588169
Eugenio Iannone, Labs on Chip: Principles, Design and Technology, Editore: CRC Press, Anno edizione: 2014, ISBN: 978-1466560727
Albert Folch, Hidden in Plain Sight: The History, Science, and Engineering of Microfluidic Technology, Anno edizione: 2022

The role of mathematics in biological modelling has considerably increased during the last twenty years and represents today a significant fraction of all research projects in applied mathematics. On the other side, the knowledge of the mechanical and, more generally, of the mathematical aspects of biological processes across the scales from cells to tissues has become enormous.
The arising mathematical problems, although they represent the translation of well-known physical laws into the realm of Biology, are often very difficult to tackle without an appropriate numerical setting and analylitic approximation.
Therefore, the course aims to give a solid mathematical background in the field of biomathematics and up-to-date knowledge of the main biomathematical models widely used in biology and biomedicine, outlining the most important mathematical tools needed for their setting and comprehension.
Each topic is treated both theoretically and practically through a project work.

Lectures and exercise sessions will allow students to:

• Analyze and understand the goals, assumptions and requirements associated to modeling of a biological system model;
• Define the analytical and computational tools to derive the model results;
• Identify and define the tools to verify and to validate the model results and their correspondence with the experimental observations.
  The project laboratory will allow students to:
• Write the numerical impementation of partial differential models starting from a code writen by others;
• Analyse the simulation results in the range of biologically admissible parameter range;
• Summarize and present the results achieved.
  The expected skills focus on the ability of the student in creating models fitting applied and experimentally verifiable situations in biology. The student must know the most important models in biomathematics treated in the course and be able to describe then critically rather than knowing formulas and expressions by heart.
  The most important skill, however, is the capability of the student of drawing rigorous conclusions from the models using the existing literature in the topic and his mathematical background.
  The student should then be able to read a scientific article or a book chapter on biomathematical modelling and recognize first the parts where physical or biological laws are set, then the approximations used and finally the conclusions, focusing on possible drawbacks or inconsistencies with respect to the observed experiments.
  Finally, it is expected that the student acquires a fairly good vocabulary of the technical terms involved in the shown models in Biology, as well as the corresponding vocabulary of terms arising from mathematics.

Introduction to biomathematical modelling; dimensional and asymptotic analysis.
Elements of dynamical systems: phase space, equilibrium and stability, bifurcations and limit cycles, homoclines and heteroclines.
Chemical kinetics and conservation laws. Law of Mass Action. Active and passive transport in electrophysiology. Electrodiffusion of ionic species across the cell membrane. Effective potential and ionic currents: cellular excitation.
The experiments and the model by Hodgkin and Huxley; the model by FitzHugh and Nagumo. Examples and computer simulations.
Cable equation for the spatial propagation of ionic currents in electrophysiology. Nonlinear wave propagation: traveling fronts, traveling pulses, spiral waves. Application of the theory to the propagation of electrical signals in neurons. Examples and computer simulations. Elements of Fourier analysis, linear stability analysis. Application of the theory to reaction-diffusion systems of equations: Turing instability and pattern formation.
Population dynamics. Lotka-Volterra model: local and global stability. Structured population: von Foerster equation. Mathematical epidemioloogy: compartment models.
Transport and drug delivery in tissues. Growth of spheroidal tumor in vitro in its avascular phase: the Greenspan model. Multiphase models: sharp versus diffuse interface approaches. Application to neurodegenerative diseases and precision oncology.

Prova orale obbligatoria
The exam will be oral and written on the blackboard. The questions during the oral exam will concern the Theory and the Esercitazioni. As for the Theory, a good knowledge of the part of general theory is required, while for the models part a deep knowledge of the finest algebraic passages is not necessary. The questions regarding the Esercitazioni will concern examples seen during the course and some calculations made in order to explain them. The evaluation will focus on mathematical rigour, knowledge appropriateness of language,
The Student shall prepare a short presentation (10 minutes approx.) based on material on models NOT covered in the Course, writing a mail to prof. Ciarletta in due time (at least 2 weeks before), choosing a topic of interest. The presentation will be evaluated mainly on the clarity of the exposition and it must be in English.

Keener-Sneyd, Mathematical Physiology
B. Perthame, Growth, reaction, movement and diffusion from biology
J.D. Murray, Mathematical Biology vol I and II, Editore: Springer

Questo corso si propone di introdurre gli studenti di ingegneria a questioni filosofiche ed etiche che emergono con l'uso delle tecnologie biomediche. Ad esempio, gli ingegneri spesso si avvalgono di simulazioni informatiche di modelli idealizzati dei loro oggetti di studio. Tuttavia, tali procedure sono affette da incertezze rappresentazionali e computazionali che sono ineliminabili. Si presentano quindi questioni filosofiche circa l'attendibilità delle predizioni risultanti, oltre che questioni etiche riguardanti la responsabilità morale dell'uso delle tecnologie utilizzate. Allo stesso modo, l'inedita abilità a trattare un'enorme quantità di dati apre scenari affascinanti, soprattutto nel campo della medicina di precisione. Eppure, anche qui si devono affrontare domande aperte sulla capacità predittiva degli algoritmi impiegati nel trattamento dei Big Data, oltre che problemi morali concernenti la privacy e il controllo delle informazioni personali.

Questo corso si propone di introdurre gli studenti di ingegneria a questioni filosofiche ed etiche che emergono con l'uso delle tecnologie biomediche. Ad esempio, gli ingegneri spesso si avvalgono di simulazioni informatiche di modelli idealizzati dei loro oggetti di studio. Tuttavia, tali procedure sono affette da incertezze rappresentazionali e computazionali che sono ineliminabili. Si presentano quindi questioni filosofiche circa l'attendibilità delle predizioni risultanti, oltre che questioni etiche riguardanti la responsabilità morale dell'uso delle tecnologie utilizzate. Allo stesso modo, l'inedita abilità a trattare un'enorme quantità di dati apre scenari affascinanti, soprattutto nel campo della medicina di precisione. Eppure, anche qui si devono affrontare domande aperte sulla capacità predittiva degli algoritmi impiegati nel trattamento dei Big Data, oltre che problemi morali concernenti la privacy e il controllo delle informazioni personali.

L'obiettivo del corso è duplice:
1. Rendere gli studenti consapevoli delle complesse dinamiche della comunicazione e della persuasione, con un'enfasi speciale sulla componente personale (mittente/destinatario).
2. Equipaggiare gli studenti con abilità comunicative perché siano in grado di produrre comunicazioni orali, scritte e in forma multimediale che siano chiare e persuasive.
Il corso adotta tre strategie:

• Lezioni frontali
• Modalità "blended" e "flipped" (gli studenti accederanno in maniera autonoma a risorse online quali esempi di discorsi - in forma scritta o di video -, articoli, casi di studio, lezioni in video)
• Tutoring in presenza o in remoto (attraverso collaborazione "cloud") sui compiti da svolgere e sul progetto finale

L'obiettivo del corso è duplice:
1. Rendere gli studenti consapevoli delle complesse dinamiche della comunicazione e della persuasione, con un'enfasi speciale sulla componente personale (mittente/destinatario).
2. Equipaggiare gli studenti con abilità comunicative perché siano in grado di produrre comunicazioni orali, scritte e in forma multimediale che siano chiare e persuasive.
Il corso adotta tre strategie:

• Lezioni frontali
• Modalità "blended" e "flipped" (gli studenti accederanno in maniera autonoma a risorse online quali esempi di discorsi - in forma scritta o di video -, articoli, casi di studio, lezioni in video)
• Tutoring in presenza o in remoto (attraverso collaborazione "cloud") sui compiti da svolgere e sul progetto finale

The main objective of this course is the detailed study of the mathematical models describing the electric activity of the heart. The course adopts a multiscale approach, starting at the single ionic channel and moving to the ionic currents, the action potential of the different cells of the heart, up to the torso. The course looks in detail at the numerical solution of the resulting equations as well as their implementation on the computer, favoring the interaction of the student with computer codes implemented in a user-friendly environment. These modeling and simulation tools are then applied to the study of arrhythmias, such as those associated with acute regional ischemia, and other pathologies.

Lectures and exercise sessions will allow students to:
Understand and describe complex engineering problems in the field of biomedical engineering (DD1)
Set up a model to simulate the electric activity of the heart, identifying the right elements composing the model and their characteristics (DD2)
Interpret the results of an electrophysiological simulation and the interactions/synergies between the different elements of the model (DD1)
The project laboratory will allow students to:
Perform continuous learning and develop strategies for autonomous learning (DD5)
Analyze software code written by others (DD2)
Summarize and present the results achieved during the analysis and specification activities (DD3 and DD4)
Communicate the results of their activity in a clear and concise manner (DD3 and DD4)

Basic physiology of the heart: functioning and structure. Modeling cardiac excitation and excitability: the cardiac action potential. Models of cardiac action potential. Numerical integration of models of action potential. The concept of stability and requirements of the time step. The muscle structure of the heart: mathematical models of cardiac anatomy. Modeling propagation in excitable media: monodomain and bidomain equations. The extracellular potential and the model of the torso. The finite element method for modeling impulse propagation: algorithms, numerical implementation, convergence, stability and performance. Influence of space and time discretization. Cardiac arrhythmias: types of arrhythmias and mechanisms causing reentries. The concept of vulnerability window. The acute ischemic heart. Study of other cardiac pathologies.
Course material:
Handouts, presentations, (accessible) papers on computational biology of the heart. For model implementation, the software OpenCore is used for single cell models, and the software package Matlab will be used for modeling the electric and electromechanical models in 1D and 2D cases.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
Students will be evaluated at the end of the course on the basis of a written examination on the theoretical parts of the course, the reports from practical sessions, and the presentation of the course project.
Final exam: 80%
Report of practical sessions and project presentation: 20%
Oral exam: Students with a final mark of 30/30 can opt for an oral exam to achieve the final mark 30 with honors

Sundnes J, Lines G T, Ca X, Nielsen B F, Mardal K A, Tveito A, Computing the Electrical Activity in the Heart, Editore: Springer, Anno edizione: 2006, ISBN: 3-540-33432-7
Panfilov AV, Holden AV (Editors), Computational Biology of the Heart, Editore: John Wiley and Sons, Anno edizione: 1997, ISBN: 0-471-96020-9
Keener J, Sneyd J, Mathematical Physiology, Editore: Springer Verlag, Anno edizione: 1994
Jaakko Malmivuo and Robert Plonsey, Bioelectromagnetism http://www.bem.fi/book/

The course introduces the students to the most important methods for the numerical computation of electromagnetic fields. Typical applications of the presented methods can be found in electrical and biomedical engineering.
Each method will be introduced theoretically and then applied to canonical problems using Matlab/Octave.
Challenging problems taken from real applications (some of them suggested by private companies or research centers) will be proposed to the students for their final project work.

Lectures sessions will allow students to know:
the most important differential and integral formulations and discretization methods for the numerical solution of quasi-stationary Maxwell equations;
one of the most common discretization methods for the numerical solution of the equations describing the propagation of an electrical signal along a transmission line;
the vectorial basis functions for the discretization of electromagnetic fields;
one of the most common discretization methods for electromagnetic wave propagation problems
how to implement the presented numerical methods in Matlab/Octave;
Laboratory sessions will lead the students to perform numerical experiments using existing codes and electromagnetic software packages.
The final project work will stimulate the ability to apply the previous knowledge to a real application, choosing the most suitable method for the electromagnetic problem at hand.
The instructor expects a deep comprehension of the subjects which should not be limited to the statement of theoretical results.
Instead, the acquired knowledge should enable students to express critical judgment.

Formulations for quasi-stationary electromagnetic problems
The Method of Moments (MOM) for magnetostatic and electrostatic problems
The Boundary Element Method (BEM) for the numerical solution of Laplace equation in two and three dimensions
BEM for eddy current problems
The Finite Element Method (FEM): theoretical background
FEM for electrostatic and eddy current problems
Vectorial basis functions for FEM discretization of electromagnetic field problems
FEM/BEM coupling
The Partial Element Equivalent Circuit (PEEC) method
The Finite Difference Time Domain (FDTD) method for transmission lines
FDTD for electromagnetic wave propagation problems

Progetto/i - Elaborato/i obbligatorio, individuale, con revisioni periodiche, con presentazione/discussione finale
Students will be evaluated at the end of the course on the basis of the development and oral presentation of a project in Matlab/Octave in order to show their ability in implementing an electromagnetic numerical formulation.

S. N. Makarov, G. M. Noetscher, A. Nazarian, Low-frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB, Editore: John Wiley & Sons, Anno edizione: 2016, ISBN: 978-1-119-05256-2
J. T. Katsikadelis, The Boundary Element Method for Engineers and Scientists, Editore: Elsevier, Anno edizione: 2016, ISBN: 9780128044933
T. Rylander, P. Ingelström, A. Bondeson, Computational Electromagnetics, Editore: Springer, Anno edizione: 2014, ISBN: 1489986022
Özlem Özgün, Mustafa Kuzuolu, MATLAB-based Finite Element Programming in Electromagnetic Modeling, Editore: CRC Press, Anno edizione: 2019, ISBN: 978-1-4987-8407-8

The aim of the course is to make students familiar with the advanced quantitative methods adopted in describing the dynamics of financial markets, in valuating and hedging financial derivatives, and in optimal investments problems. An implementation of all models and methods in Matlab is an essential part of the program. The goal is to provide students with all the instruments necessary to be able to solve a financial problem, like pricing derivatives, choosing the best model and coding to obtain a numerical solution. A part of the course is also devoted to Fintech applications.
This course is connected to the joint-course 097667 - COMPUTATIONAL FINANCE (8 cfu). This sheet defines objectives, programs and learning outcomes expected for both courses.

Lectures and coding sessions will allow students to acquire the following competences:

• Knowledge and understanding
  know some advanced concept of stochastic calculus, which are essential in quantitative finance;
  know how to choose modeling assumptions to solve a financial problem properly.
• Ability in applying knowledge and understanding
  know how to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledgements.
• Making judgements
  find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
  be able to judge the possible financial risks raising from using wrong modeling assumption (like misprice of financial products).
• Communication skills
  to be able to express mathematical and financial concepts in a clear and rigorous way.

Advanced Models for Financial Markets and Asset Allocation
Lévy processes: stochastic calculus for jump processes; fundamental properties of Lévy processes and reason why they overcome the Black&Scholes limits; Lévy-Kintchine formula; simulating Lévy processes; approximate small jumps with a Wiener process; construction of Lévy processes by subordination; Lévy-Ito formula; Extension to additive processes; example of additive processes
Stochastic Volatility models: Heston, Hull-White, Stein & Stein models.
Stochastic volatility models with jumps: Bates, BNS, time change Lévy
Numerical Methods for Finance
Monte Carlo Simulations: sampling from uniform and other distributions; simulating continuous processes; simulating jump diffusion processes; variance reduction techniques; pricing European and exotic options; pricing American derivatives: the Longstaff & Schwarz algorithm.
PDE: Finite Differences discretizations: evaluating barrier and European options via Finite Differences; pricing American derivatives: the PSOR algorithm.
FFT: Carr-Madan method for European derivatives. The Convolution method
Energy Finance
Energy commodities; Jump processes for commodities; Valuation of a Swing option on Gas
Asset Allocation
Black&Litterman approach; asset allocation and efficient portfolio frontier
For the 8 cfu version: you can choose between the Energy Finance and Asset Allocation
For the 10 cfu version: all parts are mandatory

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, senza presentazione/discussione finale
Exam Structure and Evaluation The exam consists of three components: a) Projects focusing on energy finance, asset allocation, and hedging topics. b) A theoretical and coding exam. c) A mandatory oral exam.
Project Guidelines The objective of the projects is to foster collaborative group work, allowing students to apply the approaches and principles taught in class. Projects will be assigned throughout the semester, with specific submission deadlines announced at the time of assignment. Evaluation will be based on the submitted artifacts (e.g., documentation and code). The maximum score for the projects is 12/30 (4 points per project). The hedging project will be graded with two points for document and code and two points based on the group score (2 points for the first two groups and 1 point for third and fourth positions).
Written Exam and Admission to Oral Exam: the theoretical and coding exam accounts for a maximum of 18/30 points (14 points for coding and 4 points for theory). To be admitted to the oral exam, the combined score of the projects and the written exam must be at least 14/30 and the mark on the theoretical part should be at least 2/4.
Oral Exam The oral exam is mandatory. It can increase the final grade by a maximum of 4/30 points, but it may also result in a negative adjustment with no lower limit.
097667 - COMPUTATIONAL FINANCE (8 CFU) Students enrolled in the 8 CFU version of the course may opt to skip either the portfolio project or the energy project. For these students, for these students the portfolio and the hedging project mark are rescaled accordingly.
The exam has the goal of checking whether the student has acquired the following skills:

• knowledge of advanced concepts of stochastic calculus, which are essential in quantitative finance;
• knowledge of how to choose modeling assumptions to solve a financial problem properly;
• ability to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledge;
• ability to find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
• ability to express mathematical and financial concepts in a clear and rigorous way.

R. Cont, P. Tankov, Financial Modelling with Jump Processes, Editore: CRC/CHAPMAN-HALL, Anno edizione: 2004
R. Seydel, Tool for Computational Finance, Editore: Springer-Verlag, Anno edizione: 2012

This course is part of the Computational Science and Computational Learning track in the Master Program in Mathematical Engineering. The aim is to provide students with the fundamentals of mathematical models and numerical methods for partial differential equations that describe the motion of fluids in both laminar and turbulent regimes. This is a very dynamic area of study full of new contributions. Therefore the course, in addition to the basic aspects, aims to encourage the study of the latest methodological approaches. In this part of the integrated course the focus will be on the statistical description of turbulence and on its modelling.
This course is also offered in a reduced 3 CFU version 052029 - COMPUTATIONAL FLUID DYNAMICS [2] which together with the course on 052028 - COMPUTATIONAL FLUID DYNAMICS [1] (5 CFU) defines the integrated course on 052030 - COMPUTATIONAL FLUID DYNAMICS [C.I.] (8 CFU). The present sheet defines the objectives, programs and learning outcomes for both courses.

The student will be able to know and understand:

• the statistical quantities that are useful to describe the main features of a turbulent flow;
• the Kolmogorov theory for statistically homogeneous, stationary and incompressible turbulence;
• the limitations of the Kolmogorov theory
• the main families of turbulent models: Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES)
• the properties and limits of the different turbulent models
  The student will be able to apply the knowledge and comprehension to:
• (*) characterize the main transport and diffusion properties of a passive scalar in a turbulent flow.
• (*) characterize the features of two-dimensional turbulence and the main differences with respect to three-dimensional turbulence.
• (*) characterize the features of the turbulent boundary layers.
• the implementation of wall laws in the framework of RANS turbulence models.
• calibrate the model parameters of RANS turbulence models.
• the implementation of simple turbulence models in finite element solvers.
  (*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

• Statistical description of turbulence. Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows. Limitations of Kolmogorov's theory.
• (*) Transport and diffusion of a passive scalar in a turbulent flow.
• (*) Two-dimensional turbulence.
• (*) Turbulent boundary layer.
• Turbulence models for Reynolds Averaged Navier Stokes (RANS) equation; turbulent viscosity models, mixing length,
  two equation models: k-epsilon model, k-omega model.
• Large Eddy Simulation (LES) turbulence models: filtering technique, Smagorinsky turbulent viscosity model,
  similarity scale models, dynamic models, dynamic mixed models, anisotropic models.
  (*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The student will attend a written test including theory and programming exercises and oral examinations with the two teachers of the course. The exam is passed if the student reaches a sufficient mark (>=18) in each of the three parts (written exam and two oral exams) and the final mark is the average of the three marks.
The student must prove to know the main definitions and concepts inherent in turbulent flows.
He must be able to critically discuss the different theoretical aspects of turbulent phenomena: the characteristics of the relevant statistical descriptors; the Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows and subsequent developments; (*) the transport and diffusion of a passive scalar in a turbulent flow; (*) two-dimensional turbulence; (*) the turbulent boundary layer; the turbulence models both in the framework of Reynolds Averaged Navier Stokes and of Large Eddy Simulation.
He must be able to propose the most adequate analytic and modelling approach that guarantees the best compromize in terms of accuracy and computational efficiency for a given turbulent flow.
In particular during the oral part the student should be able to present complex arguments in a rigorous, clear and concise way.
(*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

Lecture Notes available on beep channel
J. Ferziger, M. Peric, Computational Methods for Fluid Dynamics (4th edn), Editore: Springer-Verlag, Anno edizione: 2020, ISBN: 9783319996912
P.A. Davidson, Turbulence - An Introduction for Scientists and Engineers (2nd edn), Editore: Oxford University Press, Anno edizione: 2015, ISBN: 9780198722588
U. Frisch, Turbulence, Editore: Cambridge University Press, Anno edizione: 1995, ISBN: 9780521457132

The integrated course Computational Mechanics for Geomaterials consists in two strictly integrated modules:
the Computational Mechanics module (5 CFU) aims to introduce the theoretical and operational aspects of the finite element method for the solution of elastic and elasto-plastic problems and to present the main classes of constitutive laws in the non-linear field
the Geomaterials module (5 CFU) aims to present some aspects of the behaviour of soils, as two-phase materials characterized by a non-linear mechanical response, in geotechnical problems where close interactions between various physical processes may occur. These problems are typical of environmental engineering and geosciences and require, to obtain an accurate solution, the use of computational methods.

After lectures and teaching workshops attendance and exam passing, the student:
will master the main constitutive laws employed to describe the behavior of different classes of material, with particular emphasis on geotechnical materials, and will understand their field of application [D1];
will master the equations governing the elastic and elasto-plastic problems for single-phase solids and for saturated soils and will be able to describe them clearly and effectively [D1];
will be able to apply the above knowledge to solve simplified problems [D2, D3];
will master the displacement formulation of the finite element method, in the linear and non-linear regime, even in presence of saturated porous materials [D2];
will be able to independently solve typical problems of geotechnical engineering through the conscious use of a multi-purpose finite element code [D2, D3];
will be able to draw up a report on the obtained results, with clarity and language skills [D3].

Integrated course topics:
(the part related to the Computational Mechanics module, points 1,3,5,6, is written in normal font, the part relating to the Geomaterials module, points 2,4,7,8 is written in italics)
1. Elastic problem for a single-phase continuum
Three-dimensional, plane and axial-symmetric elastic problems. Isotropic and anisotropic elastic constitutive model.
2. Hydro-mechanical problem for a saturated porous continuum
Equations of equilibrium, compatibility and mass conservation for the saturated porous medium. Seepage analysis for a porous medium with rigid skeleton. Displacements analysis with uncoupled approach. The hydro-mechanical coupled problem in a deformable medium with elastic behaviour.
3. Fundamentals of the finite element method
Weak formulation of the elastic problem. General aspects of the displacement formulation of the finite element method. Finite element formulation for plane problems. Isoparametric elements.
4. The finite element method for geomaterials
Formulation of the finite element method for the hydro-mechanical coupled problem of a saturated porous medium. Fundamental characteristics and procedures of the finite element analysis in a geotechnical engineering problem. Analysis of soil response under various working conditions. Analysis of serviceability and ultimate state. Examples of finite element solutions for linear elastic problems.
5. Introduction to the mechanics of materials
Mechanical behavior of materials: elastic, visco-elastic, elastic-plastic, visco-plastic
6. Elasto-plastic constitutive models
Yield functions, hardening laws, associated and non-associated sliding laws, examples. Hints on the integration methods of nonlinear constitutive models. The finite element method for elastoplastic problems
7. Elasto-plastic models for geomaterials
Mechanical behaviour of soil, rock and discontinuities. Elasto-plasticity, softening and rheological models. Constitutive parameters and their calibration. Soil behaviour in partially saturated conditions.
8. Applications of the finite element method to geotechnical engineering problems
Examples of finite element analyses for non-linear problems. Soil-structure interaction problems. Unconfined seepage in unsaturated levees. Excavation and construction procedures. Slope stability problems.

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
The evaluation is based on an oral discussion and a written report to be prepared during the semester.
The written report focuses on the case-studies analyzed during computer laboratories through a commercial software. The students (possibly in pairs) re-elaborate the topic covered during the course in a personal and autonomous way and draw up a technical report, structured as if it were addressed to an external client. The written report must clearly describe the examined problem and comment the obtained results in a complete and critical way. The evaluation criteria include the presentation's completeness and clarity, as well as critical comments and in-depth discussions. The report is graded on a scale of 10.
The oral discussion is divided into two parts, each pertaining to a module of the integrated course and evaluated with a maximum grade of 11. The evaluation criteria are the ability to master the course topics and apply the knowledge acquired.
The final grade is the sum of the three marks, which includes the possibility of receiving the highest grade "con Lode" when exceeding 30.

General description and motivation:
Nature is the ultimate engineer — its principles underpin both the human body and the most advanced electronic systems. In this course, we will explore the deep and fascinating connections between Life Sciences and Electronics, using the language of mathematics and scientific computing to understand and model complex real-world phenomena. From charge transport in nanoscale transistors to ion flows across biological membranes, and from electrical signaling in neurons to the physics of semiconductor devices, we will discover how core principles transcend disciplines. By applying mathematical modeling and numerical methods, we will develop stable and accurate numerical simulations that bridge biology and electronics at both the systems and molecular levels.
The aim of the course is to provide students with the basic tools required to construct mathematical models of realistic problems and the theoretical foundations needed to develop and analyze numerical methods and algorithms for their stable and accurate solution on a computer. The course focuses on mathematical modeling using differential equations—both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs)—with applications in Electronics and Biomedical Engineering. Numerical methods will be presented, emphasizing stable approximations of ODEs and PDEs, particularly through the Finite Element Method and its variants. Additionally, the course will introduce a novel computational paradigm in Scientific Machine Learning: Physics-Informed Neural Networks (PINNs).
The course features hands-on computer lab sessions where students will extensively use MATLAB and python, a multi-paradigm programming language and numerical computing environment developed by MathWorks, to solve mathematical problems and perform simulations. Students are required to install and use the software on their own laptops.
The full course yields 8 CFUs and is associated with the following other two courses, each one yielding 5 CFUs:
050492 - COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS
096660 - NUMERICAL METHODS IN MICROELECTRONICS
The course pursues three specific objectives:
1. Provide a unified mathematical modeling framework for:
a) Cellular biology
b) Solid-state electronics
2. Provide numerical methods for the simulation of:
a) Cellular systems
b) Electronic devices
3. Develop critical skills for the analysis and design of complex systems in:
a) Life Sciences
b) Electronics
For students enrolled in course 050492: objectives 1.a, 2.a and 3.a.
For students enrolled in course 096660: objectives 1.b, 2.b and 3.b.

Lectures, laboratory activities and projects will:
1) Provide students with the knowledge required to formulate, analyze, and simulate mathematical models arising in engineering and life-science applications.
a) For students in Electronics Engineering (course 096660), this includes the acquisition of the fundamental principles of mathematical modeling and numerical approximation and its application to the simulation of semiconductor devices.
b) For students in Mathematical and Biomedical Engineering (course 050492, 096659, referring specifically to Module 2, see below), the course leverages these foundations to introduce advanced computational paradigms based on hybrid physics-based and data-driven models, such as Physics-Informed Neural Networks (PINNs), with perspectives towards digital-twin frameworks for engineering and biomathematical applications.
2) Enable students to quantitatively assess the physical accuracy of models and the numerical performance of computational methods through the solution of exercises and project assignments of increasing complexity.
3) Develop the ability to critically analyze, design, and validate computational models through the combined use of mathematical modeling, numerical simulation, and (for the courses 050492, 096659) modern scientific machine learning tools.
The theoretical concepts, methods, and algorithms will be validated during laboratory sessions through numerical experiments, project assignments, and critical discussion of results.
Project assignments will contribute to the final course grade.
The expected learning outcomes (according to the Dublin descriptors) are in the following.
Knowledge and understading:

• develop knowledge and understanding of the mathematical models and numerical methods for their approximation.
  Applying knowledge and understading:
• apply the numerical methods to the solution of mathematical problems arising in different applications in Engineering;
• implement numerical algorithms;
• effectively use the software library MATLAB to implement the algorithms, solve the numerical problems, and perform numerical simulations.
  Making judgement:
• choose the most appropriate numerical algorithm to solve a mathematical problem based on theoretical properties and computational aspects;
• critically interpret the numerical results based on the properties of the mathematical problem and of the numerical method.
  Communication skills:
• present a project.
  Ability to learn:
• elaborate on the material provided during lectures and laboratory sessions to choose the most appropriate numerical algorithms and solvers;
• develop projects on numerical problems that are relevant in Engineering and Life Sciences, in particular for Electronics and Biomedical Engineering.
  Students are expected to develop a deep understanding of the models and methods discussed, going beyond theoretical results and standard exercises, and applying their knowledge effectively. They should critically assess different situations, make informed decisions, and justify their reasoning. Accuracy in calculations and a well-structured presentation of the theory are also required.

The course is subdivided into three main parts or modules.
Module 1 – Foundations of Computational Modeling
a. Mathematical models based on ordinary and partial differential equations (ODEs and PDEs).
b. Numerical approximation of ODEs and PDEs through finite element methods.
c. Finite element methods for balance laws. Discretiztion of diffusion–advection–reaction models in conservative form. Discussion of stability, conservation, and convergence properties.
Module 2 – Hybrid Physics-Based and Data-Driven Models in Biomathematics
a. Review of cellular and tissue models in electrophysiology, including ion transport, membrane dynamics, action potential propagation, and cardiac electrophysiology and their approximation using the finite element method.
b. Hybrid physics-based/data-driven modeling. Artificial Neural Networks (ANNs): training, testing, validation, and learning paradigms. Physics-Informed Neural Networks (PINNs) as surrogate solvers for differential equations, inverse problems, and data assimilation.
c. Applications to cardiac electrophysiology and personalized medicine. Digital-twin perspectives for personalized modeling and simulation in life sciences.
Module 3 – Computational Models for Microelectronics
a. Drift–Diffusion and Poisson–Drift–Diffusion models for semiconductor devices.
b. Conservative numerical approximations, including finite-volume and Scharfetter–Gummel methods.
c. Nonlinear solution strategies, including Gummel iterations and Newton methods.
d. Applications to semiconductor devices, with emphasis on p–n junctions.
For students enrolled in course 096659: Modules 1, 2 and 3.
For students enrolled in course 050492: Modules 1 and 2.
For students enrolled in course 096660: Modules 1 and 3.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Progetto/i - Elaborato/i obbligatorio, individuale, senza revisioni periodiche, con presentazione/discussione finale
The exam consists of project evaluations, a written test, and an optional oral examination, with the final grade based on the combined results.
Project assignments. Evaluation of 2 project assignments during the semester, cosen among modules 1,2,3. Students attending modules 1,2 or 1,3 will take a project for each module, students taking modules 1,2,3 can choose two projects on two distinct modules. Projects will be assigned with mandatory deadlines set by the lecturer along the semester. The maximum score for each projects is 5 for a total of 10 points.
Written Test. A mandatory written test will be held during one of the 5 exam sessions scheduled by the School of Industrial and Information Engineering. The test includes theoretical and practical exercises covering all topics from the lectures and lab sessions. The use of the computer, algorithms and scripts is required for the test. Students must answer theoretical questions, formulate and solve mathematical and numerical problems, implement algorithms and critically interpret the results based on the theoretical properties of the numerical methods. The written test yields a maximum score of 30; a minimum score of 15 is required to pass the written test and the exam.
Oral Exam. It is optional and it covers all the topics of the course. It is available only if the written test is passed with a minimum score of 15. It affects only the written test score of +/- 3 points, not exceeding a total of 30 points.
The total score of the exam is the sum of the project score and the written test score, each multiplied by 0,825. The exam is passed only if the total score is 18 or higher. Cum laude is granted if the total score is larger than or equal to 32.

R. Sacco, G. Guidoboni, A. G. Mauri, A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences, Editore: Elsevier Inc. 50 Hampshire St., Cambridge MA 02139, USA, Anno edizione: 2019
A. Quarteroni, Numerical Models for Differential Problems, Editore: Springer, Anno edizione: 2017
P. Colli Franzone, L. Pavarino, S. Scacchi, Mathematical Cardiac Electrophysiology, Editore: Springer, Anno edizione: 2014
R. Muller and T. Kamins, Device Electronics for Integrated Circuits, Editore: John Wiley and Sons, Anno edizione: 2003
J. Keener and J. Sneyd, Mathematical Physiology, Editore: Springer-Verlag, Anno edizione: 2009
I. Rubinstein, Electrodiffusion of Ions, Editore: SIAM Philadelphia, Anno edizione: 1990

This is a course about exploring random systems using computer simulations. Indeed, almost every mathematical model describing systems or phenomena of interest is hampered by uncertainties, although very often uncertain features or inputs are not accounted for.
The goal of the course is to introduce computational tools aiming at: (i) describing uncertainty sources in general systems, with special emphasis on differential models, and (ii) analyzing the impact of uncertainty on systems ’ outcomes, in terms of both uncertainty propagation from inputs to outputs, and input parameter estimation from noisy observations. A wide range of additional techniques enabling uncertainty quantification for complex problems will also be considered such as, e.g., surrogate models, reduced-order models for differential problems, multi-fidelity and neural network-based strategies, data-driven dynamical systems, thus providing also a general introduction to recent paradigms in scientific machine learning.

Both versions of the course have the following common learning goals:

• At the end of the course students are expected to be able to simulate statistical models - and run with Python - computational experiments aimed at: describing possible sources of uncertainty, quantifying the impact of uncertainty on numerical models, sampling from distributions of quantities of interest involving the simulation of physics-based models, applying Monte Carlo methods and their extensions, performing parameter estimation, building surrogate or reduced-order models by handling neural network-based or GP regression models.
• Leveraging on their engineering forma mentis and on the skills in computational statistics acquired in the course, students are expected to be able to evaluate the practical and statistical significance of the outcome of their numerical simulations, to quantify its uncertainty, and to propose efficient and reliable strategy to reduce computational complexity.
• Students are expected to be able to communicate and transfer the results and interpretations of their computational experiments using effective graphical or analytical means, suitable for the problem at hand and the findings of the analysis.
  Moreover, the students of the 8 CFU version of the course are expected to have a basic understanding of further topics related with data assimilation, sensitivity analysis, and data-driven dynamical systems.

The course is organized in a series of lectures that also include practical lab sessions. Lectures will provide the theoretical background; practical Lab sessions will provide algorithms' implementation and examples of application of the considered methodologies by using Python codes.
Part 1. Monte Carlo methods & Stochastic Simulation
Generating random samples from simple distributions (inversion method, transformations), acceptance-rejection sampling.
Generating random fields. Karhunen-Loève expansion.
Monte Carlo methods
Variance reduction techniques: antithetic variables, importance sampling, control variates, stratification, latin hypercube sampling.
Quasi Monte Carlo methods
Part 2. Surrogate models & Scientific Machine Learning
Dimensionality reduction: singular value decomposition
Gaussian processes & GP regression
Neural Networks (e.g., autoencoders & variational autoencoders)
Projection-based & deep learning-based Reduced Order Models
Data-driven Dynamical Systems: dynamic mode decomposition, sparse identification of nonlinear dynamics, extensions
Part 3. Sensitivity analysis & forward Uncertainty Quantification
Sensitivity analysis of multiple parameters: one-at-a-time, elementary effect methods, variance-based methods. Nonparametric methods.
Uncertainty propagation through Monte Carlo methods. Application to differential models.
Multi-level Monte Carlo and multi-fidelity Monte Carlo methods
Part 4. Data assimilation & inverse Uncertainty Quantification
Statistical inverse problems: a Bayesian setting for parameter estimation.
Monte Carlo Markov Chain methods. Application to differential models.
Data assimilation: Gaussian Filtering (Kalman filters, extensions, particle filters). Application to differential models.
Dynamic Bayesian Networks. Predictive Digital Twins

Prova orale obbligatoria
The oral exam covers the content of both theoretical lectures and practical Lab sessions, according to the sizing (5CFU/8CFU) of the course.
During the exam, students are required to present the detailed solution of two selected assignments (among a list of assignments proposed during the practical Lab sessions), commenting both the numerical results obtained and the computational procedures employed, and to answer to theoretical questions related with the topics of the course.
Assignments will require students to apply, adapt, or extend some of the methods presented during the course to selected case studies. The assignments will be evaluated during the oral examination and must be submitted to the examiners by the deadline communicated during the classes.
Theoretical questions will assess students' knowledge of the methodologies covered throughout the course. During the examination, students will first be required to sketch written answers to the theoretical questions, before presenting and discussing them with the examiners.
In the 5+3CFU form, a n additional assignment has to be carried out, which might also take the form of a critical analysis of a recent scientific paper related to the course's topics.
The course will be based on a selection of chapters of the following books, class notes, and some selected scientific papers provided:

Ralph C Smith, Uncertainty Quantification: Theory, Implementation, and Applications, Editore: SIAM, Anno edizione: 2013
Steven L. Brunton, J. Nathan Kutz, Data-driven Science and Engineering. Machine Learning, Dynamical Systems, and Control, Editore: Cambridge University Press, Anno edizione: 2022
Jochen Voss, An Introduction to Statistical Computing. A Simulation-based Approach, Editore: John Wiley & Sons, Anno edizione: 2014
Andreas Krause, Jonas Hubotter, Probabilistic Artificial Intelligence arXiv:2502.05244
Mark Asch, Marc Bocquet, Maelle Nodet, Data Assimilation. Methods, Algorithms, and Applications, Editore: SIAM, Anno edizione: 2016
Kevin P. Murphy, Probabilistic Machine Learning: An introduction, Editore: MIT Press, Anno edizione: 2022 http://probml.github.io/book1

This is a course about exploring random systems using computer simulations. Indeed, almost every mathematical model describing systems or phenomena of interest is hampered by uncertainties, although very often uncertain features or inputs are not accounted for.
The goal of the course is to introduce computational tools aiming at: (i) describing uncertainty sources in general systems, with special emphasis on differential models, and (ii) analyzing the impact of uncertainty on systems ’ outcomes, in terms of both uncertainty propagation from inputs to outputs, and input parameter estimation from noisy observations. A wide range of additional techniques enabling uncertainty quantification for complex problems will also be considered such as, e.g., surrogate models, reduced-order models for differential problems, multi-fidelity and neural network-based strategies, data-driven dynamical systems, thus providing also a general introduction to recent paradigms in scientific machine learning.

Both versions of the course have the following common learning goals:

• At the end of the course students are expected to be able to simulate statistical models - and run with Python - computational experiments aimed at: describing possible sources of uncertainty, quantifying the impact of uncertainty on numerical models, sampling from distributions of quantities of interest involving the simulation of physics-based models, applying Monte Carlo methods and their extensions, performing parameter estimation, building surrogate or reduced-order models by handling neural network-based or GP regression models.
• Leveraging on their engineering forma mentis and on the skills in computational statistics acquired in the course, students are expected to be able to evaluate the practical and statistical significance of the outcome of their numerical simulations, to quantify its uncertainty, and to propose efficient and reliable strategy to reduce computational complexity.
• Students are expected to be able to communicate and transfer the results and interpretations of their computational experiments using effective graphical or analytical means, suitable for the problem at hand and the findings of the analysis.
  Moreover, the students of the 8 CFU version of the course are expected to have a basic understanding of further topics related with data assimilation, sensitivity analysis, and data-driven dynamical systems.

