Courses

Computer Science and System Engineering

Academic Year 2015 - 2016

Advanced Topics of Computational Mechanics

Abstract:
The course is organized as a set of seminars and lectures delivered by IMT Professors and by invited recognized international experts. It covers advanced topics of computational mechanics.
Hours:
10
Professors/Lecturers:
Marco Paggi (IMT Lucca); Andrea Bacigalupo (IMT Lucca); Pattabhi Ramaiah Budarapu (IMT Lucca)
Available for:
Computer Science and System Engineering

Advanced Topics of Computer Science

Abstract:
This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on System Modelling and Analisys (SysMA).
Hours:
40
Professors/Lecturers:
Rocco De Nicola (IMT Lucca); Tbd; Mirco Tribastone (IMT Lucca)
Available for:
Computer Science and System Engineering

Advanced Topics of Control Systems

Abstract:
In this course we will venture to go through some of the most advanced control schemes whose development has been motivated by problems in process control and economics. The course's main objective will be to bring students in touch with the state of the art in MPC theory and explore various research opportunities that emerge. We will see how the mature concept of model predictive control (MPC) can be combined with process economics to yield a unifying framework -- known as economic model predictive control (EMPC) -- for simultaneous control and process optimization. The EMPC-controlled closed-loop trajectories need not be stable/convergent, but they provide certain performance/cost guarantees for the process. We establish stability conditions for the closed-loop system and study various EMPC formulations and their properties. Special emphasis will be put on the study of MPC methodologies for uncertain systems. We will discuss various stochastic MPC methodologies and study their closed-loop properties. We will provide a comprehensive theory of Markovian systems for which we will define new notions of stability such as mean square stability, almost sure stability and uniform stability.

Prerequisites: Linear algebra & calculus; Linear discrete-time dynamical systems; Model predictive control theory.

(course topics and grading plan are available at http://dysco.imtlucca.it/atcs/)
Hours:
20
Professors/Lecturers:
Alberto Bemporad (IMT Lucca); Pantelis Sopasakis (IMT Lucca)
Available for:
Computer Science and System Engineering

Analytics and Data Science in Economics and Management I

Abstract:
Python Course for Data Science (M. Puliga):
- Introduction to the language: basic statements, cycles and functions
- Diving into the language: advanced types: sets and dictionaries, classes and modules, using PIP and ipython
- Scraping the web: introduction to BeautifulSoup, the regular expressions module re, the request module
- Introduction to Plotting: basic numpy, plotting overview
- Data science utilities: introduction to SQL (sqlite/mysql)

Getting, Organizing and Analyzing the Data (A. Petersen):
- a crashcourse in scraping and parsing XML based websites (in mathematica & python)
- a crashcourse on using Gephi (open source network visualization program)
- a crashcourse on data organization, processing, analysis and visualization

Multivariate Statistical Analysis (M. Di Lascio):
This part of the course aims at introducing the most important and widespread multivariate analysis methods. After introducing multivariate random variables and multivariate data, the course focuses on the study of the relationships between variables and on the study of the similarities between units. In particular, the course deals with:

- dimension reduction methods (principal component analysis and factor analysis);
- analysis tools for linear and nonlinear multivariate dependence (canonical correlation analysis and copula models); distance‐based and model‐based clustering techniques.

Causal Inference and Evaluation Methods (F. Mealli):
This part of the course deals with statistical methods for inferring causal effects from data from randomized experiments or observational studies. Students will develop expertise to assess the credibility of causal claims and the ability to apply the relevant statistical methods for causal analyses.

Prerequisites: Lin. Alg. + Opt. Control + Found. of Prob. & Stat. Inf.
Hours:
40
Professors/Lecturers:
Alexander Petersen (IMT Lucca); Fabio Pammolli (Politecnico di Milano); Marta Di Lascio (Libera Università di Bolzano); Michelangelo Puliga (IMT Lucca); Fabrizia Mealli (Università degli Studi di Firenze)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Applications of Stochastic Processes

Abstract:
This course offers an introduction to stochastic processes as a practical modelling tool for the quantitative analysis of systems. It covers the fundamentals of Markov chains, and presents algorithms and state-of-the-art software applications and libraries for their numerical solution and simulation. The class of Markov Population Processes is presented, with its most notable applications to as diverse disciplines as chemistry, ecology, systems biology, health care, computer networking, and electrical engineering. Finally, the course will examine the computational issues arising from the modelling of large-scale systems, reviewing effective approximation methods based ordinary differential equation (fluid) limits, moment-closure techniques, and hybrid models.

