Courses

Computer Science and System Engineering

Academic Year 2017 - 2018

Advanced Neuroimaging

Abstract:
Early brain functional studies, based on MRI , PET or EEG, focused on univariate analyses, in which the activity of each region is processed independently from each other. Nowadays, multivariate machine learning techniques have been developed to model complex, sparse neuronal populations. This course will provide an introduction to new methods and cutting-edge machine-learning techniques in the neuroimaging field by exploring multivariate statistical modeling of brain-activity data and computational modeling of brain information processing. Specifically, the course focuses on machine learning decoding and encoding perspectives in fMRI and novel methods (e.g., Representational Similarity Analysis) to explore and analyze brain data. A comprehensive review of model validation and statistical inference is provided.
In addition, hardware and software implementation recently allowed to combine different neural measures with different spatial and temporal resolutions within the same experimental session. The course also discusses the transdisciplinary approach combining different neuroimaging techniques in unique methodological frameworks and the advent of ultrahigh field neuroimaging.
Hours:
30
Professors/Lecturers:
Tbd; Nicola Vanello (Università degli Studi di Pisa); Mauro Costagli (Fondazione IMAGO7 Pisa); Andrea Leo (Centro di Ricerca "E. Piaggio")
Compulsory for:
Cognitive, Computational and Social Neurosciences
Also available for:
Computer Science and System Engineering

Advanced Numerical Analysis

Abstract:
1. General considerations on matrices

Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)


2.a Direct methods for general linear systems

Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability


2.b Direct methods for sparse linear systems

Factorizations of banded matrices
Ordering strategies to minimize the fill-in of a matrix
Solution of sparse triangular systems
Sparse matrices in Matlab: memorization and handling
Predefined functions for the direct solution of systems


3. Numerical solution of large-scale linear systems

Krylov subspace methods (CG, MINRES, GMRES, IDR family)
Structured problems
Preconditioning
Algebraic multigrid methods (hints)
Numerical experiments with Matlab and the IFISS package


4. Numerical solution of eigenvalue problems

Standard and generalized eigenproblems
Typical numerical methods
Equation of motion in structural dynamics: quadratic eigenproblems
Hours:
20
Professors/Lecturers:
Claudio Canuto (Politecnico di Torino); Valeria Simoncini (Università di Bologna)
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics

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:
20
Professors/Lecturers:
Marco Paggi (IMT Lucca); Andrea Bacigalupo (IMT Lucca); Alessio Gizzi (Campus Bio-Medico Roma)
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:
20
Professors/Lecturers:
Max Tschaikowski (IMT Lucca); Claudio Mezzina (IMT Lucca); Andrea Vandin (IMT Lucca); Hugo Torres Vieira (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.
Hours:
20
Professors/Lecturers:
Alberto Bemporad (IMT Lucca)
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 without 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 + Finance
Hours:
10
Professors/Lecturers:
Michele Bonollo (IASON ltd.)
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics

Complex Systems Theory

Hours:
20
Professors/Lecturers:
Guido Caldarelli (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences

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:
Tbd
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

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.
Hours:
20
Professors/Lecturers:
Tbd
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics

Data Science Lab

Abstract:
The aim of this class is to provide students with R language fundamentals and basic sintax. In particular, lessons will cover the following topics:

- Overview of R features
- The basics (vectors, matrices, objects, manipulation, basic statements)
- Reading data from files
- Probability distributions
- Basic statistical models
- Graphical procedures
- R packages overview
Hours:
15
Professors/Lecturers:
Valentina Tortolini (IMT Lucca)
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

Econometrics I

Abstract:
This modular sequence provides a graduate-level introduction to econometric analysis. A variety of methods are introduced theoretically and illustrated via applications drawn from recent papers in the applied literature. The aim of the sequence is to bridge the step between a technical econometrics course and actual research practice. The goal is to provide students with the necessary knowledge to understand in what contexts are certain techniques useful and how to implement each method in empirical research.