The course is organized in a series of lectures that also include practical lab sessions. Lectures will provide the theoretical background; practical Lab sessions will provide algorithms' implementation and examples of application of the considered methodologies by using Python codes.
Part 1. Monte Carlo methods & Stochastic Simulation
Generating random samples from simple distributions (inversion method, transformations), acceptance-rejection sampling.
Generating random fields. Karhunen-Loève expansion.
Monte Carlo methods
Variance reduction techniques: antithetic variables, importance sampling, control variates, stratification, latin hypercube sampling.
Quasi Monte Carlo methods
Part 2. Surrogate models & Scientific Machine Learning
Dimensionality reduction: singular value decomposition
Gaussian processes & GP regression
Neural Networks (e.g., autoencoders & variational autoencoders)
Projection-based & deep learning-based Reduced Order Models
Data-driven Dynamical Systems: dynamic mode decomposition, sparse identification of nonlinear dynamics, extensions
Part 3. Sensitivity analysis & forward Uncertainty Quantification
Sensitivity analysis of multiple parameters: one-at-a-time, elementary effect methods, variance-based methods. Nonparametric methods.
Uncertainty propagation through Monte Carlo methods. Application to differential models.
Multi-level Monte Carlo and multi-fidelity Monte Carlo methods
Part 4. Data assimilation & inverse Uncertainty Quantification
Statistical inverse problems: a Bayesian setting for parameter estimation.
Monte Carlo Markov Chain methods. Application to differential models.
Data assimilation: Gaussian Filtering (Kalman filters, extensions, particle filters). Application to differential models.
Dynamic Bayesian Networks. Predictive Digital Twins

Prova orale obbligatoria
The oral exam covers the content of both theoretical lectures and practical Lab sessions, according to the sizing (5CFU/8CFU) of the course.
During the exam, students are required to present the detailed solution of two selected assignments (among a list of assignments proposed during the practical Lab sessions), commenting both the numerical results obtained and the computational procedures employed, and to answer to theoretical questions related with the topics of the course.
Assignments will require students to apply, adapt, or extend some of the methods presented during the course to selected case studies. The assignments will be evaluated during the oral examination and must be submitted to the examiners by the deadline communicated during the classes.
Theoretical questions will assess students' knowledge of the methodologies covered throughout the course. During the examination, students will first be required to sketch written answers to the theoretical questions, before presenting and discussing them with the examiners.
In the 5+3CFU form, a n additional assignment has to be carried out, which might also take the form of a critical analysis of a recent scientific paper related to the course's topics.
The course will be based on a selection of chapters of the following books, class notes, and some selected scientific papers provided:

Ralph C Smith, Uncertainty Quantification: Theory, Implementation, and Applications, Editore: SIAM, Anno edizione: 2013
Steven L. Brunton, J. Nathan Kutz, Data-driven Science and Engineering. Machine Learning, Dynamical Systems, and Control, Editore: Cambridge University Press, Anno edizione: 2022
Jochen Voss, An Introduction to Statistical Computing. A Simulation-based Approach, Editore: John Wiley & Sons, Anno edizione: 2014
Andreas Krause, Jonas Hubotter, Probabilistic Artificial Intelligence arXiv:2502.05244
Mark Asch, Marc Bocquet, Maelle Nodet, Data Assimilation. Methods, Algorithms, and Applications, Editore: SIAM, Anno edizione: 2016
Kevin P. Murphy, Probabilistic Machine Learning: An introduction, Editore: MIT Press, Anno edizione: 2022 http://probml.github.io/book1

Descrizione sintetica dei contenuti del corso
Il corso parte da una panoramica sulla modellazione della visione umana, per arrivare a mostrare le relazioni tra una immagine prospettica ideale e la corrispondente scena tridimensionale. Vengono poi illustrate le caratteristiche di un sistema di Computer Vision reale basato su una fotocamera digitale, della quale si analizzano separatamente i diversi componenti per mostrare come questi allontanino l'immagine ripresa da quella ideale e come queste variazioni possano essere modellate matematicamente attraverso un processo di calibrazione. A partire da immagini calibrate vengono poi mostrate le tecniche per l'orientamento relativo, l'intersezione e la scalatura sulla base di riferimenti metrici sulla scena che consentono la stima di dati 3D con metodo passivo. Il corso illustra poi il principio di funzionamento dei diversi sensori 3D attivi a oggi disponibili sul mercato, li inquadra in una contesto generale specificandone le caratteristiche. Descrive le modalità con cui tali sensori devono essere utilizzati per digitalizzare la forma di un oggetto con la generazione di una nube di punti 3D che rappresenta il campionamento spaziale della superficie di interesse. Il corso fornisce poi le capacità necessarie per pianificare un progetto di acquisizione 3D con una serie di range-map prese da orientamenti diversi, tenendo conto dei possibili artefatti dovuti all'interazione luce-materiale o ad eventuali errori di orientamento tra sensore 3D e superficie di interesse. Viene poi definito il processo di costruzione di un modello tridimensionale poligonale a partire da un set di dati acquisiti, attraverso le fasi di orientamento, fusione ed editing della mesh finale. Per trasmettere questi saperi nella maniera più efficace il corso prevede una consistente attività esercitativa e di laboratorio. In un primo progetto d'aula gli studenti misurano elementi geometrici nello spazio 3D a partire dalle loro immagini piane. Tali immagini vengono acquisite con le proprie fotocamere digitali opportunamente calibrate, o, in alternativa, con camere messe a disposizione dal laboratorio. In una seconda parte del corso gli studenti realizzano modelli 3D di oggetti reali acquisendoli con scansione laser ed elaborando i dati così ottenuti con pacchetti software diffusi in ambito industriale. Le tecnologie trattate nella parte teorica sono in tal modo messe in pratica su casi di studio reali, così che gli studenti possano interagire con l'intero processo di Reverse Engineering basato su acquisizione 3D passiva con tecniche di Computer Vision, acquisizione 3D attiva, elaborazione 3D, creazione del modello e presentazione.
Sintesi dei contenuti
Introduzione teorica. Sistemi di coordinate e relative operazioni di trasformazione. Stima 3D da immagini ideali. Siste-mi di imaging reali. Sistemi 3D passivi. Sistemi 3D attivi basati su misure angolari. Sistemi 3D attivi basati su misura di distanze, Integrazione dei metodi di rilievo. Principi di metrologia 3D. Costruzione di modelli 3D con Computer Vision. Costruzione di modelli 3D con tecniche attive. Esempi applicativi.

See the program of the module in the master course

See the program of the module in the master course

L'insegnamento affronta il tema della creatività, in particolare nel campo della scienza e della tecnologia, con l'obiettivo di stimolare negli studenti la consapevolezza del fatto che esistono alcuni fattori chiave per creare ambienti di lavoro e modi di agire e pensare maggiormente creativi. Dopo una base teorica sulla creatività in generale e della creatività negli ambiti della scienza e della tecnologia, con particolare riferimento alle opere di Kuhn e Popper, vengono proposte una serie di metodologie da sperimentare in maniera laboratoriale, ispirate degli studi di Resnick, De Bono, Kelley e altri autori. L'approccio viene validato praticamente attraverso lo svolgimento di progetti di gruppo su temi dati, da affrontare in gruppi interdisciplinari.

Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
Valutazione continua obbligatoria
See the program of the module in the master course

The Critical Thinking course aims to provide, in an innovative manner, the methodological tools necessary to reason and argue soundly under conditions of risk and uncertainty in science and technology. The tools used will be those belonging to logic, philosophy, argumentation, and the psychology of thought, as applied to uncertain reasoning. The course content will be presented and discussed interactively with students. The course is intended to give students the opportunity to reflect critically on the cultural, social, and ethical impacts of science and technology

( Knowledge and understanding )
Students will:

• be acquainted with different forms of scientific reasoning
• acquire methodological skills in order to deal with risk and uncertainty
  ( Applying knowledge and understanding )
  Students will:
• foster their ability to solve problems and cope with uncertainty
• apply critical thinking to complex problems
• integrate their technical knowledge with humanistic, cognitive and ethical perspectives on science and technology
  ( Making judgements )
  Students will be able to:
• use methods and imagine scenarios in order to deal with (severe) uncertainty
• enhance creativity in thinking and reasoning
  ( Communication )
  Students will learn how to
• improve their skills in a writing an academic paper
• make academic presentations
• evaluate different forms of (risk) communication
  ( Lifelong learning skills )
  Students will
• be ready to evaluate and take decisions under conditions of uncertainty
• be better prepared to their future professional life in a socially responsible way
• be able to propose innovation solutions to complex and uncertain problems.

The course will cover different topics both from a theoretical and a more practical point of view.
The list of topics includes:

• scientific reasoning: deduction, induction, and abduction
• elements of logic and argumentation
• probabilistic reasoning: biases and paradoxes
• risk theory
• risk perception
• risk communication
• risk and moral argumentation
• decision making under severe uncertainty
• technological innovation and uncertainty
• scenario planning
• sustainability and scientific values

Progetto/i - Elaborato/i obbligatorio, individuale, senza revisioni periodiche, con presentazione/discussione finale
An individual final essay
Students are required to develop an argumentative thesis in an individual essay in which the specific claims are justified by the use of critical thinking and the relevant literature.
Students are required to read and carefully study the suggested bibliography and to apply it to case-studies.
Collective presentations
Students are encouraged to give collective presentations in order to reduce the length of the individual final essay (this option is available only for some study programs). All detailed information and the pdfs of the scientific papers that we will be used will be made available.
The individual final essay will be evaluated considering the following criteria:
1) originality of the main thesis
2) knowledge of the scientific and technological background
3) argumentative skills
4) ability to integrate technical knowledge with critical reflection
5) compliance with academic standards

Damiano Canale, Roberto Ciuni, Aldo Frigerio, Giovanni Tuzet, Critical Thinking. An Introduction, Editore: Bocconi University Press - Egea, Anno edizione: 2021, ISBN: 9788899902858
Daniele Chiffi, Stefano Moroni, Uncertainty, Innovation and the City, Editore: Edward Elgar, Anno edizione: 2025, ISBN: 9781035342662 https://www.e-elgar.com/shop/gbp/uncertainty-innovation-and-the-city-9781035342662.html?srsltid=AfmBOoooZkaZdrxskmSY2ckahsDBQ2HOVkhHF7S-AU-24J5_HcpovGK-
Mattia Andreoletti, Daniele Chiffi, Philosophy of Risk, Editore: Cambridge University Press, Anno edizione: 2027
Note: If not yet published, an advanced draft of the book will be made available to students.

Data-driven and algorithmic technologies increasingly support or automate decisions in engineering, business, science, public policy and everyday life. Their outcomes, however, are not determined by technical performance alone: they also depend on how data are generated, selected and represented, on the objectives and constraints embedded in algorithms, and on the social contexts in which technological systems are designed and deployed.
The course provides students with an interdisciplinary framework for understanding, analysing and addressing fairness-related issues in data-driven technologies. It combines a sociological perspective on data, datafication and algorithmic processes with technical methods for identifying bias, evaluating different notions of fairness and designing fairness-aware technological and decision-making solutions.
The course is intended for students from different engineering backgrounds. It aims to show that data and algorithmic fairness is not a specialised topic limited to diversity and inclusion, but a central engineering challenge concerning the quality, reliability, legitimacy and societal impact of technological systems.
The sociological module introduces students to the relationship between data and society, considering the production and use of data as both a technological activity and a socio-political process. The technical module focuses on the mechanisms through which unfair outcomes may arise in data, algorithms and decision-making processes, and on methods and frameworks for evaluating and mitigating them.
Through lectures, discussions, case studies, exercises and a group project, students will learn to connect sociological interpretation, technical analysis and engineering design.

Upon successful completion of the course, students will be able to:
Explain and critically interpret how data and algorithmic systems are shaped by social, cultural, political and technological processes, and how their design and deployment may reproduce or transform existing inequalities.
Dublin Descriptor 1 — Knowledge and understanding
Analyse data-driven and algorithmic systems from a fairness perspective, identifying potential sources of bias across the different stages of the technological lifecycle and applying suitable concepts, criteria and methods to assess their outcomes.
Dublin Descriptor 2 — Applying knowledge and understanding
Formulate and justify fairness-aware design or policy choices, critically discussing alternative solutions, conflicting objectives, limitations and trade-offs, and clearly communicating the results of the analysis to audiences with different disciplinary backgrounds.
Dublin Descriptors 3 and 4 — Making judgements and communication skills
Class activities, independent study and project work will also support students in integrating technical and sociological perspectives, using feedback constructively and autonomously extending the course concepts to new application domains.
Dublin Descriptor 5 — Learning skills

The course is organised into two closely integrated modules.
Module A — Data and society: sociological perspectives
2 CFU
The first module introduces a sociological perspective on data and algorithmic processes. Data are considered not only as technical objects, but also as the result of social choices, classifications, institutional practices and power relations.
Topics include:
introduction to sociology and to the relationship between society and technology;
data, society and processes of datafication;
the social construction of data, categories and classifications;
identity, culture and technological systems;
the relationship between technology, power and inequality;
the role of gender, race and ethnicity, age, disability and socioeconomic conditions in the production and use of data;
historical and contemporary case studies concerning data-driven technologies;
data feminism and design justice;
epistemic injustice and its relevance to data production, technological design and decision-making;
the social, cultural and political implications of algorithmic systems in scientific, business, policy, healthcare and everyday-life contexts.
The module combines lectures with in-class discussions, exercises and case-study activities. This reflects the approach proposed for the sociological module, in which data production and application are treated as both technological and socio-political phenomena.

Prova scritta obbligatoria, senza prove in itinere
Valutazione continua obbligatoria
The course adopts an interdisciplinary and student-centred approach. Teaching activities combine:
lectures introducing sociological concepts, technical methods and analytical frameworks;
guided discussions on scientific literature, technological applications and controversial cases;
individual and small-group exercises;
analysis of real or realistic case studies;
activities requiring students to compare alternative definitions and approaches to fairness;
supervised development of a group project;
final presentation and discussion of project results.
The group project requires students to select or analyse a data-driven or algorithmic application and examine it from both a sociological and a technical fairness perspective. Depending on the selected case, students may analyse data generation, model assumptions, performance across population groups, decision rules, deployment conditions, affected stakeholders and possible mitigation strategies.
The project is intended to develop the ability to integrate perspectives from different disciplines and to formulate technically informed and socially aware design recommendations.
Indicative teaching mix
Teaching activity
Hours
Didattica trasmissiva/frontale
28
Didattica interattiva/partecipativa
12
Didattica laboratoriale
4
Didattica progettuale
6
Didattica valutativa
0
Total assisted teaching
50
Independent study and project work
75
Assisted teaching hours per CFU
10
This classification is consistent with the current distinction between transmissive teaching, interactive activities, laboratory work and project-based teaching. In particular, discussions, guided exercises and case-study activities fall within interactive teaching, while the supervised development and revision of the group assignment are appropriately classified as project-based teaching.

In control and filter design problems, one deals with systems that often are affected by uncertainty so that their behavior is not deterministically known and, possibly, it is also time varying. In this situation, data-driven control design schemes can be adopted, where design is not based on a fixed model of the system, but rather modeling is progressively updated based on data obtained from the actually observed system response and the better control action to achieve the desired goal is learned through experience. This course aims at illustrating some of the main techniques in data-driven control and at demonstrating their effectiveness in counteracting the presence of uncertainty; correspondingly, advance identification and learning techniques to acquire knowledge on the system dynamics from measured data will be introduced and discussed. Computer simulations carried over during classes will be used to consolidate concepts.

Lectures and exercise sessions (including computer laboratory classes) will enable students to:

• understand how the wealth of information contained in data can be processed and exploited for control and system design purposes ( DdD1 - capability of knowledge and understanding );
• understand the assumptions and functioning principles underlying some common data-driven control design techniques ( DdD1 - capability of knowledge and understanding );
• recognize the situations where the design of control systems can profitably take advantage of learning from data and from the observation of the system behavior ( DdD1 - capability of knowledge and understanding, DdD2 - capability of applying knowledge and understanding );
• determine which approaches are most appropriate for a given application and predict the impact of algorithmic choices and data preprocessing on the robustness and effectiveness of the resulting control scheme ( DdD2 - capability of applying knowledge and understanding, DdD3 - capability of making judgements );
• implement, at an algorithmic level, some of the methods and approaches presented in the course ( DdD2 - capability of applying knowledge and understanding, DdD3 - capability of making judgements ). This last objective will be pursued in particular through the computer laboratory classes.
  Following successful completion of the examination, students will be able to communicate their knowledge clearly and convincingly ( DdD4 ).

Uncertainty, data, adaptation and robustness
Uncertainty, robustness, and adaptation in control. Principles of data-driven control. On-line and off-line schemes. Direct and indirect schemes.
Indirect data-driven control schemes
The self-tuning paradigm. Certainty equivalence principle. Identification resumed: least-squares identification, recursive identification, forgetting factor. Main properties of the self-tuning scheme: convergence of the model estimate, stability and optimality. Examples.
Direct data-driven control schemes
Principles of direct data-driven control. Taxonomy of existing approaches (IFT, VRFT,…). The VRFT (Virtual Reference Feedback Tuning) approach: principles. Frequency interpretation of PEM identification methods. Optimality and sub-optimality of the VRFT controller, optimal data pre-filtering. VRFT in presence of additive disturbances. Instrumental Variable identification. The VRFT toolbox of MATLAB.
Data-driven approaches to optimal control
Markov Chain Decision Processes (MCDP). Optimal control of a MCDP. Discounted costs. Principles of dynamic programming: the Bellman equation. Data-driven approaches to dynamic programming. Reinforcement learning. The Q-learning algorithm. Exploitation vs. exploration issues.

Prova scritta obbligatoria, senza prove in itinere
The final exam is a written exam, constituted by four questions. The duration is 2h.
More specifically:
The first three questions are theoretical open questions on topics covered throughout the course programme. These questions are intended to assess the level of knowledge and understanding achieved by the student. One of these questions may consist of a numerical exercise designed to assess the student’s ability to apply the acquired knowledge to solve problems. These questions are aimed at assessing the student’s knowledge and understanding (DdD1) and ability to apply knowledge and understanding (DdD2).
In the fourth question, the student is required to address a situation that, although related to the topics covered in the course, has not been dealt with directly in class. This question is aimed at assessing the student’s ability to establish connections among the various topics covered in the course and to apply the acquired knowledge to new and innovative contexts (DdD3).
The examination will also assess the student’s ability to communicate their knowledge clearly and convincingly (DdD4).

Notes and papers provided by the lecturer
Note: Additional information available on the course web-site http://corsi.dei.polimi.it/IMAD/SAA/
S. Bittanti, Identificazione dei modelli e sistemi adattativi, Editore: Pitagora Editrice
S. Bittanti, Teoria della predizione e del filtraggio, Editore: Pitagora Editrice
S. Bittanti (ed.), Simulazione, identificazione, controllo: il caso di uno scambiatore di calore, Editore: Pitagora Editrice

In the last decade, the notion of data has been associated with several changes, disruptions,
revolutions in various areas of our societies, as well as concerns, risks, and issues. Data
science, machine learning, artificial intelligence and big data have become central to every
aspect of social life. How can these complex and powerful technologies be managed and
governed for the benefit of all members of society now and in the future? In this course we will
address the growing attention to the embedding of data across different settings and the
challenges that such embedding brings for ethics and governance of data. The course equips
students with the knowledge and skills to reason on data governance and ethics. We introduce
key question tools on the use of data and associated technologies, reviewing ethical concerns
around data handling, and examining case studies from data collection, storage, and analysis.
Students are then encouraged to bring this increased awareness back to their own practice,

The course introduces Data Mining and overviews the most important algorithms used in this field. It consists of three main parts. The first part introduces the basics of data mining, including the representation of data, their exploration, and preparation. The second part delves into the four main areas, association rules, clustering, regression, and classification. Finally, we focus on advanced topics such as time series, anomaly detection, explainability, and AutoML.

Dublin Descriptors
Expected learning outcomes
Knowledge and understanding
Students will learn to:

• Structure a data mining pipeline
• The fundamental characteristics of the most important algorithms used in all the major steps of the pipeline
• Identify architectural styles and patterns
  Applying knowledge and understanding
  Given specific data mining process, students will be able to:
• Analize and comment on specific architectural choices
• Highlight possible criticalities
• Identify existing biases
• Apply the theory to assess the reliability of the results produced
  Making judgements
  Given a data mining task, students will be able to:
• Analyze and understand the goals, assumptions and requirements associated with that task
• Select the best environment to implement each step of the data mining process
• Select the best infrastructure
  Communication
  Students will learn to:
• Analyze the design choices that a data analytics solution entails
• Present and critically discuss the results of a data mining process
  Lifelong learning skills
  Students will learn
• how to tackle problems in real-world scenario and
• how to critically analyze a proposed solution and the result it produced.

Introduction to Data Mining
Data representation
Text representation and embeddings
Data exploration and visualization
Association rules
Clustering

• Hierarchical
• Representation-based
• Density-based
  Regression
  Classification
• Logistic regression
• Naive Bayes and Bayesian Belief Network
• k-nearest neighbor
• Decision trees
• Ensemble methods
  Advanced Topics
• Time series
• Anomaly detection
• Explainability
• Blackbox optimization
• AutoML

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The assessment is based on a written, closed-book test at the end of the course, taken in person, in class. It typically consists of questions on the course topics. It can include conceptual questions and exercises requiring a significant modeling effort. The test is worth a maximum of 30 points; three additional bonus points are awarded based on the time taken to submit the exam. 30 cum laude is assigned when the total score is 32 or above. Students have approximately 2 hours to answer the test. Students can take the test at any exam session during the year. The written test can be taken only in person. The discussion of the graded exams is also in person only. Instructors can summon students who passed the written test for an additional (in-person) oral exam covering the entire course program.
Type of assessment
Description
Dublin descriptor
Written test

• Solution of numerical problems
• Computation of score functions used in data mining algorithms- Execution of fundamental algorithms using small datasets
• Interpretation of code fragments to understand what they compute
  Exercises focusing on design aspects
• Evaluation of trade-offs between different proposed solutions
• Design of data mining pipelines for a given scenario
• Critical comparison of existing methods
  2,3,4,5

Mohammed J. Zaki and Wagner Meira, Jr.,, Data Mining and Analysis: Fundamental Concepts and Algorithms (Second Edition), Editore: Cambridge University Press, Anno edizione: 2020, ISBN: 978-1108473989
Note: Freely available at http://www.dataminingbook.info/
Pang-Ning Tan, Michael Steinbach, Vipin Kumar, Anuj Karpatne, Introduction to Data Mining, Global Edition (2nd Edition), Editore: Pearson, Anno edizione: 2016, ISBN: 978-0273769224 https://www.pearson.com/store/p/introduction-to-data-mining-global-edition/P200000005534/9781292456133
Christoph Molnar, Interpretable Machine Learning: A Guide for Making Black Box Models Explainable, ISBN: 979-8411463330 https://christophm.github.io/interpretable-ml-book/
Note: Free browsable version available online.

Neural networks are mature, flexible, and powerful non-linear data-driven models that have successfully solved many complex tasks in science and engineering. The advent of the deep learning paradigm, i.e., training (neural) networks to simultaneously learn an optimal data representation and a model solving the requested task, has further boosted neural networks research and development. These models nowadays achieve human-like performance in natural language processing, text modeling, gene expression modeling, and image recognition, to name a few examples. This course provides a broad introduction to artificial neural networks (ANN), starting from the traditional feedforward (FFNN) and recurrent (RNN) neural networks architectures, till the most successful deep-learning models including convolutional neural networks (CNN) and long short-term memories (LSTM). The course aims at providing students with a theoretical background and the practical skills to understand and use ANN and, at the same time, become familiar and with Deep Learning for solving complex engineering problems.
The primary goal of this course is to let the students design, implement and practice algorithms based on simple mathematical models from linear algebra and convex optimization, and solve challenging inverse problems in image and signal processing (denoising, deblurring, inpainting, anomaly detection). The course topics include:

• Signal/Image models based on orthonormal bases (Fourier, wavelets), data-driven basis (PCA, Gram-Schmidt) and local polynomial approximation.
• Sparsity and redundancy. Sparse coding with ^0 (OMP) ^1 norm (convex optimization ISTA, IRLS, LASSO)
• Dictionaries yielding sparse representations and dictionary learning (KSVD)
• Denoisign, in painting and anomaly detection algorithms based on sparse representation

L'insegnamento fornisce l'insieme di contenuti necessari a progettare gli esperimenti e ad analizzare i risultati utilizzando un sw a grande diffusione. Gli studenti del corso da dieci crediti, inoltre, avranno modo di applicare i concetti teorici ad un caso pratico in cui cercheranno di migliorare un processo di fabbricazione con uno o più esperimenti
I temi affrontati saranno: Analisi della varianza a un fattore e a molti fattori, Modelli a fattori fissati, casuali e misti. Tecniche DOE (Design Of Experiments) per la progettazione degli esperimenti: piani fattoriali completi e con blocco; piani 2k replicati, frazionati e con blocca; piani nested e split plot, piani alfabetici ottimi. Analisi di regressione lineare. Tecniche RSM (Response Surface Methodology) e di progettazione robusta.

L'insegnamento fornisce l'insieme di contenuti necessari a progettare gli esperimenti e ad analizzare i risultati utilizzando un sw a grande diffusione. Gli studenti del corso da dieci crediti, inoltre, avranno modo di applicare i concetti teorici ad un caso pratico in cui cercheranno di migliorare un processo di fabbricazione con uno o più esperimenti
I temi affrontati saranno: Analisi della varianza a un fattore e a molti fattori, Modelli a fattori fissati, casuali e misti. Tecniche DOE (Design Of Experiments) per la progettazione degli esperimenti: piani fattoriali completi e con blocco; piani 2k replicati, frazionati e con blocca; piani nested e split plot, piani alfabetici ottimi. Analisi di regressione lineare. Tecniche RSM (Response Surface Methodology) e di progettazione robusta.

Il corso ha lo scopo di illustrare problemi, metodi e algoritmi relativi all'analisi di sistemi complessi, con particolare riferimento allo studio delle dinamiche non lineari e delle reti di interazione tra sistemi.
Nel primo modulo (Teoria dei sistemi (dinamica non lineare)) si discutono le proprietà fondamentali dei sistemi dinamici non lineari, vale a dire i comportamenti asintotici, dai più semplici (stazionario) ai più complessi (oscillazioni persistenti, periodiche o caotiche), e le transizioni da un comportamento all'altro al variare dei parametri del sistema (biforcazioni, isteresi, catastrofi).
Nel secondo modulo (Complessità nei sistemi e nelle reti) si considerano sistemi composti da più unità tra loro interagenti, presentando dapprima gli strumenti per l'analisi delle proprietà delle reti complesse (network analysis) per poi analizzare come la struttura delle interazioni tra i sistemi caratterizzi il comportamento dinamico complessivo (sistemi multi-agente, consenso e sincronizzazione).

The course is an introduction to the fundamental notions of Discrete Mathematics, one of the fastest growing areas of modern mathematics. These notions are nowadays more and more used in the development, analysis and comprehension of mathematical models in every area of engeneering. Among the many topics that go under the name of discrete mathematics, in the course we consider set theory, enumerative combinatorics, graph theory, elementary number theory and modular arithmetics, and abstract algebra.

At the end of the course, students who have mastered contents and methodology, will be able to express the fundamental concepts of Discrete Mathematics through definitions, theorems, examples and counterexamples, to justify the effectiveness of mathematical procedures used to solve the problems presented in the course and to properly use the mathematical language while arguing (Dublin Descriptor 1, or DD1).
Regarding the application of the acquired knowledge and understanding, students will be able to:

• use formal rules for computations on symbols, independently from the meaning of the symbols (DD2);
• solve equations over the integers or over the integers modulo m (DD2);
• compute the number of elements of sets defined by a property (DD2);
• analyze graphs (DD2).

SET THEORY: Basic notions of set theory. Natural numbers and the induction principle.
ENUMERATIVE COMBINATORICS: Cardinality of a set. Basic counting principles. Principle of inclusion and exclusion. Formulas of Sylvester and Da Silva. Binomial numbers, Stiefel's formula and other identities on binomial numbers. Permutations and selections from a set. Derangements. Binomial theorem. Stirling numbers of the second kind. Partitions of a natural number. Ferrers diagrams. The Tower of Hanoi problem. Formal power series. Partial fractions. Generating functions. Linear homogeneous recursions. Fibonacci and Lucas numbers. Closed form of the Fibonacci numbers.
GRAPHS: Basic definitions. Planarity of graphs. Euler's formula. Bipartite graphs. Eulerian graphs. Hamiltonian graphs. Trees. Binary trees. Spanning trees. Vertex colorings. Chromatic number. Edge colorings. Chromatic index. K\"{o}nig's theorem. Matchings in bipartite graphs. Hall's theorem. Adjacency matrix, incidence matrix with respect to an orientation, Laplacian matrix. Theorem of Poincaré. Spectrum of a graph.
ELEMENTARY NUMBER THEORY AND MODULAR ARITHMETIC: Integers. Divisibility and prime numbers. Euler's function. Congruences. Integers modulo m. Euler's theorem. Fermat's little theorem. Chinese remainder theorem. Wilson's primality test.
ABSTRACT ALGEBRA: Elements of group, rings and fields. Finite fields.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), individuale, senza revisioni periodiche, con presentazione/discussione finale
The aim of the exam is to verify if every student has got the following expertises:
1. ability of applying theoretical results to solve exercises (DD2),
2. knowledge of definitions (DD1),
3. results on the topics of the course (DD1 and DD2),
4. proofs of the main mathematical theorems presented in the course (DD1).
The final evaluation consists of an oral exam on the topics presented in the course, part of which is devoted to the solution of exercises.

Notes of Discrete Mathematics WeBeep page of the course

To provide the main tools in dynamical systems and mathematical control theory, enabling students to address control problems of interest in applied sciences, by using the concepts learned during the course.
This course explores the fundamental mathematical principles and methods used to analyze and design control systems which are necessary tools in the design and management of systems that stem from sciences, technology, industry, or services.
Control theory analyzes properties of controlled systems, i.e., dynamic systems which can be acted upon by means of a control (or command).
The aim is to transform the system from an initial state to a particular end-state, respecting certain criteria, we might aim to stabilize the system in order to make it resistant to certain disruptions or to determine optimal solutions for a particular optimization criterion (optimal control).
Students of this course can profit of their training both in academic and in modern industry, in specialized fields such as aeronautics, aerospace, robotics, but also in life sciences, where the knowledge of the mathematical tools employed in control could help to better understand problems encountered to design, build, and optimize, or at least improve existing methods. From the mathematical point of view, due to the wide range of applications of control systems, both models involving ODEs and models involving PDEs are needed. The main part of the course deals with dynamical systems of ODEs. Control theory for PDEs is a wide field of study and research. Students will be introduced in this framework by means of some specific examples, as diffusion problems and vibrating phenomena, where they can exploit the main techniques employed to study controlled PDEs, largely used in applied sciences.

By the end of the course, students know classical problems of control theory governed by ordinary differential equations (ODEs). They also know examples of control problems involving partial differential equations (PDEs), of very large interest in various applied sciences.
Applications studied during the course include: fuel optimal landing of a space vehicle, minimum drag nose shape problem, boat guidance in a river, reproductive strategies in social insects (in the framework of controlled ODEs), heating or cooling a building in an optimal way, stabilization and controllability of a string (in the PDEs framework).
In reference to the Dublin indicators, the course emphasises:
DD1 – Knowledge and Understanding
The student will be able to clearly explain, using rigorous mathematical language, the definitions and theorems related to the course syllabus provided by the instructor.
DD2 – Applying Knowledge and Understanding
The student will be able to:
analytically use tools from control theory to various types of differential equations and systems;
set up an optimisation problem.
DD5 – Learning Skills
The nature of the subject, together with the structure of the course and the examination, is designed to foster and assess the student's learning abilities. In addition, the teaching approach adopted encourages students to develop independent learning skills and become more autonomous learners.

1. Dynamical systems. Linear systems of ODEs: general results and structure, exponential matrix. Asymptotic behavior of dynamical systems, stability (linearization, Lyapunov method), phase portraits.
2. Control Systems and asymptotic stabilization. Examples, reachable sets, linear systems, local controllability of nonlinear systems, bang-bang theorem. Stabilization of linear and nonlinear control systems.
3. Optimal control. Existence of Optimal Controls for Mayer problems and the problem of Bolza. Necessary conditions for the optimality: the Pontryagin Maximum Principle. Linear quadratic optimal control. Sufficient Conditions. Dynamic Programming. The linear quadratic case.
4. An introduction to control for partial differential equations. Controllability and stabilization of the wave and the heat equations. Optimal control for PDE’s, an introduction.
5. Further topics. Seminar of experts and students on recent advances in mathematical control theory, dealing e.g., with control problems for multiagent systems, traffic models, moving sets.
The 5cfu version of the course consists in the points 1, 2, 3, 5 of the above program.

Altro
In dependence of the number of students, several options are possibile:
Evaluation during lectures, depending on their participation. The students will be asked to contribute actively by preparing expositions and solving exercises.
Oral examination with, possibly, a preliminary presentation of some specific topic of the course or written exercises.
These options will be clarified during the first week of the course.

Bressan, Piccoli, Introduction to Mathematical Theory of Control, AIMS Book Series, 2007
Cannarsa, Gazzola, Dynamic Optimization for Beginners, EMS Press
Evans, An introduction to mathematical control theory, Berkley, Lecture notes
Li, Yong, Optimal Control Theory for Infinite-Dimensional Systems, Birkhäuser, Boston, 199

The course aims to present an in-depth analysis of the most important semiconductor devices used in modern electronics, with emphasis on the MOS Transistor and the Bipolar Junction Transistor. A main goal is to allow students to clearly understand the working principles and the electrical behavior of the devices starting from the careful investigation of their basic physics and pointing out the role played by their most relevant design parameters. This, in turn, aims to make students develop the skills and critical-thinking needed not only to address the operation but also to optimize the performance of a semiconductor device. Thanks to that, students will be able to understand what are the driving forces behind the successful trends of microelectronic technologies and why these trends are the outcome of relentless changes in device structure/geometry/materials, representing another important goal of the course. Through a series of sessions of simulation laboratory and two sessions of experimental laboratory, finally, students will also get some experience on the computer-aided analysis and on the electrical characterization of semiconductor devices. In summary, the course aims to provide students with the background and competencies needed not only to master the operation of electron devices within circuit applications but also to directly work on state-of-the-art semiconductor devices and technologies.

Knowledge and understanding (Dublin Descriptor 1)
After this course, the student knows and understands:

• the basic physics, the working principles and the electrical characteristics of the most relevant electron devices used in modern electronics;
• the dependence of the electrical behavior of the investigated electron devices on their design parameters;
• the guidelines ruling the evolution of semiconductor devices and technologies.
  Applying knowledge and understanding (Dublin Descriptor 2)
  After this course, the student is able to:
• apply suitable analysis methodologies to investigate the operation of semiconductor devices;
• determine the impact of changes in the design parameters of the investigated electron devices on their electrical behavior;
• master the operation of the investigated electron devices in circuit applications;
• discuss problems related to semiconductor devices and technologies with clarity, using technical terms and with a solid physical and mathematical background.
  Making judgements (Dublin Descriptor 3)
  After this course, the student is able to:
• determine the best solution to the trade-offs involved in the design of the most important electron devices in modern electronics;
• evaluate what should be required of the evolution of semiconductor technologies to prolong their success in the years to come.
  Learning skills (Dublin Descriptor 5)
  After this course, the student is able to:
• address the operation of electron devices different from those investigated in the course in autonomy;
• read and understand the scientific literature in the field of electron devices.

Review of basic properties of semiconductor materials

• Energy bands in a semiconductor material, dependence of the energy gap on temperature, density of states for the conduction and valence bands;
• Thermodynamic equilibrium: Fermi-Dirac and Maxwell-Boltzmann statistics, Fermi level, concentration of electrons and holes;
• Current transport by drift and diffusion of charge carriers, resistivity and sheet resistivity;
• Electrostatic potential in a semiconductor material: non-linear Poisson equation, Debye length;
• Non-equilibrium conditions: quasi-Fermi levels, continuity equation for electron and holes, dielectric relaxation time, Shockley-Read-Hall theory for carrier generation/recombination via defect-assisted processes.
  p-n junction
• Basic structure and d evice electrostatics under thermodynamic equilibrium: band diagram, built-in potential, electric field profile;
• Forward and reverse bias: band diagram, quasi-Fermi levels, potential drops and current components along the junction, Shockley ideal-diode equation, wide-base and narrow-base diodes;
• Generation/recombination currents in the space-charge region of the junction, high level of injection and parasitic resistances, Gummel plot, temperature dependence of the current-voltage characteristics of the device;
• Small-signal model of the p-n junction.
  Metal-semiconductor junction
• Basic structure and device e lectrostatics under equilibrium and non-equilibrium conditions;
• Current transport: Schottky's diffusion theory, Bethe's thermionic-emission theory, thermionic-emission-diffusion theory;
• Schottky effect;
• Tunneling ohmic contacts;
• Impact of interface states on device operation.
  MOS capacitor
• The MOS system: basic structure, working principles, band diagram under thermodynamic equilibrium and in the presence of a gate bias, working regimes of the device;
• Analysis of device electrostatics: calculation of the substrate charge as a function of the surface potential from the solution of the Poisson equation, surface potential and substrate charge as a function of the gate bias, threshold voltage;
• Small-signal capacitance: dependence on the gate bias (C-V curve), low-frequency, high-frequency and deep-depletion regimes;
• MOS capacitor with ring: split C-V, impact of the ring bias on device electrostatics, on threshold voltage and on the C-V curve;
• Oxide charge and interface states: impact on device electrostatics and on the C-V curve;
• Polysilicon gate: technological benefits, electrostatic drawbacks and impact on the threshold voltage of an n-MOS and of a p-MOS.
  MOSFET
• The long-channel MOSFET: basic structure of the device, working principles, gradual-channel approximation, electrostatic analysis and calculation of the depletion and inversion charge in the channel under subthreshold and strong-inversion conditions, general expression for the drain current;
• Current-voltage characteristics of the long-channel MOSFET above threshold: ohmic, parabolic and saturation regimes, pinch-off condition at the drain, band diagram and quasi-Fermi levels along the channel, small-signal model of the transistor, output resistance in the saturation regime and channel length modulation, carrier transit time in the channel, body-effect;
• Subthreshold conduction in the long-channel MOSFET: carrier diffusion from source to drain, subthreshold current, subthreshold slope, carrier generation in the channel, transcharacteristics of the transistor;
• Dependence of the electrical characteristics of the device on the oxide thickness, on substrate doping and on temperature, impact of oxide charge and interface states on the drain current, source/drain parasitic resistances and capacitances;
• Short-channel MOSFET: electrostatics, short-channel effect, DIBL, velocity saturation along the channel and its impact on the current-voltage characteristics of the device, early saturation of the drain current due to velocity saturation at the drain;
• MOSFET scaling: constant-field scaling and generalized scaling, scaling trade-offs and constraints, high-k dielectrics, metal gate, Tox-Wdmax space for the design of scaled MOSFETs, FinFETs and advanced MOSFET structures, relevant scaling issues in nanoscale devices, statistical variability, leakage currents.
  Bipolar junction transistor (BJT)
• Basic structure of the device, working principles, current gain, collector current of the prototype transistor;
• Electric field in the quasi-neutral base region: non-uniform doping, high injection, band-gap narrowing and engineering of the base material, expressions for the collector current;
• Base current: shallow emitter and deep emitter;
• Dependence of the current gain of the transistor on the collector current, Gummel plot, carrier recombination in the base/emitter depletion layer, parasitic resistances, Kirk effect, modulation of the base conductivity;
• Current-voltage characteristics of the BJT: saturation regime and forward-active regime, Early effect;
• Small-signal model of the BJT, frequency response, cut-off frequency and its dependence on the collector current, forward transit time;
• Evolution of device parameters, advanced device structures, polysilicon emitter, SiGe base.