Prerequisites: fundamentals of probability theory; knowledge of the topics of “Stochastic Processes and Stochastic Calculus” is useful but not necessary.
Hours:
20
Professors/Lecturers:
Mirco Tribastone (IMT Lucca)
Available for:
Computer Science and System Engineering

Banking and Finance (long seminar with optional exam)

Abstract:
One of the most challenging task in finance is the gap between theoretical models and the actual software implementation. Cross some different areas (derivatives evaluation, risk management, accounting issues) several problems arise: discretization, analytical approximation, montecarlo simulation vs. numerical probability, optmization and so on. After a short overview of the main financial areas, the course aims to give some insights on these topics, with a special focus on the risk management current hard problems and the related software algorithms.

Prerequisites: Stochastic Processes and Stochastic Calculus, Management Science and Corporate Finance, Finance
Hours:
12
Professors/Lecturers:
Michele Bonollo (IASON ltd.)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science

Basic Numerical Linear Algebra

Abstract:
The course is aimed to recall the basic notions about vectors, matrices, vector spaces and norms, along with the basic numerical methods concerning the solution of linear systems. In particular: direct methods for square linear systems and conditioning analysis; direct methods for solving over-determined linear systems in the least square sense. The course also provides an introduction to Matlab, which is used for implementing the illustrated methods.
Hours:
20
Professors/Lecturers:
Luigi Brugnano (Università degli Studi di Firenze)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Computational Contact and Fracture Mechanics

Abstract:
This course provides an overview on the theories of contact and fracture mechanics relevant for a wide range of disciplines ranging from materials science to engineering. Introducing their theoretical foundations, the physical aspects of the resulting nonlinearities induced by such phenomena are emphasized. Numerical methods (FEM, BEM) for their approximate solution are also presented together with a series of applications to real case studies. In detail, the course covers the following topics: Hertzian contact between smooth spheres; the Cattaneo-Mindlin theory for frictional contact; numerical methods for the treatment of the unilateral contact constraints; contact between rough surfaces; fundamentals of linear elastic fracture mechanics; the finite element method for crack propagation; nonlinear fracture mechanics and the cohesive zone model; interface finite elements; applications of fracture mechanics to materials science, retrofitting of civil/architectonic structures, composite materials.
Hours:
20
Professors/Lecturers:
Marco Paggi (IMT Lucca)
Available for:
Computer Science and System Engineering

Computer Programming and Methodology

Abstract:
This course aims at introducing to students principles and methodologies of computer programming. Emphasis is on good programming style, techniques and tools that allow efficient design, development and maintenance of software systems. The course focuses on the design of computer applications drawing attention to modern software engineering principles and programming techniques, like object-oriented design, decomposition, encapsulation, abstraction, and testing. A significative case study is used to allow students to experiment with the principles and techniques considered in this course. Depending on the background of the class, Java, C++, and/or Python are considered in the course.
Hours:
20
Professors/Lecturers:
Michele Loreti (Università degli Studi di Firenze)
Available for:
Computer Science and System Engineering

Convex Optimization

Abstract:
The course covers the basics of convex optimization methods, with an emphasis on numerical algorithms that can solve a large variety of optimization problems arising in control engineering, machine learning, mechanical engineering, statistics, economics, and finance.

The materials for the course are available at http://www.stanford.edu/~boyd/papers/cvx_short_course.html
Hours:
20
Professors/Lecturers:
Stephen Boyd (Stanford University); Steven Diamond (Stanford University); Enzo Busseti (Stanford University)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science

Data Science with Complex Networks

Abstract:
Complex Systems are everywhere and in the era of massive production of electronic data coming from all sort of devices it is of crucial importance to have the right tools to manage and extract from them all the valuable information. To this aim during this course we will develop both the basic theoretical tools and the practical coding technics to tackle all sort of complex systems, ranging from Trade and Financial Networks, to the World Wide Web and the Social Networks. In particular Complex Networks Theory proved to be successful in the process of handling this enormous quantity of data and in order to apply these concepts to the various cases it is crucial to define a clear strategy and guidelines to represent the system data in the shape of a network. Using the Python scripting language we will introduce state of the art methods and algorithms to cope with some reference dataset.

Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis, introduction to Networks
Hours:
20
Professors/Lecturers:
Guido Caldarelli (IMT Lucca); Alessandro Chessa (IMT Lucca)
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Econometrics

Abstract:
This course covers some of the most important methodological issues arising in any field of applied economics when the main scope of the analysis is to estimate causal effects. A variety of methods will be illustrated using theory and papers drawn from the recent applied literature. The aim is to bridge the step from a technical econometrics course to doing applied research. The emphasis will be on the applications. The goal is to provide students with enough knowledge to understand when these techniques are useful and how to implement each method in their empirical research.

Part 1 (C. Tealdi):
- The simple regression model
- Estimation
- Inference
- Dummy variables
- OLS Asymptotics
- Heteroskedasticity
- Instrumental Variables

Part 2 (A. Belmonte):
- A quick introduction to STATA
- Microeconomic data structures
- Conditional distributions and the conditional expected function concept
- A discussion of the assumptions of the GM Theorem
- Heterogeneous conditional distributions
- Dummy variables and Anova models
- Autocorrelation and the Moulton factor

Part 3 (P. Zacchia):
- Beyond Single-Equation Linear Models: Structural Models, Identification and Causality; Rubin Causal Model
- Simultaneous Equation Models
- Introduction to M-Estimation
- Generalized Method of Moments
- Maximum Likelihood Estimation
- Non-Parametric Estimation

Part 4 (A. Rungi):
- Benefits and limits of panel data structures; Review of some panel data examples for micro- and macro data; How to handle and describe panel data; basic estimation techniques
- Details for panel data estimators
- Identification problems
- Introduction to non-linear panel data estimators
- Count data models

Prerequisites: Linear Algebra + Found. of Prob. & Stat. Inf.
Hours:
60
Professors/Lecturers:
Cristina Tealdi (Heriot-Watt University); Armando Rungi (IMT Lucca); Paolo Zacchia (IMT Lucca); Alessandro Belmonte (IMT Lucca)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Finance

Abstract:
This course introduces students to the basic concepts used in quantitative finance, which forms the basis for many applications such as derivatives pricing, financial engineering and asset pricing. Anyone interested in these areas will have to acquire a good grasp of the topics in this course. We will cover: the analysis of complete and incomplete markets in discrete and continuous time models; the discussion and extension of the assumptions of the Black-Scholes-Merton equation and the introduction of common numerical techniques that are widely applied in practice (along with practical lab sessions with real data); the introduction of structured finance products, their use in risk management and valuation techniques, most notably for mortgage-backed securities, credit default swaps and collateralized debt obligations.

Students require an adequate knowledge of mathematics, particularly in matrix algebra and analysis along with stochastic processes and stochastic calculus to follow this course. Appropriate readings to refresh your knowledge are given on request.

Outline:

Part I
– Pricing Models
- Hedging of securities;
- No-arbitrage pricing;
- Pricing in multi-period models (Binomial Model);- Pricing in continuous time (Black-Scholes-Merton Model)

Part II
- Numerical techniques
- Beyond Black-Scholes-Merton Model;
- Binomial lattices;
- Monte-Carlo simulation;
- Finite differences

Part III
– Structured Finance
- Mortgage-backed securities;
- Modeling and pricing corporate default;
- Credit Default Swaps;
- Designing CDOs and exotic CDOs

Prerequisites: Management & Corporate Finance + Stochastic Processes & Stochastic Calculus.
Hours:
20
Professors/Lecturers:
Simone Giansante (University of Bath)
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Foundations of Probability and Statistical Inference

Abstract:
This course aims at introducing, from an advanced point of view, the fundamental concepts of probability and statistical inference.
Some proofs are sketched or omitted in order to have more time for examples, applications and exercises. In particular, the course deals with the following topics:

• probability space, random variable, expectation, variance, cumulative distribution function, discrete and absolutely continuous distributions, random vector, joint and marginal distributions, joint cumulative distribution function, covariance,
• conditional probability, independent events, independent random variables, conditional probability density function, order statistics,
• multivariate Gaussian distribution,
• probability-generating function, Fourier transform/characteristic function,
• types of convergence and some related important results,
• point estimation, interval estimation, hypothesis testing, linear regression, introduction to Bayesian statistics.
Hours:
35
Professors/Lecturers:
Irene Crimaldi (IMT Lucca)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Funding and Management of Research and Intellectual Property (long seminar without exam)