Module 1 (P. Zacchia and A. Rungi) – Multiple Linear Regression
o Theory and Algebra of OLS
o Non-spherical Errors and Inference
o Functional Form
o Analysis of Variance

Module 2 (P. Zacchia) - Core Econometric Theory
o Review of Asymptotic Theory
o Structural Models, Identification and Causality
o Simultaneous Equation Models, 2SLS and 3SLS
o Introduction to M-Estimation
o Generalized Method of Moments
o Maximum Likelihood Estimation

Module 3 (A. Rungi) - Panel Data, Dynamic Models and Nonlinear Models
o Linear and Static Panel Data Models
o Linear and Dynamic Panel Data Models
o Non-Linear Models
o Multinomial Models

Prerequisites: Introduction to Economics + Matrix Algebra + Foundations of Probabilistic and Statistical Inference
Hours:
40
Professors/Lecturers:
Armando Rungi (IMT Lucca); Paolo Zacchia (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
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: Stochastic Processes and Stochastic Calculus
Hours:
20
Professors/Lecturers:
Tbd
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics

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.

Students may be exonerated up to a maximum of 10 hours according to their background.
Hours:
30
Professors/Lecturers:
Irene Crimaldi (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences

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)
Available for:
Analysis and Management of Cultural Heritage; Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

Game Theory

Abstract:
The course covers the basics of non-cooperative game theory and information economics. The goal is to equip students with an in-depth understanding of the main concepts and tools of game theory in order to enable them to successfully pursue research in applied areas of economics and related disciplines, and to provide a solid background for students who are planning to concentrate on economic theory.
The course starts with a detailed description of how to model strategic situations as a game. It proceeds by studying basic solution concepts and their main refinements (dominance and iterative dominance, Nash equilibrium, correlated equilibrium, subgame perfect equilibrium, weak perfect Bayesian equilibrium, sequential equilibrium), strategic interaction under incomplete information (Bayesian games, Bayesian Nash equilibrium), and asymmetric information (adverse selection, signaling, screening, moral hazard, and the principal agent problem). The discussion of all theoretical concepts will be accompanied by representative applications from economics.
The course is mostly self-contained, but students should be familiar with basic concepts from calculus, linear algebra, and probability theory.
Hours:
20
Professors/Lecturers:
Kenan Huremovic (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences

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)
Available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics

Introduction to Cognitive and Social Psyschology

Abstract:
This course will provide an introduction to general themes in Cognitive and Social Psychology. In the first part of the course, we will review seminal findings that had a major impact on our knowledge of cognitive processes and social interactions, as well as more recent studies that took advantage of neuroimaging, electrophysiology and brain stimulation methods to shed new light on decision-making and social behaviors. During the second part of the course, students will be asked to perform a brief presentation of a research article and to critically discuss positive aspects and limitations of the study. The course will include seminars and lectures by renowned researchers in the field and will educate PhD candidates about the influence of social aspects of the human nature on cognitive and brain functioning (and vice-versa) in an intellectually motivating manner.
Hours:
24
Professors/Lecturers:
Pietro Pietrini (IMT Lucca); Emiliano Ricciardi (IMT Lucca)
Available for:
Analysis and Management of Cultural Heritage; Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

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)
Compulsory for:
Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences
Also available for:
Analysis and Management of Cultural Heritage; Computer Science and System Engineering

Machine Learning

Abstract:
The course provides an introduction to basic concepts in machine learning. Topics include: learning theory (bias/variance tradeoff; Vapnik-Chervonenkis dimension and Rademacher complexity, cross-validation, feature selection); supervised learning (linear regression, logistic regression, support vector machines); unsupervised learning (clustering, principal and independent component analysis); semisupervised learning (Laplacian support vector machines); online learning (perceptron algorithm); hidden Markov models.
Hours:
20
Professors/Lecturers:
Giorgio Stefano Gnecco (IMT Lucca)
Specializing course for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences

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:
20
Professors/Lecturers:
Tbd
Compulsory for:
Analysis and Management of Cultural Heritage
Also available for:
Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

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

Neuroscience in Bio-Engineering and Robotics

Hours:
18
Professors/Lecturers:
Tbd; Domenico Prattichizzo (Università degli Studi di Siena); Enzo Pasquale Scilingo (Università di Pisa)
Compulsory for:
Cognitive, Computational and Social Neurosciences
Also available for:
Computer Science and System Engineering

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, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

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.
An economic application of optimal control: a dynamic limit pricing model of the firm.