Prova orale obbligatoria
The exam consists in an oral test. During the test, the student is asked questions related to all the topics debated in the course and has to prove not only his/her knowledge and understanding (see Dublin Descriptor 1) but also his/her ability to apply the acquired knowledge and understanding (see Dublin Descriptor 2). Demonstrating the skills needed to make correct judgements in the design of electron devices (see Dublin Descriptor 3) and the capability to extend what learned during the course (see Dublin Descriptor 5) is something relevant to achieve a high grade. The test may last up to, but not more than, one hour per student. The student is free to withdraw from the test at any moment; in that case, his/her test is considered as failed. At the end of the test, the student is told whether he/she passed the exam or not. In the former case, the student receives a grade from 18 to 30 (cum laude) out of 30. In the latter, the student has to repeat the test on another date, after improving his/her preparation.
The student who passes the oral test has his/her grade increased by up to two extra points depending on his/her successful participation in the laboratory activities carried out during the course. In particular, one extra point is given after each of the two sessions of experimental laboratory to the student who: i) took part in the session of experimental laboratory and performed the required electrical characterizations and analyses; ii) submitted, in due time, a report summarizing the activities performed and the results achieved during the session of experimental laboratory; and iii) had his/her report on the session of experimental laboratory positively evaluated. It is worth pointing out that, in order to perform the required analyses on the measurement data during the sessions of experimental laboratory, the student has to make use of Mathworks Matlab. Taking part in the sessions of simulation laboratory allows the student to develop the needed skills in that software.
The final outcome of the exam in terms of pass/fail and final grade (given by the sum of the points collected through the oral test and through the laboratory activities) is officially recorded in the report of the examination call.

Y. Taur, T. H. Ning, Fundamentals of modern VLSI devices, Editore: Cambridge Univ. Press, Anno edizione: 2021, ISBN: 9781108480024
Note: 3rd ed.

A partire da una solida comprensione e modellizzazione dei principi e dei fenomeni fisici sfruttati nei dispositivi elettronici,
l'insegnamento fornisce una panoramica dei principali campi di applicazione dell'elettronica illustrandone problematiche e metodologie.

DdD 1: conoscenza e comprensione
A seguito del superamento dell’esame, lo studente:
conosce le problematiche di base e i campi di applicazione dell'elettronica
conosce i principi fondamentali sui quali si basa il funzionamento dei dispositivi elettronici
conosce le architetture circuitali di base dell'elettronica analogica e ne comprende il funzionamento
conosce le architetture circuitali di base dei circuiti retroazionati basati su amplificatori operazionali e ne comprende il funzionamento
DdD 2: capacità di applicare conoscenza e comprensione
A seguito del superamento dell’esame, lo studente:
è in grado di analizzare analiticamente il funzionamento di dispositivi elettronici quali transistori MOS e giunzioni pn
è in grado di affrontare l'analisi di circuiti elettronici analogici, lineari e non
è in grado di comprendere il ruolo funzionale dei blocchi circuitali di un circuito

1. Introduzione
Segnali e circuiti elettrici.
Sistemi elettronici: definizione, classificazioni, esempi.
Breve storia dell'evoluzione delle tecnologie elettroniche.
2. Richiami di elettrotecnica
Reti elettriche resistive.
Circuiti dinamici con commutazione degli ingressi.
Circuiti dinamici lineari in regime sinusoidale e arbitrario.
Risposta in frequenza. Circuiti nel dominio della trasformata di Laplace: poli e zeri e loro significato circuitale. Diagrammi di Bode. Il metodo delle costanti di tempo. Individuazione delle funzioni di trasferimento per ispezione circuitale.
Legame tra il comportamento in frequenza e la risposta nel tempo.
Circuiti con elementi non lineari: il modello linearizzato per piccoli segnali.
3. Fisica dei semiconduttori
Legge di ohm e mobilità dei portatori. Introduzione ai semiconduttori. Semiconduttori intrinseci ed estrinseci. Drogaggio p e n. Compensazione. Legge di azione di massa. Correnti di deriva e diffusione. Relazione di Einstein. Relazione tra concentrazione di portatori e differenza di potenziale. Derivazione della distribuzione di Boltzmann. Equazione di continuità.
4. Il diodo
La giunzione pn: relazione funzionale corrente-tensione basate sulla distribuzione di Boltzmann. Elettrostatica della giunzione: estensione della zona di carica spaziale. Corrente nel diodo pn a base corta e lunga, in diretta ed inversa. Estensione della zona di carica spaziale nella giunzione polarizzata.
Analisi delle approssimazioni: neutralità delle regioni neutre, caduta di tensione sulle regioni neutre, quasi equilibrio della zona svuotata, lunghezza di Debye.
Il significato della lunghezza di diffusione. Il tempo di transito dei minoritari nelle zone neutre del diodo a base corta. Carica di minoritari accumulata nel diodo a base lunga e corta e relativa formulazione alternativa per la corrente. Capacità di giunzione e di diffusione. Ionizzazione da impatto: calcolo del campo elettrico critico.
Modelli e circuiti equivalenti per diodi. Circuiti di taglio e vincolo, clamper, allungatore di picco per la demodulazione AM. Rettificatore a semionda e ad onda intera. Calcolo del ripple e della corrente massima nel diodo. Ponte di diodi.
Il diodo polarizzato in inversa come fotorivelatore. Strutture pin.
5. Il transistore MOS
Il concetto di transistore come generatore comandato. Breve storia del transistor. BJT e JFET (cenni).
MOS: calcolo della tensione di soglia. Calcolo della corrente nel MOSFET in approssimazione di canale graduale. La zona di saturazione nel MOSFET. Modello per piccoli segnali.
Polarizzazione del MOS e impiego come amplificatore per piccoli segnali.
Circuiti elementari a MOS: source comune, source follower, source degenerato, gate comune. Resistenza viste nei terminali del MOSFET. La resistenza di uscita. Il MOSFET come generatore di corrente. Stadio differenziale e specchio di corrente.
Effetti dello scaling.
6. Amplificatore Operazionale
Sistemi retroazionati: stabilizzazione del guadagno ed effetto sulle non linearità del blocco di andata. Guadagno ideale, reale e d’anello.
L'amplificatore operazionale retroazionato ovvero il nullore. Configurazione invertente e non invertente. L'elaborazione analogica del segnale con l'A.O: nodo sommatore, buffer di tensione, amplificatore alle differenze, integratore ideale e reale.
Risposta in frequenza. Cenni alla stabilità. Polo ad anello chiuso della configurazione non invertente. Trade-off tra banda e guadagno.
La retroazione e la risposta in frequenza. La stabilità e i relativi criteri di verifica.
L'A.O. reale: effetti delle principali non idealità: correnti di bias, offset di tensione, corrente di uscita, slew-rate, resistenze di ingresso e uscita.
8. Rumore nei circuiti elettronici (cenni)
Processi casuali, processi stazionari, processi ergodici. La funzione di autocorrelazione e la densità spettrale di potenza. Rumore termico e rumore shot. Generatori equivalenti di rumore.

Prova scritta obbligatoria, senza prove in itinere
La verifica dell'apprendimento avviene esclusivamente tramite prove scritte volte a verificare: la capacità di risolvere esercizi di tipo dispositivistico, e la capacità di analizzare e risolvere circuiti elettronici analogici lineari e non.
In particolare, in sede d'esame lo studente dovrà dimostrare:
-di essere in grado di analizzare analiticamente il funzionamento di dispositivi elettronici quali transistori MOS e giunzioni pn, sfruttando i principi di fisica dei dispositivi appresi
-di saper risolvere (in polarizzazione e su piccolo segnale) circuiti elettronici analogici, riconoscendo le architetture circuitali di base apprese e sfruttandone le note proprietà
-di saper risolvere circuiti elettronici non lineari basati su diodi

• saper risolvere circuiti analogici retroazionati basati su amplificatori operazionali, riconoscendo le configurazioni circuitali apprese e sfruttandone le note proprietà
  Non sono previste prove in itinere.

G. Giustolisi e G. Palumbo, Introduzione ai dispositivi elettronici, Editore: FrancoAngeli, Anno edizione: 2005, ISBN: 9788846469489
Adel S. Sedra, Kenneth C. Smith, Circuiti per la Microelettronica V edizione, Editore: Edises, Anno edizione: 2019, ISBN: 9788833190549
Note: uso solo parziale (<15%). Traduzione italiana della settima edizione in inglese
Adel S. Sedra, Kenneth C. Smith, Tony C. Carusone, Vincent Gaudet, Microelectronic Circuits (8th edition), Editore: Oxford University Press, Anno edizione: 2019, ISBN: 0190853549
Note: uso solo parziale (<15%)
R. C.Jaeger, T. B. Blalock e B. J. Blalock, Microelettronica VI edizione, Editore: McGraw-Hill, Anno edizione: 2023, ISBN: 8838656517
Note: uso parziale, in alternativa a Sedra Smith

Il corso affronta le principali questioni teoriche relative all'innovazione socio-tecnica (quali i concetti di base dell'innovazione tecnologica, le dinamiche di diffusione delle innovazioni, i limiti del determinismo tecnologico, l'agency degli oggetti tecnologici, la flessibilità interpretativa della tecnologia, genere e tecnologia) e analizza esempi rilevanti di tecnologie d'avanguardia che hanno un impatto sulla società e sulla vita umana, come l'Internet delle cose, la fabbricazione digitale, la realtà aumentata e l'intelligenza artificiale. Anziché focalizzarsi sul loro funzionamento, le prestazioni e i problemi tecnici, il corso affronterà le questioni etiche che esse sollevano e gli impatti sociali che producono.

Il corso affronta le principali questioni teoriche relative all'innovazione socio-tecnica (quali i concetti di base dell'innovazione tecnologica, le dinamiche di diffusione delle innovazioni, i limiti del determinismo tecnologico, l'agency degli oggetti tecnologici, la flessibilità interpretativa della tecnologia, genere e tecnologia) e analizza esempi rilevanti di tecnologie d'avanguardia che hanno un impatto sulla società e sulla vita umana, come l'Internet delle cose, la fabbricazione digitale, la realtà aumentata e l'intelligenza artificiale. Anziché focalizzarsi sul loro funzionamento, le prestazioni e i problemi tecnici, il corso affronterà le questioni etiche che esse sollevano e gli impatti sociali che producono.

The main objective of the course is to study the climate change challenge using quantitative, numerical tools. Specifically, the aim is to learn the basic elements of the global energy and climate problems, evaluate the solutions with a focus on the energy sector, and use optimization and simulation models to evaluate the emission reduction and adaptation strategies.
To do so, a discussion of the fundamentals of the global economy, energy, land and climate systems will be complemented by development and applications of mathematical models integrating these key components. The course will also involve programming languages used in energy-climate planning, such as AMPL and python, among others.
The course uses innovative teaching methods, in particular, it is a flipped classroom course: students will form groups of 4-5 and work on projects to improve one or more numerical models to deal with climate change solutions, either on mitigation or adaptation.
Students based in Leonardo (e.g., Mathematical Engineers) may attend part of the course virtually.

At the end of course, students will be able to:

• Explain the foundations of climate science / climate change and how climate change affects energy and economic systems
• Describe the main historical landmarks of climate- energy policy (IPCC)
• Explain the link between climate change and energy systems
• Discuss advantages and limitations of the different mitigation and adaptation strategies
• Describe the different components of an energy system
• Distinguish between major modeling paradigms (IAMs, bottom-up and top-down energy models, etc.) and choose the appropriate type of model for a given question
• Answer specific questions using optimization models and critically interpret / analyse results
• Translate a real-world problem into an optimization formulation
• Write a mathematical model in a specific programming language
• Identify the main sources of uncertainty and calculate their impact on model outcomes
• Present a project in class, and thus create a presentation and be able to communicate it properly

The specific list of topics is as follows
Topic 1: Introduction to the climate change challenge: physics and causes of climate change, consequences and impacts.
Topic 2: Global energy and climate policies and agreements
Topic 3: The role of technology in climate change mitigation
Topic 4: Fundamentals of continuous and discrete optimization
Topic 5: Mathematical modeling and optimization using AMPL
Topic 6: Fundamentals of climate economics
Topic 7: Introducing the tools of Integrated Assessment Models
Topic 8: The simplest integrated energy-economy-climate model: the DICE model
Topic 9: Introduction to energy systems
Topic 10: Energy models: EnergyScope and PyPSA
Topic 11: Climate risks, adaptation and climate engineering
Topic 12: Accounting for risks and uncertainty: sensitivity and uncertainty analysis methods, stochastic and robust optimization

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
Final grade will be based on two main components. A group project which involves model development and presentation during the course lectures. An additional written exam which will be done during the standard exams timeline.
1) Model development and group presentation (2/3): This will be done in class during the course, and we will evaluate both the modeling work as well as the communication skills. In particular, the teacher will assess the relevance of the chosen project, the validity of the software development (also looking at the code) as well as the presentation and oral skills.
2) Written exam (1/3): This will test knowledge of programming and of the theoretical concepts. The theoretical questions will cover the topics examined in class.

Global Energy Assessment - Toward a Sustainable Future, Editore: Cambridge University Press, Anno edizione: 2012 http://www.globalenergyassessment.org/
IPCC 6th assessment report, Anno edizione: 2023 https://www.ipcc.ch/assessment-report/ar6/
DICE 2013 http://www.econ.yale.edu/~nordhaus/homepage/documents/DICE_Manual_100413r1.pdf
The AMPL Book https://ampl.com/resources/books/ampl-book/

The course of Engineering Seismology aims at providing students with the following key elements, introductory to different topics of Earthquake Engineering:
1) the physical background for understanding the earthquake process, from the seismic source, to the seismic wave propagation, up to the ground reponse;
2) numerical, analytical and experimental tools for the engineering characterization of earthquake ground motion;
3) methods and data for probabilistic seismic hazard evaluations;
4) background to the evaluation of seismic actions for design and assessment according to the seismic norms;
5) introduction to concepts of seismic risk at a territorial scale.

At the end of the course, the student is expected to have acquired the following skills:
1) understanding how the physical process governing the earthquake ground motion affects the seismic response of soils and structures (DdD 1);
2) acquisition of in depth knowledge of seismic hazard and seismic risk, and of the seismic norms (especially Italian and European, but also worldwide) as regards definition of seismic actions for design (DdD 1);
3) mastering open source software for the evaluation of seismic wave propagation and local seismic amplification effects due to surface geology, with some applications to real case studies (DdD 2);
4) mastering open source software for the probabilstic seismic hazard assessment, with some applications to real case studies (DdD 2);
5) solving realistic complex engineering problems related to earthquake engineering (DdD 2);
6) ability to make a presentation and defense of the technical results obtained within the homeworks during the oral evaluation (DdD 3,4,5);

Origin of earthquakes and world seismicity
Mechanics of the seismic source, seismic moment earthquake magnitude
Review of recent earthquakes from the main tectonic areas worldwide
Earthquakes in Italy
Introduction to macroseismic scales
Earthquake records: analysis and processing
Analysis of an earthquake record in the time and frequency domain
Parameters associated to ground motion intensity
Introduction to signal processing: baseline correction, filtering, integration
Seismic wave propagation and site effects
P and S waves
Introductory boundary condition problems.
1D wave propagation in heterogeneous media
Applications to site effects evaluation for earthquake engineering: the case of Mexico City
Propagation in linear visco-elastic media
Introduction to non-linear dynamic soil response and linear-equivalent models
2D and 3D complex site effects
Elastic response spectra
Dynamic equilibrium of a single degree-of-freedom system
Response spectrum of an accelerogram
Seismic hazard assessment
Deterministic and probabilstic approaches to seismic hazard assessment
Seismic catalogs
Gutenberg-Richter recurrence relationship
Ground motion prediction equations
The Cornell method for probabilistic seismic hazard analyses
Seismic input in the norms
The Italian seismic hazard map
Elastic spectra for design
Site classification
Criteria of selection of accelerograms for seismic analyses
The seismic input in other worldwide norms: Eurocode8 and US
Seismic vulnerability and risk analysis
Seismic vulnerability elements of masonry structures
Seismic vulnerability elements of reinforced concrete structures
Macroseismic scales
Fragility curves
Introductory elements to seismic risk analysis

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
Students will prepare several homeworks to cover by practical case studies the various subjects of the course.
The homeworks will be delivered and discussed during the oral exam, where a comprehensive evaluation of different topics related to the course will be made. Prior to the oral exam, a written session of the exam is foreseen, with introductory questions.

Faccioli E., Paolucci R., Elementi di Sismologia applicata all'Ingegneria, Editore: Pitagora, Anno edizione: 2005
Kramer S., Geotechnical Earthquake Engineering, Editore: Prentice Hall, Anno edizione: 1996

The course aims to prepare graduate students in scientific and technical disciplines to reason about the ethical consequences of their work, with specific reference to the impact on the environment. Specifically, the first part of the course will introduce students to important topics in the ethics of climate change: e.g., what principles should guide our preservation of the human species? What are the possible policy responses to climate change and how should they be evaluated from a moral standpoint? What, if anything, do we owe to the natural environment and to non-human animals? In the second part, we will bring the discussions of the first part to bear on the question of what constitutes 'due diligence' for technologists in light of climate change, using case-studies from scientific and technical sectors to illustrate the issues at stake. This will help bring out the dimensions of responsibility that are incumbent upon technological production today.

From theory to practice in finance. The course presents with a case-study approach some significant examples where a financial engineer could provide a relevant contribution:
Credit Risk: single-name and multi-name products;
Quantitative Risk Management (RM): from RM measures to RM techniques;
Structured products: calibration, valuation and some hedging issues.
This teaching includes a version of 10 cfu, which is linked to a joint-course teaching by 8 cfu called FINANCIAL ENGINEERING (course 052505). This form defines objectives, programs and learning outcomes expected for both courses.

Both versions of the course have the following common learning goals:
1. to know and to understand

• fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);
• their limits of applicability;
• some risk management techniques;
• single name and multi-name credit problems and models;
• main structured product typologies.
  2. to apply this knowledge on some "Quantitative Case Studies" via the
• valuation of the relevant financial quantities (e.g. Net Present Value of some financial portfolios, risk measurement);
• calibration of underlying models;
• selection of an adequate risk management instrument/trading strategy.
  It is expected an understanding by the student not limited to the definitions, the main results and the solution of standard exercises, but a critical knowledge able to discriminate different financial situations and a conscious model selection, justifying the chosen approaches.
  Moreover the student should obtain correct solutions, explain adequately the codes, and expose properly the theory.

0. Basic derivatives’ concepts

• Forward & option: Exchange-traded Markets vs OTC markets, Forward vs Futures. Forward Price: deduction via a no-arbitrage argument. European Option (Call/Put): decomposition in Intrinsic Value & Time Value; Put Call Parity. CRR & Black Model and examples. Monte-Carlo technique.
• Main Greeks: Delta, Gamma, Vega e Theta. Volatility Smile.
• Basic Interest Rate (IR) instruments: Fundamental year-fractions in IR Derivatives. Depos, Forward Depos, FRA, STIR Futures, IR Swaps & Fwd Swap, Cap/Floor, Swaptions, “InterBank Floaters”.
• IR bootstrap. Sensitivities: BPV, DV01 and duration. For a linear portfolio, sensitivity analysis and hedging of IR risk with IRS.
  1. Credit Risk
• Introduction to credit risk.
• Basic FI instruments in presence of Credit Risk: Fixed Coupon Bond, Floater Coupon Bond, Asset Swap, CDS. SPOL, CDS, ASW relations. Bootstrap Credit Curve.
• Firm-value (Merton, KMV calibration, Black-Cox) & Intensity Based Models (Jarrow & Turnbull, inhomogeneous Poisson).
• Multiname products (ABS, MBS, CDO) and models for HP and LHP (Vasicek).
• O'Kane & Schloegl model, double t-Student, General Threshold Model.
• Copula approach and Li model with examples (Archimedean and Gaussian Copulas).
• Implied Correlation in CDO trances.
  2. Quantitative Risk Management
• Basel Accords, Risk Management Policy.
• VaR/ES: examples, Variance-Covariance method, Historical Simulation, Weighted Historical Simulation, Bootstrap, Full valuation Monte-Carlo, Delta-normal & Delta Gamma method, plausibility check, scaling rule.
• Coherent measures: assioms, VaR subadditivity (counterexample, elliptic case), ES coherence.
• Backtest VaR: Base approach, unconditional backtest, conditional backtest. [Only for 10 cfu version]
• Capital Allocation: Euler Principle & Contribution to VaR & ES.
  3. Structured products main typologies with examples
• Certificates, Equity and IR Structured bond: the general Monte-Carlo approach for pricing non-callable structured products. Callable & Autocallable products.
• Deal structuring and Issuer hedging.
• Digital Risk: Slope impact & Black Correction in Autocallable products, FFT technique. Lewis formula for option pricing and analytic strip via an example: Exponential Levy model (NIG & VG). Global calibration and pricing via a Monte-Carlo (NIG & VG). Sticky Strike & Sticky Delta. Parsimony and smile symmetry.
• IR products and models: plain vanilla and exotics. HJM models: Main equation under Risk Neutral measure. Equivalence with a ZC bond approach and Fundamental Lemmas. Main examples:
  o Market models: forward measure and application in the general derivative premium case. LMM and caplet solution. Calibration: Flat Vol vs Spot Vol in Cap/Floor markets.
  o Hull White model (Extended Vasicek): Cap/Floors solution, Bond Options & Swaptions exact solution. Calibration issues. Pricing: Trinomial Tree Construction.
  The 10 cfu version of the course (course 052500) uses some "Innovative teaching methods" designed and realized in collaboration with the financial industry (most of these methods are not included in the 8 cfu version, course 052505). Often this teaching methodology uses some "Quantitative Case Studies" that present some concrete problems for a financial institution, but simplified in order to be treated in a classroom. This approach requires the student to propose and realize quantitative solutions within a group (composed by 3 to 5 students) and with strict time constraints.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
The are five possible examination appeal dates, established in the academic calendar (two in June/July, one in September, two in January/February). Each exam appeal is composed by a written part and an oral part.
In the written part, the student is required to write:

• Matlab codes that solve some financial engineering problems;
• a document describing the chosen methodology, numerical results and problems/criticalities (if present).
  The written and the oral part contribute to the final score with the same weight (15/30).
  The examination appeal for the 8 cfu version, called FINANCIAL ENGINEERING (course 052505), does not include arguments specific of the 10 cfu version (both in the written and oral part).
  The examination has the objective to verify whether the student has acquired the following skills:
  1. The knowledge of
• fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);
• their limits of applicability;
• some risk management and quantitative finance approaches;
• single name and multi-name credit problems and models.
  2. The ability in applying the acquired knowledge in the computational/mathematical approaches for the
• calibration of financial models from real datasets;
• valuation/risk measurement/risk management of portfolios of elementary/structured products in presence of market and credit risks.

A. J. McNeil, R. Frey & P. Embrects, Quantitative Risk Management: Concepts, Techniques and tools, Editore: Princeton University Press, Anno edizione: 2005, ISBN: 0691122555
Note: Risk Management
P.J. Schonbucher, Credit Derivatives Pricing Models, Editore: Wiley, Anno edizione: 2003, ISBN: 0470842911
Note: Credit Risk
J. Hull, Options, futures and other derivatives, Editore: Pearson Prentice Hall, Anno edizione: 2009, ISBN: 0136015867

The course aims to let Students to:
Understand roles and functions of financial markets and how they support the real economy;
Know what are the major activities of banks and other financial institutions;
Share the impact coming from digital innovation and sustainability on financial markets and institutions.

At the end of the course, Students will be able to indicate and understand:
how financial systems and financial intermediaries operate;
what are the main figures of banks and financial institutions and how they are related to the businesses;
main trends related to the financial and digital innovation and sustainability.

OVERVIEW
The course focuses on financial markets and institutions. In particular, it concentrates on the features, the objectives, the role and the typologies of financial markets and of the different categories of financial intermediaries and institutions. A major attention will be dedicated on banks. Moreover, some lectures will provide insights about the banks P&L, their supervision and regulation and the Banking Union. The course will also focus on the asset management industry and on corporate governance and sustainable value creation. All the items will include a description about how the digital transformation and the fintech as well as sustainability are playing a major role on financial markets.
CONTENTS DESCRIPTION
Fundamentals of the financial system
Financial and economic systems
Financial markets and institutions
The theory of financial intermediation
Fintech and digital transformation
Financial markets and instruments
Securities: bonds, equity, derivatives, forex
Banks: structure, supervision and management
Banks
Bank supervision, prudential regulation and the Banking Union
Banks P&L, economic and financial equilibrium, asset liability management
Banks risk management: RAF and IXAAP
Asset management
Industry value chain (players, products, relationship with other intermediaries…)
ESG investing
Corporate governance and sustainability
Internal and external governance
Governance and sustainable value creation
ORGANIZATIONAL ISSUES
The contents are provided through class lectures, which consist in both theoretical lessons and exercises. Lectures have a strong correspondence with the suggested textbook. Students should attend class regularly and actively participate, contributing to class learning and discussion. Some sessions will be given through practitioners coming from the most important and highly-reputed financial risk management departments.

Prova scritta obbligatoria, senza prove in itinere
Individual written test at regular calls.
Students may re-take the exam in any regular exam session, as many times as they wish; doing so requires formally rejecting the previous grade.

A. Saunders, Financial Markets and Institutions., Editore: McGraw Hill, Anno edizione: 2021

How can financial institutions turn data into better services, smarter investment tools, and more informed decisions? How do algorithms execute trades in modern markets? And what can blockchain bring to financial services?
This course explores Fintech through the business and financial problems it can help solve. It combines essential theoretical foundations with a strong practical focus, connecting machine learning, algorithmic trading, and blockchain to concrete applications.
The course covers three complementary areas:
Machine Learning for Finance and Business (50%) — Learn to translate business questions into data-driven solutions through extensive hands-on work with datasets and Python notebooks. Applications include segmenting banking clients, identifying financial and insurance needs to support personalized recommendations, replicating investment portfolios, and building early warning systems to detect abnormal market conditions. Students explore data, develop and compare models, interpret results, and communicate their business implications.
Algorithmic Trading and Market Microstructure (25%) — Discover how modern financial markets operate and how algorithms support trade execution. Topics include limit order books, liquidity, market making, execution strategies, and price impact, with an emphasis on the practical constraints and trade-offs that shape trading decisions.
Blockchain and Digital Assets (25%) — Understand the foundations of blockchain and examine smart contracts, tokens, cryptoassets, stablecoins, and central bank digital currencies. Explore their potential applications and limitations, including the role of cryptoassets in investment portfolios.
Learning by doing is central to the Machine Learning component: students tackle business cases, experiment with alternative approaches, and present their findings. The emphasis is on developing the judgment to choose appropriate methods, assess their limitations, and connect analytical results to business decisions.
5-CFU version: Students complete the Machine Learning component and choose either Algorithmic Trading or Blockchain, tailoring the course to their interests.

Lectures and coding sessions will allow students to acquire the following competences:

• DD1 Knowledge and understanding
  know some advanced concept of stochastic calculus, which are essential in quantitative finance;
  know how to choose modeling assumptions to solve a financial problem properly.
• DD2 Ability in applying knowledge and understanding
  know how to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledge.
• DD3 Making judgements
  find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
  be able to judge the possible financial risks raising from using wrong modeling assumption (like misprice of financial products).
• DD4 Communication skills
  to be able to express mathematical and financial concepts in a clear and rigorous way.

Machine Learning for Finance and Business (50%)
Core concepts and methods: supervised and unsupervised learning; clustering, classification, and regression; decision trees, random forests, and neural networks; model evaluation and interpretability; introduction to reinforcement learning and its financial applications.
Hands-on business cases using datasets and Python notebooks:
Customer segmentation: identify client profiles and build data-driven personas to support tailored financial services.
Needs estimation and personalized recommendations: use customer data to identify financial and insurance needs and support next-best-action decisions.
Portfolio replication: use observed returns to construct portfolios that track an investment strategy or index.
Early warning systems: detect abnormal market conditions to support risk monitoring and investment decisions.
Practical activities cover data exploration and preparation, model development and comparison, interpretation of results, and communication of business implications.
Algorithmic Trading and Market Microstructure (25%)
Market participants and trading venues; limit order books and order types; liquidity, bid–ask spreads, and market making; adverse selection; execution algorithms, including TWAP and VWAP; transaction costs and price impact; technological aspects of algorithmic trading. Connections with reinforcement learning for sequential trading and execution decisions.
Blockchain and Digital Assets (25%)
Blockchain foundations: hash functions and Merkle trees, transactions, distributed consensus, and mining. Bitcoin and wallets. Smart contracts, tokens, and initial coin offerings. Stablecoins and central bank digital currencies (CBDCs). Financial characteristics of cryptoassets and their role in portfolio allocation. Business applications and limitations of distributed ledger technologies.
5-CFU version: The Machine Learning component is combined with either Algorithmic Trading or Blockchain.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, senza presentazione/discussione finale
The exam consists of:
a) projects on the ML topics;
b) written theoretical exam.
The objective of projects is to let students work in groups, applying the approaches and principles taught in class. Projects will be assigned through the semester. Project artifacts are expected to be released at fixed deadlines that will be defined by the time the project will be assigned. The evaluation of projects will be based on the produced artifacts (documentation, code, …).
The written theoretical exam is mandatory.
The exam has the goal of checking whether the student has acquired the following skills:

• knowledge of advanced concepts of stochastic calculus, which are essential in quantitative finance;
• knowledge of how to choose modeling assumptions to solve a financial problem properly;
• ability to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledgements;
• ability to find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
• ability to express mathematical and financial concepts in a clear and rigorous way.

Atomi:massa e dimensioni.Distribuzione di Boltzmann e teorema dell'equipartizione dell'energia. Radiazione di corpo nero. Effetto fotoelettrico e effetto Compton. Modello atomico di Bohr. Dualismo onda particella e lunghezza d'onda di de Broglie. Principio di indeterminazione di Heisenberg. Equazione di Schroedinger. Buca di potenziale rettangolare. Oscillatore armonico. Particella libera. Barriere di potenziale ed effetto tunnel. Operatori:autofunzioni e autovalori. Operatore momento angolare. Atomi a un elettrone. Teoria delle perturbazioni dipendenti dal tempo e transizioni ottiche. Dipoli magnetici elementari. Spin dell'elettrone. Interazione spin-orbita. Principio di esclusione di Pauli e interazione di scambio. L'atomo di Elio. Atomi a molti elettroni: teoria di Hartree. Tabella periodica. Spettri di emissione di raggi X. Sistemi a molte particelle: meccanica statistica quantistica. Distribuzione di Fermi-Dirac e di Bose-Einstein.

Students attending the course are expected to gain a full understanding of aspects such as the consequences of the presence of defects and geometric irregularities and of the ensuing stress concentrations.
Issues such as the scale or size effect and the effect of cyclic loading will also be clarified.
Attendees will also be interactively involved in the use of the finite element code Abaqus for the computation of fracture parameters such as the stress concentration factor, the stress intensity factor and the strain energy release rate in simple 2D structural configurations.

Students will have to show their knowledge and understanding of subjects treated in undergraduate courses, such as strength of materials and structural mechanics, and master courses of the first semesters, such as the finite element method and limit analysis methods.
At the end of the course they will be required to show their ability in applying their knowledge and understanding to the conceptual treatment of structural problems involving the possibility of defect propagation up to structural failure. In particular, they will have to show their knowledge and understanding of concepts like stress concentration, role of defects and the conditions for their propagation, brittle versus ductile failure, size effects, different approaches to fatigue failure and they will be required to apply their gained knowledge and understanding to the computation of fracture parameters such as the stress concentration factor, the stress intensity factor and the strain energy release rate and the J integral in simple 2D structural configurations.

Plane problems in linear elasticity. Formulation of Beltrami’s problem. Airy’s function. Formulation of Beltrami’s problem in cylindrical coordinates. Stress concentrations in linear elasticity. Lamé’s analytical solution for the thick pipe. Kirsch’s analytical solution of the plate with a circular hole. Williams’ formulas for the stress singularity near a reentrant corner. Stress intensity factor.
Basic notions of linear elastic fracture mechanics. Griffith’s approach: strain energy release rate. Irwin’s approach. Crack tip plastic zone width estimate: Irwin and Dugdale models. Range of applicability of linear elastic fracture mechanics. Case histories concerning failures due to brittle fracture and fatigue. Computation of fracture parameters using the finite element method. X-FEM approach to the simulation of crack propagation.
Ductile elastoplastic fracture mechanics. Crack tip opening displacement. Nonlinear strain energy release rate. J integral. J integral finite element computation.
Experimental fracture behavior of structural materials: metals, polymers, quasi-brittle materials (e.g. concrete).
Strain localization. Notion of characteristic length. Size effects.
Quasi-brittle fracture mechanics: cohesive models. Cohesive modeling of delamination.
High-cycle fatigue. Experimental evidences: Wohler’s diagrams. Total life and defect tolerant approaches to fatigue. Paris-Erdogan law. Safe Life and Fail Safe design philosophies.
Experimental measurement of fracture parameters.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The exam consists of a written test on the course subject matter. The written test will be followed by a short colloquioum where the student work will be revised and possibly integrated with oral questions.
The written questions in the test are aimed at verifying the student knowledge and understanding of the different conditions for structural failure, the role of defects, the effects of stress concentrations, the size effect and the effect of cyclic loading. The student will also have to prove to know and to have understood the methods for the computation of fracture mechanics parameters such as the stress intensity factor, the strain energy release rate and the J integral.

T.L. Anderson, Fracture Mechanics - Fundamentals and Applications, Editore: CRC Taylor and Francis, Anno edizione: 2005, ISBN: 978-0-8493-1656-2
Alberto Carpinteri, Meccanica della Frattura, Editore: Pitagora Editrice Bologna, Anno edizione: 1992, ISBN: 88-371-0543-6
K. Bertram Broberg, Cracks and Fracture, Editore: Academic Press, Anno edizione: 1999, ISBN: 978-0-12-134130-5
L. B. Freund, Dynamic Fracture Mechanics, Editore: Cambridge University Press, Anno edizione: 1990, ISBN: 978-0521303309
Zdenek P Bazant, Luigi Cedolin, Stability Of Structures: Elastic, Inelastic, Fracture And Damage Theories, Editore: World Scientific, Anno edizione: 2010, ISBN: 9789814464482

The course concerns the fundamentals of the mathematical theory of interactions between agents.
Starting from the main assumptions of the theory, it discusses both cooperative and non cooperative games, and it also provides an introduction to evolutionary game theory. The goal is to explain how rationality can explain and/or predict and/or suggest the behavior of interacting agents, where "agents" may refer not only to people, but also to computers, animals, microorganisms and so on.

Knowledge and understanding
1) To know the fundamentals of interactive decision theory.
2) To know some of the proofs of fundamental theorems in non cooperative game theory.
3) To know some of the proofs of fundamental theorems in cooperative game theory.
4) To know some of the proofs of fundamental theorems in evolutionary game theory.
5) To know some of the main ideas of matching theory, social choice, and differential games.
Ability in applying knowledge and understanding
1) To be able to modelize simple interactive situations as games.
2) To be able to state and explain the proofs of fundamental theorems in game theory.
3) To solve exercises.
Making judgements
1) To be able to state translate a problem in a game and analyze it.
Communication skills
1) To be able to explain and illustrate (in written form) the importance or the meaning of a definition or a theorem.
2) To be able to explain the applications of the theory.

1) Main assumptions of the theory. Main differences between decision theory and interactive decision theory.
2) Non cooperative games. Games in estensive form. Games with perfect information, backward induction. Combinatorial games.
3) Zero sum games. Conservative values. The case of equilibrium in pure strategies. Extending the finite game to mixed strategies. The von Neumann theorem. Finding optimal strategies and the value of a finite game by means of Linear Programming.
4) The Nash non cooperative model, Nash equilibrium and existence of (mixed) equilibria in finite games. Examples. Potential games, how to find a potential. Examples: congestion games, routing games, network games, location games. Price of stability and of anarchy. Correlated equilibria.
5) Cooperative games, definitions, examples. Core, nucleolus, the Shapley value and power indices.
6) The bargaining problem: the Nash and the Rosenthal approaches.
7) Problems of matching.
8) Social choice and Arrow’s theorem.
9) Evolutionary game theory.
10) Mechanism design.
11) Differential games.

Prova scritta obbligatoria, senza prove in itinere
The exam consists of two parts.
Part One, on Moodle. Six exercises (2 points each), and two sets of multiple choice questions on the theory (6 points each set).
Part Two, on paper. Two open questions on the theory (5+3 points). The first one requires an introduction to the topic, a presentation of the main ideas and results and the proof of a theorem. The second one is a specific question.
Points are rounded to the closest integer. Students obtaining strictly more than 30 points are graded 30 e lode.

Maschler, Solan, Zamir, Game Theory, Editore: CUP, Anno edizione: 2013, ISBN: 9780511794216
Note: New edition 2020
Sigmund, Introduction to Evolutionary Game Theory https://homepage.univie.ac.at/Karl.Sigmund/psapm573.pdf

Geophysical methods based on the ecographic or tomographic principle generate the final results through a complex data processing procedure. The goal of the course is to introduce the student to the 2D and 3D data processing algorithms that are used to process geophysical data from seismic or georadar surveys. Algorithms are presented in simple and intuitive ways during the lectures and are tested by the student on real data during the laboratory hours. Students attending the laboratories and wishing to develop a project will be organized in small groups. Real data and tasks will be assigned to each group. Each group will work on the data with the specific processing software that they have been trained to use in preliminary lab sessions. Many lab hours will be dedicated to discussions with the teacher to evaluate the results and to solve doubts and problems either in presence or in remote sessions. Any group will be asked to edit and submit a short report about the processing of the assigned real data.

After having attended the course and passed the exam, the student:
DdD 1 (knowledge and understanding)
Is familiar with the analysis of geophysical signals either in time or in frequency domain.
Knows the principles of the data processing algorithms used in seismic and georadar prospecting.
DdD 2 (applying knowledge and understanding)
Can define and apply a proper data processing sequence to produce a seismic or georadar 2D or 3D section.
Has some practice with a geophysical professional software so that he can rapidly get familiar with any other geophysical software that might be used by his company.
DdD 3 (making judgements)
Can properly select and optimize the input parameters required by each algorithm.
Is able to critically evaluate the results of each processing step and the final quality of the processed dataset.
DdD 4 (communication skills)
Has improved his attitude to work in a team and to write technical reports.

1. Hints of signal theory: Fourier transform, linear systems, impulse response, transfer function, convolution, autocorrelation and cross-correlation, analog and digital signals, sampling, Nyquist theorem.
2. Processing of georadar data: hints on acquisitions, filters, time-calibration, background subtraction, gain, topographic corrections, velocity analysis, time-depth conversion, focusing methods for monostatic and bistatic systems, focusing of 3D data.
3. Processing of seismic refraction data: hints on acquisitions, first arrival picking, reciprocal methods, Generalized Reciprocal Method, tomographic inversion.
4. Processing of seismic reflection data: hints on acquisitions, gain, bandpass filters, FK filters, time-variant filters, velocity analysis, static and dynamic corrections, muting, residual statics, stack, deterministic and statistical deconvolution, pre-stack and post-stack multiple suppression, 2D and 3D migration, pre-stack migration, calibration with VSP data.
5. Processing of MASW data: Rayleigh waves, hints on acquisitions, spectral analysis through fk transform or tau-p transform, dispersion curve picking, inversion.
6. Tomographic inversion: hints on acquisitions, traveltime picking, time-calibration, inversion grid design, traveltime inversion, amplitude picking, divergence correction, radiation pattern correction, amplitude inversion.
Laboratory: Part of the course consists of a large number of laboratory sessions with Matlab and with professional software for radar and seismic data processing.