Abstract:
The long seminar aims at providing an overview on the management of intellectual property rights (copyright transfer agreements, open access, patents, etc.). Funding opportunities for PhD students, post-docs, and researchers are also presented (scholarships by the Alexander von Humboldt Foundation; initiatives by the Deutscher Akademischer Austausch Dienst; scholarships offered by the Royal Society in UK; bilateral Italy-France exchange programmes; Fulbright scholarships; Marie Curie actions; grants for researchers provided by the European Research Council). For each funding scheme, specific hints on how to write a proposal are given.
Hours:
10
Professors/Lecturers:
Marco Paggi (IMT Lucca); Tbd
Available for:
Computer Science and System Engineering; Economics, Management and Data Science; Analysis and Management of Cultural Heritage

Game Theory

Abstract:
Mechanism Design. Revelation principle, Dominance and Nash Implementation. Strategic and Axiomatic Bargaining. Asymmetric Information and Optimal Contracts. Moral Hazard and Adverse Selection models. Signaling and Screening Models. Applications. Static games of complete information: definition of a game; normal form representation; strongly and weakly dominated strategies; Nash Equilibrium (NE); mixed strategy equilibrium. Applications of NE and introduction to market competition; Cournot competition; Bertrand competition; externalities; public goods. Dynamic games of complete information: definition of a dynamic game; extensive form representation; perfect and imperfect information; Backward Induction equilibrium; Subgame Perfect equilibrium. Repeated games: Definition; one-shot deviation property; folk theorem; application to Rubinstein bargaining. Static games of incomplete information: Bayesian games; Bayesian Nash equilibrium. Dynamic games of incomplete information: perfect Bayesian equilibrium; signalling games, cheap talk.
Hours:
30
Professors/Lecturers:
Nicola Dimitri (Università degli Studi di Siena)
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Identification, Analysis and Control of Dynamical Systems

Abstract:
The course provides an introduction to dynamical systems, with emphasis on linear systems. After introducing the basic concepts of stability, controllability and observability, the course covers the main techniques for the synthesis of stabilizing controllers (state-feedback controllers and linear quadratic regulators) and of state estimators (Luenberger observer and Kalman filter). The course also covers data-driven approaches of parametric identification to obtain models of dynamical systems from a set of data, with emphasis on the analysis of the robustness of the estimated models w.r.t. noise on data and on the numerical implementation of the algorithms.
Hours:
20
Professors/Lecturers:
Alberto Bemporad (IMT Lucca); Dario Piga (IMT Lucca)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science

Introduction to Networks

Abstract:
The course will provide an introduction to the mathematical basis of Complex Networks and to their use to describe, analyze and model a variety of physical and economic situations.

LIST OF LECTURES

Lecture 1 Graph Theory Introduction:
Basic Definitions, Statistical Distributions, Universality, Fractals, Self-Organised Criticality

Lecture 2 Properties of Complex Networks:
Scale-Invariance of Degree Distribution, Small-World Effect, Clustering

Lecture 3 Applications:
Internet, WWW, Socio-technological systems, Economics, Biology

Lecture 4 Communities:
Community Detections, Algorithms to explore Graphs

Lecture 5 Different kind of graphs:
Vertices differences, Layered Vertices, Trees and Taxonomies

Lecture 6 Ranking:
Hierarchies, Spanning Trees,HITS, PageRank,

Lecture 7 Static Models of Graphs:
Erdos-Renyi, Small World,

Lecture 8 Dynamical Models of Graphs:
Barabasi-Albert, Configuration models

Lecture 9 Fitness models:
Fitness model and Self-Organised Fitness Model

Lecture 10 Basic Ingredients of Models:
Growth Preferential Attachments, Log Normal Distribution, Multiplicative Noise
Hours:
10
Professors/Lecturers:
Guido Caldarelli (IMT Lucca)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science; Analysis and Management of Cultural Heritage

