Courses

Advanced Numerical Analysis
Corpo:

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

Ore:
20
Professors:
Valeria Simoncini (Università di Bologna), Benedetta Morini (Università degli Studi di Firenze)
Advanced Topics in Network Theory: Algorithms and Applications
Corpo:

Centrality metrics and spectral properties of graphs.
Community detection.
Bipartite and multilayer networks.
Applications: World Trade Web

Lecture 1: Centrality metrics
Lecture 2: Spectral properties
Lecture 3: Ranklings and reputation on graphs
Lecture 4: Community detection in networks I
Lecture 5: Community detection in networks II
Lecture 6: Bipartite networks
Lecture 7: Multilayer networks
Lecture 8: World Trade Web
Lecture 9: Infrastructural network I
Lecture 10: Infrastructural network II

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca), Fabio Saracco (IMT Lucca), Angelo Facchini (IMT Lucca)
Advanced Topics in Network Theory: Algorithms and Applications
Corpo:

Centrality metrics and spectral properties of graphs.
Community detection.
Bipartite and multilayer networks.
Applications: Worls Trade Web
Lecture 1: Centrality metrics
Lecture 2: Spectral properties
Lecture 3: Ranklings and reputation on graphs
Lecture 4: Community detection in networks I
Lecture 5: Community detection in networks II
Lecture 6: Bipartite networks
Lecture 7: Multilayer networks
Lecture 8: World Trade Web
Lecture 9: Infrastructural network I
Lecture 10: Infrastructural network II 

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca), Fabio Saracco (IMT Lucca), Angelo Facchini (IMT Lucca)
Advanced Topics in Network Theory: Brain Networks
Corpo:

TBD

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca), Tommaso Gili (IMT Lucca)
Advanced Topics in Network Theory: Brain Networks
Corpo:

TBD

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca), Tommaso Gili (IMT Lucca)
Advanced Topics in Network Theory: Complex Networks and Python
Corpo:

TBD

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca)
Advanced Topics in Network Theory: Complex Networks and Python
Corpo:

TBD

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca)
Advanced Topics in Network Theory: Dynamical Processes of Networks
Corpo:

Mean field and master equations.
Percolation and epidemic models.
Contagion: the case of financial networks.

Applications of network theory.

Lecture 1: Master equations for network models
Lecture 2: Fitness and relevance models
Lecture 3: Epidemic processes in mean fields
Lecture 4: Epidemics on networks
Lecture 5: Scaling and percolation on networks
Lecture 6: Contagion in financial network I
Lecture 7: Contagion in financial network II
Lecture 8: Game theory on networks
Lecture 9: Evolutionary network games
Lecture 10: Networks from time series and visibility graph

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca) Giulio Cimini (IMT Lucca)
Advanced Topics in Network Theory: Dynamical Processes of Networks
Corpo:

Mean field and master equations.
Percolation and epidemic models.
Contagion: the case of financial networks.
Applications of network theory.
Lecture 1: Master equations for network models
Lecture 2: Fitness and relevance models
Lecture 3: Epidemic processes in mean fiels
Lecture 4: Epidemics on networks
Lecture 5: Scaling and percolation on networks
Lecture 6: Contagion in financial network I
Lecture 7: Contagion in financial network II
Lecture 8: Game theory on networks
Lecture 9: Evolutionary network games
Lecture 10: Networks from time series and visibility graph 

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca), Giulio Cimini (IMT Lucca)
Analytics in Economics and Management
Corpo:

The aim of this course is to teach students how to produce a research paper in economics and management using hands-on empirical tools for different data structures. We will bridge the gap between applications of methods in published papers and practical lessons for producing your own research. After introductions to up-to-date illustrative contributions to literature, students will be asked to perform their own analyses and comment results after applications to microdata provided during the course

How productive is a firm, an industry or a country? Why? Where is it more profitable to locate an economic activity? Who buys what products? How long can we expect a company to outlive its competitors? What is the relationship between economic welfare and size of a city? How do economic agents interact socially in a geographic space or in a workplace?

The objective is to develop a critical understanding of the iterative research process leading from real economic data to the choice of the best tools available from the analyst kit. Students are expected to be familiar with macroeconomics, microeconomics and econometrics from the first-year sequence.

Final scores will be based 50% on individual presentations of a selected supplemental reading and 50% on an individual homework.