Prova orale obbligatoria
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), di gruppo, con revisioni periodiche, senza presentazione/discussione finale
Evaluation is based on an oral exam, during which the student may be asked to design a data processing procedure or discuss a specific algorithm. The aim is to assess whether, and to what extent, the student has achieved the expected learning outcomes in terms of knowledge, understanding, application, and communication skills (as outlined in the dedicated section).
For students who attended the lab sessions and chose to develop a project, part of the exam will consist on the discussion of the technical report and the data processing procedure applied to the real dataset assigned to the group. The discussion on the report and the other part of the oral exam will be evaluated as a whole since the discussion on the report is part of the oral exam. The purpose of the project is not to split the exam into two independently graded parts (project and oral), but rather to facilitate students in achieving the expected learning outcomes of the course—particularly those related to DdD 2, 3, and 4. The project will be a great opportunity for the students to check their skill in designing and optimizing the processing procedure and in critically evaluating the results. Besides, it will be an opportunity to work in a team, to interact with the instructor and to prepare a report thus improving some important communication skills. Thus, the project is strongly recommended but since it requires the students to regularly attend the course, it is not mandatory. Students that will not attend the class cannot work on a project and will not submit a report. However, in order to make practice in geophysical data processing applications, they will have the opportunity to do the lab sessions independently by working on specific training datasets following the guidelines made available on WeBeeP.
Exam appointments are scheduled upon request. Please book your appointment at least one week in advance.

L. Zanzi: Handouts of PowerPoint presentations https://webeep.polimi.it
L. Zanzi: Lecture videos https://webeep.polimi.it
L. Zanzi: Notes on GPR https://webeep.polimi.it
P. Annan: GPR data processing notes https://webeep.polimi.it
L. Zanzi and A. Hojat: Notes on seismic methods https://webeep.polimi.it
D. Palmer: Generalized Reciprocal Method https://webeep.polimi.it
O. Yilmaz, Seismic data analysis http://wiki.seg.org/wiki/Seismic_Data_Analysis

The course deals with some important network and graph optimization problems arising in several fields of application such as telecommunication, transportation and logistics. The course presents optimization models for different classes of problems and describes the main methods that have been proposed to tackle them.
The aim of the course is to provide students with a classification of optimization problems related to networks and other applications. Further, the course aims at providing the students with the knowledge of a wide range of optimization methods. The students will learn to model optimization problems arising in real life applications, to represent them as particular case of well known optimization problems, and to deal with them applying both exact and heuristic approaches. Beside theoretical knowledge, the course will provide practical experience in developing and applying the optimization techniques. During lab sessions, the students will be asked to apply their knowledge to deal with problems.

Knowledge and understanding (DdD 1)
The student will learn

• some of the main families of optimization problems (network design and flows, location, scheduling)
• the key heuristic methods, their features and properties
• the principal relaxation approaches
• the valid inequalities and some classical examples
  Applying knowledge and understanding (DdD 2)
  The student will be able to
• identify the mathematical model underlaying an application and, if possible, map it to existing families of optimization problems
• design a heuristic algorithm to tackle a problem, implement it and evaluate its performance
• apply relaxation techniques and implement them to obtain a bound for a problem
• derive valid inequalities based on classical examples and implement them to improve the bound
  Learning skills (DdD 3, DdD 5)
  The students will learn how to tackle complex optimization problems stemming from a variety of real-world applications. They will be able to devise advanced solution algorithms to such problems, and possibly map them to a graph structure to utilize computational efficiency. Moreover, students will be able to verify the quality of their algorithms through the development of adequate bounds.

Introduction. Brief review of mathematical programming models for graph and network optimization problems (paths, trees, minimum cost flow, maximum flow, travelling salesman problem, knapsack problem). Brief review of the Branch-and-Bound method and Cutting Plane algorithms (Gomory cuts).
Flow routing and Fixed Charge Network Design problems. Classification: splittable vs unsplittable flow, single vs multiple paths, multicommodity flows, node and arc fixed costs. Arc-based and path-based ILP models.
Column generation method. Dual problem and complementary conditions, the pricing problem.
Heuristic methods. Greedy algorithm. Local Search. Metaheuristics: tabu search, simulated annealing, variable neighborhood search. Very large scale neighborhood and ILP based neighborhood. Examples of application of heuristic methods.
Location problems. Classification: set covering and set partitioning, p -center and p -median problems, uncapacitated and capacitated facility location problems, single assignment and multiple assignment.
Valid inequalities and cutting planes. Cover inequalities for knpasack problem. Valid inequalities for network design and connectivity requirements.
Relaxation. Continuous relaxation, surrogate relaxation. Lagrangian relaxation: general framework and application to facility location problems and network design problems.
Scheduling problems. Introduction to scheduling problems. Classification: single machine scheduling with different objective functions (total weighted completion time, makespan, lateness, tardiness), parallel machines scheduling problems, flow shop, job shop. Models and algorithms for scheduling problems.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The exam includes a written test and a lab exam.
The written test includes:

• exercises: the student is required to apply the knowledge for solving small examples and for applying the optimization methods to a given problem
• theoretical questions on course topics with open answer: the student is required to demonstrate his/her knowledge of the optimization methods
  The lab part includes homeworks: the student is required to apply the methods and implement them to solve problems

R. Ahuja, T. Magnanti, J. Orlin, Network flows: Theory, Algorithms, and Applications, Editore: Prentice Hall, Anno edizione: 1993
D. Bertsekas, Network Optimization: Continuous and Discrete Models, Editore: Athena Scientific, Anno edizione: 1998
F.W.Glover, G.A.Kochenberger, Handbook of Metaheuristics, Editore: Springer-Verlag, Anno edizione: 2003
J. Desrosiers, M. Lübbecke, G. Desaulniers, J. B. Gauthier, Branch-and-Price, Anno edizione: 2026
H.W. Hamacher, Z. Drezner, Facility Location: Applications and Theory, Editore: Springer, Anno edizione: 2001
B. Korte, J. Vygen, Combinatorial Optimization: Theory and Algorithms, Editore: Springer Verlag, Anno edizione: 2001
M.L. Pinedo, Scheduling - Theory, Algorithms, and Systems, Editore: Springer, Anno edizione: 2008
V.J. Rayward-Smith, I.H. Osman, C.R. Reeves, G.D. Smith, Modern heuristic search methods, Editore: Wiley and Sons, Anno edizione: 1996
M. Piòro, D. Medhi, Routing, Flow, and Capacity Design in Communica- tion and Computer Networls, Editore: Elsevier, Anno edizione: 2004
S.Martello, P.Toth, Knapsack problems, Editore: Wiley, Anno edizione: 1990
Laurence A. Wolsey, Integer Programming, Anno edizione: 2020, ISBN: 1119606527

Groundwater circulation. Basics of groundwater hydraulics. Darcy's Law. Characterization of hydraulic properties of porous media. Mass balance equation. Two- and three-dimensional flow models. Analytical solutions. Well hydraulics and field etsts interpretation. Analytical solution, including storage and non-linear effects at the well. Interpretation of well-interference testing in complex hydrogeological systems.
Transport processes in porous media. Basic processes and equations governing reactive transport. Dual porosity models. Multi-component reactive transport. Modeling under uncertainty. Flow and transport processes in randomly heterogeneous aquifers. perturbation theory. Effective parameters for flow and transport. Inverse modeling. General formulation of non-linear inverse problems in porous media. Interpretation of tracer tests. Aquifers' characterization.

The purpose of the Image Analysis and Computer Vision course is to study both the foundations on image formation, image analysis, 3D scene reconstruction, and the methodologies underlying the solution techinques to the main problems involved.
Image analysis addresses the extraction of the content of one or several images; Computer Vision addresses the methodologies to obtain a representaton of the observed 3D scene. Optical, geometric, and algorithmic aspects are studied, as well as aspects connected to signal processing and data analysis.
A project allows to closely examine, possibly from a practical point of view, one or more of the discussed topics.

1. Knowledge and understanding: Geometric foundations of the image projection; Image analysis as a signal
2. Applying knowledge and understanding: Use geometric knowledge to devise techniques to interpret an observed scene; Use knowledge on signal processing to develop techniques to extract relevant features from images
3. Making judgements: Given a complex and realistic scene reconstruction problem, try to infer a sufficient set of constraints from the particular circumstances of the problem instance
4. Communication skills: presenting own ideas to the teacher/gruop mates relative to a complex problem to solve, reporting adopted solution and results
5. Learning skills: learning to correlate items from an eterogeneous corpus of knowledge to solve a complex and realistic Computer Vision problem, use foundations to allow lifetime learning in Image Analysis and Computer Vision

0. Introduction.
1. Camera sensors: transduction, optics, geometry, distortion
2. Basics on Projective geometry: modelling basic primitives (points, lines, planes, conic sections, quadric surfaces) and projective spatial transformations and projections.
3. Camera geometry, and single view analysis: calibration, image rectification, localization of 3D models.
4. Multi-view analysis: 3D shape reconstruction, self-calibration, 3D scene understanding.
5. Linear filters and convolutions, space-invariant filters, Fourier Transform, sampling and aliasing.
6. Nonlinear filters: image morphology and morphology operators (dilate, erode, open, close), median filters.
7. Edge detection and feature detection techniques. feature matching and feature tracking along image sequences.
8. Inferring parametric models from noisy data (including outliers), contour segmentation, clustering, Hough Transform, Ransac (random sample consensus).
9. Applications: object tracking, object recognition, classification.

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, senza presentazione/discussione finale
Altro
EVALUATION.
The standard examination consists of two parts: an individual homework (max 10/30 pts) and an application project (max 20/30 pts) on a topic from a list proposed by the teacher (project can possibly be extended to Master Thesis).
A. Written individual homework: study the geometric aspect of the assigned problem, exploit problem specification to derive useful constraints (1,2, 3); implement the solution (including the extraction of the needed image features), while addressing noise and uncertainty on the extracted image features, and evaluate experimental results (3, 5); carefully write a self-sufficient report (4).
B. Assessment of project artifact with written report and presentation: Assessment of the design and experimental work done either individually or in small groups (up to three participants): 2, 3, 4, 5.
Project can be either full or short. Full project evaluation outcome contributes maximum 20/30 pts -possibly, with laude assignment- to the final mark. Short project evaluation contributes maximum 16/30 to the final mark (no laude). In both cases, the submission of a well written, self-explaining report plus a presentation file is required.
If the homework is submitted and a good score is obtained (minimum 8/10), the student can ask to compose his final mark basing only on the evaluation of the full project. A " laude" grade can only be granted if both the Homework and the Project are excellent, i.e., respectively 10/10 and 20/20.
ESCAPE STRATEGIES.
1) Project but no homework: the exam will include a written proof, including difficul exercizes. Final grade ranges up to a maximum of 28/30.
2) Homework but no project: the exam will include a full written proof, including some difficult exercizes. Final grade ranges to maximum of 27/30.
3) No homework, no project: the exam will consist in a full written proof, including some difficult exercizes. Final grade ranges to maximum 25/30.

R. Hartley - A. Zisserman, Multi-view Geometry for Computer Vision, Editore: McGraw- Hill, Anno edizione: 2003
Slides of the course https://webeep.polimi.it/course/view.php?id=1047§ion=2

This course is about how to measure, represent, and communicate information efficiently. It explains why bits have become the universal currency for information exchange and how information theory underpins the design and operation of modern technologies such as smartphones, the Internet, and cloud computing. Information measures are first introduced and then applied to the analysis of the fundamental performance limits achievable in data compression and communication over noisy channels.
The goal of the course is to teach students how the concepts of source coding and channel capacity are used to model, analyze, and design modern communication systems in order to enable efficient information processing. Since these concepts constitute a fundamental foundation of virtually every digital communication system, another objective is to establish concrete links between information theoretic principles and advanced communication technologies. To this end, students will have the opportunity to work on projects that apply the concepts and methodologies learned during the course.
In addition to the foundations of classical information theory, the course provides an introduction to Quantum Information Theory. Whereas classical information theory is based on the representation, processing, and transmission of information using classical bits, quantum information theory considers information encoded in quantum bits, or qubits, which obey the principles of quantum mechanics. This part of the course introduces the fundamental concepts of quantum information and highlights the similarities and differences between the classical and quantum frameworks.
The course also includes project activities carried out in collaboration with industrial partners. Depending on the assigned topic, students will address either classical information theory problems, including source coding and channel coding, or introductory applications of quantum information theory. These projects are designed to connect the theoretical concepts presented during the course with practical engineering problems arising in industrial applications.

1 - Knowledge and understanding
Lectures and exercise sessions will allow students to:

• know how to measure information quantitatively
• know theoretical and methodological skills related to the concept of classical and quantum information
• understand properties of entropy, mutual information as applied them to information processing
  2 - Applying knowledge and understaning
  After the end of the course, students should be able to:
• understand and solve complex problems in different interdisciplinary areas
• integrate and individually find and re-adapt known solutions to growing problems
• analyse uncertainty in terms of information entropy and other information measures
• summarize and present the results achieved during the analysis and specification activities
• to communicate the results of their activity in a clear and convincing way
  3 - Making judgements
  After the end of the course, students should be able to:
• define mathematical models by considering the informational aspects of a system and the related measures
• evaluate concrete schemes for compression and communication

1 – Introduction to Information Theory
Historical background. Introduction to information theory and its applications.
2 - Entropy and Source Coding
Entropy of a memoryless source. Coding of memoryless sources. Prefix codes. Kraft inequality. Huffman codes and Shannon codes. Source coding theorems for memoryless sources. Joint entropy and conditional entropy. Chain rules. Entropy of sources with memory. Source coding theorem for memory sources. Practical source coding methods. Universal coding. Arithmetic coding.
3 - Channel Capacity
Channel models. Discrete memoryless channels. Mutual information. Relative entropy. Data processing inequality. Channel capacity. Reliable communication over discrete memoryless channels. Entropy, mutual information, and channel capacity for continuous channels. Additive white Gaussian noise (AWGN) channel. Channel coding theorem. Error exponent. Fano's inequality.
4 – From Classical to Quantum Information Theory
Motivation for quantum information theory. Quantum states. Qubits. Bra–ket notation. Unitary evolution. Quantum gates. Quantum measurement and the Born rule. Density operators. Pure and mixed states. Composite quantum systems. Entanglement. Bell states. No-cloning theorem. Quantum entropy. Properties of quantum entropy. Quantum mutual information. Coherent information.
5 – Project on Selected Topics
A voluntary project laboratory will be assigned during the semester. All projects will be related to the course topics covered in Sections 1–4 and will be carried out either in collaboration with industrial partners, who will propose engineering problems, or on topics proposed by the students and approved by the course instructors. Depending on the selected project, students will address classical information theory, including source and channel coding, or introductory topics in quantum information theory.
Projects will be carried out in groups of two or three students during the second half of the semester. Their objective is to apply the concepts learned in the course to realistic engineering problems. The evaluation will be based on the produced artifacts, such as documentation, software, or experimental results, together with a final presentation. Technical discussions with the course instructors and researchers from the participating companies will complement the project activities.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The written exam evaluates Knowledge and understanding (DD1) and Applying knowledge and understanding (DD2) through numerical exercises and open questions on the topics addressed in the course. It can assign up to 23 points, which form the basis for the final mark before the oral examination.
The oral examination evaluates Making judgements (DD3), Communication skills (DD4), and Learning skills (DD5). It can assign up to 10 points.
Students may choose to complete a voluntary project in place of the oral examination. The project evaluates Applying knowledge and understanding (DD2), Making judgements (DD3), and Communication skills (DD4) in the context of an applied study. It can assign up to 10 points.
The mark of 30 cum laude is awarded when the total score after the project presentation reaches 33.

Lecture notes https://webeep.polimi.it/course/view.php?id=14728
Luca Barletta, Gianluigi Liva, Maurizio Magarini, Lecture Notes on Channel Coding https://webeep.polimi.it
Note: Supplemental Material for the Courses Channel Codes for of Iterative Decoding (TUM) and Information Theory (PoliMi).
T. M. Cover, J. A. Thomas, Elements of information theory (1st or 2nd edition), Editore: John Wiley & Sons, 1991 (1st ed.), 2006 (2nd ed.). First edition available online for PoliMi students (http://onlinelibrary.wiley.com/book/10.1002/0471200611)
Sandro Bellini, Information Theory https://webeep.polimi.it/mod/folder/view.php?id=337337
D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms, Editore: D. J. Cambridge University Press, 2003
R. G. Gallager, Information Theory and Reliable Communication, Editore: John Wiley & Sons, 1968

The aim of the course is twofold.
In the Insurance module, students are introduced to actuarial mathematics and learn models and methods used to price insurance contracts and analyse insurance portfolios, both in the life and non-life insurance cases.
In the Econometrics module, students are equipped with the skills needed to thoroughly and appropriately model, analyse, and forecast financial time series.

Lectures and computer laboratory sessions allow students to acquire the following competences.

• Knowledge and understanding.
  Students know the main models and methods used in actuarial mathematics, both in the life and in the non-life insurance cases.
  Students understand the main concepts of statistics and econometrics used to analyse and forecast financial time series.
• Ability to apply knowledge and understanding.
  Students can apply the models and methods of actuarial mathematics to price life insurance benefits, and to model and analyse insurance portfolios to guarantee profitability and solvability of insurance companies.
  Students can analyse in a proper way a financial time series.
• Making judgements.
  Students can judge the main risks in insurance contracts and quantify their impact on insurance portfolios.
  Students can find proper modelling assumptions to analyse and forecast financial time series.
• Communication skills.
  Students are able to express mathematical and financial concepts in a clear and rigorous way.

Actuarial mathematics.
Life insurance: survival models, life tables, pricing of insurance benefits and annuities, reserves, modelling life insurance portfolios, Solvency II regulation.
Non-life insurance: collective risk models for general insurance portfolios, premium calculation principles, the Cramér-Lundberg model.
Econometrics.
Financial time series; stationary processes and selection, estimation, and forecasting of ARMA models; unit root processes, vector autoregressive (VAR) models, and key concepts such as Granger causality and cointegration (Engle and Granger theorem); discrete-time models for heteroskedasticity, including ARCH and GARCH.
Throughout the course, numerous applications to financial market time series are discussed, including volatility estimation and topics in green finance.
Computer laboratory sessions are an integral part of the course. Two group project works, one for each module, are assigned during the semester and evaluated at the end of the course.

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The evaluation consists in two project works, one for the Insurance module and the other one for the Econometrics module, and an oral exam.
Project works need to be carried out in groups. Students are expected to apply the models and methods taught in class to actual case studies and real-world data, and to develop teamworking skills.
Project works are assigned during the semester and specific deadlines for submission are communicated in due time, for each of them.
Project works are evaluated at the end of the course, each on a scale 0-12, based on the submitted documents (report, MATLAB or R code, etc.). Students are required to show:
Knowledge and understanding of actuarial mathematics models and methods and the Solvency II regulation;
The ability to price insurance contracts and to analyse the profitability of an insurance company;
The ability to discern and analyse the main sources of risk of insurance portfolios;
Knowledge and understanding of econometrics models and methods, time series volatility modelling and cointegration, and multivariate time series models;
The ability to properly analyse and forecast financial time series;
The ability to express mathematical and financial concepts in a clear and rigorous way.
The oral exam is individual, distinct for the Insurance and the Econometrics modules, each evaluated on a scale 0-20. The oral exam can be taken only during official exam sessions; a midterm oral exam will also be scheduled.
The oral exam consists of three questions for each module on the whole program of the course. To pass the oral exam, students must correctly answer to two questions for each module.
Students are expected to show:
Knowledge and understanding of the models and methods taught in class;
The ability to prove in a rigorous way the results discussed during lectures;
The ability to interpret the concepts from an actuarial and/or financial perspective;
The ability to apply the acquired knowledge to examples and case studies;
The ability to express mathematical and financial concepts in a clear and rigorous way.
The final grade of each module, on a scale 0-32, is given by:
Insurance module: sum of project work (0-12) and oral exam (0-20);
Econometrics module: sum of project work (0-12) and oral exam (0-20).
The exam is passed if and only if the grade of each module is 16 or higher and their arithmetic average, denoted by AVG, is 18 or higher. In this case, the final grade of the exam is:
AVG/30, if AVG is between 18 and 30;
30/30, if AVG is higher than 30; in this case, the teachers may award the grade 30/30 cum laude, at their own discretion.
The grades of the project works and of the midterm exam are valid up to the last exam session for this edition of the course (January-February 2027); they are erased afterwards.
If during an exam session only one of the grades of each module is 16 or higher, then the student may retain that grade for the next exam sessions, up to the last one for this edition of the course (January-February 2027); it is erased afterwards.

D. Dickson, M. Hardy and H. Waters, Actuarial Mathematics for Life Contingent Risks, Editore: Cambridge University Press, Anno edizione: 2020, ISBN: 978-11-08-47808-3 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma99632799908776
H. Schmidli, Risk Theory, Editore: Springer, Anno edizione: 2017, ISBN: 3-319-72005-8 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma99590686508776
A. Olivieri and E. Pitacco, Introduction to Insurance Mathametics, Editore: Springer, Anno edizione: 2015, ISBN: 9783319213774 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/fpq6t9/cdi_askewsholts_vlebooks_9783319213774
H. Schmidli, Stochastic control in insurance, Editore: Springer, Anno edizione: 2008, ISBN: 1-281-13740-5 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/1nvvje2/alma9948777108776
Brooks, Chris., Introductory econometrics for finance., Editore: Cambridge university press, Anno edizione: 2019, ISBN: 978-0-13-348686-2
R. Tsay, Financial Time Series, Editore: Wiley Finance

Machine learning deals with the problem of building programs that learn from experience. While artificial intelligence focuses on the representation of knowledge and the algorithms for reasoning about such knowledge, machine learning deals with the problem of extracting knowledge from experience gathered solving problems to be used to solve unseen instances of similar problems.
This course provides the theoretical and methodological foundation of machine learning methods and algorithms that are used in several application areas, including, Data Mining, Robotics, Autonomous Agents, Bioinformatics, Recommender Systems, Social Networks, etc.

Dublin Descriptors
Expected learning outcomes
Knowledge and understanding
Students will learn how to:
Model supervised learning and reinforcement learning problems
Train their models
Select the model complexity
Evaluate the performance of their models
Applying knowledge and understanding
Given specific project cases, students will be able to:
Model the learning problem
Select the most appropriate learning technique
Tune the hyperparameters of the studied techniques
Assess the performance of the learned model.
Making judgements
At the end of this course, students will be able to:
Correctly assess the performance of the proposed solutions
Be aware of fairness issues involved in the training of machine learning methods
Lifelong learning skills
Students will learn the trade-off between bias and variance and hot to manage it by selecting the proper complexity of the learning model
Students will learn to develop algorithms to solve relevant learning problems.

Introduction (1 class)
Basic concepts.
Learning theory. (4 classes)
Bias/variance tradeoff. Union and Chernoff/Hoeffding bounds.
VC dimension. Worst case (online) learning.
Practical advice on how to use learning algorithms.
Supervised learning. (8 classes)
Supervised learning setup. LMS.
Logistic regression. Perceptron. Exponential family.
Kernel methods: Radial Basis Networks, Gaussian Processes, and Support Vector Machines.
Model selection and feature selection.
Ensemble methods: Bagging, boosting.
Evaluating and debugging learning algorithms.
Reinforcement learning and control. (6 classes)
MDPs. Bellman equations.
Value iteration and policy iteration.
TD, SARSA, Q-learning.
Value function approximation.
Policy search. Reinforce. POMDPs.
Multi-Armed Bandit.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The assessment will be based on a written exam at the end of the course, where both theoretical competence and modeling skills will be tested.
Type of assessment
Description
Dublin descriptor
Written test
Solution of numerical problems: exercises on supervised learning and reinforcement learning problems
Solution of modeling problems: exercises where the student needs to properly model the machine learning problem and choosing the most appropriate solution technique
Theoretical questions with open answers.
1,2
1,2,3,5
1,2,5

Christopher M. Bishop, Pattern Recognition and Machine Learning, Editore: Springer-Verlag Berlin, Heidelberg, Anno edizione: 2006, ISBN: 0387310738 https://www.microsoft.com/en-us/research/people/cmbishop/prml-book/
Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, Editore: MIT Press, Cambridge, MA, Anno edizione: 2018, ISBN: 0262039249 http://incompleteideas.net/book/the-book-2nd.html
Murphy, K. P., Probabilistic Machine Learning: An introduction, Editore: MIT Press, Anno edizione: 2022 https://probml.github.io/pml-book/book1.html
Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, Mathematics for Machine Learning, Editore: Cambridge University Press, Anno edizione: 2020 https://mml-book.com/

The course presents the two most important manifestation of ordering phenomena in solids beyond the crystal lattice: magnetism and superconductivity. The two are crucial for the understanding of the transport properties of crystalline materials, and can be exploited in a multitude of applications. Magnetism and superconductivity are governed by microscopic interactions, ultimately among electrons, but the macroscopic phenomenology is the result of interatomic interactions and dimensionality. Bose-Einstein condensation (BEC) and superfluidity are also presented as they share with magnetism and superconductivity the property of being macroscopic quantum phenomena.
The objective of the course is thus to provide a broad knowledge and understanding of ordering phenomena in solids. Phenomenology, experimental methods and theoretical models are considered and confronted. More broadly the goal is to introduce the students to the real world of advanced condensed matter research, with special emphasis on phenomenology and experimental insight.

Lectures and seminars will allow students to:
Know the fundamental concepts of ordering phenomena
Recognize the different types of magnetic order
Know the general phenomenology of superconductivity, superfluidity and BEC
Determine which experimental methods can be used in the study of magnetism and superconductivity and, in general, of ordering phenomena in solids
Read and understand original research papers in the fields of magnetism and superconductivity
Present a brief seminar on basic concepts and advanced examples on modern magnetism and superconductivity
Therefore, after passing the exam, the student will be able to:
DD1 - Understand the principles of magnetism and order phenomena, know the terminology related to them, employ the basic models applicable to them
DD2 - Recognize analogue of magnetism and superconductivity in other contexts and apply models ant techniques in new contexts of physics and technology
DD4 - Communicate their own perception of physics phenomena in a formal presentation and elaborate on them

Magnetism of isolated magnetic moments
Phenomenology: recalling diamagnetism, paramagnetism.
Weiss model for ferromegnetism and antiferromagnetism
Atomic moments.
Hunds rules
Crystal field: origin of CF, quenching of orbital moments, Jahn-Teller effect.
Exchange interaction
Examples of simple 3d transition metal oxides (NiO, MnO, Fe3O4)
Goodenough Kanamori rules
Perovskites
Manganites and cuprates
Magnetic order and magnetic structures.
Order parameters
Heisenberg and Ising models
Magnetism in metals
Pauli paramagnetism
Landau diamagnetism
Stoner model
RKKY interaction, Kondo effect
Excitations in magnetic systems
Spin waves
Stoner excitations
Magnetism at low dimensionality
Spin chains and spin ladders
2 dimensional magnets
Thin films
Bose-Einstein Condensation (BEC) and Superfluidity:
Bose-Einstein statistics
BEC principles
BEC of ultra-cold atomic gas
Macroscopic wave function and quantum fluids
Superfluid HeII
Superfluid flow and vortices
Superconductivity:
Phenomenology: transport, susceptibility, thermodynamics
London equations
Josephson effect
Ginzburg-Landau model
BCS theory
Cuprate superconductors (also as an example of 2D antiferromagnets).
Experimental techniques.
Magnetic resonances, Mössbauer spectroscopy, muon spin rotation.
Elastic and inelastic scattering of neutrons and x-rays for magnetic structure and magnetic excitations.
Synchrotron radiation based techniques for magnetism: selected examples of X-ray spectroscopy.

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, individuale, senza revisioni periodiche, con presentazione/discussione finale
The exam consists of two parts held during a single interview, in English.
1) A seminar of 20-25 minutes, on a subject pre-assigned by the teacher. The student has to present the general concepts of the theme in a correct and complete way, providing some examples at the level of the lectures and of the text book. The student is also invited to look for original examples, applications, interconnections with other subjects, to demonstrate a higher level of understanding. A PowerPoint presentation is best suited for the seminar, but black/white board option is also possible.
2) Two or three questions on the core of the course as presented in the lectures. The student is requested to answer at the black/white board to show their understanding of the basic concepts and notions of the course. Theoretical and experimental aspects will be valued equally important.
A fully successful exam (27-30/30) will be deemed when a solid and broad mastering of the concepts of ordering phenomena in solids is demonstrated.
An average grade (22-26/30) will be the result of fairly complete understanding of individual themes but with limited interconnection among subjects.
A pass level (18-21/30) will correspond to a minimum knowledge of individual notions.

S. Blundell, Magnetismm in condensed matter, Editore: Oxford University Press, ISBN: 978-0198505914
James F. Annett, Superconductivity, Superfluids and Condensates, Editore: Oxford university Press, Anno edizione: 2013, ISBN: 978-0-19-860756-7
Harald Ibach, Hans Lüth, Solid-State Physics: An Introduction to Principles of Materials Science, Editore: Springer, ISBN: 978-3540938033

The main objective of the course is to acquire knowledge of mathematical and physical modeling of physical systems and to develop critical skills for their application in solving engineering problems.
The first goal of part [2] of the course is to provide students with a theoretical and application-oriented understanding of perturbative approa ches, including the rigorous use of asymptotic series. A second objective is to introduce advanced topics in continuum mechanics, such as materials with microstructure, and to explore how perturbative methods are applied within the framework of continuum mechanics.

The student is expected:

• to master the mathematical develoment of all the mathematical and physical methods exposed during the course;
• to use dimensional analysis and asymptotic methods to analyse the proposed physical problem;
• to develop the critical skills for selecting the most adapted method and for providing a rigorous derivation of the required mathematical solution;
• to use widespreadly adopted symbolic programming languages for object and modeling management (e.g. Mathematica);
• to become articulate and fluent in expressing and communicating all the key ideas and proofs of the basic theorems and concepts.

Introduction to asymptotic analysis. Asymptotic analysis of equations, simple and multiple roots. Dominant balance. Introduction to regular and singular perturbation theory. Linearization of constitutive relation for elasticity. Infinitesimal strain tensor. Elasticity tensor. Linear constitutive relation. Symmetry group. Isotropic linear elasticity. Lame constants. Navier equations. Plane wave propagation in linear isotropic elasticity: transverse and longitudinal wave propagation. Elements of surface waves.
Boundary layer theory. Matching conditions: Van Dyke rule and intermediate variable method. Flow past a plate at high Reynolds number. Prandtl's equations, Blasius self-similar solution. Multiple-scale method: perturbation on unbounded domains, nonlinear oscillations, stability of the Kapitza pendulum.
Continua with microstructure. Nematic liquid crystals. The Frank-Oseen Elastic Energy. Equilibrium Equations. Anchoring and boundary conditions. Freedericksz transition, linear analysis of the bifurcation. Elements of nonlinear analysis of bifurcations. Dynamic Theory of Nematics: The Ericksen-Leslie equations.

Prova scritta obbligatoria, senza prove in itinere
The exams wil be organized in agreement with the Academic Calendar and the Rules of the School of Engineering.
The verification of knowledge and capabilities acquired by the student is based, for each part, on a written test of about 1h 30min, possibly followed by an oral part.
The two written tests can be taken together during the same exam session, or separately in different exam sessions.
The final grade is based on an overall evaluation of the two parts of the exam.
The verification of knowledge and capabilities acquired by the student in part [2] of the course is based on a written test of about 1h 30min, possibly followed by an oral part or a presentation.
The written test consists in two problems, either theoretical or practical, in which the student is expected to provide answers to few itemized questions.
In the oral part the student is expected to answer theoretical questions on course topics, and to verify student's skills at making connections between course topics and previous courses.

Bender, Orszag, Advanced mathematical methods for scientists and engineers, Editore: Springer, ISBN: 978-1475730692
Holmes, Introduction to Perturbation Methods, Editore: Springer, Anno edizione: 2013, ISBN: 978-1461454762

The aim of the course is to present the methodological foundations of arbitrage theory in continuous time and to provide students with the main mathematical models and methods used in modern quantitative finance. These will be applied to describe financial markets from a mathematical point of view, to tackle the problem of pricing financial derivatives, and to construct hedging strategies.

Students are expected to acquire the following competences.
Knowledge and understanding.
Students know the main models and methods used in modern mathematical finance.
Students understand the main techniques used to price financial derivatives and construct hedging strategies.
Students understand the assumptions of arbitrage theory in continuous time, the advantages and drawbacks of each model, and the differences between them.
Ability in applying knowledge and understanding.
Students are able to apply the models and methods used in modern mathematical finance to correctly price financial derivatives and to construct hedging strategies.
Students are able to select the most appropriate model to solve a financial problem.
Students are able to apply the general theory to derive analytical results starting from a given model.
Students are able to correctly interpret the results obtained in the solution of a problem, from the theoretical, numerical, and financial points of view.
Making judgements.
Students can judge which model and/or method is more suited to solve a financial problem.
Students can judge the main advantages and limitations of the studied models, both from a mathematical and a financial point of view.
Communication skills.
Students are able to express mathematical and financial concepts in a clear and rigorous way, both in written and in oral form.

• Introduction. Financial markets and financial derivatives. Review of basic financial principles.
• Discrete-time models. Portfolios and arbitrage opportunities. First and second fundamental theorems of asset pricing. Risk-neutral valuation of financial derivatives and hedging strategies. No-arbitrage option inequalities. Put-call parity.
• Portfolio dynamics in continuous-time. The classical Black & Scholes model. Derivation of the Black & Scholes equation via no-arbitrage arguments. Probabilistic representation via the risk-neutral measure. Valuation formulae for simple contingent claims, European options, forward and futures contracts, options on futures. Dynamic hedging of simple contingent claims. Volatility estimation. Greeks. Buy-and-hold strategies.
• The multidimensional Black & Scholes model. Derivation of the Black & Scholes equation via no-arbitrage arguments. The market price of risk vector. Probabilistic representation via the risk-neutral measure. Valuation formulae for simple contingent claims. Dynamic hedging of simple contingent claims.
• The Black & Scholes model for dividend-paying assets.
• Currency derivatives and quanto products. The Garman-Kohlhagen model.
• Valuation of exotic derivatives in the Black & Scholes model.
• The optimal stopping problem. Discrete-time formulation, the backward recursion algorithm, characterization of the value function via the Snell envelope. Continuous-time formulation, the variational inequality and the free boundary problem. Valuation of American options.
• The martingale approach to arbitrage theory. A general market model. Equivalent martingale measures. The first and second fundamental theorem of asset pricing. Absence of arbitrage and completeness of the Black & Scholes model. Change of numéraire.
• Incomplete markets. Calibration to market data.
• (Only for 10 ECTS exam) Interest rate models. General facts on interest rates and valuation of fixed-income derivatives. Short-rate models, affine models and affine term structures. The Vasicek, Ho-lee, Cox-Ingersoll-Ross, Hull and White Models. The Heath-Jarrow-Morton framework to model forward rates. The LIBOR market model. Valuation of Caps, Floors and Swaptions.
  Exercise sessions will be devoted to the application to the valuation of financial derivatives and hedging problems of the models and methods discussed in class, both from a theoretical and algorithmic point of view.
  In laboratory sessions students will discuss and implement in MATLAB, with a hands-on approach, the numerical valuation of derivatives in the Black & Scholes model, the bootstrap method and the numerical valuation of interest rates derivatives.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
The exam includes two assignments, a written and an oral exam.
Assignments.
The two assignments are small group works based on computer laboratory sessions, which will be devoted to the valuation of plain vanilla derivatives and to interest rate models. They are mandatory only for the 10 ECTS exam. Deadlines are communicated during the course. The overall grade for assignments is on a scale 0-3.
Written exam.
The written exam is based on exercises and applications of mathematical finance, with some aspects of the general theory. It is evaluated on a scale 0-30. Students are expected to show knowledge and understanding of the concepts taught during the course, the ability to rigorously apply stochastic calculus in the context of mathematical finance, to perform an appropriate valuation of financial derivatives, to correctly apply models and methods of mathematical finance to solve problems, to adequately intepret the results obtained.
Oral exam.
The oral exam is based on the whole program of the course. The oral exam can be taken only if the sum of the assignments and the written exam grades is 18 or higher. The oral exam is evaluated on a scale 0-33, with grades in the interval 31-33 assigned only in case of exceptionally brilliant exams.
Students are expected to show knowledge and understanding of the concepts taught during the course, the ability to rigorously prove mathematical statements, to provide the correct financial interpretation of the results, and to present adequate examples to illustrate the concepts.
Final grade.
The exam is passed if and only if the arithmetic average, denoted by AVG, between the sum of the assignments and the written exam grades, and the oral exam grade, is 18 or higher. In this case, the final exam grade is:

• AVG/30, if AVG is between 18 and 30;
• 30/30, if AVG is higher than 30; in this case, the teacher may assign the grade 30/30 cum laude, at his own discretion.

T.Bjork,, Arbitrage theory in continuous time, Editore: Oxford University Press, Anno edizione: 2009 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
E. Rosazza Gianin, C. Sgarra, Mathematical finance: theory review and exercises, Editore: Springer, Anno edizione: 2013 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
M. Musiela, M. Rutkowski, Martingale methods in financial modelling, Editore: Springer, Anno edizione: 2005 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma9953003008776
S. E. Shreve, Stochastic Calculus for Finance I. The Binomial Asset Pricing Model, Editore: Springer, Anno edizione: 2004 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99902417508776
S. E. Shreve, Stochastic Calculus for Finance II. Continuous-Time Models, Editore: Springer, Anno edizione: 2004 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99915720808776
J. Hull, Options, futures, and other derivatives, Editore: Pearson, Anno edizione: 2022 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99915720808776
D. Filipovic, Term-structure models, Editore: Springer, Anno edizione: 2009 https://www.bibliosearch.polimi.it/permalink/39PMI_INST/tn5umn/alma99926232908776

The primary goal of this laboratory course is to let the students design, implement and practice algorithms based on simple mathematical models from linear algebra and convex optimization, and solve challenging inverse problems in image processing (denoising, deblurring, inpainting, anomaly detection).
Teaching Organization
The course consists of traditional classes and computer-laboratory hours. During the laboratory hours, students will be guided in implementing simplified versions of the presented algorithms on their laptops. A set of homeworks will be provided to students for consolidating their understanding. Imaging problems, including denoising, inpainting, and anomaly detection, will be considered as running examples through the computer labs. Python will be the homework programming language, and students will be invited to work on their own laptops.

Dublin Descriptors
Expected learning outcomes
Knowledge and understanding
Students will learn:
· How to formulate relevant restoration problems in imaging.. How basic notions of linear algebra are used in widely used image models.. The modeling assumptions underpinning the mainstream image processing algorithms.. A large number of very general optimization algorithms solving image restoration problems.
Applying knowledge and understanding
Given a specific imaging problem, the student will be able to:
· Describe with a formal notation the image formation / degradation process.
· Apply transform-domain paradigm in image processing.
· Implement fundamental algorithms.. Implement a solution, possibly leveraging on core functions presented during lecture. Assess algorithm performance
Making judgments
Given an imaging problem, students will be able to:
· Formulate an effective modeling assumption for a specific imaging problem at hand
· Identify the viable approaches to solve the problem and then the best algorithms among those presented in the course
· Discuss the pros and cons of different algorithms and approaches. Identify limitations of selected algorithms
Communication
The student will learn to:. Describe the major steps underpinning transform-domain and optimization algorithms presented during lectures. Present an algorithmic solution with mathematical rigour
Lifelong learning skills
The student will learn to:
· Face real-life imaging problems with a mathematical modeling and algorithmic approach.
· Implement algorithms that cover fundamental blocks in image processing pipelines.. Develop practical skills to apply simple mathematical models and algorithms in image processing.. Consolidate their linear algebra and optimization background to be applied in other domains.