Machine Learning and Pattern Recognition

Abstract:
Basics of pattern recognition and machine learning and real world applications in imaging, internet, finance. Similarities and differences. Supervised vs unsupervised learning. Linear regression in many ways. The logistic regression. Support vector machines for classification and regression. Random Forests for classification. Linear and quadratic discriminant analysis. Unsupervised learning (k-means, c-means, kernel k-means, spectral clustering, EM). Feature extraction and selection (PCA, ICA, kernel PCA, and manifold learning). Current trends in Machine Learning.
Prerequisites: Probability and basic random processes, linear algebra, basic computer programming, numerical methods.
Hours:
20
Professors/Lecturers:
Sotirios Tsaftaris (The University of Edinburgh)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science

Management of Complex Systems: Approaches to Problem Solving

Abstract:
Methods and approach to problem solving. Problem analysis; analysis of complex systems (related to cultural heritage, such as a city of art organization, promotion, etc.). The course will include practical simulations. The course will be linked to a seminar on specific Case studies.
Hours:
40
Professors/Lecturers:
Andrea Zocchi; Tbd
Compulsory for:
Analysis and Management of Cultural Heritage
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Management Science and Corporate Finance

Abstract:
The first part of the course is also designed for the curriculum AMCH as “Basics of Management” (20 hours).

The course aims at introducing doctoral students to fundamental concepts and to theoretical research in management science and corporate finance. The first classes will focus on a few classic readings in management and organization theory, and then we will move to corporate finance. The main goal is to expose students to classic and fundamental background readings on the structure of Organizations, Decision Making in Organizations, and Corporate Finance. Specific Chapters will be selected for class discussions.

Prerequisites: The course will emphasize intuition over technical detail wherever possible, while more technical readings will be made available and discussed with students with a quantitative background. Those who are willing to catch up with some reading on their own should not have too many problems, under the Lecturer's supervision.
Hours:
30
Professors/Lecturers:
Fabio Pammolli (Politecnico di Milano); Luca Regis (IMT Lucca)
Compulsory for:
Economics, Management and Data Science; Analysis and Management of Cultural Heritage
Also available for:
Computer Science and System Engineering

Micromechanics

Abstract:
The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour. Topics addressed in the course concern the evaluation of the bounds to the effective elastic properties of heterogeneous materials, local (Cauchy continuum) and non-local (micromorphic and multipolar continuum) homogenization methods of materials with periodic and quasi-periodic microstructure using heuristic computational approaches or asymptotic techniques and multiscale modeling of materials with disordered microstructure based on computational and variational homogenization methods.
Hours:
10
Professors/Lecturers:
Marco Paggi (IMT Lucca); Andrea Bacigalupo (IMT Lucca)
Available for:
Computer Science and System Engineering

Model Predictive Control

Abstract:
Quick review of linear dynamical systems in state-space form, stability, state-feedback control and observer design, linear quadratic regulation and Kalman filtering. Basic model predictive control (MPC) algorithm and the receding horizon principle. Linear MPC: formulation, quadratic programming, stability properties. Multiparametric programming and explicit MPC. MPC of hybrid dynamical systems subject to linear and logical constraints. Stochastic MPC. Selected applications of MPC to automotive and aerospace systems, supply chains, financial engineering. Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis, optimization.
Hours:
20
Professors/Lecturers:
Alberto Bemporad (IMT Lucca)
Available for:
Computer Science and System Engineering

Modelling and Verification of Reactive Systems

Abstract:
Computing systems are becoming increasingly sophisticated and control key aspects of our lives. In light of the increasing complexity of such computing devices, one of the key scientific challenges in computer science is to design and develop computing systems that do what they were expected to do, and do so reliably. The aim of this course is to introduce models for the formal description of computing systems, with emphasis on parallel, reactive and possibly real-time systems, and the techniques for system verification and validation that accompany them. As an important component of the course, we shall introduce industrial-strength software tools for modelling and analyzing the behaviour of (real-time) reactive systems.
Hours:
20
Professors/Lecturers:
Rocco De Nicola (IMT Lucca)
Available for:
Computer Science and System Engineering

Networks

Abstract:
The course is structured into three modules: the first one will cover advanced topics in complex network theory, whereas, the second one will focus on economic and financial networks, dealing with both theory and applications.