Prerequisites: Matrix Algebra
Hours:
20
Professors/Lecturers:
Giorgio Stefano Gnecco (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering

Philosophy of Science (long seminar without exam)

Abstract:
This is an introduction to the basic concepts and problems in the analysis of scientific reasoning and inquiry. The course will focus on some central patterns of reasoning and argumentation which in science and critically discuss their features and limitations. Topics covered include the nature of theory and evidence, the logic of theory testing, and the debate about the aims of science and the trustworthiness of scientific results. Classical examples and case-studies from the history and practice of scientific inquiry will be employed to illustrate the relevant problems and theoretical positions. No previous knowledge of either logic or philosophy is required.
Hours:
10
Professors/Lecturers:
Gustavo Cevolani (IMT Lucca)
Available for:
Analysis and Management of Cultural Heritage; Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

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

Python Programming for Complex Networks

Abstract:
We present in this course the latest results in the field of complex networks. They can solve immediate problems when studying the Internet and the WWW, and they can help sort information on a variety of other systems. This course is structured in such a way as to start with a specific problem and then present the theoretical tools needed to model or to sort out the most relevant information.

In the course we shall follow the various students from the setup of the software in their pc (a basic in Python will be provided in another course) to the application of existing software and the writing of specific one for the personal line of research of the students.
Hours:
20
Professors/Lecturers:
Guido Caldarelli (IMT Lucca)
Compulsory for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences

Qualitative and Quantitative Formal Methods for Computer Science

Abstract:
This course offers an introduction to core topics in formal methods for the specification and analysis of systems, both for functional and nonfunctional properties. Students will be exposed to basic models of computation such as labelled transition systems and process algebra, formal approaches to specifying the semantics of programming languages (such as operational and denotational semantics), and quantitative analysis methods based on Markov processes.
Hours:
20
Professors/Lecturers:
Rocco De Nicola (IMT Lucca); Mirco Tribastone (IMT Lucca)
Available for:
Computer Science and System Engineering

Research Topics in Computer Science

Abstract:
The goal of this course is to get students acquainted with research methods in computer science, including publication strategies and a classification of its main outlets (workshops, conferences, and journals). Students will receive a broad perspective on the major sub-fields computer science (e.g., programming languages, verification, software engineering, security, …) by means of guest lectures delivered by leading experts in the respective areas.
Hours:
20
Professors/Lecturers:
Rocco De Nicola (IMT Lucca); Mirco Tribastone (IMT Lucca)
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.
Hours:
8
Professors/Lecturers:
Luca Aceto (Reykjavik University)
Available for:
Analysis and Management of Cultural Heritage; Computer Science and System Engineering; Economics, Networks and Business Analytics; Cognitive, Computational and Social Neurosciences

Software Verification

Abstract:
Software verification is the process by which a computer program is analysed in order to prove its correctness or to discover bugs. This course will introduce students to this topic with an overview of several techniques based on both testing and static verification, such as abstract interpretation, model checking, and satisfiability modulo theories. Students will be exposed to both theory and practice of software verification by means of practical sessions with state-of-the-art software tools.
Hours:
20
Professors/Lecturers:
Tbd
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).

Prerequisites: Matrix Algebra + Foundations of Probability and Statistical Inference
Hours:
30
Professors/Lecturers:
Irene Crimaldi (IMT Lucca)
Specializing course for:
Economics, Networks and Business Analytics
Also available for:
Computer Science and System Engineering; Cognitive, Computational and Social Neurosciences