The course topics include:
Image models based on orthonormal bases (DCT), data-driven bases (PCA)
Image models based on sparsity and redundancy:
Away from an Orthonormal Basis, representations with respect to a redundant set of generators.
Sparse coding with ℓ^0 (OMP) or ℓ^1 norm (convex optimization ISTA, IRLS, LASSO), extended models (Group LASSO)
Dictionaries yielding sparse representations and dictionary learning (KSVD, MOD)
Applications of sparse models to image denoising, inpainting, and anomaly detection.
Polynomial Models: Local Polynomial Approximation and Intersection-of-Confidence Interval Rule and applications to image denoising
Non-Local Self-Similarity models for image denoising (NLMS, BM3D).
Robust fitting methods (RANSAC, LMEDS).
Multi-model fitting: Sequential Ransac and Hough transform.
Detailed Syllabus
Linear Algebra and Image Models: patch-based modeling & denoising via DCT thresholding.
Introduction to Inverse Problems for Images: Denoising and Spatial Aggregation, Noise estimation, Wiener Filtering
Data-driven basis and PCA Denoising
Away from an Orthonormal Basis, a redundant set of generators:
Solution of Linear Systems and Tikhonov regularization
Sparsity as a regularization prior
Sparse coding in ell0 sense, Greedy algorithms: MP and all the variants (Thresholding, Weak-MP, MP, OMP, LS-OMP)
Sparse coding and ell1 (convex optimization):
Gradient descent
Basis Pursuit Denoising (BPDN): proximal mapping (ISTA), FISTA, IRLS.
Connections between BPDN and LASSO.
Learning Dictionary yielding Sparse Representations by block coordinate descent: M ethod of Optimal Directions (MOD), KSVD.
Extended Sparse models:
Structured sparsity: Joint sparsity, group sparsity,
Elastic Net
Image Processing Applications using Dictionaries: denoising, inpainting, anomaly detection.
Local Polynomial models for images:
Local Polynomial approximation (LPA)
LPA + adaptive scale selection (LPA-ICI)
Applications of LPA -ICI to Image Denoising
Self-similarity models for Images:
Non-local Means
BM3D
Robust Fitting methods in image analysis
Fitting a single model: M-estimators, RANSAC, LMEDS, MSAC
Multimodel Fitting: Sequential Ransac, Hough Transform

Prova orale obbligatoria
The final assessment will be based on an oral exam in which students will be invited to illustrate the course materials (theory and algorithms).
Most lectures come with an assignment where students need to fill in Python Notebooks, which are fundamental for understanding the course materials. To access the oral exam, it is mandatory to submit the assignments by the day the exam is scheduled in the online system. Assignments will be assessed on a pass/fail basis. The oral exam includes questions on the algorithms implemented in the assignments.
Type of assessment
Description
Dublin descriptor
Oral exam
Students are requested to demonstrate proficiency in:
Implementing the algorithms presented during the course
Describe their own codes, with particular emphasis on image modeling and the algorithmic steps
Discuss limitations and possible improvements
Illustrate the modeling assumptions underpinning imaging problems presented in the course
Addressing the presented image processing problems with a principled approach.
Govern the most important algorithms presented in the literature, illustrating their rationale and major steps.
1, 2, 3, 4, 5

Lectures Slides and Demo Codes will be provided
Michael Elad,, Sparse and redundant representations: from theory to applications in signal and image processing, Editore: Springer, Anno edizione: 2010, ISBN: 978-1441970107

The key goal of the course is to provide a very successful example of a mathematical rigorous formulation of a physics theory - quantum mechanics -, starting from first principles (postulates) down to the discussion of concrete phenomena in atomic physics. In this respect, the course is meant to illustrate some typical features of modern mathematical physics and some insights on contemporary research lines in the field.
A self-contained presentation of quantum mechanics and its mathematics, suited in particular for students with mathematical background, is given. It is shown that a fully rigorous mathematical construction can lead to non-trivial physics results, so testifying that mathematical physics can in fact shed light on physics phenomena. Indeed, all the most intriguing and counter-intuitive phenomena of quantum mechanics (uncertainty, probabilistic behavior, interference etc.) as well as their mathematical formulation are discussed. On the other hand, several mathematical tools on functional analysis, operator theory, functional inequalities, etc., are introduced and discussed in details so that the mathematical content of the course is valuable as well for students more oriented towards abstract mathematics.
We denote by (*) the topics covered by the 5 CFU version of the course.

From the physics point of view, we expect that students without any previous knowledge of quantum mechanics acquire a basic understanding of the main features of the theory, while those who have already attended physics courses on the topic discover a more mathematically sounded presentation of quantum mechanics.
In addition, we expect that the students at the end of course

• know the first principles of quantum mechanics and are able to translate them in the mathematical language (*);
• are able to describe how the core physical aspects of quantum mechanics (uncertainty, probabilistic behavior, dispersion, interference, etc.) follow from the postulates of the theory (*);
• know the rigorous mathematical modelling of simple quantum systems as the free particle, the harmonic oscillator and the hydrogen atom (*);
• know the key features of the quantum description of atomic matter and many-body systems;
• understand the mathematical framework of non-relativistic scattering theory;
• know the basics of second quantization and quantum field theory;
• get an introduction to some research lines about the mathematical features of quantum mechanics.

1. Postulates of Quantum Mechanics (*)
2. Observables and States (*)
Brief recap of operator theory; Heisenberg uncertainty relation; self-adjointness criterion and self-adjoint extensions; spectral theorem and probabilistic interpretation of quantum mechanics; spectral decomposition; mixed states and density matrices; Stone theorem and existence of the dynamics.
4. Free Particle and Harmonic Oscillator (*)
Free particle: time evolution of wave packets, dispersion and interference, semiclassical limit; harmonic oscillator: spectrum, creation and annihilation operators, coherent states.
5. Hydrogen Atom (*)
Self-adjointness and stability; spectrum; angular momentum; eigenfuctions.
6. Perturbation Theory (*)
Perturbation theory in finite dimensions; analytic perturbation theory; perturbation of spectral projectors; variational methods: min-max principle; physical applications: Zeeman effect, anharmonic oscillator.
7. Many-body Quantum Mechanics & Atomic Matter
Spin and identical particles: bosons and fermions; reduced density matrices; non-interacting many-particle systems; atomic Hamiltonians and stability of matter of the first kind; Lieb-Thirring inequalities; stability of matter of the second kind; Bose-Einstein condensation, superfluidity and superconductivity; nonlinear models for condensed matter physics.
8. Scattering
Scattering by a potential; time-dependent scattering theory; asymptotic completeness; Lippman-Schwinger equation and generalized eigenfunctions.
9. Quantum Field Theory
Fock spaces: the mathematics of second quantization; annihilation and creation operators; Fock space calculus; free and regular field theories: time-zero and spacetime fields, spin-boson and Nelson models; interacting field theories and renormalization.

Prova orale obbligatoria
Valutazione continua facoltativa (a scelta dello studente)
The exam consists of two components: a final oral exam (worth up to 27 points) and ongoing assessments (optional, worth up to 6 additional points).
The two assessment sessions (up to 3 points each), held halfway through the course and at its end, are optional and consist of exercises completed during the exercise classes. They may be replaced by a question session covering the entire syllabus during the final exam.
The final oral exam may take the form of a presentation on a topic chosen from a list provided by the instructor, followed by questions on that topic, or a traditional oral examination covering all the material discussed during the course.
The exam for the 5 CFU version of the course consists in a traditional oral examination.

lecture notes on WeBeep
Note: (handwritten)
lecture notes on WeBeep
Note: (in italian)
Alessandro Teta, A Mathematical Primer in Quantum Mechanics, Editore: Springer, Anno edizione: 2018, ISBN: 9783319778938
Alberto Galindo, Pedro Pascual, Quantum Mechanics I, Editore: Springer, Anno edizione: 1990, ISBN: 978-3-642-83854-5
Alberto Galindo, Pedro Pascual, Quantum Mechanics II, Editore: Springer, Anno edizione: 1991, ISBN: 978-3-642-84129-3
J. Blank, P. Exner, M. Havlícek, Hilbert Space Operators in Quantum Mechanics, Editore: Springer, Anno edizione: 2010, ISBN: 9789048180127
E.H. Lieb, R. Seiringer, The Stability of Matter in Quantum Mechanics, Editore: Cambridge University Press, Anno edizione: 2009, ISBN: 9780511819681
M. Lewin, Spectral Theory and Quantum Mechanics, Editore: Springer Cham, Anno edizione: 2024, ISBN: 9783031668777
A. Arai, Analysis on Fock Spaces and Mathematical Theory of Quantum Fields, Editore: World Scientific Publisher, Anno edizione: 2018, ISBN: 9789811288425
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 1 - Functional Analysis, Editore: Academic Press, Anno edizione: 1981, ISBN: 9780125850506
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 2 - Fourier Analysis, Self-adjointness, Editore: Academic Press, Anno edizione: 1975, ISBN: 9780125850025
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 3 - Scattering Theory, Editore: Academic Press, Anno edizione: 2012, ISBN: 9780123958273
M. Reed, B. Simon, Methods of Modern Mathematical Physics vol. 4 - Analysis of Operators, Editore: Academic Press, Anno edizione: 2012, ISBN: 9780123958280

Aims and scope
The course aims to derive the macroscopic properties of gaseous systems starting from
their microscopic (molecular dynamics) analysis.
In this perspective, analytical and numerical methods for the solution of kinetic equations
are presented.

Knowledge and understanding
At the end of the course the students are expected to:
-know the basic mathematical properties of the Boltzmann and related kinetic equations
-be able to solve kinetic equations both analytically and numerically
-be able to model various problems in science

Program
1-Introduction to Statistical Mechanics

• The postulate of classical statistical mechanics.
  -Microcanonical Ensemble.
  -Canonical Ensemble.
  -Grand Canonical Ensemble.
  2-The Boltzmann equation
• Derivation (Lanford Theorem). Existence of solutions (Diperna-Lions Theorem).
  -The BBGKY Hierarchy.
  -Elementary properties of the collision operator.
  -Boundary conditions and the gas-surface interaction.
  -The H-Theorem and the problem of irreversibility.
  -Kinetic Models.
  3-Methods of solution of the Boltzmann equation
• Variational Methods.
  -Transformation into Integral Equations.
  -Numerical methods.
  4-Quantum kinetic equations
  -The Boltzmann-Nordheim equation.
  -Equilibrium states and the H-Theorem.
  -Quantum BBGKY-like Hierarchies.
  -Kinetic theory of Bose-Einstein condensation.
  5-Application of the Boltzmann equation to Microfluidics
• Analytical and numerical investigation of microchannel flows (Poiseuille, Couette and
  Thermal-Creep problems; sound waves propagation).
  -Slip boundary conditions for the Navier-Stokes equations.
  -Kinetic modeling of gas mixtures.
  6-Mathematical Models and Methods in Micro-Nano-Technologies
  -Characterization of Micro-Electro-Mechanical Systems (MEMS) devices.
  -Analysis of damping forces in low-frequency and radio-frequency MEMS devices.
  7-Kinetic equations for Biomedical applications
  -The Smoluchowski equation.
  -Two-scale homogenization.
  -Mathematical models of neurodegenerative diseases.

Prova scritta facoltativa (a scelta dello studente), senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Examination
The final exam consists either in an oral discussion on the whole program,
or in a written project in which one of the topics, dealt with during the course,
is investigated thoroughly.

Kerson Huang, Statistical Mechanics, Editore: John Wiley & Sons, Anno edizione: 1987, ISBN: 978-0-471-81518-1
Carlo Cercignani, The Boltzmann Equation and Its Applications, Editore: Springer-Verlag, Anno edizione: 1988, ISBN: 3-540-96637-4
Carlo Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations, Editore: Cambridge University Press, Anno edizione: 2000, ISBN: 0-521-65992-2

The increasing computer power is nowadays essential to deal with the numerical solution of large dimensional problems, however a computational reduction is still determinant whenever interested in real-time simulations and/or repeated output evaluations for different values of some inputs of interest. In order to reduce this computational burden, we may rely on suitable reduced order models (ROMs), which are faster and cheaper to simulate, yet accurately represent the original high-fidelity (or full-order) system behavior. Within this class of techniques, parametric model reduction has emerged only in the last decade as a very active research area. Parametric ROMs target the broad class of problems for which the equations governing the system behavior depend on a set of parameters, such as in the case of parameterized PDEs. These parameters may represent, for instance, material properties, system geometry, boundary or initial conditions. The goal of parametric ROMs is thus to generate rapid but reliable models that characterize the system’s response over the whole parametric range. Such a strategy proves to be necessary in order to speedup design, control, optimization, and uncertainty quantification settings, usually requiring several repeated model evaluations.
This course surveys the state-of-the-art of parametric reduced order models, describing the most popular approaches related to physics-driven techniques (such as reduced basis methods and proper orthogonal decomposition) and data-driven techniques (such as non intrusive ROMs based on interpolation, surrogate models involving, e.g., neural networks, and model discovery techniques), providing also a comparative discussion that lend insights to potential advantages/disadvantages entailed by their application.

Besides the knowledge of theoretical results and numerical methods presented during lectures and Lab sessions, a critical comprehension of the class’ topics is expected by the students at the end of the class, justifying the followed procedures. Attending the course, students are expected to:
know and understand how to perform numerical simulation of problems of interest in mechanical engineering (e.g., heat and mass transfer, linear and nonlinear elasticity/elastodynamics, fluid dynamics) in many-query contexts (e.g., repeated simulations in multiple scenarios; control and optimization) or real-time contexts (e.g., predictive digital twins);
set, analyze and apply reduced order modeling techniques for differential problems built on top of classical numerical methods (e.g., finite element method), of both physics-driven and data-driven type;
exploit already acquired numerical methods in Engineering to set up physics-based ROMs (e.g., reduced basis methods);
exploit recent strategies in scientific machine learning for the efficient numerical simulation of physical systems through data-driven ROMs (including, e.g., simple neural networks);
adapt the proposed methodologies to more general problems of applied interest in Engineering;
interpret the results, assessing both accuracy and efficiency of simulation strategies, from both a numerical and a statistical point of view.

The course is organized in a series of lectures and practical lab sessions. Lectures will provide the theoretical background; practical Lab sessions will provide algorithms' implementation and examples of application of the considered methodologies by using basic (e.g., Matlab or Python) codes. After reviewing basic concepts in numerical methods for differential problems, the course will focus on the following topics:
Dimensionality reduction algorithms
Singular value decomposition, optimal low-rank approximations, proper orthogonal decomposition. Autoencoders.
Projection-based reduced order modeling techniques
The reduced basis method for (linear) parametrized partial differential equations: reduced space construction, (Petrov-)Galerkin projection, a posteriori error estimation. Affine parameter dependence.
Hyper-reduction techniques
Extension of the reduced basis method to nonlinear and/or nonaffinely parametrized problems. Empirical interpolation method.
Non-intrusive reduced order modeling techniques
POD with interpolation (e.g., Neural Networks, Gaussian Process) strategies. Autoencoders and basic ideas on deep-learning reduced order models for parametrized systems.
Data-driven dynamical systems
Dynamic mode decomposition. Sparse identification of nonlinear dynamics (SINDy). Neural ODEs. Model discovery techniques for the latent dynamics.
Physics-informed machine learning
SINDy Autoencoders: extension of SINDy to high-dimensional systems. Shallow recurrent decoder networks for reduced order models embedding sensor data. Learning nonlinear operators (e.g., deep operator networks).

Prova orale obbligatoria
The oral exam covers the content of both theoretical lectures and practical Lab sessions.
During the exam, students are required to present the detailed solution of two selected assignments (among a list of assignments proposed during the practical Lab sessions), commenting both the numerical results obtained and the computational procedures employed, and to answer to theoretical questions related with the topics of the course.
Assignments will require students to apply, adapt, or extend some of the methods presented during the course to selected practical case studies. The assignments will be evaluated during the oral examination and must be submitted to the examiners by the deadline communicated during the classes.
Theoretical questions will assess students' knowledge of the methodologies covered throughout the course. During the examination, students will first be required to sketch written answers to the theoretical questions, before presenting and discussing them with the examiners.
The course will be based on a selection of chapters of the following books, class notes, and some selected scientific papers provided:

A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations. An Introduction, Editore: Springer, Anno edizione: 2016
Steven L. Brunton, J. Nathan Kutz, Data-Driven Science and Engineering. Machine Learning, Dynamical Systems, and Control, Editore: Cambridge University Press, Anno edizione: 2022

The course aims to provide a general introduction to the computational methods which can be used to model the behaviour of molecular systems and materials. The lectures will introduce the theoretical concepts, first in qualitative terms and then in the form of equations and algorithms. The practical hand-on computational sessions will introduce the students to the usage of freely available programs for molecular simulation and visualization. The students will become aware of the meaning of "modelling", "simulation" and "computing", in a way which may be useful also in other, unrelated contexts.

The students will learn some theoretical principles underlying current molecular modelling methods. This will allow them to read an understand the scientific literature emplying these methods. (Dublin descriptor 1: Knowledge and insight).
They will learn how to use some common codes for the calculation and interpretation of the properties of molecules, liquids and materials, and specifically: VMD (visualization), ORCA (quantum chemistry), Tinker and LAMMPS (molecular dynamics and Monte Carlo). They will also learn some basics of scientific data analysis, using Python-based tools: Jupyter notebooks, numpy, scipy, matplotlib. (Dublin descriptor 2: Applying knowledge and insight).
They will be expected to gain some critical understanding of the methods, in order to choose the right method for a specific problem and assess the results of their calculations. (Dublin descriptor 3: Judgement).
The students will be expected to present the results of a computational project, both as a written report and during a subsequent oral discussion. (Dublin descriptor 4: Communication).

Introduction to molecular modelling: overview of problems and approaches.
Elements of molecular quantum mechanics: Schroedinger equation, Born-Oppenheimer approximation, electronic wavefunctions, independent-particle model, molecular orbital (MO) theory, basis sets. Molecular properties: the electron density and the molecular electrostatic potential. Electron correlation and the bond dissociation problem. Concepts from density functional theory (DFT): Hohenberg-Kohn theorem, Kohn-Sham scheme, exchange-correlation functionals. Semiempirical molecular orbital methods.
Empirical models: force fields for organic and biological molecules, shell model for ionic polarization, the embedded-atom model for metals, empirical "reactive" potentials for semiconductors and carbon-based systems. Coarse-grained models.
Exploring potential energy surfaces: stationary states, energy minimization and saddle point location methods. Conformations of large molecules.
Introduction to simulation methods: elements of statistical mechanics, ensembles and calculation of thermodynamic properties, boundary conditions, treatment of short- and long-range interactions.
Molecular dynamics (MD) simulations: integration algorithms, introduction of constraints. Choice of initial conditions. Controlling temperature and pressure in MD. Analysis of trajectories: pair distribution functions, analysis of molecular conformations, time correlation functions. Evaluation of transport properties. Non-equilibrium methods. Enhanced sampling for "rare" events.
Monte Carlo (MC) simulations: general principles (Markov processes, transition probabilities, detailed balance) and Metropolis Monte Carlo for the NVT ensemble. Generalization to other ensembles. Example: the Ising model.
Application examples:

• calculation of molecular energies, geometries, vibrational spectra, electron densities, interactions, etc.
• structure and properties of solids, liquids, soft materials, interfaces, etc.

Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The students will be evaluated on the basis of written reports on the practical modeling problems, followed by an oral examination covering the reports and the theoretical concepts underlying the empoyed methods. Projects can be carried out individually or in groups of two.
The final grade will be based on:

• understanding of the theoretical principles of the chosen computational model(s) (Dublin descriptor 1: knowledge and insight).
• capability to run the numerical simulation codes, extract and analyze the results from them (Dublin descriptor 2: Applying knowledge and insight).
• soundness of the computational method(s) for a specific problem, capability to interpret the results and identify possible problems or limitations (Dublin Descriptor 3: Judgement).
• presentation of the results, both in writing (report) and orally (final discussion) (Dublin Descriptor 4: Communication).

Frank Jensen, Introduction to computational chemistry (3rd. edition), Editore: JohnWiley & Sons, Ltd, Anno edizione: 2017, ISBN: 9781118825990
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, 2nd edition, Editore: Oxford University Press, Anno edizione: 2017, ISBN: 9780198803201
Andrew R. Leach, Molecular Modelling: Principles and Applications (2nd ed.), Editore: Prentice Hall, Anno edizione: 2001, ISBN: 0582382106
Peter Atkins, Julio de Paula, ATKINS' PHYSICAL CHEMISTRY, Editore: W. H. Freeman and Company, New York, Anno edizione: 2006, ISBN: 0-7167-8759-8

This course explores innovative web technologies, guiding students in understanding how interaction on the Web can be extended and enhanced through the integration of advanced multimodal interactive technologies.
The course is structured into three specialised modules:
Web-Visual: Focuses on traditional paradigms for organizing and navigating visual content.
Web-Conversational: Explores the integration of conversational AI and Large Language Models into web platforms to enable fluid, natural-language interaction.
Web-eXtended Reality: Deepens immersive interactive technologies and their integration into web platforms.
By combining theoretical insights with hands-on exercises, this course guides students to learn how to address the growing demand for innovative multimodal web solutions. It is ideal for those students eager to create impactful and engaging multimodal web technologies.

By the end of the course, students will be able to:
Manage the design and development of advanced web applications, with a strong focus on user interaction and experience
Design and prototype conversational systems for the Web, based on Conversational AI models and Large Language Models (LLMs).
Integrate eXtended reality (XR) components into web applications to create immersive user experiences.
Dublin Descriptors
Knowledge and Understanding Students will learn how to:
understand the principles and paradigms underlying multimodal interaction and their relevance to the Web;
master the phases of a human-centered design process for advanced multimodal interactive applications;
analyze users, contexts, and tasks to identify opportunities for integrating multimodal interaction;
recognize the affordances and limitations of web-based frameworks supporting visual, conversational, and extended reality (XR) modalities;
evaluate multimodal web applications in terms of usability, user experience, and interaction quality.
Applying Knowledge and Understanding Given specific design and development scenarios, students will be able to:
specify requirements for multimodal interactive web applications;
design and prototype visual, conversational, and XR components to extend web interaction;
integrate Conversational AI and Large Language Models (LLMs) into web platforms to enable natural-language interaction;
combine immersive XR technologies with web standards to create engaging, interactive experiences;
develop functional multimodal web prototypes using contemporary frameworks and tools.
Making Judgments Students will be able to:
analyze and model multimodal interaction workflows and architectures;
critically assess trade-offs among different modalities and technologies according to project goals and constraints;
select and justify appropriate design principles, frameworks, and integration strategies for multimodal web solutions.
Communication Students will learn how to:
communicate design decisions and technical solutions clearly, using appropriate levels of abstraction for technical and non-technical audiences;
document multimodal architectures and design rationales effectively, highlighting usability and user experience aspects.
Lifelong Learning Skills Students will learn how to:
autonomously explore emerging multimodal interaction paradigms and web technologies;
apply a continuous learning approach to adapt to the evolution of interactive technologies and frameworks;
transfer the acquired design and development methodologies to new domains and interaction contexts.

The course is structured across three modules, each combining the introduction of methodological concepts and technological frameworks in an integrated format of lectures, guided exercises, and hands-on development sessions.
Module 1: Web-Visual:
Web design and principles
Web usability and accessibility
Key concepts of Web architectures and architectural patterns
Fundamentals of Web technologies and languages (client-side and server-side)
Module 2: Web-Conversational:
Design of Conversational Agents for the Web
Integration of Conversational AI and LLMs into web platforms; hands-on sessions with major frameworks and libraries (e.g., OpenAI).
Automatic Speech Recognition, Text-to-Speech and Speech-to-Text technologies.
Modulo 3: Web-eXtended Reality:
Overview of the XR interaction paradigm.
Design of AR experiences.
Integration of XR technologies into web platforms; hands-on sessions with major frameworks for XR on the web (e.g., WebXR, Three.js).
Introduction to additional AI-based input channels for Web interaction, such as image processing and object recognition.

Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
Valutazione continua facoltativa (a scelta dello studente)
The exam is mainly project-based. A project consists of the conceptual design, grounded in the design principles introduced during the lectures, and the development of a mid-fidelity prototype demonstrating the application of the learned technologies to the implementation of the proposed design. The design and implementation will be guided by a set of specifications and requirements provided by the instructor at the beginning of the course.
Teamwork is strongly encouraged, although individual projects might also be permitted.
Throughout the course, intermediate assignments will support students in gradually applying the concepts discussed in class to their projects. These deliverables will contribute to the incremental construction of the final project outcome. Regular review sessions will provide formative feedback on the intermediate submissions and support the ongoing development of the project.
On the official exam dates, each team will present the final result of their work. The assessment will focus on both the overall quality of the final project and the technical skills demonstrated during its development, with particular attention to each team member's individual contribution. The final exam will therefore:

• Evaluate the project outcome along with the completeness of the designed prototype in relation to the assigned requirements; the methodological and technical correctness of the solution; the originality of the solution; and the effort invested in the project activity.
• Verify students’ understanding of the course content with attention to the individual comprehension of each team member.
  T ype of assessment
  Description
  Dublin descriptor
  Assessment of project artefacts
  Assessment of the quality of the design and experimental work developed by students in groups, and of the correct understanding of concepts, paradigms, and technologies
  1, 2, 3, 5
  Oral presentation
  Assessment of the presentation of the work developed by students in groups
  2, 3, 4, 5

Il corso "Natural Language Processing" introduce gli studenti ai problemi e alle metodologie relativi all'analisi e alla produzione di frasi di linguaggio naturale, sia scritte che parlate. Il corso presenta il ruolo attuale dei modelli stocastici e del Deep Learning, illustra nuove opportunità di combinare modelli tradizionali, basati sull'analisi formale, con modelli stocastici, per la morfologia, la sintassi, la semantica, la pragmatica, la voce, la prosodia, il discorso, il dialogo e la sentiment analysis. Il corso offre sessioni di esercitazione pratica, in cui gli studenti possono testare modelli e tecniche presentati durante le lezioni. Le applicazioni includeranno: l'analisi dell'interazione uomo-macchina e uomo-uomo, basate sul linguaggio; l'analisi linguistica e prosodica e la loro generazione per la riabilitazione; la ricerca e il riconoscimento di pattern per l'analisi del sentiment nell'interazione critica; l'analisi della complessità, nel testo e in generale nella comunicazione basata sulla parola; la definizione di profili utente che tengono conto delle preferenze in merito alle modalità di espressione (nel contesto forense, educativo e clinico).

The primary objective of the course is for students to learn the fundamental abstractions and features of available networked software platforms while gaining concrete practical experience on their use in different application scenarios. Specific domains covered in the course are the Internet of Things, Edge Computing, Big Data Analytics, Concurrent Systems, Event-driven Applications, and High-performance Computing. The course promotes a practical approach, as the explanation of system abstractions and features is tightly linked to their practical application. The lecturers adopt a novel teaching methodology that enables students to invest most of their time in in-class lab sessions and hands-on work, with support from the lecturers.
For each software platform covered in the course, the learning activities use a combination of online videos and in-class lab sessions. The online videos introduce abstractions and fundamental features of a given platform. The lab sessions allow students to clarify doubts with the lecturers and experiment with the technology at hand.

By the end of the course, students are expected to be familiar with the primary abstractions and features in the software platforms covered in the course, be able to design and implement complete applications of medium complexity, and be acquainted with the practical issues arising when deploying and running these systems in realistic settings. The Dublin Descriptors applicable to the course follow:
Dublin Descriptor 1 (knowledge and understanding): the lab sessions of the course provide the opportunity to test the students’ understanding while facing the practical issues in deploying and running the systems.
Dublin Descriptor 2 (applying knowledge and understanding): the students apply the learned abstractions and features of each software platform in selected settings, drawing connections between theoretical concepts and experimentation.
Dublin Descriptor 5 (lifelong learning skills): the students are expected to acquire the ability to solve medium-complexity experimental problems on their own, using either the software platforms covered in the course or others that are based on similar abstractions or offer similar features.

For each of the software platforms we consider, we provide first an introduction to the specific domain, followed by a description of key abstractions and features, intertwined with concrete examples. A different software platform is considered for each of the aforementioned domains:
Internet of Things: ContikiNG
Computing Continuum: Node.js and Node-RED
Big Data Analytics: Apache Spark
Concurrent Systems: Akka
Event-driven Applications: Apache Kafka
High-performance Computing: MPI

Prova orale facoltativa (a scelta dello studente) o condizionata (a scelta del docente)
Valutazione continua facoltativa (a scelta dello studente)
Altro
The course adopts two evaluation modes: continuous evaluation or oral examination.
The continuous evaluation (DD2, DD5) is accomplished in student groups. Groups are randomly formed by the lecturers and different for each of the software platforms considered in the course. The goal is to combine the students’ learning with in-class experimental activities that allow the teachers to assess their preparation as learning proceeds throughout the semester. In addition to online videos, in-class Q&A sessions, and lab sessions, dedicated evaluation labs are scheduled throughout the semester. The evaluation labs build on what the students learned and experimented with online videos and regular lab sessions, and are instrumental to check their understanding of a given platform. During an evaluation lab, the student groups are to complete an exercise the lecturer hands out at the beginning of the lab. The work accomplished at the end of an evaluation lab is graded by the lecturers and contributes to determining the final grade, possibly integrated by selected oral discussions. This mode allows students to complete the coursework by the end of the lecture period.
The oral examination (DD2, DD5), differently, seeks to test the individual students’ preparation by verifying the students' understanding of the software platforms discussed in the course in an oral discussion, and may also include questions on selected programming assignments. The oral examinations are individual and scheduled during the exam period after the end of the lecture period.
Groups may start with the continuous evaluation but individual students may possibly switch, at any time during the semester, to the oral examination mode.

Teaching material provided by the lecturer

Nonlinear systems exhibit richer phenomena than their linear counterparts, at the price of increased complexity.
To navigate this complexity, the course first presents the main tools to analyze dynamical properties of nonlinear systems, among which Lyapunov methods and changes of variable play a prominent role. Through these tools, then, the course illustrates well-established techniques to design controllers for relevant classes of nonlinear systems, as described below. Mechanical and robotic systems, oscillators and electrical circuits are used to exemplify these techniques.
The course is methodological and aims at providing students with a toolkit of techniques for nonlinear (control) systems with an eye towards computational implementations of some of these techniques. This toolkit and the understanding gained in the course should enable students to deal with the instances of nonlinear (control) systems they will encounter and to autonomously delve into more advanced topics within the broad area of nonlinear control.

After the lectures and exercise sessions of this course, the student

• knows the fundamental tools for the analysis of dynamical properties of nonlinear systems (DD1);
• knows some of the most used techniques for control design of nonlinear systems (DD1);
• is able to explain these techniques (DD5), rigorously justify the main steps in their derivation (DD2), and suitably apply them according to the context (DD2).
  After the computer sessions of this course, the student
• is able to numerically implement control design algorithms (DD2);
• is familiar with some computational tools for the analysis and design of classes of nonlinear systems (DD2).
  DD1-DD5 refer to Dublin descriptors 1-5.

The course covers some selected topics within control design of nonlinear systems.

• Review on autonomous nonlinear systems.
• Passivity.
• Input/output models, L2 gain and its application to antiwindup design.
• Special nonlinear forms.
• Feedback linearization.
• State feedback stabilization for nonlinear systems.
  The course comprises
• lectures, where theoretical notions and methods are presented;
• exercise sessions, where the theoretical notions and methods are illustrated on numerical examples of nonlinear systems;
• computer sessions, where more realistic examples of nonlinear systems and computational tools (such as linear matrix inequalities and sum-of-squares) are illustrated.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The final assessment is a written exam consisting of

• exercises, where the students will show their knowledge on analysis and design methodologies for nonlinear control systems (DD1) as well as their capability to apply these methodologies to some numerical problems (DD2);
• theoretical questions, where the students will demonstrate their ability in explaining how to address (DD4) and solve (DD2) an analysis/design problem for a nonlinear control system, according to a given methodology.
  An oral exam is not part of the assessment, unless the lecturer deems one necessary for the evaluation after the written exam.
  DD1-DD5 refer to Dublin descriptors 1-5.

H. K. Khalil, Nonlinear Control, Editore: Pearson, Anno edizione: 2015, ISBN: 978-0133499261
C. M. Kellett and P. Braun, Introduction to Nonlinear Control: Stability, Control Design, Estimation, Editore: Princeton University Press, Anno edizione: 2023, ISBN: 978-0691240480
H. K. Khalil, Nonlinear Systems Third Edition, Editore: Prentice Hall, Anno edizione: 2002, ISBN: 978-0130673893
M. Vidyasagar, Nonlinear systems analysis, Editore: SIAM, Anno edizione: 2002, ISBN: 978-0-89871-526-2
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Editore: SIAM, Anno edizione: 1994, ISBN: 978-0-89871-485-2

Nonparametric Statistics is a course that aims at providing students with statistical and algorithmic tools for the analysis of complex data, i.e., data for which the identification of standard and classical probabilistic models is hard or not possible, through a nonparametric approach. The course is organized in theoretical classes and lab sessions and a data analysis team project. Knowledge in probability, statistical inference and multivariate statistics is required.

Lectures and exercises sessions will allow students to acquire the following competences:
Knowledge and understanding.
Having successfully taken the course examination, the students are expected to

• know the principles of nonparametric descriptives, inference, prediction and forecasting;
• know the correct terminology of nonparametric statistics and to be able to correctly argument the theory.
  The students’ knowledge and comprehension is expected not be limited to the enunciation of definitions and results and to the solution of standard exercises, but rather to be critical and enabling to distinguish among different situations and to take appropriate choices, justifying the followed procedures.
  Ability of applying knowledge and understanding.
  Having successfully taken the course examination, the students are expected to
• be able to apply the attained knowledge to specific problems of data analysis;
• be able to select the principles which are useful to obtain the solutions to the problems at hand.
  Communication skills.
  Having successfully taken the course examination, the students are expected to
• be able to effectively and efficiently communicate the developed solutions and the corresponding results.

Part I (Non parametric Multivariate Exploration)
Depth measures
Depth measures for functional data [only for the 8 CFU version]
Part II (Non parametric Inference)
Rank Tests
Permutational Inference (Tests and Confidence Intervals for means, linear regression and Anova)
Booststrap Inference (Tests and Confidence Intervals for means, linear regression and Anova)
Permutation Inference for functional data [only for the 8 CFU version]
Part III (Non parametric Regression)
Nonparametric and Semiparametric Regression (Binning; KNN; Kernel methods; Splines; Spline with differential penalization)
Quantile Regression
Nonparametric and Semiparametric estimation in Survival Analysis (Kaplan-Meier and Nelson-Aalen estimators, Cox model)
Part IV (Nonparametric Forecasting)
Conformal prediction
Conformal prediction for functional data [only for the 8 CFU version]

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The course assessment will consist of a composite individual evaluation (home-work + oral discussion) and a team project for both the 5CFU and 8CFU version of the course.
The composite individual evaluation will consist of two parts: fi rstly, a homework where each student will be required to provide the solution of an execise in terms of code necessary for getting the solution; then, an oral discussion where the student will be required to solve an exercise and to answer some theoretical questions. Failing the rst part will prevent to access the second part of the composite evaluation.
The composite individual evaluation will be scored on a scale from 0 to 30, the maximum evaluation being 32/30.
It will be passed upon obtaining a score larger or equal to 18/30. The exam evaluation will account for the degree of clarity of the exposition and for the correctness of methods and computations. For each question students will be asked to report both the method used and the numerical solution obtained, and to critically discuss the latter one.
The team project will consist of an analysis of a real dataset, to be conducted in teams of 2 to 4 students, using the models and methods introduced in the course. The team projects will be presented during and at the end of the course in an open workshop that will take place after the end of the semester. For the groups whose students are not willing to give the written exam during the winter semester a second date will be available during the summer session.
Each team will receive an evaluation in a scale from 0 to 30. More details about the expected project development will be given in a dedicated lesson.
The final individual grade will be obtained as a weighted average of the grades obtained by the student in the two parts of the evaluation: 2/3 grade of the composite exam + 1/3 grade of the project.
During the exam, the students will have to:

• Demonstrate the degree of knowledge and comprehension of the key aspects of the course, presenting the used methodologies in a clear and exhaustive way;
• Demonstrate their ability to apply the learned notions to solve exercises and real problems, on any of the topics covered in the course.

Regina LiuJ. M. PareliusK. Singh, Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference, Editore: The Annals of Statistics, Anno edizione: 1999, Fascicolo: 27(3):783-858
Note: A further selection of scientific papers for each topic will be provided by the teachers.
Fortunato Pesarin; Luigi Salmaso, Permutation Tests for Complex Data: Theory, Applications and Software, Editore: John Wiley & Sons, Anno edizione: 2010
Trevor Hastie; Robert Tibshirani; Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction: Data Mining, Inference, and Prediction, Editore: Springer
Hosmer, D.W., Lemeshow, S., Applied Survival Analysis, Editore: John Wiley & Sons, Anno edizione: 2008
Vladimir Vovk; Alex Gammerman; Glenn Shafer, Algorithmic learning in a random world, Anno edizione: 2005

Nonparametric Statistics is a course that aims at providing students with statistical and algorithmic tools for the analysis of complex data, i.e., data for which the identification of standard and classical probabilistic models is hard or not possible, through a nonparametric approach. The course is organized in theoretical classes and lab sessions and a data analysis team project. Knowledge in probability, statistical inference and multivariate statistics is required.

Lectures and exercises sessions will allow students to acquire the following competences:
Knowledge and understanding.
Having successfully taken the course examination, the students are expected to

• know the principles of nonparametric descriptives, inference, prediction and forecasting;
• know the correct terminology of nonparametric statistics and to be able to correctly argument the theory.
  The students’ knowledge and comprehension is expected not be limited to the enunciation of definitions and results and to the solution of standard exercises, but rather to be critical and enabling to distinguish among different situations and to take appropriate choices, justifying the followed procedures.
  Ability of applying knowledge and understanding.
  Having successfully taken the course examination, the students are expected to
• be able to apply the attained knowledge to specific problems of data analysis;
• be able to select the principles which are useful to obtain the solutions to the problems at hand.
  Communication skills.
  Having successfully taken the course examination, the students are expected to
• be able to effectively and efficiently communicate the developed solutions and the corresponding results.

Part I (Non parametric Multivariate Exploration)
Depth measures
Depth measures for functional data [only for the 8 CFU version]
Part II (Non parametric Inference)
Rank Tests
Permutational Inference (Tests and Confidence Intervals for means, linear regression and Anova)
Booststrap Inference (Tests and Confidence Intervals for means, linear regression and Anova)
Permutation Inference for functional data [only for the 8 CFU version]
Part III (Non parametric Regression)
Nonparametric and Semiparametric Regression (Binning; KNN; Kernel methods; Splines; Spline with differential penalization)
Quantile Regression
Nonparametric and Semiparametric estimation in Survival Analysis (Kaplan-Meier and Nelson-Aalen estimators, Cox model)
Part IV (Nonparametric Forecasting)
Conformal prediction
Conformal prediction for functional data [only for the 8 CFU version]

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The course assessment will consist of a composite individual evaluation (home-work + oral discussion) and a team project for both the 5CFU and 8CFU version of the course.
The composite individual evaluation will consist of two parts: fi rstly, a homework where each student will be required to provide the solution of an execise in terms of code necessary for getting the solution; then, an oral discussion where the student will be required to solve an exercise and to answer some theoretical questions. Failing the rst part will prevent to access the second part of the composite evaluation.
The composite individual evaluation will be scored on a scale from 0 to 30, the maximum evaluation being 32/30.
It will be passed upon obtaining a score larger or equal to 18/30. The exam evaluation will account for the degree of clarity of the exposition and for the correctness of methods and computations. For each question students will be asked to report both the method used and the numerical solution obtained, and to critically discuss the latter one.
The team project will consist of an analysis of a real dataset, to be conducted in teams of 2 to 4 students, using the models and methods introduced in the course. The team projects will be presented during and at the end of the course in an open workshop that will take place after the end of the semester. For the groups whose students are not willing to give the written exam during the winter semester a second date will be available during the summer session.
Each team will receive an evaluation in a scale from 0 to 30. More details about the expected project development will be given in a dedicated lesson.
The final individual grade will be obtained as a weighted average of the grades obtained by the student in the two parts of the evaluation: 2/3 grade of the composite exam + 1/3 grade of the project.
During the exam, the students will have to:

• Demonstrate the degree of knowledge and comprehension of the key aspects of the course, presenting the used methodologies in a clear and exhaustive way;
• Demonstrate their ability to apply the learned notions to solve exercises and real problems, on any of the topics covered in the course.