Ore:
20
Professors:
Massimo Riccaboni (IMT Lucca)
Behavioral Economics
Corpo:

TBD

Ore:
20
Professors:
Ennio Bilancini (IMT Lucca)
Behavioral Economics
Corpo:

TBD

Ore:
20
Professors:
Ennio Bilancini (IMT Lucca)
Business Model for Emerging Markets
Corpo:

Teaching contents:

1. The economy of the intangibles
2. Manufacturing and robot
3. Strategy and business model
4. How to model a business
5. How to model a business in a complex scenario
6. What make market emerging? Not only new lands.
7. The Blockchain technology and the future
8. Initial Coins Offering (ICO) compressed between Business plan and White paper
9. Possible value of Blockchain technology for Small and medium Italian sized business
10. A global value chain approach to protect and foster strategic identity

Business case

Students will learn how to evaluate strategies, as well as how to locate sources of potential competitive advantage from a perspective that, for the purpose of this course, encompasses the internal and dynamic fit of a strategy. They will also learn how to identify organizational barriers and corporate behaviors that sustain or challenge the development and execution of strategies, and the competitive advantage of a company.

Ore:
20
Professors:
Nicola Lattanzi (IMT Lucca)
Business Model for Emerging Markets
Corpo:

Teaching contents:

1. The economy of the intangibles
2. Manufacturing and robot
3. Strategy and business model
4. How to model a business
5. How to model a business in a complex scenario
6. What make market emerging? Not only new lands.
7. The Blockchain technology and the future
8. Initial Coins Offering (ICO) compressed between Business plan and White paper
9. Possible value of Blockchain technology for Small and medium Italian sized business
10. A global value chain approach to protect and foster strategic identity 

Business case

Students will learn how to evaluate strategies, as well as how to locate sources of potential competitive advantage from a perspective that, for the purpose of this course, encompasses the internal and dynamic fit of a strategy. They will also learn how to identify organizational barriers and corporate behaviors that sustain or challenge the development and execution of strategies, and the competitive advantage of a company.

Ore:
20
Professors:
Nicola Lattanzi (IMT Lucca)
Computer Programming and Methodology
Corpo:

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.

Ore:
20
Professors:
Mirco Tribastone (IMT Lucca)
Computer Programming and Methodology
Corpo:

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.

Ore:
20
Professors:
Mirco Tribastone (IMT Lucca)
Critical Thinking (long seminar without exam)
Corpo:

Constructing and evaluating arguments is fundamental in all branches of science, as well as in everyday life. The course provides the basic skills and tools to recognize correct forms of inference and reasoning, detect the unsound or fallacious ones, and assess the strength of various kinds of argument. The toolbox includes elementary deductive logic, patterns of inductive and abductive inference, the basics of statistical and probabilistic reasoning, and the analysis of heuristics and biases in cognitive psychology. We shall discuss real-world examples of correct and incorrect reasoning from both scientific and non-scientific literature (newspapers, social media, and so on). No previous knowledge of logic, philosophy, or advanced mathematics is required.

Ore:
10
Professors:
Gustavo Cevolani (IMT Lucca)
Data Science Lab
Corpo:

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

Ore:
15
Professors:
Valentina Tortolini (IMT Lucca)
Data Science Lab
Corpo:

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

Ore:
15
Professors:
Valentina Tortolini (IMT Lucca)
Decision-Making in Economics and Management
Corpo:

The main goals of the course are:
(1) to take economic theories and methodologies out into the world, applying them to interesting questions of individual behavior and societal outcomes;
(2) to develop a basic understanding of human psychology and social dynamics as they apply to marketing contexts;
(3) to become familiar with the major theory and research methods for analyzing consumer behavior;
(4) to develop market analytics insight into consumer actions.

Most of time will be devoted to close reading of research papers, including discussion of the relative merits of particular methodologies. Students will participate actively in class discussion, engage with cutting-edge research, evaluate empirical data, and write an analytical paper. The course aims at enabling students to develop and enhance their own skills and interests as applied microeconomists.

