# Courses

## Economics, Management and Data Science

Academic Year 2016 - 2017

### 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); Benedetta Morini (Università degli Studi di Firenze)
- Available for:
- Computer Science and System Engineering; Economics, Management and Data Science

### Advanced Topics of Networks

- Abstract:
- Complex Networks are an ubiquitous presence in Economic and Financial systems 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 these kind of systems, ranging from the International Trade and the 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.

We shall present some cases of study and introduce the computational instruments to handle this data. The course will be based on the text "Data Science and complex networks" G. Caldarelli A. Chessa OUP 2016.

Prerequisites: Networks - Hours:
- 20
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca); Alessandro Chessa (IMT Lucca); Michelangelo Puliga (IMT Lucca)
- Specializing course for:
- Economics, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering

### Analytics and Data Science in Economics and Management I

- Abstract:
- A) Python Course for Data Science (A. Chessa):

1) Introduction to the language: basic statements (if, else, type casting), cycles and functions, examples and exercices;

2) Diving into the language: advanced types: sets and dictionaries, classes and modules, using PIP and ipython, examples and exercises;

3) Scraping the web: introduction to BeautifulSoup, the regular expressions module re, the request module, examples and exercises;

4) Introduction to Plotting: basic numpy, plotting overview, examples and exercises;

5) Data science utilities: introduction to SQL (sqlite/mysql).

B) 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. Examples from many disciplines: economics, education, other social sciences, epidemiology, and biomedical science. Evaluations of job training programs, educational voucher schemes, changes in laws such as minimum wage laws, medical treatments, smoking, military service.

This course involves using the software R, which is available for free. No previous experience with R is necessary. However, those without previous R experience should expect to spend extra time on assignments as they familiarize themselves with the program.

Prerequisites: Matrix Algebra + Optimal Control + Foundations of Probability & Statistical Inference - Hours:
- 30
- Professors/Lecturers:
- Alessandro Chessa (IMT Lucca); Fabrizia Mealli (Università degli Studi di Firenze)
- Compulsory for:
- Economics, Management and Data Science
- Also available for:
- Computer Science and System Engineering

### Analytics and Data Science in Economics and Management II

- Abstract:
- 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. - Hours:
- 30
- Professors/Lecturers:
- Massimo Riccaboni (IMT Lucca); Armando Rungi (IMT Lucca)
- Compulsory for:
- Economics, Management and Data Science

### Applied Econometrics I

- 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 (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 3 (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: Introduction to Economics + Matrix Algebra + Foundations of Probabilistic and Statistical Inference - Hours:
- 50
- Professors/Lecturers:
- Cristina Tealdi (Heriot-Watt University); Armando Rungi (IMT Lucca); Paolo Zacchia (IMT Lucca)
- Compulsory for:
- Economics, Management and Data Science
- Also available for:
- Computer Science and System Engineering

### Applied Econometrics II

- Abstract:
- This course deals with the following topics:

1) Regression and Causality: a) Properties of the Conditional Expectation Function; b) Bad controls; c) Omitted variable bias; d) Measurement errors; e) Simultaneous equations; f) How to write an empirical project.

2) The Evaluation Problem and Randomised Experiments: a) Introduction to the evaluation problem; b) Randomised Experiments; c) Practical problems when running experiments; d) Duflo et al (2007) on randomization in development; e) Application I: Krueger (1999) on class size and educational test scores; f) Application II: Blundell et al (2004) on education and earnings in the UK.

3) Quasi-Experiments: a) Matching; b) Propensity Score Matching; c) Evaluating the validity of matching estimators; d) Application I: Caliendo et al., (2005) on job creation in Germany; e) Application II: Jones and Olken (2009) on assassination and institutions.

4) Differences-in-Differences: a) Basics; b) Regression Differences-in-Differences; c) The Synthetic Control Method; d) Application I: Card & Krueger (1994) on minimum wage and unemployment; e) Application II: Abadie & Gardeazabal (2003) on the effect of terrorism in the Basque region; f) Application III: Autor (2003) on unjust dismissal doctrine and employment.

5) Regression Discontinuity Design: a) Sharp RD; b) Fuzzy RD; c) Running RD Models; d) Application I: Lee (2008) on U.S. House elections; e) Application II: Angrist & Lavy (1999) on scholastic achievement.