Regina LiuJ. M. PareliusK. Singh, Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference, Editore: The Annals of Statistics, Anno edizione: 1999, Fascicolo: 27(3):783-858
Note: A further selection of scientific papers for each topic will be provided by the teachers.
Fortunato Pesarin; Luigi Salmaso, Permutation Tests for Complex Data: Theory, Applications and Software, Editore: John Wiley & Sons, Anno edizione: 2010
Trevor Hastie; Robert Tibshirani; Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction: Data Mining, Inference, and Prediction, Editore: Springer
Hosmer, D.W., Lemeshow, S., Applied Survival Analysis, Editore: John Wiley & Sons, Anno edizione: 2008
Vladimir Vovk; Alex Gammerman; Glenn Shafer, Algorithmic learning in a random world, Anno edizione: 2005

The course provides students with the physical foundations required to understand, critically assess and select nuclear techniques for advanced materials characterization.
Emphasis is placed on understanding the physical principles governing each technique, the type of information that can be extracted, the achievable sensitivity and spatial resolution, and the strengths and limitations of each method. Particular attention is devoted to the comparison of complementary techniques and, where appropriate, to their relationship with widely used non-nuclear characterization methods, in order to highlight the specific information uniquely provided by nuclear techniques.
Complementary classes of techniques based on nuclear reactions, ion beams, neutrons, hyperfine interactions and positron annihilation are presented, highlighting the information provided by each method, their capabilities and their limitations in materials characterization.
An introductory review of the nuclear physics concepts required for the subsequent topics is included, making the course accessible to students from different educational backgrounds.
The final part of the course adopts an active learning approach based on Blended Learning, in which students critically analyse recent scientific papers illustrating advanced applications of the techniques discussed during the lectures.

The student
knows the physical principles underlying the main nuclear techniques for materials characterization and the type of information provided by each technique (DdD1);
knows the capabilities, limitations and complementarity of the different techniques, including their sensitivity, spatial or depth resolution, and typical fields of application (DdD1);
is able to select and critically compare the most appropriate technique, or combination of techniques, for a given materials characterization problem (DdD2);
is able to interpret the scientific literature employing nuclear techniques for materials characterization and discuss their applications using appropriate scientific terminology (DdD2).

Module 1 – Introduction to materials characterization and nuclear techniques
Role of materials characterization techniques in materials science
Information accessible through different characterization methods (elemental composition, depth profiling, crystal structure, local atomic environment, point defects)
Overview of nuclear techniques for materials characterization and their complementarity with other characterization methods
Module 2 – Physical foundations
Review of the physical concepts underlying the techniques presented in the course:
collisions
multipole expansion of electromagnetic fields and interaction of multipoles with electromagnetic fields
magnetic dipoles in magnetic fields
X-ray emission: continuous and characteristic X-ray spectra
interaction of X-rays and gamma rays with matter: scattering and absorption
For students without previous background in nuclear physics, the introductory lectures also provide the fundamental concepts of nuclear structure, radioactivity and nuclear reactions needed for the subsequent modules.
Module 3 — Photon-based techniques
Physical principles of X-ray emission
X-ray Fluorescence (XRF)
Particle-Induced X-ray Emission (PIXE)
Comparison between XRF and PIXE
Information provided, capabilities, limitations, detection limits and typical applications
Module 4 — Ion Beam Analysis techniques
Rutherford Backscattering Spectrometry (RBS)
Elastic Recoil Detection Analysis (ERDA)
Nuclear Reaction Analysis (NRA)
Particle-Induced Gamma-ray Emission (PIGE)
Integration of complementary Ion Beam Analysis techniques
Information provided, capabilities, limitations, depth resolution and typical applications
Module 5 – Neutron-based techniques
Neutron Activation Analysis (NAA)
Neutron diffraction
Inelastic neutron scattering
Comparison with X-ray diffraction
Information provided, capabilities, limitations and typical applications in structural and dynamical characterization of materials
Module 6 – Nuclear spectroscopies and positron-based techniques
Hyperfine interactions
Mössbauer spectroscopy
Nuclear Magnetic Resonance (NMR)
Positron Annihilation Spectroscopy (PAS): positron lifetime spectroscopy; Doppler broadening spectroscopy.
Comparison of complementary techniques
Information provided, capabilities, limitations and typical applications for the characterization of local atomic environments, vacancy-type defects and free volume
Module 7 – Applications and case studies (Blended Learning and active learning)
Critical analysis and discussion of recent scientific papers
Student presentations
Selection and critical comparison of techniques for specific materials characterization problems
Integration of complementary characterization techniques

Prova orale obbligatoria
Assessment consists of an oral examination aimed at evaluating the student's understanding of the physical principles underlying the techniques presented in the course, their capabilities and limitations, and their applicability to specific materials characterization problems.
Students are expected to discuss and compare different nuclear techniques for materials characterization, justify the choice of the most appropriate experimental approach for a given investigation, and critically interpret examples drawn from the scientific literature.
Students participating in the Blended Learning activities through the presentation of a scientific paper will have this activity taken into account in the overall assessment.

H.R. Verma, Atomic and Nuclear Analytical Methods: XRF, Mössbauer, XPS, NAA and Ion-Beam Spectroscopic Techniques, Editore: Springer, Anno edizione: 2007, ISBN: 3-540-30277-8
Note: Covers several nuclear techniques. - Available as E-book at Politecnico library
editor-in-chief: John C. Lindon, Encyclopedia of Spectroscopy and Spectrometry, Editore: Elsevier, Anno edizione: 2000, ISBN: 978-0-12-226680-5
Note: Note: Available as E-book at Politecnico library

Numerical methods are ubiquitous in Machine Learning. The aim of this course is twofold:
on the one hand, to systematically address the mathematical and numerical background at
the heart of machine learning, with particular attention to applications in Science and
Engineering; on the other hand, to sustain the theoretical analysis with laboratory sessions.
Extensive hands-on sessions are planned.
The course is part of a pilot program on the use of AI tools in teaching.

Knowledge and understanding (Dublin Descriptor 1)
At the end of the course and after successfully passing the exam, the student will learn how to know, understand and be able to implement numerical methods for machine learning.
Applying knowledge and understanding (Dublin Descriptor 2)
At the end of the course and after successfully passing the exam, the student will be able to:

• Construct and analyze numerical algorithms for Machine Learning.
• Understand and master the theoretical properties of numerical algorithms for solving Machine Learning Problems.
• Write and interpret algorithms;
• Develop implementation skills and numerical verification abilities.
  Autonomy of judgment (Dublin Descriptor 3), Communication skills (Dublin Descriptor 4) and Learning ability (Dublin Descriptor 5).
  At the end of the course and after successfully passing the exam, the student will be able to:
• choose the most appropriate numerical scheme for solving a given problem;
• critically reason and interpret the results;
• model and numerically simulate problems stemming from applications in Science and
  Engineering.

1. Numerical Linear Algebra Tools
Singular value decomposition, principal components and best low rank matrix.
Eigenvalues. Least square methods. QR factorization.
Toeplitz matrices and shift invariant filters. Convolution.
Randomized SVD
2. Automatic differentiation
Wenger list, Direct Acyclic Graphs, Forward mode of AD
Dual numbers
Backward mode of AD
3. Numerical Optimization and Training of Neural Networks
Loss functions.
Stochastic gradient methods, accelerated gradient methods, coordinate descent methods.
Second order methods: Newton and Inexact Newton Methods.
4. Approximation properties of Neural Networks
Stone-Weierstrass theorem and universality results for shallow neural networks
Approximation theory of deep neural networks: error bounds, optimality
properties and regularity classes (e.g, Sobolev, Besov).
5. Sparse hints to Artificial Intelligence/Machine Learning applications.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of a written test, an oral colloquium and a project. The written test takes place in
the computer room and it covers all the theoretical and practical arguments
considered during the lectures and lab sessions. The problems mainly focus on definition,
application of important lemmas and theorems, and important examples. Light calculations
may be needed. The exam is open book. The maximum grade of the written test is
28/30. To get a grade > 28, students are required to take an oral exam. The assessment of the
oral exam will be based on subject knowledge matters and quality of the oral delivery.
Exam (written and oral). It covers:

• The student's ability to apply the subject-specific knowledge and techniques acquired during the course (Descriptors 1 and 2).
• The student's ability to choose the most appropriate numerical algorithms and critically interpret the results (Descriptors 2 and 3).
  Project. It covers:
• The students' ability to integrate knowledge for problem-solving, collaborate effectively in teams, and communicate results (Descriptors 3, 4, and 5).

G. Strang, Linear Algebra and Learning from Data, Editore: Wellesley-Cambridge Press, Anno edizione: 2019, ISBN: 978-0692196380
J. Nocedal, S. J. Wright, Numerical Optimization, Editore: Springer Nature, Anno edizione: 2006, ISBN: 978-0387303031
A. Griewank, A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Editore: SIAM, Anno edizione: 2008, ISBN: 978-0898716597
I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, Editore: Mit Press, Anno edizione: 2017, ISBN: 978-0262035613 http://www.deeplearningbook.org/
O. Calin, Deep Learning Architectures: A Mathematical Approach, Editore: Springer Nature, Anno edizione: 2020, ISBN: 978-3-030-36723-7

Numerical methods are ubiquitous in Machine Learning. The aim of this course is twofold:
on the one hand, to systematically address the mathematical and numerical background at
the heart of machine learning, with particular attention to applications in Science and
Engineering; on the other hand, to sustain the theoretical analysis with laboratory sessions.
Extensive hands-on sessions are planned.
The course is part of a pilot program on the use of AI tools in teaching.

Knowledge and understanding (Dublin Descriptor 1)
At the end of the course and after successfully passing the exam, the student will learn how to know, understand and be able to implement numerical methods for machine learning.
Applying knowledge and understanding (Dublin Descriptor 2)
At the end of the course and after successfully passing the exam, the student will be able to:

• Construct and analyze numerical algorithms for Machine Learning.
• Understand and master the theoretical properties of numerical algorithms for solving Machine Learning Problems.
• Write and interpret algorithms;
• Develop implementation skills and numerical verification abilities.
  Autonomy of judgment (Dublin Descriptor 3), Communication skills (Dublin Descriptor 4) and Learning ability (Dublin Descriptor 5).
  At the end of the course and after successfully passing the exam, the student will be able to:
• choose the most appropriate numerical scheme for solving a given problem;
• critically reason and interpret the results;
• model and numerically simulate problems stemming from applications in Science and
  Engineering.

1. Numerical Linear Algebra Tools
Singular value decomposition, principal components and best low rank matrix.
Eigenvalues. Least square methods. QR factorization.
Toeplitz matrices and shift invariant filters. Convolution.
Randomized SVD
2. Automatic differentiation
Wenger list, Direct Acyclic Graphs, Forward mode of AD
Dual numbers
Backward mode of AD
3. Numerical Optimization and Training of Neural Networks
Loss functions.
Stochastic gradient methods, accelerated gradient methods, coordinate descent methods.
Second order methods: Newton and Inexact Newton Methods.
4. Approximation properties of Neural Networks
Stone-Weierstrass theorem and universality results for shallow neural networks
Approximation theory of deep neural networks: error bounds, optimality
properties and regularity classes (e.g, Sobolev, Besov).
5. Sparse hints to Artificial Intelligence/Machine Learning applications.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam consists of a written test, an oral colloquium and a project. The written test takes place in
the computer room and it covers all the theoretical and practical arguments
considered during the lectures and lab sessions. The problems mainly focus on definition,
application of important lemmas and theorems, and important examples. Light calculations
may be needed. The exam is open book. The maximum grade of the written test is
28/30. To get a grade > 28, students are required to take an oral exam. The assessment of the
oral exam will be based on subject knowledge matters and quality of the oral delivery.
Exam (written and oral). It covers:

• The student's ability to apply the subject-specific knowledge and techniques acquired during the course (Descriptors 1 and 2).
• The student's ability to choose the most appropriate numerical algorithms and critically interpret the results (Descriptors 2 and 3).
  Project. It covers:
• The students' ability to integrate knowledge for problem-solving, collaborate effectively in teams, and communicate results (Descriptors 3, 4, and 5).

G. Strang, Linear Algebra and Learning from Data, Editore: Wellesley-Cambridge Press, Anno edizione: 2019, ISBN: 978-0692196380
J. Nocedal, S. J. Wright, Numerical Optimization, Editore: Springer Nature, Anno edizione: 2006, ISBN: 978-0387303031
A. Griewank, A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Editore: SIAM, Anno edizione: 2008, ISBN: 978-0898716597
I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, Editore: Mit Press, Anno edizione: 2017, ISBN: 978-0262035613 http://www.deeplearningbook.org/
O. Calin, Deep Learning Architectures: A Mathematical Approach, Editore: Springer Nature, Anno edizione: 2020, ISBN: 978-3-030-36723-7

The goal of this course is to introduce numerical linear algebra solvers for scientific computing and their implementation on HPC architectures. The course emphasises the importance of numerical approximations for solving large linear systems and analysing the properties of large, potentially sparse, matrices. These tasks are crucial to overall efficiency and are the most resource-intensive steps in complex numerical simulations, large-dataset analysis, and Machine Learning applications. The course covers algorithms for large-scale computing, their practical implementation, and their analysis in terms of computational and communication complexities. For algebraic linear systems stemming from the numerical approximation of differential problems, the course will also address how the choice of the numerical technique depends on factors such as the specific differential problem, the numerical discretisation method, and the HPC environment.
Extensive computer lab sessions will be carried out using the C programming language on significant test cases. Additionally, the course aims to train students to use programming languages for algorithm development and numerical computations, enabling them to critically apply advanced simulation tools.
Throughout the course, students are stimulated to:

• Develop specialised knowledge of numerical linear algebra for large-scale scientific computing problems (Dublin Descriptor 1).
• Analyse, implement, and apply numerical algorithms effectively (Dublin Descriptor 1, Dublin Descriptor 2).
• Select the most appropriate technique and critically use advanced simulation tools by motivating the choices made (Dublin Descriptor 3, Dublin Descriptor 4, Dublin Descriptor 5).

According to the Dublin descriptors, the expected learning outcomes are the following.
DD1. Knowledge and understading.

• Develop knowledge and understanding of the main Numerical Linear Algebra algorithms, as well as evaluate their properties.
  DD2. Ability to apply knowledge and understading.
• Construct and analyse the main Numerical Linear Algebra algorithms.
• Understand and master the theoretical properties of numerical algorithms for solving algebraic problems.
• Write and interpret algorithms;
• Develop implementation skills and numerical verification abilities:
  DD3. Autonomy of judgment, DD4. Communication skills, DD5. Learning ability.
• Choose the most appropriate numerical scheme for solving a given problem;
• Critically interpret of the numerical results in the light of the theory;
• Motivate the choice of the adopted methods and tools;
• Integrate knowledge for problem-solving, collaborate effectively in teams, communicate the results.

The topics that will be covered in the course are listed below. The methods presented during the lectures will be numerically investigated during the Computer Lab sessions.
Lectures will cover the following topics:
Iterative methods for large linear systems: Sparse matrix storage formats; Krylov subspace iterative methods (CG, GMRES, BiCG, BiCGstab,....); HPC programming and implementation of iterative solvers; Domain decomposition preconditioners: non-overlapping and overlapping techniques; (Algebraic) multigrid/multilevel methods.
Direct methods for sparse linear systems: Graph reordering and fill-in; Graph partitioning and parallelisation; The multifrontal method.
Numerical algorithms for Machine Learning: Least square approximations; Numerical techniques for QR factorisation; (L)-BFGS (hints).
Numerical approximation of eigenvalues: Lanczos methods; Numerical algorithms based on approximate factorisations.
Computer Labs. The Computer Lab sessions are based on the parallel software library LIS (Library of Iterative Solvers for linear systems, https://www.ssisc.org/lis/index.en.html). A quick overview of HPC linear algebra libraries such as Eigen, MUMPS, and LAPACK will also be covered.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Valutazione continua obbligatoria
The exam includes a written test and a coursework challenge, with an optional oral test available.

• The written test, which accounts for 80% of the final grade, takes place in the computer lab. It covers all theoretical and practical topics discussed in lectures and lab sessions, including theoretical concepts and the implementation and programming of numerical algorithms.
• A coursework challenge, which accounts for 20% of the final grade. Students work in small groups on an assigned task and actively participate in a summative assessment and evaluation process.
• The optional oral consists of a discussion on course topics and the written elaborate.
  Assessment. The assessment covers:
  -The student's ability to apply the subject-specific knowledge and techniques acquired during the course (Descriptors 1 and 2).
• The student's ability to choose the most appropriate numerical algorithms and critically interpret the results (Descriptors 2 and 3).
• In coursework challenges, the students' ability to integrate knowledge for problem-solving, collaborate effectively in teams, and communicate results (Descriptors 3, 4, and 5).
  The lecturer reserves the right to require an oral examination after the written examination to assess and verify students' knowledge and competencies.

N. Trefethen, D. Bau, Numerical Linear Algebra, Editore: SIAM, Anno edizione: 2022
Y. Saad, Iterative Methods for Sparse Linear Systems, Anno edizione: 2003

This comprehensive course dives into the intricate world of mathematical and numerical modeling, specifically focusing on the simulation of various physical phenomena within the geosciences field. With a keen emphasis on subsurface flow and deformation, the course aims to provide a gradual introduction to numerical complexities while concurrently exploring the mathematical modeling principles that underpin these phenomena.
Throughout the course, we will cover an array of fascinating topics, ensuring a parallel progression between mathematical and numerical modeling. From the modeling point of view we will focus on the modeling of flow, transport and poroelastic deformation in subsurface porous media. From the point of view of numerical methods we will address advanced topics such as:

• mixed formulations
• advanced discretization methods for general grids
• hybrid dimensional PDEs
• conservation laws
• stiff advection-diffusion-reaction problems
• strategies for the solution of nonlinear and coupled problems.

At the end of this course, students will have acquired a solid foundation in the mathematical models pertaining to relevant phenomena in porous media flow. By delving into the intricacies of these mathematical models, students will develop a comprehensive understanding of the underlying principles and governing equations that drive these phenomena. Armed with this knowledge, students will be well-equipped to analyze and interpret the behavior of fluids in porous media, gaining insights into the complex dynamics at play.
In addition to the comprehensive understanding of mathematical models, the course offers an extensive overview of the numerical challenges associated with simulating these phenomena. Through engaging exercise sessions and practical assignments, students will have the opportunity to tackle real-world scenarios and apply numerical methods to solve complex problems. By actively engaging in these exercises, students will enhance their ability to comprehend and evaluate numerical results in a discerning and critical manner.
The exercise sessions are designed to foster the development of analytical and problem-solving skills, enabling students to effectively interpret and assess the outcomes of numerical simulations. By actively engaging with the exercises, students will learn to identify potential sources of error, evaluate the reliability of the results, and discern the accuracy and limitations of different numerical approaches. This process of critical analysis will empower students to make informed judgments and draw meaningful conclusions from the numerical data generated during simulations.
Furthermore, the course emphasizes the importance of effective communication and the ability to articulate findings in a clear and concise manner. Students will be encouraged to present their numerical results, explain their methodologies, and provide insightful interpretations of the outcomes. By developing these communication skills, students will gain the confidence to engage in scholarly discussions, collaborate effectively with peers, and convey their understanding of the numerical challenges associated with porous media flow phenomena.
Ultimately, upon completion of the course, students will possess a strong foundational knowledge of the mathematical models governing porous media flow phenomena. They will also have acquired the essential skills to navigate the numerical challenges inherent in simulating these phenomena. Armed with this knowledge and expertise, students will be well-prepared to contribute to the field of geosciences, leveraging their discerning understanding of numerical results to drive advancements in the understanding and management of porous media flow.

The course covers a diverse range of topics related to porous media flow and deformation. Here is a detailed list of the subjects that will be explored:
1- Single phase flow in porous media: This module begins with an introduction to the fundamental concepts, including definitions and the governing equation. The weak formulation of the primal and mixed versions of the problem will be discussed, along with their well-posedness results. Students will also delve into numerical approximations, such as finite volume methods, specifically the two-point flux approximation and multi-point flux approximation. Additionally, finite element approximation will be explored, focusing on the numerical approximation of the mixed version of the problem using consistent discretization subspaces, such as the Raviart-Thomas finite elements. This section will also highlight the advantages and comparisons of the different approaches, particularly in the presence of heterogeneities in material properties.
2- Discretization methods for complex domains: This module explores the challenges associated with discretizing layered and heterogeneous media, as well as the presence of thin inclusions like fractures. Reduced models for flow in fractured porous media will be discussed, along with an abstract framework for mixed-dimensional PDEs. Students will learn about various numerical schemes tailored specifically for fractures and flexible numerical methods designed to handle non-standard grids. The geometrical complexity associated with real-world problems will also be addressed.
3- Transport phenomena in porous media: This section focuses on the extension of single-phase flow models to encompass two-phase flow and unsaturated flow. Students will gain insights into passive transport models and explore implicit and explicit discretization schemes. Time step restrictions, the choice of numerical flux, and their effects on the accuracy and stability of the simulations will be discussed in detail.
4- Reactive transport: In this module, mathematical modeling by advection-diffusion-reaction PDEs will be covered. Students will study models for mineral precipitation and dissolution, including the effects of fast and slow chemical reactions. Solution strategies for fully coupled versus iterative and non-iterative splittings will be explored, along with considerations for choosing the time advancing scheme. Special attention will be given to stiffness resulting from the coexistence of different time scales and the importance of maintaining solution positivity.
5- Poro-elasticity: This module provides a primer on linear elasticity and introduces Biot's theory, which describes the interaction between fluid flow and deformation in porous media. Students will gain an understanding of the coupled mathematical model that arises from poro-elasticity. Solution strategies for solving the Biot problem, including monolithic versus iterative splittings, will be discussed.
Throughout the course, practical laboratory sessions will utilize the PorePy (https://github.com/pmgbergen/porepy) and PyGeoN (https://github.com/compgeo-mox/pygeon) packages, written in Python. These packages offer powerful tools for implementing numerical methods and conducting simulations in the field of porous media flow and deformation.
To enrich the learning experience, several topical seminars will be conducted by esteemed national and international experts in the field. These seminars will provide valuable insights and perspectives, enhancing students' understanding of the latest advancements and research trends in porous media flow and deformation.
By the end of the course, students will have gained comprehensive knowledge in the mathematical modeling and numerical simulation of various phenomena in porous media. They will possess practical skills in implementing numerical methods, analyzing results, and interpreting findings in a discerning manner.

Prova orale obbligatoria
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), individuale, senza revisioni periodiche, con presentazione/discussione finale
The final assessment consists of two parts, taking place on the same day: i) an in-depth analysis of a research paper and ii) a brief oral exam.
For what concerns part i) students will study a research paper on one of the topic of the course (proposed by the teacher or agreed upon). They will give a 10-15 minutes presentation demonstrating their understanding of the topic.
For part ii) students will choose and prepare a topic from the course program, which should be different from the research paper. This will be the subject o a short oral exam.
Part i) could be replaced by a small project (code develompent starting from the examples seen during laboratories). The topic should be discussed with the teacher. In this latter case, students should deliver the code and a short presentation.

Jan M. Nordbotten and Micheal A. Celia, Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation, Editore: Wiley, ISBN: 978-0-470-88946-6 https://www.wiley.com/en-gb/Geological+Storage+of+CO2:+Modeling+Approaches+for+Large+Scale+Simulation-p-9780470889466
Rainer Helmig, Multiphase Flow and Transport Processes in the Subsurface, Editore: Springer, ISBN: 978-3-642-64545-7 https://link.springer.com/book/9783642645457
Olivier Coussy, Poromechanics, Editore: Wiley, ISBN: 9780470849200 https://onlinelibrary.wiley.com/doi/book/10.1002/0470092718

The goal of the course is to provide advanced skills in machine learning and optimization for challenging real-world data-driven applications. More precisely, the course explores mathematical models, optimization algorithms, and machine learning tools. The course focuses on four real-world applications in which computational data science is crucial: pricing in e-commerce, digital advertising, matching, and non-stationary environments. For every real-world application, the goals of the course are: providing a description of the real-world scenario, providing mathematical models of the scenario, providing optimization algorithms for the scenario, providing machine learning tools to deal with uncertainty. The treatment of the topics will be both from a theoretical point of view, describing models/algorithms and their properties, such as approximation guarantees and computational efficiency, and from a practical point of view, applying the algorithm during some laboratory sessions.

DdD1. Knowledge and Understanding

• Analyze real-world applications through mathematical models derived from microeconomics.
• Examine and interpret the properties and assumptions of such models.
• Evaluate the performance of algorithms and compare them with theoretical lower bounds.
  DdD2. Applying Knowledge and Understanding
• Model real-world applications as learning problems.
• Identify the most suitable class of algorithms to solve a given problem.
• Apply existing computational tools to implement and test practical solutions.
  DdD3. Making Judgments
• Assess the performance and robustness of proposed solutions.
• Make informed decisions among alternative methods offering different theoretical or empirical guarantees.
  DdD4. Communication
• Present and discuss problem formulations, modeling choices, and obtained results using appropriate technical language.
  DdD5. Lifelong Learning Skills
• Design algorithms to address problems for which no existing methods are available.
• Analyze and critically discuss the theoretical properties of newly developed algorithms.

0. Introduction to online learning
0.1. Online learning setting
0.2. Learning with full feedback
0.2.1 Online gradient descent
0.2.2. Adversarial expert problem
0.3. Learning with bandit feedback
0.3.1. Stochastic multi-armed bandits
0.3.2. Adversarial multi-armed bandits
1. Pricing in e-commerce
1.1. Introduction to pricing
1.2. Learning in pricing
1.2.1. Learning with discrete prices
1.2.2. Learning the demand curve
1.3. Implementing learning algorithms for pricing
2. Matching and combinatorial bandits
2.1. Introduction to matching
2.2. Matching algorithms
2.3. Combinatorial bandits
2.3.1. Combinatorial bandits with UCB
2.3.2. Combinatorial bandits with TS
2.4. Implementing learning algorithms for combinatorial bandits
3. Advertizing and learning with budget
3.1. Introduction to advertizing
3.2. Online learning with budget constraints
3.2.1. UCB for online learning with budget constraints
3.2.2. Primal-dual methods for online learning with budget constraints
3.3 Implementing learning algorithms for online problems with budget
4. Contextual Bandits
4.1. Introduction to contextual bandits
4.2 Online learning in contextual bandits
4.2.1 Learning with a small number of contexts
4.2.2 Learning in linear contextual bandits
4.3 Implementing learning algorithms for contextual bandits
5. Non-stationary enviroments
5.1. Introduction to non-stationary environments
5.2. Sliding window
5.3. Change detection
5.4. Implementing learning algorithms for non-stationary environments

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
The exam is structured as follows:

• Written exam (2 hours --- max 16 points). The exam is composed of 4 questions relative to all the topics. Here, the students are required to answer some theoretical questions about topics discussed during the course. The capabilities the students must show are:
• Understanding the theoretical properties of the algorithms (DdD1).
• Modeling real-world applications by means of mathematical models (DdD2).
• Identifying the most suitable class of algorithms to solve a problem, using the already available tools to solve a problem in practice (DdD2, DdD3).
• Project work (max 16 points). The project work can be carried out by groups of students, where each group is composed of at most 4 students. The students can exploit the lectures delivered by the teaching assistant to organize the project work. However, attending the lectures delivered by the teaching assistant is not mandatory. Here, the students are required to solve problems that are beyond the topics discussed during the course. The capabilities the students must show are:
• Design an algorithm for a problem not discussed during the course (DdD3, DdD5).
• Present orally the proposed algorithms and discuss their properties (DdD3, DdD4, DdD5).

Aleksandrs Slivkins, Introduction to Multi-Armed Bandits, Editore: Now Publishers, Anno edizione: 2019
Elad Hazan, Introduction to Online Convex Optimization, Editore: MIT Press, Anno edizione: 2022

The 8 credit OPTIMIZATION course is linked to the two joint courses: 051822 - NONLINEAR OPTIMIZATION (5 credits) and 051823 - DISCRETE OPTIMIZATION (5 credits), which correspond to two overlapping parts of the overall course. The details concerning the topics and organization of the two joint courses are reported below in "Argomenti trattati".
This description contains the objectives, programs and expected learning outcomes of the three courses.
The aim of the overall OPTIMIZATION course is to present the main concepts and methods of nonlinear (continuous) optimization and discrete optimization, which allow to tackle a wide variety of decision-making problems arising in science, engineering and management. Modeling and application-related aspects are also covered. Optimization problems from, among others, data mining, economics, energy, healthcare, machine learning, logistics, production, telecommunications and transportation, are discussed.
After the introduction and the fundamentals of convex analysis for optimization (common to the two joint courses), the overall course is subdivided into two parts. The first one is devoted to Nonlinear Optimization with continuous variables. The second one is devoted to Discrete Optimization and in particular to Integer Linear Programming, that is, optimization problems with a linear objective function and linear constraints where some (or all) variables are restricted to take discrete (integer) values.
During the computer lab meetings, the students will learn how to use a modelling language based on Python (with state-of-the-art solvers) to build optimization models and solve (mixed) integer linear optimization problems and nonlinear optimization problems.

In the following, the expected learning outcomes related to the joint courses NONLINEAR OPTIMIZATION and DISCRETE OPTIMIZATION are labelled with, respectively, (1) and (2).
Knowledge and understanding (DdD 1)
The students will learn:

• the key convex analysis concepts and results for optimization (1,2)
• the optimality conditions for unconstrained nonlinear optimization (1)
• the gradient, conjugate directions, Newton and quasi-Newton methods, with their convergence properties (1)
• the subgradient method for convex non-smooth optimization (1)
• the optimality conditions for constrained nonlinear optimization (1)
• the concepts and results of Lagrangian duality (1)
• the null-space and active set methods for quadratic programming problems (1)
• the quadratic penalty method and the augmented Lagrangian method (1)
• the logarithmic barrier method (1)
• the fundamentals of quadratic sequential programming (1)
• a wide selection of optimization models arising in a variety of fields of application (2)
• the main modeling techniques for Integer Linear Programming (ILP) problems (2)
• the concepts of strong and ideal formulations, and how to stregthen a given formulation (2)
• some important relaxations, in particular the Lagrangian relaxation with the subgradient method (2)
• the cutting plane methods for generic and structured ILP problems (2)
• the general scheme of the Banch-and-Cut method (2)
• the column generation method (2)
• some heuristics (2)
  Applying knowledge and understanding (DdD 2)
  The students will be able to:
• build optimization models starting from the decision problem descriptions, solve them using a mathematical modeling language and/or a state-of-the-art optimization solver (1,2)
• establish whether a given nonlinear optimization problem is convex (1)
• identify an appropriate method to tackle a given nonlinear optimization problem and apply it to small examples (1)
• solve a constrained nonlinear optimization problem via the Karush-Kuhn-Tucker optimality conditions (1)
• construct the Lagrangian dual of a given problem and establish the relationship with the primal problem (1)
• solve (un)constrained nonlinear optimization problems with some of the studied methods in Matlab (1)
• enhance (linearize and strengthen) ILP formulations (2)
• recognize an ideal ILP formulation based on the concept of totally unimodular matrices (2)
• apply the studied methods, such as for instance cutting planes, column generation, and heuristics, to some small problems (2)
• devise a Lagrangian relaxation for an assigned discrete optimization problem and discuss its strength (2)
• leverage on the acquired theoretical and algorithmic knowledge to answer relevant questions. (1,2)
  Communication skills (DdD 4)
  The students will be able to clearly describe any studied method, its main properties and its (dis)advantages with respect to other alternative algorithms. (1,2)

In the following, the topics related to the joint courses Discrete Optimization and Nonlinear Optimization are labelled with respectively (1) and (2).
1. Introduction (1,2)
Discrete (integer) and nonlinear (continuous) optimization models, local and global optima. Three examples: 3-D image reconstruction (computed tomography), location and transportation problem, winner determination in combinatorial auctions. Some fields of application.
2. Fundamentals of convex analysis (1,2)
Separating/supporting hyperplanes, main consequences (Farkas Lemma), characterization of convex functions, subgradients.
3. Unconstrained nonlinear optimization (1)

• Examples: statistical estimation, traning artificial neural networks.
• Optimality conditions based on feasible directions.
• Line search methods and convergence rate.
• One-dimensional optimization (Wolfe conditions).
• Line search methods: gradient, conjugate directions, Newton and quasi-Newton methods (DFP and BFGS).
• Subgradient method for convex non-smooth optimization.
  4. Constrained nonlinear optimization (1)
• Examples: designing linear classifiers and training Support Vector Machines (SVMs).
• Necessary optimality conditions: constraint qualification, Karush-Kuhn-Tucker conditions.
• Sufficient optimality conditions: Lagrange function, saddle points, weak and strong duality.
• Quadratic programming: examples from portfolio optimization and machine learning, null space method for equality constrained problems, active set methods for problems with also inequality constraints.
• Quadratic penalty and augmented Lagrangian methods.
• Barrier method and an application to linear programming (interior point method).
• Fundamentals of quadratic sequential programming.
  3. Discrete optimization (2)
• Integer linear programming (ILP) problems and modeling techniques with illustrative examples, including covering, packing, partitionning, location, routing, network flows, lot sizing and scheduling.
• Valid inequalities. Alternative, strong and ideal formulations.
• "Easy" ILP problems and totally unimodular matrices.
• Linear, surrogate and combinatorial relaxations.
• Lagrangian relaxation: Lagrangian subproblem, dual problem, subgradient method, choice of Lagrangian dual. Examples: symmetric travelling salesman and generalized assignment problems.
• Branching and bounding strategies for the Branch-and-Bound method (the general method is a prerequisite).
• Cutting plane methods: Chvátal-Gomory procedure, fractional and mixed integer Gomory cuts, facets of polyhedra, strong valid inequalities for structured ILP problems (cover inequalities for the binary knapsack problem, clique and odd cycle inequalities for the independent set problem, cut-set inequalities for TSP), separation problem and lifting procedure.
• Branch-and-Cut method: general scheme and main components.
• Column generation method and Branch-and-Price scheme.
• Some heuristics.
  A few topics will be assigned for independent study before related lectures or sessions devoted to exercises.
  Organization
  Besides the lectures, the course includes 9 sessions devoted to exercises (seven two-hour sessions and two one-hour sessions) and 6 two-hour sessions devoted to computer laboratory work. Every week the students will be assigned a set of exercises to be solved before the next exercise session and to be discussed in classroom.
  Joint courses: NONLINEAR OPTIMIZATION and DISCRETE OPTIMIZATION
  The courses NONLINEAR OPTIMIZATION (5 credits) and DISCRETE OPTIMIZATION (5 credits) correpond to two overlapping parts of the course OPTIMIZATION (8 credits).
  While OPTIMIZATION includes all the material presented during the lectures, the exercise and computer laboratory sessions,
• the course NONLINEAR OPTIMIZATION (5 credits) includes Chapters 1, 2, 3 and 4, the exercise sets n. 1-5 and the computer laboratory sessions n. 1-3 using Python,
• the course DISCRETE OPTIMIZATION (5 credits) includes Chapters 1, 2 and 5, the exercise sets n. 1, 6-9 and the computer laboratory sessions n. 3-6 using Python.
  The students enrolled in both courses NONLINEAR OPTIMIZATION (5 credits) and DISCRETE OPTIMIZATION (5 credits) must take the written exam of OPTIMIZATION (8 credits) and conduct a project or an individual study (2 credits) to be defined with one of the two instructors.

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
For the Optimization course, a written exam covering all the material presented during the lectures, the sessions devoted to the exercises, and the computer laboratory sessions and assignments. For the joint courses NONLINEAR OPTIMIZATION and DISCRETE OPTIMIZATION, the material is that related to the lectures, exercises and computer laboratories of the corresponding part of the course, as detailed in the above program.
The written exam consists of several questions aimed at evaluating the level of (applying) knowledge and understanding of the main concepts, models, results and methods covered in the course as specified in the expected learning outcomes. In particular, it includes: a modeling question; questions involving the application of the studied methods to assigned problems or the solution of numerical problems with appropriate algorithms; theoretical questions related to the main concepts, methods and results; and a question concerning the material covered in the computer laboratory sessions and assignments. An open-answer question will also allow assessment of the communication skills. (DdD 1, DdD2, DdD4)
A few points may be assigned based on some formative assesments or computer lab assignments during the semester, further details will be provided at the beginning of the course.
The students enrolled in both courses NONLINEAR OPTIMIZATION (5 credits) and DISCRETE OPTIMIZATION (5 credits) must take the written exam of OPTIMIZATION (8 credits) and conduct a project or an individual study (2 credits) to be defined with one of the instructors. The project or individual study will be evaluated on the basis of an oral presentation. (DdD 1, DdD2, DdD 3, DdD4, DdD5)

Slides of the lectures, material for the exercise and computer laboratory sessions
Note: The material will be made progressively available (during the semester) on WeBeep.
M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming: Theory and Algorithms. Third edition, Editore: Wiley Interscience, Anno edizione: 2006
S. Boyd, L. Vandenberghe, Convex Optimization, Editore: Cambridge Univeristy Press, Anno edizione: 2004 http://www.stanford.edu/~boyd/cvxbook/
J. Nocedal, S. Wright, Numerical Optimization, Editore: Springer, Anno edizione: 2006
Note: Second edition
L. A. Wolsey, Integer Programming, Second edition, Editore: J. Wiley & Sons, Anno edizione: 2021

Il Corso "Personalità Teambuilding e Leadership" introduce lo studente alla conoscenza delle strutture di personalità che orientano l'immagine di Sé, l'atteggiarsi, l'agire, il pensare, l'interagire, il comunicare e il cooperare: per lo studio, il lavoro e le relazioni interpersonali e con particolare riferimento allo sviluppo di competenze per il teambuilding e la leadership. Porta lo studente: - a valorizzare le proprie risorse e migliorare il proprio rendimento nell'acquisizione di nuove abilità e competenze; - a conoscere e ad affrontare meglio situazioni difficili a livello personale o di gruppo; - a prepararsi alla cooperazione e alla leadership; - ad affrontare al meglio le prime esperienze di inserimento lavorativo. Il corso offre laboratori esperienziali per lo sviluppo di soft skill nelle aree trattate, presenta i principi e modelli (di area costruttivista e relazionale) che guidano le esperienze di laboratorio e che possono essere adottati nella futura vita professionale e personale.

Il Corso "Personalità Teambuilding e Leadership" introduce lo studente alla conoscenza delle strutture di personalità che orientano l'immagine di Sé, l'atteggiarsi, l'agire, il pensare, l'interagire, il comunicare e il cooperare: per lo studio, il lavoro e le relazioni interpersonali e con particolare riferimento allo sviluppo di competenze per il teambuilding e la leadership. Porta lo studente: - a valorizzare le proprie risorse e migliorare il proprio rendimento nell'acquisizione di nuove abilità e competenze; - a conoscere e ad affrontare meglio situazioni difficili a livello personale o di gruppo; - a prepararsi alla cooperazione e alla leadership; - ad affrontare al meglio le prime esperienze di inserimento lavorativo. Il corso offre laboratori esperienziali per lo sviluppo di soft skill nelle aree trattate, presenta i principi e modelli (di area costruttivista e relazionale) che guidano le esperienze di laboratorio e che possono essere adottati nella futura vita professionale e personale.