Module 1: Advanced Theory of Complex Networks
Lecture 1 Models of Evolving Networks
Lecture 2 Fitness & Relevance models
Lecture 3 The Master Equations approach
Lecture 4 Percolation
Lecture 5 Epidemic Models on Networks
Lecture 6 Advanced Topological Properties
Lecture 7 Complex Networks Randomization
Lecture 8 Exponential Random Graphs
Lecture 9 Parameter Estimation via Maximum Likelihood
Lecture 10 Applications: Bipartite, Directed and Weighted Networks.

Module 2: Economic & Financial Networks
Lecture 1 Evolutionary Network Games
Lecture 2 Heterogeneous Mean-Field Theory
Lecture 3 Financial Networks
Lecture 4 Systemic Risk
Lecture 5 DebtRank
Lecture 6 Economic Networks
Lecture 7 The WTW & COMTRADE dataset
Lecture 8 Gravity Models of Trade
Lecture 9 Early Warning Signals
Lecture 10 Network Reconstruction from Partial Information

Module 3 Social and Infrastructural Networks
Lecture 1 Introduction to Social Network Data
Lecture 2 Tecniques and Methodologies of Analysis in Social Networks
Lecture 3 Twitter data and Models
Lecture 4 Clustering and Classification of Facebook Data
Lecture 5 Automatic Topic Extraction
Lecture 6 Introduction to Infrastructural Networks
Lecture 7 Electric Grids
Lecture 8 Cascade Phenomena
Lecture 9 Modelling of infrastructural networks
Lecture 10 Smart Grids and Renewables

Prerequisites: Linear algebra, Introduction to Networks, Found. Prob. & Stat. Inf.
Hours:
30
Professors/Lecturers:
Guido Caldarelli (IMT Lucca); Antonio Scala (CNR - Istituto di Sistemi Complessi); Tiziano Squartini (IMT Lucca); Giulio Cimini (IMT Lucca); Fabio Saracco (IMT Lucca)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Neural Bases of Conceptual Representation, Emotion and Behavior

Abstract:
This course will discuss the state-of-the-art of knowledge into the neural bases of human brain function. Students will learn about the brain correlates of cognition, emotion and behavior in humans, including perception, conceptual representation and decision-making processes. Among the questions what will be examined, how do we perceive the external world? How do we acquire knowledge and form a conceptual representation? Do we really need vision to see? How do we make a decision? How do genetic and environmental factors affect our choices? The Course will also discuss how it is now possible to decode neural information about thinking and consciuosness itself.
Hours:
12
Professors/Lecturers:
Pietro Pietrini (IMT Lucca)
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering; Analysis and Management of Cultural Heritage

Numerical Methods for the Solution of Partial Differential Equations

Abstract:
The course introduces numerical methods for the approximate solution of initial and boundary value problems governed by linear partial differential equations (PDEs) ubiquitous in physics, engineering, and quantitative finance. The fundamentals of the finite difference method and of the finite element method are introduced step-by-step in reference to exemplary model problems related to heat conduction, linear elasticity, and pricing of stock options in finance. Notions on numerical differentiation, numerical integration, interpolation, and time integration schemes are provided. Special attention is given to the implementation of the numerical schemes in Matlab and in the finite element analysis program FEAP fast intensive computations.
Hours:
20
Professors/Lecturers:
Marco Paggi (IMT Lucca)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science

Optimal Control

Abstract:
Discrete-time optimal control: dynamic programming for finite/infinite horizon and deterministic/stochastic optimization problems. LQ and LQG problems, Riccati equations, Kalman filter. Deterministic continuous-time optimal control: the Hamilton-Jacobi-Bellman equation and the Pontryagin’s principle. Examples of optimal control problems in economics.
Hours:
30
Professors/Lecturers:
Giorgio Stefano Gnecco (IMT Lucca)
Compulsory for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Philosophy of Science (long seminar without exam)

Abstract:
We know a lot of things – or, at least, we think we do. Epistemology is the branch of philosophy that studies knowledge: its main features, the dynamics of its growth, as well as its claims for truth, validity, and progress. In this course – which is designed as a series of seminars held by the students, preceded by a few introductory lectures – we will consider some of the key contributions to the philosophical debate about the growth of scientific knowledge in the twentieth century, from Logical Positivism to Karl Popper, from Thomas Kuhn to Paul Feyerabend. We shall read some of their (as well as others’) works, and critically consider the content and limits of the different methodologies they advanced.
Finally, we will reflect on the extent to which such debates affected the methodology of the social sciences, and consider in what ways hard and social sciences differ: as to their inner nature, the context in which they operate, the data they employ and rely upon, and the prescriptive methodology they more or less explicitly adopt.
Hours:
10
Professors/Lecturers:
Stefano Gattei (Chemical Heritage Foundation, Philadelphia)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science; Analysis and Management of Cultural Heritage