Prerequisites: Applied Econometrics 1 - Hours:
- 20
- Professors/Lecturers:
- Vincenzo Bove (University of Warwick)
- Compulsory for:
- Economics, Management and Data Science

### 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 & Stochastic Calculus + Finance - Hours:
- 10
- Professors/Lecturers:
- Michele Bonollo (IASON ltd.)
- Available for:
- Computer Science and System Engineering; Economics, Management and Data Science

### 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:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### 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, Management and Data Science

### Critical Thinking (long seminar without exam)

- Abstract:
- Critical Thinking is an introductory course in the principles of good reasoning. Its main focus lies in arguments, their nature, their use and their import. Unlike a course in pure Logic, which would spell out universal formal rules of correct reasoning, Critical Thinking is more concerned with the unruly nature of real argumentation that does not allow unambiguous and definite formalization. The course is designed to serve as a methodical preparation for more effective reasoning and improved cognitive skills. Its ambition is to develop those intellectual dispositions that are essential for effective

evaluation of truth claims as well as for making reasonable decisions based on what we know or

believe to know. It is more about the quality of our beliefs and the reasons that support them than about their content. It will make ample use of examples taken from real world case studies, books, scientific or newspaper articles. Students will be encouraged to participate in the discussion over each example, and to find out more of their own. - Hours:
- 10
- Professors/Lecturers:
- Stefano Gattei (Chemical Heritage Foundation, Philadelphia)
- Compulsory for:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences
- Also available for:
- Economics, Management and Data Science

### 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:
- Tbd; Valentina Tortolini (IMT Lucca)
- Available for:
- Economics, Management and Data Science

### Decision-Making in Economics and Management

- Abstract:
- 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. - Hours:
- 20
- Professors/Lecturers:
- Massimo Riccaboni (IMT Lucca); Zhen Zhu (IMT Lucca)
- Compulsory for:
- Analysis and Management of Cultural Heritage; Economics, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences

### 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:
- 24
- Professors/Lecturers:
- Simone Giansante (University of Bath)
- Specializing course for:
- Economics, Management and Data Science
- Also available for:
- Computer Science and System Engineering

### Forensic and Legal Psychology

- Abstract:
- tbd
- Hours:
- 12
- Professors/Lecturers:
- Pietro Pietrini (IMT Lucca)
- Available for:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences; Economics, Management and Data Science

### 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, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences; 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)
- Available for:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### 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.

Prerequisites: Optimal Control - Hours:
- 30
- Professors/Lecturers:
- Nicola Dimitri (Università degli Studi di Siena)
- Compulsory for:
- Economics, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences; 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)
- Available for:
- Computer Science and System Engineering; Economics, Management and Data Science

### Innovation and Industrial Dynamics

- Abstract:
- This course will survey recent developments in theory and empirics of firm dynamics and its importance for aggregate outcomes such as innovation, growth and international trade. In particular, this class will center around the following questions:

a) what are the key empirical regularities on firm dynamics and what are the principal measurement issues?

b) what drives firms’ size and growth dynamics?

c) what determines the dynamics of entrepreneurial growth and innovation by firms?

d) how do different sources of firm-level heterogeneity influence aggregate outcomes?

e) what drives the rise and fall of inter-firm collaboration and trade networks?

This is a second year Ph.D. course. Students are expected to be familiar with macroeconomics, microeconomics and econometrics from the first-year sequence. - Hours:
- 20
- Professors/Lecturers:
- Massimo Riccaboni (IMT Lucca)
- Specializing course for:
- Economics, Management and Data Science

### 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:
- 32
- Professors/Lecturers:
- Pietro Pietrini (IMT Lucca); Emiliano Ricciardi (IMT Lucca)
- Available for:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### Introduction to Economics

- Abstract:
- (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.

(A. Belmonte): 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. - Hours:
- 20
- Professors/Lecturers:
- Paolo Zacchia (IMT Lucca); Alessandro Belmonte (IMT Lucca)
- Available for:
- 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)
- Compulsory for:
- Cognitive, Computational and Social Neurosciences
- Also available for:
- Analysis and Management of Cultural Heritage; Computer Science and System Engineering; Economics, Management and Data Science

### Machine Learning and Pattern Recognition

- Abstract:
- Basics of pattern recognition and machine learning and real world applications in imaging, internet, finance. Similarities and differences. Decision theory, ROC curves, Likelihood tests. Linear and quadratic discriminants. Template based recognition and feature detection/extraction. Supervised learning (Support vector machines, Logistic regression, Bayesian). Unsupervised learning (clustering methods, EM, PCA, ICA). 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:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### Macroeconomics