Ore:
10
Professors:
Massimo Riccaboni (IMT Lucca)
Econometrics I
Corpo:

- Review of Asymptotic Theory
- Theory and Algebra of OLS
- Inference, non-spherical Errors and Clustering
- Structural Models, Identification and Causality
- Simultaneous Equation Models, 2SLS and 3SLS
- Introduction to M-Estimation
- Generalized Method of Moments
- Maximum Likelihood Estimation

Ore:
20
Professors:
Paolo Zacchia (IMT Lucca)
Econometrics I
Corpo:

- Review of Asymptotic Theory
- Theory and Algebra of OLS
- Inference, non-spherical Errors and Clustering
- Structural Models, Identification and Causality
- Simultaneous Equation Models, 2SLS and 3SLS
- Introduction to M-Estimation
- Generalized Method of Moments
- Maximum Likelihood Estimation 

Ore:
20
Professors:
Paolo Zacchia (IMT Lucca)
Econometrics II
Corpo:

- Microdata and Heterogeneity
- Potential Outcome Framework
- Difference-in-difference and treatment effects
- Linear and Static Panel Data Models
- Linear and Dynamic Panel Data Models
- Non-Linear Models
- Categorical variables and count data
- Multinomial models

Ore:
20
Professors:
Armando Rungi (IMT Lucca)
Econometrics II
Corpo:

- Microdata and Heterogeneity
- Potential Outcome Framework
- Difference-in-difference and treatment effects
- Linear and Static Panel Data Models
- Linear and Dynamic Panel Data Models
- Non-Linear Models
- Categorical variables and count data
- Multinomial models

Ore:
20
Professors:
Armando Rungi (IMT Lucca)
Finance
Corpo:

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

Ore:
20
Professors:
Tbd
Finance
Corpo:

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  

Ore:
20
Professors:
Tbd
Firms, Business Analytics and Managerial Behavior
Corpo:

Teaching contents:

1. Theory of the Firm
2. The system of force in a business organization
3. The balance between efficiency of the production and effectiveness in results
4. Business performance and ways to represent
5. The financial statement
6. How to read and comprehend performances and results
7. Methodology and tools for Balance sheet analysis
8. Prevision versus prediction and business analytics
9. Entrepreneurship and management in complex scenario
10. Neuroscience, decision making process and managerial behavior

Business case

Students will learn how to evaluate strategies, as well as how to locate sources of potential competitive advantage from a perspective that, for the purpose of this course, encompasses the internal and dynamic fit of a strategy. They will also learn how to identify organizational barriers and corporate behaviors that sustain or challenge the development and execution of strategies, and the competitive advantage of a company.

Ore:
20
Professors:
Nicola Lattanzi (IMT Lucca)
Firms, Business Analytics and Managerial Behavior
Corpo:

Teaching contents:
1. Theory of the Firm
2. The system of force in a business organization
3. The balance between efficiency of the production and effectiveness in results
4. Business performance and ways to represent
5. The financial statement
6. How to read and comprehend performances and results
7. Methodology and tools for Balance sheet analysis
8. Prevision versus prediction and business analytics
9. Entrepreneurship and management in complex scenario
10. Neuroscience, decision making process and managerial behavior

Business case

Students will learn how to evaluate strategies, as well as how to locate sources of potential competitive advantage from a perspective that, for the purpose of this course, encompasses the internal and dynamic fit of a strategy. They will also learn how to identify organizational barriers and corporate behaviors that sustain or challenge the development and execution of strategies, and the competitive advantage of a company. 

Ore:
20
Professors:
Nicola Lattanzi (IMT Lucca)
Forensic Psychology and Psychiatry
Corpo:

TBD

Ore:
12
Professors:
Pietro Pietrini (IMT Lucca)
Foundations of Probability and Statistical Inference
Corpo:

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

Ore:
30
Professors:
Irene Crimaldi (IMT Lucca)
Foundations of Probability and Statistical Inference
Corpo:

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. 

Ore:
30
Professors:
Irene Crimaldi (IMT Lucca)
Funding and Management of Research and Intellectual Property (long seminar without exam)
Corpo:

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.

Ore:
10
Professors:
Marco Paggi (IMT Lucca)
Funding and Management of Research and Intellectual Property (long seminar without exam)
Corpo:

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.

Ore:
10
Professors:
Marco Paggi (IMT Lucca)
Game Theory
Corpo:

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.

Ore:
20
Professors:
Kenan Huremovic (IMT Lucca), Ennio Bilancini (IMT Lucca)
Game Theory
Corpo:

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. 

Ore:
20
Professors:
Kenan Huremovic (IMT Lucca), Ennio Bilancini (IMT Lucca)
Identification, Analysis and Control of Dynamical Systems
Corpo:

The course provides an introduction to dynamical systems, with emphasis on linear systems in state-space form. 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 briefly 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.

Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis.

Ore:
20
Professors:
Alberto Bemporad (IMT Lucca)
Identification, Analysis and Control of Dynamical Systems
Corpo:

The course provides an introduction to dynamical systems, with emphasis on linear systems in state-space form. 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 briefly 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.

Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis.

Ore:
20
Professors:
Alberto Bemporad (IMT Lucca)
International Economics
Corpo:

This course introduces students to the analyses of the most important up-to-date topics in international economics. The objective is to gain an in-depth understanding of the causes and consequences of economic globalization. Emphasis will be given on the internationalization strategies of firms, the organization of production in a global economy, and consequences on labor markets.

Part 1 (F. Serti):
o Overview of Theories of International Trade
o International trade and firm heterogeneity: evidence from firm level data
o Trade and the Labor Market: evidence from local labor markets
o Trade and the Labor Market: evidence from worker and firm level data
o Offshoring and tasks

Part 2 (A. Rungi):
o Gravity Models for International Trade
o The Role of Multinational Enterprises
o Organization of Global Value and Supply chains
o Income inequality and Economic Globalization
o Trade and Investment Policies 

Prerequisites: Microeconomics + Econometrics I + Econometrics II…

Ore:
20
Professors:
Massimo Riccaboni (IMT Lucca), Armando Rungi (IMT Lucca)
Introduction to Cognitive and Social Psyschology
Corpo:

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.

Ore:
24
Professors:
Pietro Pietrini (IMT Lucca), Emiliano Ricciardi (IMT Lucca)
Introduction to Cognitive and Social Psyschology
Corpo:

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.

Ore:
24
Professors:
Pietro Pietrini (IMT Lucca), Emiliano Ricciardi (IMT Lucca)
Introduction to Complex Systems and Networks
Corpo:

Complexity, self-similarity, scaling, self-organised criticality.
Definition of graphs, real networks and their properties.
Models of static networks, models of network growth.

Lecture 01 Graph Theory Introduction
Lecture 02 Properties of Complex Networks
Lecture 03 Communities
Lecture 04 Different Kind of Graphs
Lecture 05 Ranking
Lecture 06 Static Models of Graphs
Lecture 07 Dynamical Models of Graphs 
Lecture 08 Fitness Models
Lecture 09 World Trade Web
Lecture 10 Financial Networks

Ore:
10
Professors:
Guido Caldarelli (IMT Lucca)
Introduction to Economics
Corpo:

(P. Zacchia): Brief introduction to microeconomics designed for students without previous exposure to it.
This module will cover the following topics, focusing on the interplay between formal models and intuitions:

- Individual choice;
- Equilibrium in competitive markets;
- Imperfectly competitive markets;
- Issues of market failures;
- Concepts of information economics 

(F. Serti): This course will provide with a basic introduction of the main notions in Macroeconomics. Its main goal is to give students a big picture of the macroeconomy and the link between output, employment, and inflation in the short term.
After introducing the fundamentals, the course will then introduce basic macroeconomic models such as the Keynesian AD-AS model and the IS-LM model.
The course will also give some introductory notions of the Phillips curve and its relation with the IS-LM model.

Ore:
20
Professors:
Paolo Zacchia (IMT Lucca), Francesco Serti (IMT Lucca)
Machine Learning
Corpo:

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.

Ore:
20
Professors:
Giorgio Stefano Gnecco (IMT Lucca)
Management of Complex Systems: Approaches to Problem Solving
Corpo:

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.

Ore:
30
Professors:
Andrea Zocchi
Numerical Methods for the Solution of Partial Differential Equations
Corpo:

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.

Ore:
20
Professors:
Marco Paggi (IMT Lucca)
Numerical Optimization
Corpo:

Optimization plays a key role in solving a large variety of decision problems that arise in engineering (design, process operations, embedded systems), data science, machine learning, business analytics, finance, economics, and many others. This course focuses on formulating optimization models and on the most popular numerical methods to solve them. The topics covered in the course include: modeling (linear programming models, convex optimization models), basic optimization theory (optimality conditions, sensitivity, duality), algorithms for constrained convex optimization (active-set methods for linear and quadratic programming, proximal methods and ADMM, stochastic gradient, interior-point methods), line-search methods for unconstrained nonlinear programming, sequential quadratic programming.

Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis.

Ore:
20
Professors:
Alberto Bemporad (IMT Lucca)
Optimal Control
Corpo:

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.

Ore:
20
Professors:
Giorgio Stefano Gnecco (IMT Lucca)
Philosophy of Science (long seminar without exam)
Corpo:

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.

Ore:
10
Professors:
Gustavo Cevolani (IMT Lucca)