Principles of Concurrent and Distributed Programming

Abstract:
The course objective is to introduce the basics of concurrent programming problems through an illustration of the concepts and techniques related to modeling systems in which there are more components that are simultaneously active and need to coordinate and compete for the use of shared resources. At the end of the course the student will have a good understanding of the constructs for concurrent programming and be able to use them to write and analyze concurrent programs.
Hours:
20
Professors/Lecturers:
Rocco De Nicola (IMT Lucca)
Available for:
Computer Science and System Engineering

Probabilistic and Stochastic Model Checking

Abstract:
Model checking is an automated formal verification technique whose main idea is to formally specify both the system specification and its properties (typically, by means of temporal logic) and automatically verify that such properties are satisfied (or to which extent they are). This course aims at presenting the fundamentals of model checking techniques for the verification of distributed and concurrent systems. Different classes of temporal logics will be introduced that rely on the use of semantic models to provide a logical framework for the analysis and verification of complex systems. The first part of the course will cover the fundamentals of qualitative model checking, while the second part of the course will cover the fundamentals of probabilistic model checking and its application to performance evaluation.
Hours:
20
Professors/Lecturers:
Mirco Tribastone (IMT Lucca)
Available for:
Computer Science and System Engineering

Qualitative and Quantitative Formal Methods for Computer Science

Abstract:
TBD
Hours:
40
Professors/Lecturers:
Tbd
Available for:
Computer Science and System Engineering

Scientific Writing, Dissemination and Evaluation (long seminar without exam)

Abstract:
In order to ensure their widest possible dissemination, research results need to be presented in academic publications and in talks. The first goal of this course is to introduce students to basic principles of academic writing and on basic techniques to plan and deliver good academic talks. In addition, the course discusses the key principles of peer review, which is what makes science reliable knowledge. In particular, the course focuses on how to write a professional referee report.

Further information is available at http://www.ru.is/kennarar/luca/IMTHOWTO/
Hours:
8
Professors/Lecturers:
Luca Aceto (Reykjavik University)
Available for:
Computer Science and System Engineering; Economics, Management and Data Science; Analysis and Management of Cultural Heritage

Software Verification

Abstract:
TBD
Hours:
20
Professors/Lecturers:
Gennaro Parlato (University of Southampton)
Available for:
Computer Science and System Engineering

Stochastic Processes and Stochastic Calculus

Abstract:
This course aims at introducing some important stochastic processes and Ito stochastic calculus. Some proofs are sketched or omitted in order to have more time for examples, applications and exercises.

In particular, the course deals with the following topics:

- Markov chains (definitions and basic properties, classification of states, invariant measure, stationary distribution, some convergence results and applications, passage problems, random walks, urn models, introduction to the Markov chain Monte Carlo method),
- Conditional Expectation and Conditional Variance,
- Martingales (definitions and basic properties, Burkholder transform, stopping theorem and some applications, predictable compensator and Doob decomposition, some convergence results, game theory, random walks, urn models),
- Poisson process, Birth-Death processes,
- Wiener process (definitions, some properties, Donsker theorem, Kolmogorov-Smirnov test) and Ito calculus (Ito stochastic integral, Ito processes and stochastic differential, Ito formula, stochastic differential equations, Ornstein-Uhlenbeck process, Geometric Brownian motion, Feynman-Kac representation formula).

The topics of “Foundations of Probability and Statistical Inference” are supposed to be known.
Hours:
25
Professors/Lecturers:
Irene Crimaldi (IMT Lucca)
Specializing course for:
Economics, Management and Data Science
Also available for:
Computer Science and System Engineering

Timed Automata and Logics for Real-Time Systems

Abstract:
TBD
Hours:
20
Professors/Lecturers:
Luca Aceto (Reykjavik University)
Available for:
Computer Science and System Engineering