The course aims at providing the students with a critical understanding of the philosophical foundations of science and technology. But what is the relation between philosophy and science? On the one hand, the discoveries by scientists are often inspired by philosophical ideas. On the other hand, scientific achievements and technological advancements pose deep conceptual questions to philosophers. The connection between these disciplines is thus so tied that it becomes difficult to even draw a border between them. This course explores such a connection through the study of important episodes in the history of science. Outstanding issues of philosophy of science and technology, such as scientific progress, the method of science and the confirmation of theories and laws, will be addressed. Moreover, a particular focus will be devoted to philosophical questions concerning the nature of space as they emerge in the foundations of science, especially in relation to the famous debate between Leibniz and Newton.

The course aims at providing the students with a critical understanding of the philosophical foundations of science and technology.
But what is the relation between philosophy and science? On the one hand, the discoveries by scientists are often inspired by philosophical ideas. On the other hand, scientific achievements and technological advancements pose deep conceptual questions to philosophers. The connection between these disciplines is thus so tied that it becomes difficult to even draw a border between them. This course explores such a connection through the study of important episodes in the history of science. Outstanding issues of philosophy of science and technology, such as scientific progress, the method of science and the confirmation of theories and laws, will be addressed. Moreover, a particular focus will be devoted to philosophical questions concerning the nature of space as they emerge in the foundations of science, especially in relation to the famous debate between Leibniz and Newton. Finally, in the context of philosophy of technology, we will explore epistemic tools that are used to draw scientifically-informed inferences, such as computer simulations and thought experiments.
Here's below a list of the main topics:

• Method of science
• Demarcation between science and pseudo-science
• Confirmation
• Scientific Progress
• Philosophy of Space: Absolutism vs Relationism
• Scientific Reasoning
• Philosophy of Technology

Prova scritta obbligatoria, senza prove in itinere
Altro
Final written exam based on general questions about the topics of the lectures: specifically, the students are assigned to write several essays, which have to be emailed directly to the instructors at the following address: [email protected]. There are also individual class presentations scheduled during the term

Alan Chalmers, What is This Thing Called Science?, Editore: Hackett Pub Co Inc
Nick Huggett, Space from Zeno to Einstein: Classic Readings With a Contemporary Commentary, Editore: Bradford Books

To provide the basic knowledge necessary for the understanding of the properties of ultrashort light pulses, their generation mechanisms, their propagation in linear and nonlinear media, their characterization techniques. The acquired knowledge will enable the student to work in advanced research laboratories as well as in high tech companies developing laser sources or using them for applications in micromachining, telecommunications, sensing or biomedicine.

At the end of the course the student will acquire knowledge and understanding of the underlying physics and the technical working principles of ultrashort pulse laser systems (DD1).
The student will be able to apply this knowledge and understanding to different scientific and industrial systems using ultrashort pulse lasers (DD2).
The student will be able to make judgements on the design of such systems for applications to spectroscopy, imaging or material processing (DD3).
The student will acquire learning skills that will enable her/him to read andvanced, graduate-level textbooks on nonlinear optics and photonics as well as papers on peer-reviewed scientific journals (DD5).

1. Properties of ultrashort laser pulses
introduction to ultrafast optics;
linear propagation equation for ultrashort pulses; dispersion and techniques for its compensation;
nonlinear ultrashort pulse propagation in second order media; three-fields coupled equations; second harmonic generation, sum and difference frequency generation;
nonlinear ultrashort pulse propagation in third order media; Kerr effect, nonlinear Schrödinger equation, solitons, self-phase-modulation;
ultrashort pulse characterization techniques: non-collinear and interferometric autocorrelation, FROG, SPIDER, 2DSI
2. Ultrashort pulse generation techniques
mode-locked lasers and passive mode-locking techniques;
ultrashort pulse amplification, chirped pulse amplification technique;
optical parametric amplifiers;
carrier-envelope phase and frequency combs.

Prova scritta obbligatoria, senza prove in itinere
The evaluation will consist of a written exam with questions and/or problems covering the topics of the lectures.
The exam will test the depth of understanding by the student of the handled topics, the developed critical skills and the capabilities to effectively organize the presented material, using a proper lexicon and efficiency and linearity of the discussion.

Andrew M. Weiner, Ultrafast Optics, Editore: Wiley, Anno edizione: 2009, ISBN: 978-0-471-41539-8
Sandro De Silvestri, Rocio Borrego Varillas, Aurelio Oriana, Cristian Manzoni, Giulio Cerullo, Tunable few-optical cycle pulses and advanced ultrafast spectroscopic techniques, Editore: Societa Italiana di Fisica, Anno edizione: 2018, ISSN: 0393697X, Fascicolo: 41 DOI: 10.1393/ncr/i2017-10143-7
Cristian Manzoni, Giulio Cerullo, Design criteria for ultrafast optical parametric amplifiers, Editore: Institute of Physics, Anno edizione: 2016 doi:10.1088/2040-8978/18/10/103501

FISICA DEI PLASMI
L'insegnamento intende fornire le conoscenze essenziali della fisica della materia allo stato di plasma, con particolare attenzione ai
plasmi fortemente ionizzati e ad alta temperatura, ed approfondirne alcune importanti tematiche. Elenco sintetico dei contenuti: Richiami
di elettromagnetismo; Elementi di elettrodinamica dei mezzi continui; Caratteristiche fondamentali di un plasma; Teoria delle orbite; Modelli per la descrizione del plasma; Onde in un plasma I; Emissione di radiazione elettromagnetica in un plasma; Fusione termonucleare controllata I; onde in un plasma II; collisioni in un plasma; elementi di fisica dei plasmi confinati magneticamente; interazione laser-plasma; Fusione termonucleare controllata II.

We live in an era in which data are pervasive, and data mining tools — Machine Learning and Artificial Intelligence — offer unprecedented opportunities for extracting value from them. In this scenario, quality remains a key driver of competitiveness and value creation for products and services.
The course presents a set of quantitative tools and methods for managing, modeling, and monitoring quality data in industrial and business scenarios. After successfully completing the course, students should be able to:

• Understand and master all the main concepts of quality data modelling, monitoring and improvement.
• Extract relevant information from complex, high-dimensional data.
• Identify models to predict quality data and performance indicators. Design and manage appropriate data-driven tools for industrial and business scenarios.

The course fits into the overall program curriculum, pursuing some of the defined general learning goals. In particular, it contributes to the development of the following capabilities:
Understanding the context, functions, and processes of a business/industrial environment, and the impact of these factors on business performance.
Designing solutions through a scientific and engineering approach (analysis, learning, reasoning, and modeling grounded in a solid, rigorous multidisciplinary background) to address problems and opportunities in business and industrial settings.
Developing new ideas and solutions for business and industrial scenarios evolving over time.
Lectures will provide the basic tools to understand functions and processes, using appropriate quantitative tools for data analysis.
Recitations in computer labs will show how the learned tools can be effectively used to design new solutions using a scientific approach to face the problems at hand (applying knowledge and understanding).
The lab project will foster an additional insight to develop new ideas and solutions in business and industrial scenarios (making judgements and learning skills).

The role of quality data in the current geopolitical scenario
High value-added products and services: industrial competition
Introduction to Big Data
Why quality is still important and related to product value
Quality data modeling and monitoring for "big" data streams — the four"V" of Big Data
Big Data: modeling patterns via linear models
Data Velocity: modeling patterns in autocorrelated data
Data Volume: modeling and monitoring multivariate data
Data Reduction: Principal Component Analysis and feature extractions
Data Variety: from product to process quality monitoring: on-line sensors, image and video-image data
Quality monitoring - Toward zero-defect manufacturing
Basic tools for anomaly detection and detection of out of control states.
Control charts for summary statistics – mean and variance
Control charts for residuals – pros and cons
Control charts for high-value added products – Exponentially weighted and Cusum Control charts.
AI for Quality: Neural Networks and Generative AI
Neural Networks (NN) and Deep Neural Networks (DNN) for image and signal data:anomaly detection with AI (one-class classifiers)
Generative AI: GAN and Diffusion models for anomaly detection and synthetic data generation/augmentation of rare defect classes
New frontiers: LLM for quality data analysis (hints)

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente) o condizionata (a scelta del docente)
Progetto/i - Elaborato/i facoltativo (a scelta dello studente), di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
Written Exam
The written exam is aimed at verifying if the students have successfully acquired knowledge of the basic tools to understand functions and processes. One of the test in the written exam is aimed at testing if students are able to use the newly acquired knowledge to design solutions for qualitative data analysis, using the data and information at hand.
The final mark in the written exam can range from "fail" to "30L".
Project work
An optional (highly suggested) project work is possible. In this case the students will be facing a real industrial problems using complex data sets to be analysed and monitored. The project work allows students to enhance their skills to develop new ideas and solutions in real industrial scenarios.
Oral exam
The professor may require an oral examination to further assess the student’s overall understanding of the course topics. The oral exam is also optional for the student and can be undertaken only if the written exam grade is sufficient (mark higher than 18). A maximum increase of 3/30 in the final grade can be achieved through the oral exam.

D.C. Montgomery, Introduction to Statistical Quality Control, Editore: Wiley
L. C. Alwan, Statistical Process Analysis, Editore: Irwin Mc Graw Hill
E. del Castillo, Statistical Process Adjustment for Quality Control, Editore: Wiley

The course focuses on quantitative methods for modeling, monitoring and improving quality of products and services in actual productive scenarios, characterized by multi-dimensional quality indicators. Techniques for both continuous and ordinal quality data (e.g., survey data) are presented.
After successfully completing the course, students should be able to do the following:
1. Understand the philosophy and basic concepts of quality monitoring and improvement.
2. Extract relevant information from complex, high-dimensional quality data
3. Identify models to predict the expected pattern of quality indicators
4. Design and use appropriate tools to design and manage quality in industrial and service scenarios.

The course ‘Quantum circuits and devices’ offers an overview of quantum hardware technology including qubits, quantum gates and full quantum processors. From the initial conceptualization of Richard Feynman in 1982, quantum computing has emerged in the last twenty years thanks to remarkable progress on both algorithms and qubit technology. Quantum computing can speed up the solution of hard problems, which are non-tractable by conventional computers, in various topics, such as cryptography, machine learning and the simulation of chemical molecules. Such a ‘quantum advantage’ has stimulated strong investments in research from major industries to explore the feasibility and the scaling of quantum computers. The course ‘Quantum circuits and devices’ will illustrate the state of the art of this ongoing technological race, addressing the main concepts, the opportunities and the challenges of quantum computing and providing the basic tools for understanding and designing quantum circuits.

Knowledge and understanding (Dublin Descriptor #1)
At the end of the course the students are expected to:
possess a good understanding of quantum computing in terms of basic concepts and main algorithms
possess a good understanding of qubits in terms of wavefunction, physical structure and operation including initialization, read and quantum gates
possess a basic knowledge of the main hardware implementation of qubits
possess a basic knowledge of quantum computer system architecture
Applying knowledge and understanding (Dublin Descriptor #2)
At the end of the course the students are expected to:
be able to analyze a quantum computer algorithm and architecture
be able to analyze a qubit structure and operation
be able to design an analogue control circuit for a qubit operation
Making judgements (Dublin Descriptor #3)
At the end of the course the students are expected to:
evaluate the most appropriate qubit technology for a set of application requirements
evaluate the most appropriate frequency and timing of operations for a given qubit technology

The course is organized in four phases. First, the basic principle of quantum computing will be explained. Then, the hardware implementation of quantum computing will be shown with reference to the two main quantum technologies, namely (i) the superconducting qubits and (ii) the spin qubits. Finally, the design, synthesis and operation of full quantum circuits will be described, including initialization, processing, read and quantum error correction. The following provides a detailed breakdown of the course topics:
Introduction (8 hours)
Qubits. Bloch sphere for representing the qubit state. Single qubit and multiple qubits. Superposition and entanglement. Relaxation and dephasing times. Quantum gates: NOT, Pauli, Hadamard, CNOT, CPHASE and SWAP. Universal gates and no-cloning theorem. Two-level systems: Hamiltonian, time evolution and Rabi oscillations. Avoided crossing. Quantum circuits: initialization, control, coupling and readout. DiVincenzo criteria for quantum circuits.
Semiconductor spin qubits (8 hours)
Quantum dots and donor impurities. Electron spin, Larmor precession, Zeeman effect and electrical tuning of the spin splitting. Spin-charge conversion for initialization and readout. Quantum point contacts and single-electron transistors for spin-charge conversion. Coulomb blockade. Electron spin resonance (ESR) and Rabi oscillations. Microwave transmission lines. Quantum gates for single and two qubits. Dephasing effects and silicon isotopic purification. Design/simulation tools. Technology state of the art and hardware demonstrators.
Superconducting qubits (8 hours)
Superconductivity: Bardeen-Cooper-Schrieffer (BCS) theory, Cooper-pair, superconductive energy gap. Flux quantization, Cooper pair box, superconducting quantum-interference device (SQUID). LC quantum oscillators. Circuit quantum electrodynamics. Josephson junction, effective inductance and Josephson relationships. Phase qubit, flux qubit, charge qubit and transmon. Quantum gates for single and two qubits. Superconducting qubit circuits: Initialization, readout and calibration. Flux line, drive line and read resonator. Design/simulation tools and hardware demonstrators.
Hardware quantum circuits (6 hours)
Quantum circuit design and synthesis: Clifford + T universal gate, summation and multiplication. Quantum fidelity and error correction. Randomized benchmarking and gate set tomography. Status of QC hardware and major developers. Alternative approaches: topological qubits, trapped ion qubits, trapped neutral atoms and adiabatic quantum computing. Cryogenic systems and CMOS electronic control.
Exercises (10 hours)
Numerical exercises will be illustrated on the following topics: quantum gates, quantum algorithms, spin qubits (Coulomb blockade, single electron transistor), superconducting qubits (Josephson junctions, phase/flux/charge qubits, transmons), analog control circuits.
Laboratory (10 hours)
Numerical laboratory sessions will be carried out on the design and simulation of superconducting quantum circuits with IBM’s Qiskit Metal ( https://qiskit.org/metal/ ). Experimental laboratory sessions will also be carried out remotely aimed at understanding the calibration and control of superconducting qubits.

Prova scritta obbligatoria, senza prove in itinere
The assessment will rely on a written exam with problems and questions covering the whole course, including theoretical lectures, exercises and laboratory experiments. The number of problems may vary from 5 to 10, with each answer contributing to the overall score with a specific weight, that will be shown in the text.

Ray LaPierre, Introduction to Quantum Computing, Editore: Springer Nature Switzerland AG, Anno edizione: 2021, ISBN: 978-3-030-69317-6
Daniel D. Stancil and Gregory T. Byrd, Principles of Superconducting Quantum Computers, Editore: Wiley, Anno edizione: 2022, ISBN: 9781119750727

Aim of the course is to give to the students the knowledge of the principles at the basis of Quantum Communications. The applications of these principles to some relevant examples of quantum communication protocols, like quantum key distribution for secure transmission of information, also exploiting the quantum resource of entanglement (as in quantum teleportation and in quantum repeaters), will be presented.

Dublin descriptor DD1 (knowledge and understanding). Students will learn the basic quantum principles for the understanding of the applications of quantum communications.
Dublin descriptor DD2 (applying knowledge and understanding). Students will be able to analyze and describe quantum circuits for manipulating qubits as combination of quantum gates and representing them by means of the Bloch sphere. Students will acquire the capability of implementing the main quantum communication protocols and to calculate the performance of quantum key distribution systems.
Dublin descriptor DD5 (lifelong learning skills). Students will acquire the tools for comprehending the main aspects of present and future applicative developments in the field of quantum communications.

Theoretical bases: Quantum states, observables and quantum measurement. Uncertainty principle. Complementary observables. Quantum bits (qubits). Dirac notation. Single-qubit quantum gates. Pauli operators. Measurement of qubits. Bloch sphere representation. Pure and mixed states. Density operator. Von Neumann entropy. Entanglement of qubits. Partial trace. Bell states. Bell inequality. Multiple-qubit gates. CNOT gate. No-cloning theorem. Accessible information and Holevo bound.
Quantum communications protocols: Quantum key distribution (QKD). BB84 protocol. Quantum bit error rate (QBER), secure key rate and security threshold. Trusted nodes. Examples of physical implementation of QKD. Photon-number splitting attack and QKD with decoy states. Entanglement-based QKD. E91 and BBM92 protocols. Superdense coding. Quantum teleportation. Entanglement swapping. Entanglement distillation. Entanglement distribution. Quantum repeaters.

Prova scritta obbligatoria, senza prove in itinere
The examen is written, with open questions and exercises on the topics explained during the lectures. It is possible to use at the examen only a standard calculator and a printed formulario. In detail the examen comprises:

• exercises to be solved numerically, in order to assess the expected learning outcomes related to Dublin descriptors DD1 and DD2;
• questions of theoretical type with open response, in order to assess the expected learning outcomes related to Dublin descriptors DD1, DD2 and DD5.
  The maximum score of the examen is 33 and the grade of 30 cum laude is obtained when the score is at least 32.

Reference notes for theory/examples/exercises presented on the blackboard during the lessons https://webeep.polimi.it/login/index.php
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Editore: Cambridge University Press, Anno edizione: 2000

Provide a basic understanding of the principles of quantum computing. Provide the notions required to understand if solving a problem may profit from quantum computing. Enable a hands-on experience on existing quantum computer simulators, to allow further experimentation by the candidate.

This course provides an introductory overview on the basic principles of quantum optics, their use to understand the fundamental mechanisms of light-matter interaction and the possibility to exploit these concepts to manipulate information in a completely new way as in quantum communication and quantum computation protocols. The course is conceived as a starting point for more advanced studies.

Knowledge and understanding (DD1)
Attending the lectures and passing the exam will allow the student to:

• U nderstand the physical basis of quantum optical phenomena;
• Learn the fundamental mechanisms governing light-matter interaction;
• Learn the principles and the main protocols of quantum information.
  Apply knowledge and understanding (DD2)
  The student will be able to apply the basic knowledge described above to:
• explain the operating principles of some prototypal optical devices developed for quantum information;
• deepen the understanding of physical phenomena encountered in other courses with a new perspective;
  Communication skills (DD4)
  The exam requests the students to communicate clearly what they have learnt, with rigorous argumentation.

Prelude to Quantum Optics
1. Introduction: theoretical and experimental foundations for the quantization of the electromagnetic field
2. Photodetection statistics: semiclassical model, violation of the semiclassical model by sub-Poissonian light
3. Formalism of quantum mechanics: axioms, bra-ket notation, matrix notation, Schroedinger and Heisenberg pictures
Quantization of the electromagnetic field
4. Quantization of the electromagnetic field: normal modes and normal variables for the classical electromagnetic field, postulate of the Hamiltonian of the field, Fock states and their properties
5. Quasi-classical states of the radiation field: definition and decomposition in the Fock basis, Glauber displacement operator, properties of quasi-classical states
Quantum interferometry
6. Quantum description of the beam splitter and simple notions of quantum interferometry
7. Squeezed states: definition and properties, the homodyne detection technique
Atoms and photons
8. The Jaynes-Cummings model for the interaction of a two-level atom with a quantized field: analysis of the uncoupled Hamiltonian, dressed states of the full Hamiltonian
9. Rabi oscillations induced by n photons, collapse and revival of Rabi oscillations induced by a coherent field
10. Single photon sources: single photon purity, indistinguishability, brightness; qualitative discussion of different types of single-photon sources
Quantum information
11. Single-qubit states and transformations, observables in the qubit space, no-cloning theorem
12. Quantum cryptography: elements of classical cryptography, the BB84 protocol for quantum key distribution
13. Entanglement and Bell states, Bell inequalities, the quantum teleportation protocol
14. Fundamentals of quantum computing: two qubit gates, quantum function evaluation, examples of quantum algorithms (Deutsch, Grover,...)

Prova scritta obbligatoria, senza prove in itinere
Prova orale condizionata (a scelta del docente)
The exam is in written form, and typically consists of 3 open questions, each on a different topic. An optional oral exam, requested by the student or by the teacher, may complete the evaluation.
The aim of the exam is to ascertain:

• the understanding of the physical basis of quantum optics and information (DD1);
• the knowledge of the definitions, theorems and general concepts related to quantum optics and quantum information (DD1);
• the capability to present and discuss in writings, both qualitatively and quantitatively, the quantum physical models and protocols relevant for the course, with clear and rigorous argumentations (DD2, DD4).

Chirstopher Gerry and Peter Knight, Introductory quantum optics, Editore: Cambridge University Press, Anno edizione: 2005, ISBN: 978-0-521-52735-4
Serge Haroche, Jean-Michel Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, Editore: Oxford University Press, Anno edizione: 2006, ISBN: 9780198509141
Giuliano Benenti, Giulio Casati, Davide Rossini, Giuliano Strini, Principles of Quantum Computation and Information, Editore: World Scientific, Anno edizione: 2019, ISBN: 9789813279995
Mark Fox, Quantum optics: an introduction, Editore: Oxford University Press, Anno edizione: 2006, ISBN: 978-0-19-856673-1

Reaction-Diffusion Equations (RDEs) are a common modeling tool that can be found in physics, biology and sociology. They constitute a natural framework to describe the evolution of one or many densities (of mass, population, information...) that grow, interact, and move randomly, at the microscopic level, in an environment. The scope of application of RDEs includes chemical reactions, combustion theory, population dynamics, epidemiology, diffusion of gossip and fake news. The aim of the course is two-fold: firstly, to provide a solid mathematical background on the classical initial-boundary value problems for single density models; secondly, to face different variations and improvements of such model, providing an introduction to several contemporary research topics in this field.

At the end of the course the student is expected to:
1. know the basic theory of stationary and evolutive RDEs: well posedness of the initial value problem, both in bounded domains with different types of boundary conditions and in the whole space (global Cauchy problem); both elliptic and parabolic maximum and comparison principles; existence and qualitative properties of stationary solutions, linear stability analysis; travelling fronts, speed of propagation;
2. be familiar with improved reaction-diffusion models, such as reaction-interaction-diffusion systems or equations involving anomalous diffusion;
3. be able to read contemporary research papers/books on the topic, and to discuss, with property of language, the strengths and weaknesses of a reaction-diffusion model, as well as the implications of the mathematical analysis on the described phenomenon.

0. Introduction: examples, models and motivations. Pure reaction ODEs systems.
1. Mathematical analysis of the standard model for a single density in a bounded domain.
1.1. Initial value problem (semilinear parabolic equations): well-posedness with Dirichlet, Neumann or Robin boundary conditions; maximum and comparison principles.
1.2. Stationary solutions (semilinear elliptic equations): existence, multiplicity, qualitative behavior; stability issues, principal eigenvalues.
1.3. Long-time behavior: convergence to equilibria, survival vs extinction.
2. Complements and generalizations, particular models, contemporary research topics (some of these arguments may just be object of the students' seminars).
2.1. Reaction-diffusion in unbounded domains: global Cauchy problem, eternal solutions, traveling waves, speed of propagation, invasion.
2.2. Anomalous diffusion: random walks with long jumps/long rests; fractional laplacian, non-local (integro-differential) operators; memory effects, fractional derivative in time.
2.3. Critical points theory and omega-limits of RDEs: direct method of the calculus of variations, stability of local minimizers; minimization on the Nehari manifold.
2.4. Qualitative and symmetry properties of solutions: moving plane method and applications; rearrangments, Faber-Krahn inequality.
2.5. Cooperative/competitive systems: strong competition and segregation, pattern formation, territoriality.
2.6. Optimization and shape optimization problems: optimal design of a habitat; best dispersal strategy.
2.7. Reaction-diffusion in non-conventional domains: equations on graphs or stratified structures.

Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i condizionato (a scelta del docente), individuale, con revisioni periodiche, con presentazione/discussione finale
The final exam consists: a) either in the presentation of a research article/book chapter (related to the course but not treated during the lessons), to be held during the last lessons (the choice of the research paper/book chapter must be agreed upon well in advance; to choose this modality, the student has to be up to date with the content of the course); b) or in an oral test about basic concepts of the program, with a closer look on an advanced subject chosen from the second part of the program.
The oral examination consists in answering theoretical questions and solving exercises on the topics treated during the semester, in order to assess the knowledge of theorems and the ability to exploit the mathematical tools presented in the frontal lessons. Referring to the Dublin Descriptors, the exam is aimed at evaluating acquired skills, understanding of mathematical tools and the ability to apply knowledge (DD1, DD2, DD3, DD4).

R.S. Cantrell, C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Editore: John Wiley & Sons, Ltd
S. Salsa, G. Verzini, PDEs in Action. From Modelling to Theory, Editore: Springer, Anno edizione: 2022, ISBN: 978-3-031-21852-1
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Editore: Springer
N. Abatangelo, E. Valdinoci, "Getting acquainted with the fractional laplacian" https://arxiv.org/pdf/1710.11567.pdf

The aim of the course is to teach the fundamental facts that lead to a radical rethinking of the common concepts of space and time and to the formulation of the theory of relativity. The approach adopted is Lagrangian and a particular emphasis is placed on the role of symmetry. The implications of the theory of relativity on mechanics, electromagnetism and quantum mechanics will be discussed. Finally, we will talk about the equivalence principle and the fundamental aspects of the general theory of relativity.

• Knowledge and understanding (DD1) The students will learn the fundamental properties of the underlying scenario on which physical phenomena take place: the spacetime. Due to the universal character of these laws the students will be also exposed to their usage also in different fields of physics such as mechanism, electromagnetism, quantum mechanics.
• Apply knowledge and understanding (DD2) The students will acquire the correct perspective concerning the experimental techniques and the theoretical methods nowaday employed in the field of relativity. The students will also be made aware of the possible applications of the argumests of the course and their consequences on the human life.
• Making Judgements (DD3) The students will develop a correct perception of the orders of magnituds of the physical quantities involved in the processes taking place in relativistic phenomena. The students will be stimulated to learn how to implement a true research project starting from the basic physical ideas and by making the proper strategic choices, with a particular emphasiys on aspects such as the feasibility of the project as far as the human and economical resources available are concerned.
• Lifelong learning skills (DD5) Students will acquire the capability to focus on the relevant aspects of a particular phenomenon and forecast the steps necessary, both on the experimental and on the theoretical ground, for understanding and exploiting it. All this in the perspective of a team work where eve though the activity is splitted between the team components, each of them will maintain an integrated vision of its specific duty.

Galilean relativity
The constancy of the speed of light and the einsteinian principle of relativity
The crisis of the concepts of space and time: time dilation and lenght contraction
Events, lines of universe, intervals and Minkowski diagrams
Light cone, poper time
Lorentz transformations
Velocity transformations
Four-vectors, four-tensors, tensor analysis, metric tensor
Four-velocity, four-acceleration, four-impulse
Mechanics: lagrangian approach and role of simmetry
Relativistic lagrangian
Energy, momentum and equivalence of mass and energy
Relativistic scattering
Maxwell equations: deduction from special relativity
Lagrangian of the electromagnetic field
Covariant form of the Maxwell equations
Brief introduction to quantum relativity: the Klein - Gordon and Dirac equations
General relativity

Prova scritta obbligatoria, senza prove in itinere
The final exam will be in written form and will consist in a series of questions on a series of specific topics covered during the course. Each question will not simply involve the exposition of a specific topic but will be conceived in order to be multidisciplinary and aimed to verify, aside from the knowledge acquired by the student on individual arguments, also its comprehension of the discipline as a whole and its capacity to cross correlated the various arguments covered by the course.

E. Puppin, Relativity and its implications, Anno edizione: 2023
Note: Text available in italian, english and chinese.
V. Barone, Relatività, Editore: Boringhieri, Anno edizione: 2011, ISBN: 978-88-339-5757-9
Lev Landau - Eugeni Lifshitz, Course on Theoretical Physics - Vol II: The Classical Theory of Fields, Anno edizione: 1980, ISBN: 0750627689

Modern complex industrial systems require a systematic approach to design and operation, with specified safety and reliability constraints/objectives (safety-based and reliability-based design and operation).
The goal of this course is to provide the students with the adequate competences on methods and computational tools for the evaluation, the analysis and the control of the risk associated to the operation of industrial equipment and systems. These competences, typical of safety and reliability analysts and managers, are necessary in all modern engineering for the design and operation of safe and reliable systems.

PART A
The student knows:

• ELO A.1 - the basics of probability theory, system analysis and simulation methods for reliability and availability assessments;
• ELO A.2 - the basics of maintenance engineering.
  The student is able to:
• ELO A.3 - estimate reliability and availability indicators of industrial equipment and systems;
• ELO A.4 - develop stochastic simulation methods for estimating system reliability and availability indicators;
• ELO A.5 - apply methods of maintenance engineering to industrial equipment and systems.
  PART B
  ELO B.1 - the student understands the concept of risk and the probabilistic framework for its assessment;
  ELO B.2 - the student is able to apply the methods and tools for the probabilistic risk assessment of industrial equipment and systems;
  ELO B.3 - The student knows the methodological tools to treat the uncertainty in the reliability and risk assessments and can make judgments on the confidence in the results obtained, for robust decision-making.

PART A
Basics of probability theoryfor applications to reliability analysis and risk assessment (ELO A.1);
Estimationof reliability parameters from field data(ELO A.3);
Reliability of simple systems:series, parallel, redundancies, standby (ELO A.3);
Reliability and availability of complex systemssubject to realistic procedures of inspection, maintenance, repair, renewal (ELO A.3);
Monte Carlo simulation methods for reliability and availability analysis:stochastic simulation framework; random sampling; definite integrals estimation; variance reduction techniques to increase simulation efficiency,estimation of reliability and availability of complex systems (ELO A.4);
Maintenance engineering (ELOs A.2 and A.5).
PART II
Risk:qualitative and quantitative definitions (ELO B.1);
Probabilistic risk assessment framework:identification and quantification of accident sequences (Failure Mode and Criticality Analysis, Hazard Operability Analysis, Fault and Event Tree Analyses, and Bayesian Belief Networks); risk curves and matrices; risk analysis as a tool in support of regulatory licensing and operating requirements (ELOs B.2 and B.3);
Dependent failures (ELO B.2);
Importance measures (ELOs B.2 and B.3);
Uncertainty and Sensitivity Analysis (ELOs B.2 and B.3)
Seminars on advanced topics (e.g. digitalization in Industry 4.0, integrated deterministic and probabilistic safety assessment, Prognostics and Health Management);
Case studies taken from real industrial systems and plants will be illustrated, and quantitative exercise classes will be carried out in support to the comprehension of the material covered in class.

Prova scritta obbligatoria, senza prove in itinere
Modalità di valutazione
The evaluation consists in a written exam consisting of numerical exercises theory questions.
The numerical exercises will evaluate the student abilities in applying the techniques for quantifying the reliability and availability and control the risk of industrial equipment and systems (ELOs A.3 and B.2).
The theory questions aimsat verifying the student understanding of the risk concept, the probabilistic framework for its assessment, the basics of probability theory and stochastic methods for reliability, availability and risk analysis, dependent failures, importance measures, the maintenance engineering approaches (ELOs -A.5 and B.1, B.2). Furthermore, it verifies the student ability of making judgments on the confidence in the results obtained, for robust decision-making (ELO B.3).

The final goal of the course is to provide methods to control uncertain linear dynamical systems.
Three main steps are needed to lead the students to such a goal.
First, techniques are provided for the shaping and quantification of the uncertainties, in terms of suitable definition of system norms.
Second, the problem of robust stability at the face of uncertainties are tackled via a Lyapunov function approach.
Finally the problem of feedback control of uncertain systems is deal with through parametrization and model matching synthesis.
Some classical, as well as modern techniques, will be covered so that the student will acquire the methodological skills to tackle a wide corpus of robust analysis and robust control problems for uncertain systems.
The theoretical and exercise lessons are complemented with laboratory sessions using Matlab/Simulink to test some topics of the course.
DD1 – Knowledge and Understanding
Students will acquire advanced knowledge of modelling uncertainties in linear dynamical systems, robustness measures based on system norms, Lyapunov-based methods for robust stability analysis, and methodologies for robust controller synthesis. They will understand both classical and modern approaches to robust analysis and control design, together with their theoretical foundations and applicability conditions.
DD2 – Applying Knowledge and Understanding
Students will be able to model uncertain dynamical systems, quantify uncertainty using appropriate mathematical tools, assess robust stability properties, and design feedback controllers that guarantee prescribed performance in the presence of uncertainty. They will be able to apply robust control techniques to engineering problems and validate the obtained solutions through numerical simulations and software tools such as Matlab/Simulink.
DD3 – Making Judgements
Students will be able to critically evaluate modelling assumptions, uncertainty descriptions, and alternative robust-control design methodologies. They will develop the ability to select appropriate analysis and synthesis techniques based on system characteristics, performance requirements, computational complexity, and robustness specifications.

Lectures, exercise, and lab sessions will allow students to:
Compute the norms of a dynamical system
Check robust stability
Define a robust control problem in terms of modelization of uncertainties
Solve a robust control problem via parametrization and model matching
Learn specific Matlab toolboxes (control & optimization) to work out suitable algorithms based on Linear Matrix Inequalities for the points above.

The course is structured in two parts, the first one dealing with analysis and the second one with design.
Part 1: Robust performance analysis of uncertain systems

• Norm bounded uncertainties and system norms (H2-Hinf)
• Polytopic uncertainties and switching
• Checking robust stability via linear matrix inequalities (LMIs)
• Passivity
• Application examples
  Part 2: Robust performance design of uncertain systems
• Robust H2 control and filtering
• Robust Hinf control and filtering
• Switching control (sketch)
• Robustness in digital implementation (sketch)
• Application examples

Prova scritta condizionata (a scelta del docente), senza prove in itinere
Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i condizionato (a scelta del docente), di gruppo, senza revisioni periodiche, senza presentazione/discussione finale
Valutazione continua condizionata (a scelta del docente)
The course comprises lectures and specific sessions devoted to illustrative examples and the use of computational tools.
The final assessment consists of a written or oral examination covering the theoretical contents of the course.
The assessment is aimed at verifying:
DD1 (Knowledge and Understanding): understanding of uncertainty modelling techniques, robust stability analysis methods, and robust controller synthesis approaches for linear dynamical systems;
DD2 (Applying Knowledge and Understanding): ability to formulate and solve analysis and control-design problems for linear systems affected by polytopic and norm-bounded uncertainties using the methodologies introduced in the course;
DD3 (Making Judgements): ability to evaluate modelling assumptions, select appropriate robust-control methodologies, and assess the robustness properties of the proposed solutions.
Students are expected to demonstrate the ability to use the acquired theoretical tools to analyse and design control systems for uncertain linear dynamical systems.

Patrizio Colaneri, Jose' C. Geromel, Arturo Locatelli, Control Theory and Design: an Rh2 and RHinf viewpoint, Editore: Academic Press, Anno edizione: 1997
Note: Only for a few chapters
Okko H. Bosgra, Huibert Kwakernaak, Gjerrit Meinsma, Design Methods for Control Systems
Paolo Bolzern, Patrizio Colaneri, Arturo Locatelli, Controllo e filtraggio in H2-Hinf, Editore: Polipress
Patrizio Colaneri, Notes on Robust Control
Note: In preparation

The course aims to:
strengthen modeling and mathematical-numerical skills to face inter-disciplinary challenges by exploiting a learn-by-doing training model;
consolidate the critical sense of identification of an appropriate modeling approach according to the problem under examination;
to foster teamwork skills and strengthen communication skills;
strengthen the ability to develop simulation scenarios using appropriate software. In this regard, for each assigned problem, a range of possibilities will be offered (Python, Matlab, Octave, C++, and, where possible, specific options in light of the development frameworks most used in the reference industrial world).
Problems will focus on engineering applications from different interdisciplinary fields.

After passing the exam, the student should be able to:
DD1 - Knowledge and understanding:
l earn and understand how to approach real-world engineering problems by applying data analysis and mathematical modeling;
l earn and understand how to exploit available software to build goal-oriented numerical schemes for solving engineering problems;
DD2 - Applying knowledge and understanding:
select an appropriate modeling approach and provide a rigorous m athematical formulat ion of a given problem;
d esign and implement numerical schemes for the approximation of the problem solution;
a nalyze, synthesize and visualize the numerical results;
DD3 - Making judgment:
identify the appropriate modeling approach for a given problem;
select an appropriate implementation strategy and software tool for the numerical approximation of the mathematical model;
assess and compare the performance of different models and methods;
i nterpret and critically analyze the numerical results;
DD4 - Communication skills:
describe an engineering problem, its mathematical form ulation, and its numerical approximatio n;
explain and motivate the modeling and methodological choices;
summarize and present the numerical results;
DD5 - Lifelong learning skills:
approach a generic engineering problem and implement a practical solution based on suitable numerical schemes.

The course aims at provid ing a systematic approach to solving real-world engineering problems. Students will address the problems assigned during the semester by working in small groups and under the lecturer’s supervision. This collaborative learning supports the strengthening of decision-making, critical thinking, and problem-solving skills.
T he assigned problems will guide the students in deepen ing and strengthen ing the following skills/methodologies:
mathematical formalization of a problem and identification of the appropriate modeling approach;
data analysis: preprocessing techniques, data fitting, noise models, machine learning, and dimensionality reduction techniques;
mathematical modeling and numerical approximation: ordinary and partial differential equations and numerical discretization techniques;
data-model integration: optimization techniques, neural networks, sampling methods, and data-assimilation techniques;
implementation of the proposed solution strategies using open-source P ython or C++ libraries, Matlab/Octave tools, or commonly used options in the industrial world;
visualization, interpretation, and communication of the numerical results.
The final evaluation of the student will result from an oral discussion of the assigned problems. The student will present the identifi ed and implemented approximation strategies and the numerical results. In addition, the final grade will comprise the assessment of the solutions' performance based on the checkpoints established by the lecturer. In the 5 CFUs version of the course, students will focus on a proportional subset of the projects.

Prova orale obbligatoria
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
Valutazione continua obbligatoria
The course assessment focuses on the solutions provided by the student to the proposed real-world engineering problems. During the semester, the student will develop and implement approximation strategies for their solution by working in small groups. Checkpoints will monitor the progress of the student, contributing to the final evaluation.
The student will discuss the assigned problems, the design and implementation of numerical strategies, and the numerical results during an oral exam, which will assess:
the mathematical form ulation of the problems and the identification of appropriate modeling approaches (DD1, DD2 and DD3);
the capability in choosing and adapting suitable numerical methods and relative programming tools (DD1, DD2 and DD3);
the performance of the numerical strategies (DD3);
the ability to explain and motivate the modeling and methodological choices (DD4);
the quality and the originality of the adopted solution strategies (DD5).
Both checkpoints’ assessment and oral exam contribute to the final grade.

Course material at disposal on the webeep website of Politecnico di Milano https://webeep.polimi.it/login/index.php
Brunton, S. L. and Kutz, J. N., Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.), Editore: Cambridge: Cambridge University Press, Anno edizione: 2022, ISBN: 9781009089517
Quarteroni, A., Numerical Models for Differential Problems, 3rd Edition, Editore: Springer, Series: MS&A, Vol 16, Anno edizione: 2017, ISBN: 978-88-470-5522-3

The course aims to introduce and explain important physical processes at the heart of the optical properties of semiconductor devices, such as light emitting diodes (LEDs) and semiconductor lasers.

• Knowledge and understanding – DD1
  Students will learn and understand the physical processes at the heart of photonics devices and the technological characteristics of semiconductor lasers.
• Applying knowledge and understanding – DD2
  Students will be able to transfer the physical concepts to applications requiring the generation and detection of optical radiation
• Making judgements – DD3
  Students will gain the capability of modeling photonics devices and their behaviour in engineering systems.
• Learning skills – DD5
  Students will develop the expertise to design photonics based applications and systems exploiting the knowledge acquired in the course.

1. Electrons in semiconductors
Bloch’s theorem, crystal momentum, effective mass.
Band structure of selected semiconductors.
Density of states in 3D, 2D, 1D and 0D semiconductors.
Carrier statistics: Fermi-Dirac distribution function.
Intrinsic semiconductors.
Mass-action law.
Doped semiconductors.
2. Basic concepts of quantum mechanics
Harmonic perturbation.
Transition probability. Fermi’s golden rule.
Density matrix formalism.
Charged particles in an electromagnetic field: interaction Hamiltonian.
3. Optical properties of semiconductors
Bulk semiconductors and Quantum Wells.
Transition selection rules.
Joint density of states.
Absorption and gain coefficient.
Intersubband absorption in quantum wells.
Strained quantum wells.
Spontaneous emission.
Radiative recombination dynamics: low and strong injection regimes.
Excitons in semiconductors.
4. Light Emitting Diodes (LED)
Internal quantum efficiency and photon flux.
Double heterostructure LEDs.
Carrier overflow and carrier leakage over barrier.
External quantum efficiency.
Blue LEDs.
5. Semiconductor Lasers
Quantum well lasers.
Distributed Feedback (DFB) lasers: coupled mode equations and threshold conditions.
Distributed Bragg Reflector (DBR) Lasers.
Quantum dot (QD) lasers: introduction and growing techniques of QDs.
General scheme of QD lasers.
Optical transitions in QDs.
Absorption and gain in QDs.
Quantum Cascade Lasers.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
The final assessment will be based on a written exam typically consisting of two questions. Generally, one question covers the theory taught in the course, while the second is a numerical exercise to evaluate the ability to solve practical, yet simplified, problems. Texts of previous examinations are available on the course website. An oral exam can be requested by either the students or the teacher to complete the evaluation process. This option is available exclusively to students who have achieved a grade of 18/30 or higher on the written exam.

Mauro Nisoli, Semiconductor Photonics: Principles and Applications, Editore: Societa' Editrice Esculapio, Anno edizione: 2016, ISBN: 9788893850025

As modern technology moves ever further into the nanoscale, it becomes possible to realistically consider the development of quantum computing based on solid state technology. The course on Semiconductor Qubits will develop tools to understand charge transport in high mobility two-dimensional (2D) systems, such as semiconductor quantum wells and sheets of 2D materials, based on the behaviour of electrons in solids in electric and magnetic fields. By electrostatically confining the electrons into quantum dots, their quantum states can be manipulated and measured. The study of the rich physics seen in these systems at low temperatures and high magnetic fields allows us to design qubits and carry out quantum computations, on the way to the near-future development of quantum technology.

• Knowledge and understanding
  The students will learn about the main physical phenomena relevant to low-dimensional semiconductor structures and devices.
  The students will study the electronic properties of semiconductor materials, with particular emphasis on silicon, germanium, and the SiGe alloy system.
  The students will learn the formalism of single and multiple qubit state representation and manipulations.
• Apply knowledge and understanding
  The students will learn how to recognise relevant physical phenomena in terms of their manifestation in experimental results.
  The students will understand how to extract important parameters and figures of merit from experimental transport data.
  The students will understand how the physical realization of qubits in semiconductors relies on their electronic properties.
• Making judgements
  The students will understand how to design experiments which can measure relevant parameters and figures of merit.
  The students will understand the merits and drawbacks of different physical qubit systems.
  The students will understand how to design quantum circuits to carry out simple operations and algorithms.
• Lifelong learning skills
  The students will further develop some of the concepts introduced in the first part of the integrated course.
  The students will be prepared to begin a masters' thesis project in a research laboratory working on semiconductors and/or semiconductor-based qubits.
  The students will be introduced to the extremely relevant current topic of quantum computing.

Quantum transport:
2-dimensional carrier gases: high-mobility 2DCG in a semiconductor quantum well.
Linear transport theory and Boltzmann equation: scattering mechanisms and screening, quantum and transport relaxation lifetimes, electrical conductivity and Hall effect.
M agnetic fields at low temperature: Landau levels, Shubnikov-de Haas oscillations, and the quantum Hall effect. Weak localization and spin-orbit coupling.
Split gate quantum dots:
Electrostatically confined quantum dots: definition, quasi-bound energy levels.
Quantized conductance: Coloumb blockade, tunneling.
Coupled quantum dots: charge sensing, spin-to-charge conversion.
Qubits in a semiconductor quantum well: physical realization, properties.
Q ubits:
Qubit formalism: quantum mechanics of qubit states, single qubit operations.
Multiple qubit states: separable states, entanglement.
Physical qubits: qubits in different physical systems, qubit operations, entanglement.
Quantum computing:
Quantum circuits: programming a quantum computer.
Algorithms: Bernstein-Vazirani for interrogating a hidden function, quantum Fourier transform, Shor’s factoring algorithm, Grover’s search algorithm, Quantum phase estimation.

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
The student will be evaluated by written and oral examinations according to the calendar of the course.
The student will be expected to discuss the physical phenomena which give rise to certain results or experimental effects, and what information regarding the characterization of the sample or device under test can be extracted from the experimental results. Emphasis is placed on the comprehension of real experimental data rather than calculation of simplified systems or reproduction of text-book derivations.
Students will be expected to understand and discuss the physical implementation of qubits and quantum gate operations.
Students will be expected to understand and design simple quantum circuits, discuss the advantages and disadvantages of quantum computation, and discuss the operation of the more well-known algorithms.

J. H. Davies, The Physics of Low-Dimensional Semiconductors, Editore: Cambridge University Press, Anno edizione: 1998
Thomas Ihn, Semiconductor Nanostructures: Quantum States and Electronic Transport, Editore: Oxford University Press, Anno edizione: 2010
Neil W. Ashcroft and N. David Mermin, Solid State Physics, Editore: Thomson Learning

Statistical signal processing provides the foundation for the informed development and critical use of many AI systems. Time series analysis is needed in several interdisciplinary areas of engineering such as audio/video, digital communications, finance, mechanical vibration analysis, imaging and remote sensing, GPS navigation systems, machine learning aiged problem solving, just to mention some.
The teaching activity aims to balance the fundamentals of discrete-time signals and the estimation theory with a set of engineering use-cases. Goal is to strength the capability of student to have a pragmatic, but still rigorous, way to solve stochastic signal related problems. More specifically, students will learn to approach an engineering problem that involves stochastic signals, formalize it into a mathematical model where all the unknowns are stochastic and/or deterministic variables, and find the most appropriate solving method always validated by the knowledge of the statistical bounds in idealistic connditions. The theory on statistical signal processing (60hours) are interleaved with numerical exercising (30hours) on simple settings to consolidate the concepts.
Labs and practical problems are first discussed in class providing real data, then after few days students can prepare for solving the assigned tasks by using Matlab in collaborative Labs where students are randomly grouped in 3-4 to compare and improve their problem-solving capability under the supervision of a tutor. The grouping within the same class enables students to experience intra/inter-group dynamics with other unknown and randomly chosen students, this small-scale simulation of their professional life aims to better refine their mutual professional relationships.
Part of the laboratory activity is in cooperation with industry-teams dedicated to one topic, to be defined during the semester (past was Google data analytics team)

Lectures and exercise sessions will allow the student to (DdD1):
Consolidate the theoretical tools to handle with finite-length single/multiple signals
Have solid knowledge of the estimation theory for statistical signal processing
Know what method to choose depending on statistical properties of stochastic part.
Handle with adaptive time-varying systems and design Bayesian parameters tracking
Introduction to spectral analysis
2D signals and properties
Handle multiple signals from arrays, and extract the relevant parameters
Extract a pattern from data in supervised/unsupervised forms
Design the Matlab flowchart for some essential kernels such as estimation of frequency and delays, extraction signals from noise by filtering and by convolution/deconvolution matrixes.
The project laboratory part of innovative-teaching will allow the student to (DdD2):
Analyze the requirements and write the algorithm flow
Write Matlab-code that solves the required problem
Evaluate multiple solutions for the same problem and develop a criticism.
Write a short document structured as a technical report
Work in team with other students on the same working-group and learn to interact each-other
Overall the teaching will give the student at the end of the course and after passing the exam the capability to design estimators and processing methods for limited-length data, to evaluate the reliability and accuracy of the algorithms, and tools for manipulating and classifying multiple-dimensions discrete signals. At the end of the course and after passing the exam, the student will be able to solve problems involving stochastic stationary or time-varying signals, and to evaluate the cost/benefit tradeoff with a deep knowledge of the corresponding statistical bounds. The laboratory activity in the classification and prediction is in cooperation with Google within the framework Google adopts ADSP course
Outcomes of the students:
Knowledge and understanding: students will learn how to manipulate signals using algebraic tools; apply the estimation theory and bounds to signals related problems; manipulate multidimensional signals for estimation and decision.
Applying knowledge and undestanding: students will be able to define a statistical model for signals' related problems and their solution with fundamental estimation theory methods; solve a broad range of statistical signals' related engineering problems.
Making judgements: students will be able to evaluate the fundamental limits on statistical signal processing applications even in presence of uncomplete/inaccurate conditions; tailor and adapt the statistical methods to complex problems.
Communication: student will learn how to describe a method and sinthetize the limits and results; write a technical report.

The course focuses on statistical signal processing and covers the following topics:
Review of basics: matrix and linear algebra; quadratic and constrained optimization problems.
Introduction to the estimation problem and models: definitions, performance, sufficient statistics, linear and non-linear models.
Estimators: best linear unbiased estimation (BLUE), maximum likelihood estimation (MLE), least squares method. Cramer Rao lower bound.
Bayesian estimators: a-posteriori estimation (MAP, MMSE and LMMSE); Wiener filter; linear prediction and Yule-Walker equations.
Adaptive filters: LMS, RLS methods, convergence analysis and step-size selection.
Bayesian tracking: dynamic model and Kalman filter; examples of positioning.
2D signals properties and physical filters
Array processing and beamforming methods.
Pattern and sequence recognition: Bayesian classification of signals in noise, linear discriminant and support vectors, clustering methods, supervised classification, deep learning methods and updates.
Montecarlo simulation and numerical analysis on some use cases.
Labs and practical problems are assigned during the semester and solutions are discussed within the workshops dedicated to these problems.

Prova scritta obbligatoria, con prove in itinere
Prova orale condizionata (a scelta del docente)
Progetto/i - Elaborato/i obbligatorio, di gruppo, con revisioni periodiche, con presentazione/discussione finale
The exam is in written form with at least one small project complete of the reporting activity and, optionally, the oral exam. More specifically, the written exam lasts 2.5h and it covers the entire theory part of the program with exercises to spot the degree of understanding of the concepts. Exercises are more than necessary to pass the exam, the sum of total marks allotted for all the exercises in written exam usually ranges in 42-45, so each student can choose what exercises to do and how much in depth according to her/his skill. Each exercise is in increasing-difficulty, and marks are ranked accordingly. Marks of the entire written exam saturate to 24. During written students can use the course textbook and for computations, students can use computers only with Matlab.
In parallel, the students have to develop at least one of the 3 projects (called Homeworks, or Hw, within the teaching jargon as they can be freely carried out at home): Hw#1, Hw#2, Hw#3. During the teaching semester, the Hws’ text and data are released to the students so that they can start solving Hws at home while studying theory and exercising. Solving the Hw during the teaching semester is recommended as let the students take benefit of the Project Laboratory as Hws have similar structure except should be completed independently on their own. Hws are of incremental complexity, with increasing marks 1,2,3, so that max Hw marks is 1+2+3=6. Hw#1 is mandatory and there is no restrictions on when to solve the Hws, but students can deliver the Hw-reports only after passing the written exam >17.
For students that wish to have to oral exam, the written exam should be passed with unsaturated mark >27, with at least Hw#1. Oral exam is a discussion that aims to evaluate the maturity and the knowledge of the topics when solving some use cases; during oral the student can use the textbook and notes. Notice that 30Lode is only by Oral exam.
There is an intermediate written exam, typically the end of October, covering half of the program. The second half can be completed in any written exam dates till the end of the winter session of exams. The written exam can be repeated anytime without penalty.

U.Spagnolini, Statistical Signal Processing in Engineering, Anno edizione: 2017, ISBN: 978-1-119-29397-2
Note: Note:
Notes/slides on the book can be downloaded from the folder of the course shared with students during the semester

The course aims at providing basics and advanced techniques for data mining and statistical learning in healthcare context. In particular, the course will provide tools in order to perform data analysis. A particular attention will be given to the main characteristics of health data, for example, granularity, missing values, multiclass and multilevel classification, high-dimensional problem (the number of features much larger than observations), etc… The students will work in teams under the supervision of the lecturers and will be asked to work on a project to answer specific questions on a assigned dataset.
This is a course with a limited number of available places. Application are regulated by the procedure defined by Biomedical and Mathematical engineering master programme (for Biomedical engineering see https://www.ccsbio.polimi.it/corso/laurea-magistrale; for Mathematical engineering the procedure is managed by the secretariat)

At the end of the course, the students will be able:
[Knowledge and understanding]

• to understand the basics tool of health data pre-processing (e.g. dealing with outliers and missing values)
• to understand the basic tools for data mining and multivariate analysis
  [Applying knowledge and understanding]
• to design and implement data mining algorithms and tools
• to make choices in order to adapt algorithms to the different characteristics of the dataset
• to implement algorithms and tools with commonly used software for statistical analysis (e.g R, Python)
  [Making judgements]
• to evaluate the suitability of the algorithms in relation to the specificity of the dataset.
• to select the best options and decide the best strategy
• to compare and evaluate the performances of different algorithms
  [Communication]
• to describe the algorithms and tools used during the course
• to defend the project choice in front of an audience and the lecturer.
  [Lifelong learning skills]
• to understand the necessary competencies required to solve data mining problems

• Introduction to software tools for data mining and statistical learning (e.g. R, Python)
• Pre-processing and data cleaning: collinearity, dimensionality reduction (the filter strategy, the wrapper strategy, the embedded strategy), missing values, outliers.
• Supervised approaches: binary and multiclass classification, generalized linear models for classification (e.g. logistic regression and shrinkage methods, linear discriminant analysis, partial least square discriminant analysis), model assessment and selection (cross validation, bootstrap methods)
• Unsupervised approaches: cluster analysis (e.g. k-means clustering), principal component analysis
• Example of applications in real data set will be illustrated. Practical implementation of the algorithms will support a learning by doing approach.

Progetto/i - Elaborato/i obbligatorio, di gruppo, senza revisioni periodiche, con presentazione/discussione finale
During the course, students will work in small teams under the supervision of the lecturer. The teams will work on a project to answer specific questions on assigned dataset.
The students will produce a report with the description of the analyses performed (pre-processing, data cleaning and algorithms with the adopted options) and will discuss the results with the lecturer as an oral examination.
Class participation, project quality, awareness of methods and their possible alternatives, ability in motivating the project choices and in illustrating the results, will contribute to the final grade.

https://beep.metid.polimi.it/
Note: Il portale delle attività didattiche del Politecnico di Milano
Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics), Editore: 9781461471370 https://www.statlearning.com
Trevor Hastie, Robert Tibshirani, Jerome Friedman, "The Elements of Statistical Learning" (2nd edition), Editore: Springer-Verlag, ISBN: 9780387848570 https://web.stanford.edu/~hastie/ElemStatLearn/
Wes Mckinney, Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython, Editore: Oreilly & Associates Inc, ISBN: 9781491957660
Jake VanderPlas, Python Data Science Handbook: Tools and Techniques for Developers: Essential Tools for working with Data, Editore: O'Reilly Media, ISBN: 9781491912058

This course provides an in-depth exploration of the theoretical and computational tools used to analyze and predict the macroscopic behavior of complex systems. Beginning with a concise review of equilibrium statistical mechanics and the fundamental properties of microcanonical and canonical ensembles, the course introduces key models, such as the Ising model and its disordered variants (e.g., spin glasses), to study phase transitions and mean-field theories.
The curriculum emphasizes universal aspects of phase transitions and critical phenomena, including scaling laws, critical exponents, and the Renormalization Group framework.
A significant component of the course involves a hands-on numerical laboratory, where students will design and conduct numerical experiments using Monte Carlo simulations, providing practical experience in simulating and analyzing complex systems.

[DD1: Knowledge and insight]
Lectures and exercise sessions will allow students to:

• understand Statistical Mechanics. Students will improve their understanding of the collective phenomena emerging in interacting systems, with particular focus on the behavior of random and disordered systems
• gain insight on phase transitions. Students will explore the phenomenon of phase transitions and understand how Statistical Mechanics is able to explain the discontinuous changes in physical response that occur when a system undergoes a transition between different phases. We will identify critical points, draw phase diagrams, and analyze the concepts of order parameters and symmetry breaking.
  [DD2: Applying knowledge and insight]
  The numerical laboratories will develop the students' ability to build and run numerical simulations (and in particular Monte-Carlo simulations) to test, analyze and describe the behavior of complex mechanical systems.
  [DD3: Judgement]
  During the numerical lab and in the final project, students will develop their critical thinking and problem-solving skills by applying statistical mechanics concepts to analyze and solve complex problems emerging in real-world systems.
  [DD4: Communication]
  Students will be prepared to review critically, communicate and discuss the results of the simulations during the final exam.
  [DD5: Learning skills]
  A number of selected topics related to the course will be presented to invite the students to study in autonomy.

Programme
Introduction and Recap
Fundamentals of Equilibrium Statistical Mechanics
Ensembles and time averages: Microcanonical, Canonical, and Grand Canonical ensembles
Non-convex Helmholtz free energy and its role in phase transitions
Magnetic Systems and Mean-Field Theory
The Ising Model: Microscopic description and macroscopic behavior
Phase transitions: Classification, order parameters, and critical temperature
Mean-Field Theory: Concepts and applications
Spin Glasses: Introduction and methods
The Replica Method and its implications
Critical Phenomena and Universality
Scaling laws and universal behavior in phase transitions
Ginzburg-Landau Theory of critical phenomena
Critical exponents: Definitions, significance, and computation
Gaussian approximation for critical exponent analysis
Renormalization Group Techniques
Fixed points, flow diagrams, and scale invariance
Numerical Laboratory
Basics of Pseudo-Random Number Generators
Monte Carlo Simulation Techniques:
Importance sampling and the Metropolis algorithm
Simulated annealing: Optimization and applications
Direct Simulation Monte Carlo: Methods and challenges
Practical exercises in simulating phase transitions and solving optimization problems

Prova scritta obbligatoria, senza prove in itinere
Prova orale facoltativa (a scelta dello studente)
Valutazione continua facoltativa (a scelta dello studente)
The assessment includes:

• a numerical lab test (splitted in two parts) in which the students will solve exercises related to the topics analyzed in the numerical labs; this part provides up to 12 points
• a written examination on the theoretical part of the course; this part provides up to 21 points
• an optional oral exam, either on the numerical lab or on the theoretical part of the exam, which modifies the grade obtained in that part.

K. Huang, Statistical Mechanics - 2nd Ed., Editore: Wiley, Anno edizione: 2008, ISBN: 978-8126518494
M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics, Editore: Clarendon Press, Anno edizione: 1999
Slides, and notes distributed by the Professor https://webeep.polimi.it/
Note: webeep platform of the course
S.K. Ma, Modern Theory of Critical Phenomena, Editore: Westview Press, Anno edizione: 2000
Wolfram Mathematical tutorial https://www.wolfram.com/broadcast/video.php?c=89&v=327&disp=list&p=1
Note: The software Wolfram Mathematica will be used during the course (licensed software provided by Politecnico di Milano).
No prior knowledge is assumed, but knowledge of matlab and/or programming languages (e.g., C) would help

The course provides the foundational concepts, methods, languages, and systems for ingesting, processing, and analyzing data that flows to enable real-time decisions. The course covers the topics of Streaming Data Engineering and Streaming Data Science.

Dublin Descriptors
Expected learning outcomes
Knowledge and understanding
Students will learn how to:
Identify problems that can be addressed with big data techniques tailored for velocity
apply the stream data analysis technologies for solving real-world problems
Applying knowledge and understanding
Given specific project cases, students will be able to:
Define and implement a streaming data analysis solution for the problem
Apply it on real data streams from smart IoT sensors
Making judgements
Given specific project cases, students will be able to:
Learn how to decide which streaming data analysis solution to apply and how to evaluate this decision
Communication
Students will learn to:
Write a report on a project describing and motivating the decisions taken and the results obtained
Present their work in front of their colleagues and teachers
Lifelong learning skills
Students will learn how to develop a realistic streaming data analysis project in all its phases

Streaming Data Engineering
This Streaming Data Engineering part of the course covers theoretical and practical aspects of Event-Based Systems (EBS), Data Stream Management Systems (DSMS), and Complex Event Processing (CEP). It uses the Event Processing Language (EPL) to illustrate typical DSMS and CEP operations. This segment equips students with essential skills for real-time data processing and analysis.
Event-Based Systems emphasizes efficient data collection and integration from various sources and redistribution of events to sinks, ensuring high throughput and fault tolerance. In particular, it presents Apache Kafka because it enables handling large-scale data streams, making it essential for robust data pipeline architectures.
Stream ingestion and Event-based Architectures
Apache Kafka as an essential building block of streaming data pipelines
hands-on producer-consumer APIs
Case study: ingesting data for a global retail
The Event Processing Language is a rich language that allows users to specify typical operations present in DSMS and CEP easily. It provides the ability to filter, aggregate, and transform data as it arrives. Moreover it allows identifying meaningful patterns and relationships in real-time data streams, enabling the detection of complex events from simple events.
Filtering, aggregating, and windowing data streams
Joining Data streams
Using the "every" clause and pattern guards to tame the torrent effect *
Hands-on with EPL on case studies in Retail, IoT, and Industry 4.0
Scaling stream processing with Apache Spark Structured Streaming focuses on the real-time processing and analysis of large datasets. Apache Spark's structured streaming capabilities provide scalability, fault tolerance, and high performance, enabling advanced analytics on streaming data.
Efficient DSMS operations
Hard to implement CEP operations
Hands-on practice with Spark Structured Streaming
Streaming Data Science
The Streaming Data Science part of the course covers the theoretical and practical aspects of time Series Analytics, Streaming Machine Learning, and Continuous Learning, equipping students with essential skills for real-time data analysis.
Time Series Analysis (TSA) focuses on developing models to analyze and forecast data points in chronological order. TSA approaches capture temporal dependencies and patterns, such as trends and seasonality, enabling accurate predictions and insights. TSA methods are also adept at handling non-stationarity in data.
⁠Stationarity and ⁠Decomposition
Time Series Forecasting baselines
⁠Temporal Dependence and SARIMAX forecasting models
⁠Advanced approaches to Time Series Forecasting
⁠Hands-on with the Statsmodels e Darts Python libraries
Streaming Machine Learning (SML) proposes models able to learn from data streams over-time. These models are incrementally updated as soon new data becomes available, avoiding retraining them from scratch, and adapting to many forms of non-stationarity (a.k.a. Concept Drift).
⁠Learning one sample at a time
⁠⁠Learning in the presence of Concept Drifts
⁠Streaming algorithms for classification and regression
⁠Hands-on with the River Python library
Continual Learning (CL) proposes strategies to address the problem of catastrophic forgetting when learning from a data stream using Deep Learning models. Forgetting happens when the model forgets what it learned before while learning a new concept after a drift. The goal is to achieve a balance between the ability to acquire new knowledge (plasticity) and the ability to remember past knowledge (stability).
CL Scenarios
Stability-plasticity dilemma
Evaluation metrics
⁠CL strategies
Hands-on with the Avalanche Python library

Prova scritta obbligatoria, senza prove in itinere
Progetto/i - Elaborato/i condizionato (a scelta del docente), individuale, senza revisioni periodiche, con presentazione/discussione finale
Valutazione continua facoltativa (a scelta dello studente)
The exam consists of a theoretical (written exam, with a possible oral discussion if necessary by the instructor) and an optional practical part (project work with oral presentation). Further contributions to the mark may come from optional continuous evaluations along the course using in-presence quizzes during the lessons and other interactive modalities in class (max two marks).
The written exam comprises a mix of theoretical questions regarding any course subjects and exercises regarding the technical content and how to apply it in practice. Students can get up to 30 in the written test. The whole exam is a closed-book evaluation. A minimum score on each part is requested.
The optional practical project requires using one or more of the technologies presented in the lectures. It solves a realistic streaming data analysis problem based on real or realistic datasets publicly available or provided by the teachers. Only students who get at least 27/30 in the written exam can opt for it. The maximum increment for the optional project is three marks.
The final grade is computed as follows: written text result + optional continuous evaluation result + optional practical project result. E.g., written text 27 + optional continuous evaluation 1 + optional practical project 3 = 30L
Type of assessment
Description
Dublin descriptor
Written test / continuous evaluation
Theoretical questions
Exercises focusing on streaming data analysis aspects
1,4
1, 2, 3
Assessment of project artefacts
Assessment of the design and implmenetation of the practical peoject work developed by the student
2, 3, 5
Oral presentation
Assessment of the presentation of the practical peoject developed by the student
2, 3, 4, 5

the event processing language (EPL) https://esper.espertech.com/release-9.0.0/reference-esper/html_single/
Kreps, Jay, I Love logs: Event data, stream processing, and data integration., Editore: O'Reilly Media, Inc., Anno edizione: 2014 https://books.google.it/books?id=gdiYBAAAQBAJ&lpg=PR3&ots=3yOdY3Vi7S&dq=I%20love%20logs&lr&pg=PR3#v=onepage&q=I%20love%20logs&f=false
Spark Structured Streaming https://spark.apache.org/docs/latest/structured-streaming-programming-guide.html
George E. P. Box, Gregory C. Reinsel, Gwilym M. Jenkins, Greta M. Ljung, Time Series Analysis: Forecasting and Control, 5th Edition, ISBN: 978-1-118-67502-1 https://www.wiley.com/en-us/Time+Series+Analysis%3A+Forecasting+and+Control%2C+5th+Edition-p-9781118675021
Geoff Holmes, Ricard Gavaldà, Albert Bifet, Bernhard Pfahringer, Machine Learning for Data Streams: With Practical Examples in MOA, Editore: MIT Press, Anno edizione: 2018 https://www.google.it/books/edition/Machine_Learning_for_Data_Streams/0C9ZDwAAQBAJ?hl=en&gbpv=1
Lesort, T., Lomonaco, V., Stoian, A., Maltoni, D., Filliat, D., Rodríguez, N.D., Continual learning for robotics: Definition, framework, learning strategies, opportunities and challenges https://www.sciencedirect.com/science/article/am/pii/S1566253519307377

Applicazioni di Simmetria nella Fisica Classica e Quantistica: L'obiettivo del corso è illustrare l'importanza della simmetria in diversi ambiti della fisica. In particolare, agli studenti verrà presentata la teoria dei gruppi e le sue applicazioni alla fisica quantistica. Impareranno a derivare proprietà generali attraverso considerazioni di simmetria.
Gli argomenti trattati sono: Introduzione. Simmetrie e leggi di conservazione. Elementi di teoria dei gruppi. Teoria delle rappresentazioni: concetti e risultati fondamentali, relazione con le proprietà fisiche di un sistema. Gruppi finiti e il loro ruolo nella fisica molecolare e dello stato solido. Gruppi continui: O(3) e momento angolare, SU(2) e spin.

Gli obiettivi principali sono quelli di impartire nozioni basilari sulla termodinamica e sulla trasmissione del calore per lo studio dei processi di conversione-trasferimento dell’energia e per la comprensione dei limiti fisici cui questi processi sono soggetti. In particolare, verrà sviluppata la comprensione del significato fisico di grandezze come energia, disponibilità adoabatica, energia disponibile, entropia, exergia, dei diversi tipi di processi e modalità di interazione fra sistemi, e dei meccanismi di scambio termico. Si faranno riferimenti all'impiantistica relativa alla produzione di energia elettrica, alla motoristica a propulsione endotermica, ai dispositivi di raffreddamento e riscaldamento in uso in campo tecnico.

Descrittori di Dublino
Expected learning outcomes
1. Conoscenza e comprensione
Sintetizzare ed interpretare i principi della Termodinamica nelle varie formulazioni, oltre a descrivere in dettaglio i nessi logici e matematici tra le grandezze che vi compaiono
Identificare con precisione le limitazioni cui sono soggetti tutti i processi reali e di comprendere le principali implicazioni ingegneristiche dei principi della Termodinamica
Descrivere sia qualitativamente sia in forma matematica il principio di funzionamento dei principali componenti delle macchine motrici e operatrici
Descrivere sia qualitativamente sia in forma matematica gli aspetti di base della Trasmissione del calore
2. Capacità di applicare conoscenza e comprensione
Applicare e risolvere bilanci di massa, energia ed entropia
Calcolare le proprietà delle sostanze pure e di miscele mediante modelli di diversa complessità
Esaminare impianti e processi termodinamici di media complessità
Risolvere semplici dimensionamenti di apparati per lo scambio termico
3. Autonomia di giudizio
Valutare la correttezza delle operazioni e dei calcoli svolti
Individuare le strutture dati e le procedure più adatte per risolvere gli specifici problemi proposti
Confrontare i benefici e gli svantaggi di diversi approcci modellistici
5. Capacità di apprendimento
Essere in grado di utilizzare le conoscenze e competenze apprese per affrontare in maniera metodologica problemi complessi di tipo ingegneristico e impiantistico

Modulo 1 Fondamenti di Termodinamica
Sistemi, stati e proprietà. Interazioni, pareti e processi; processi meccanici, spontanei, reversibili. Primo principio della termodinamica: energia; bilancio di energia. Tipi di stato. Secondo principio della termodinamica: disponibilità adiabatica, energia disponibile ed entropia. Principio di non decrescita dell'entropia; bilancio di entropia. Condizioni per l'equilibrio: temperatura, pressione, potenziale di massa. Diagramma Energia-Entropia. Processi quasi statici. Lavoro e calore nei processi quasi statici.
Modulo 2 Proprietà delle sostanze
Introduzione al calcolo delle proprietà delle sostanze. Gradi termodinamici di libertà; potenziali termodinamici; relazioni di Maxwell; calori specifici e coefficienti volumetrici; derivazione delle equazioni di stato e di interrelazioni notevoli; stabilità intrinseca. Sistemi omogenei: gas ideali, calori specifici e struttura microscopica; liquidi e solidi incomprimibili; introduzione ai gas reali; miscele di gas, pressione parziale, miscele ideali. Sistemi eterogenei: fasi, regola delle fasi, transizioni di fase; equazione di Clapeyron-Clausius; punti triplo e critico; diagrammi di stato.
Modulo 3 Termodinamica dei processi
Stato di flusso di massa e sistema aperto; equazioni globali di bilancio di massa, energia ed entropia. Analisi di componenti notevoli di impianto: turbine, compressori, pompe; miscelatori e scambiatori di calore; valvole; ugelli e diffusori. Flusso di energia disponibile/exergia, analisi energetica di macchine motrici e operatrici. Cicli termodinamici: classificazione, caratteristiche generali, rendimento. Cicli standard ad aria (diretti): Joule-Brayton per impianti fissi e turbogetti, introduzione alla rigenerazione. Cicli a vapore: ciclo Rankine. Cicli inversi: efficienza, cicli a gas (Brayton) e a compressione di vapore.
Modulo 4 Introduzione alla Trasmissione del calore
Introduzione ai meccanismi di trasporto dell’energia: conduzione, convezione ed irraggiamento.
Argomento 4.1 - Conduzione
Legge di Fourier e conduttività termica, equazione della diffusione termica. Conduzione in regime stazionario: geometria monodimensionale piana, cilindrica e sferica; resistenze termiche e reti elettriche equivalenti; alette: equazione della conduzione, efficienza ed efficacia. Conduzione in regime variabile: approssimazione a parametri concentrati, il numero di Biot.
Argomento 4.2 – Convezione
Convezione forzata all’esterno di superfici e all’interno di condotti: fenomenologia, numeri adimensionali di Reynolds, Nusselt, Prandtl, Peclet e uso di correlazioni adimensionali. Temperatura di miscelamento adiabatico e suo andamento lungo un condotto; differenza media logaritmica di temperatura. Introduzione alla convezione naturale: numeri adimensionali di Grashof e Rayleigh. Scambiatori di calore: classificazione, andamento delle temperature negli scambiatori equicorrente e controcorrente; potenza massima ed efficienza.
Argomento 4.3 – Irraggiamento
Radiazione termica: natura, intensità di radiazione e grandezze caratteristiche monocromatiche e totali. Corpo nero: proprietà e leggi caratteristiche. Superfici reali: emissività, superfici diffuse, grigie e opache; coefficienti di riflessione, assorbimento e trasmissione; relazione fra emissione e assorbimento (teorema di Kirchhoff), radiatori. Scambio termico radiativo tra superfici grigie e diffuse: fattore di vista e sue proprietà, calcolo della potenza termica netta irraggiata tra due superfici grigie. Superfici reirraggianti.

Prova scritta obbligatoria, senza prove in itinere
Prova orale obbligatoria
Modalità di verifica
Descrizione
Risultato di apprendimento perseguito
Prova scritta e Prova orale
Gli studenti dovranno superare un esame scritto ed un esame orale.
Gli studenti saranno valutati sulla base:

• delll’apprendimento dei concetti teorici ed in particolare che lo studente conosca i principali concetti, definizioni, enunciati ed equazioni inerenti alla Termodinamica e Trasmissione del calore;
• della capacità di applicare tali concetti – organizzando ed utilizzando sinergicamente i principali risultati modellistici ed analitici ed effettuando le opportune ipotesi per la soluzione di problemi.
  Più specificamente viene accertata la capacità di:
• impostare ed eseguire bilanci di massa, energia ed entropia per sistemi chiusi e aperti;
• calcolare le proprietà di gas, liquidi e solidi nonché di sistemi liquido-vapore e gas-vapore lungo processi termodinamici;
• analizzare dal punto di vista termodinamico le configurazioni di base di macchine e impianti (caratterizzazione di stati e trasformazioni, calcolo degli indici di prestazione);
• valutare le caratteristiche di scambio termico, come potenze, temperature, tempi e dimensioni, adottando i modelli più adatti a descrivere le modalità di trasporto (conduzione, convezione e irraggiamento).
  Valutazione finale
  La verifica della preparazione avviene mediante esame che potrà essere sostenuto nel periodo di valutazione finale al termine del semestre o in qualsiasi altro appello disponibile.
  L’esame consta di una prova scritta e di una orale che devono essere sostenute nello stesso appello.
  Prova scritta: è necessario riportare una votazione dello scritto di almeno 16/30 per essere ammessi alla prova orale.
  Prova orale: La prova orale inizia dalla discussione della prova scritta e mira all’accertamento del grado di comprensione degli aspetti fondamentali dell’insegnamento come pure della consapevolezza dell’uso dei modelli di calcolo utilizzati.
  1,2,3,5

G.P. Beretta, Termodinamica, Editore: Catolibreria Snoopy, Anno edizione: 2002
E.P. Gyftopoulos, G.P. Beretta, Thermodynamics: Foundations and Applications, Editore: Dover, Anno edizione: 2010, ISBN: 0-486-43932-1 http://web.mit.edu/lienhard/www/ahtt.html
Note: Parti: 1-3
M. Moran, H.N. Shapiro, B.R. Munson, D.P. DeWitt, Elementi di Fisica Tecnica per l'Ingegneria, Editore: McGraw-Hill, Anno edizione: 2011, ISBN: 978-88386-65509 http://web.mit.edu/lienhard/www/ahtt.html
Note: Parti: 3-6
J.H. Lienhard IV, J.H. Lienhard V, A Heat Transfer Textbook, 4th edition http://web.mit.edu/lienhard/www/ahtt.html
G. Casagrande, E. Lanzarone, L.D. Marocco, F. Miglietta, Esercizi di fisica tecnica, Editore: Pitagora, Anno edizione: 2013, ISBN: 88-371-1215-7

L'insegnamento si propone di
descrivere alcune strutture algebriche elementari con relative proprietà;
introdurre alcune delle idee alla base dello studio delle proprietà di uno spazio topologico mediante strumenti algebrici;
illustrare i temi principali dell'omologia simpliciale;
spiegare come utilizzare tali strumenti per lo studio di proprietà topologiche sia in ambito teorico che applicato;
introdurre le principali tecniche topologiche di analisi dati utili per il Machine Learning con i relativi strumenti informatici.

Al termine dell'insegnamento, chi supererà l'esame
(DdD1) conoscerà e comprenderà
le definizioni e proprietà basilari riguardanti i complessi simpliciali e l'omologia simpliciale;
le idee e gli strumenti fondamentali dell'omologia persistente e alcune sue possibili applicazioni nell'ambito della topological data analysis e del machine learning;
i principali algoritmi per il calcolo esplicito degli oggetti studiati;
(DdD2) sarà in grado di
applicare quanto appreso in situazioni specifiche, per studiare proprietà di spazi topologici al fine di costruirne approssimazioni e/o distinguerli e classificarli;
applicare gli strumenti studiati nell'analisi di dati provenienti da situazioni reali anche integrandoli in processi di Machine Learning;
(DdD3) sarà in grado di
interpretare i risultati di analisi di dati condotte con l'utilizzo dei principali software dedicati (R e/o Python).

Elementi di algebra e topologia. Relazioni di equivalenza e insiemi quoziente. Gruppi abeliani liberi e campi finiti. Topologia di un insieme, topologia quoziente, continuità di funzioni tra spazi topologici.
Omologia simpliciale. Simplessi e complessi simpliciali geometrici e astratti. Simplessi orientati. Catene e operatore bordo. Gruppi di omologia. Omologia ridotta. Calcolo dei gruppi di omologia. Prime applicazioni dell’omologia.
Omologia persistente. Filtrazione di un complesso simpliciale. Complessi di Čech, complessi di Vietoris-Rips, complessi alpha. Filtrazioni associate ad un point cloud. Omologia persistente e diagrammi di persistenza. Distanze tra diagrammi di persistenza e stabilità.
Topological data analysis e machine learning. Studio della forma dei dati: esempi di estrazione di features topologiche da dati multi-dimensionali. Applicazione in una pipeline di ML (clustering, classificazione, riduzione della dimensione,...). Discussione della versatilità e della robustezza. Comprensione della forma di un modello: aggiunta di un termine topologico nella funzione di loss di un processo di ML, analisi topologica di una rete neurale.
Nella seconda parte del corso verranno presentati numerosi esempi concreti mediante l’utilizzo di pacchetti software dedicati (R e/o Python).

Progetto/i - Elaborato/i obbligatorio, individuale, senza revisioni periodiche, con presentazione/discussione finale
L'esame consiste nello sviluppo di un progetto concordato con il docente riguardante l'applicazioni di metodi topologici in un contesto di analisi dati e/o machine learning. Le metodologie da utilizzare saranno quelle discusse durante il corso (o loro estensioni/generalizzazioni). Il docente cercherà di proporre ad ogni partecipante un caso di studio e una tipologia di dato da analizzare coerenti con il persorso di laurea magistrale del singolo.
Una volta completato il progetto, ogni studente preparerà una presentazione del lavoro e la discuterà oralmente in presenza del docente e degli altri partecipant al corso. Al termine della presentazione, il docente formulerà alcune domande inerenti sia al progetto che al contenuto dell'insegnamento.

James R. Munkres, Elements of Algebraic Topology, Editore: Addison-Wesley Publishing Company, Anno edizione: 1984, ISBN: 0-201-04586-9
Herbert Edelsbrunner, John L. Harer, Computational Topology - an introduction, Editore: American Mathematical Society, Anno edizione: 2010, ISBN: 978-0-8218-4925-5
Hal Schenck, Algebraic Foundations for Applied Topology and Data Analysis, Editore: Springer, Anno edizione: 2022, ISBN: 978-3-031-06666-5
Allen Hatcher, Algebraic Topology, Editore: Cambridge University Press, Anno edizione: 2002, ISBN: 0-521-79160-X