- Abstract:
- TBD
- Hours:
- 30
- Professors/Lecturers:
- Alessia Paccagnini (University College Dublin); Fabrizio Coricelli (Paris School of Economics)
- Compulsory for:
- 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:
- 20
- Professors/Lecturers:
- Andrea Zocchi
- Compulsory for:
- Analysis and Management of Cultural Heritage
- Also available for:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### Management Science and Corporate Finance

- Abstract:
- Thi course has been cancelled.
- Hours:
- 30
- Professors/Lecturers:
- Tbd
- Compulsory for:
- Economics, Management and Data Science
- Also available for:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering

### Matrix Algebra

- Abstract:
- This course is aimed to review the basic concepts of linear algebra:

1. Systems of linear equations: solution by Gaussian elimination, PA=LU factorization, Gauss-Jordan method.

2. Vector spaces and subspaces, the four fundamental subspaces, and the fundamental theorem of linear algebra.

3. Determinant and eigenvalues, symmetric matrices, spectral theorem, quadratic forms.

4. Cayley-Hamilton theorem, functions of matrices, and application of linear algebra to dynamical linear systems.

5. Iterative methods for systems of linear equations.

6. Ordinary lest squares problem, normal equations, A=QR factorization, condition number, Tikhonov regularization.

7. Singular-value decomposition, Moonre-Penrose pseudoinverse.

8. An economic application of linear algebra: the Leontief input-outpul model. - Hours:
- 10
- Professors/Lecturers:
- Giorgio Stefano Gnecco (IMT Lucca)
- Available for:
- Cognitive, Computational and Social Neurosciences; Economics, Management and Data Science

### Microeconomics

- Abstract:
- The course deals with some fundamental topics in Microeconomics. It aims at bringing the students from an intermediate to an advanced level of exposure and understanding of the material. The course will give emphasis to problem solving. For this reason problem sets will be assigned during the course at dates to be communicated in class. Students will then rotate on the board in a following lecture to discuss the problems.

Topics:

1 ) Consumer theory

2) Production theory

3) General equilibrium

4) Expected utility and choice under uncertainty

5) Contract theory and asymmetric Information

6) Mechanism design (if time)

Prerequisites: Introduction to Economics - Hours:
- 40
- Professors/Lecturers:
- Nicola Dimitri (Università degli Studi di Siena)
- Compulsory for:
- Economics, Management and Data Science

### 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: Matrix Algebra, Introduction to Networks, Foundations of Probability & Statistical Inference - Hours:
- 30
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca)
- Compulsory for:
- Economics, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering

### Neurobiology of Emotion and Behavior

- Abstract:
- This course will provide an introduction to general themes in Affective and Social Neurosciences, particularly focusing on the neural correlates of emotion and behavior.
- Hours:
- 12
- Professors/Lecturers:
- Pietro Pietrini (IMT Lucca)
- Compulsory for:
- Cognitive, Computational and Social Neurosciences
- Also available for:
- Analysis and Management of Cultural Heritage; Economics, Management and Data Science

### 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:

### 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, 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:
- Analysis and Management of Cultural Heritage; Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering; Economics, Management and Data Science

### Political Economy

- Abstract:
- The course is a relatively advanced (i.e. at the beginning graduate level) but essentially self-contained introduction to the methods and some major applications of modern political economy.

Topics:

• Institutions and “exogenous” differences in institutions

• At the origin of institutions: From Social Choice to Political Economics

• Median voter models

• Probabilistic voting models

• Agency models of politics: Electoral accountability and career concerns

• Partisan politicians

• Redistributive politics

• Dynamic policy problems with a focus on economic growth.

Prerequisites: The course assumes a good knowledge of macro and microeconomics (especially some growth theory, elementary taxation theory and game theory, including games with asymmetric/incomplete information and the theory of repeated games), of mathematical and statistical methods (especially static and dynamic optimization), and of econometrics (especially familiarity with the issue of causality in econometrics and IV estimation), at the level of the relevant courses offered at IMT.

In addition, students will be asked to read and present some articles along the way as a part of the final exam. - Hours:
- 30
- Professors/Lecturers:
- Alessandro Belmonte (IMT Lucca)
- Compulsory for:
- Economics, Management and Data Science

### Project Management

- Abstract:
- Project management; event management; communication and marketing; practical tools of organization; budgeting. Dealing with multiple stakeholders/ Risk management / Time management / PM tips to run an international research/Management plan concept on heritage sites / When applying for funds how do we measure project success / How we manage the output of the management plan / Flat organisations.
- Hours:
- 30
- Professors/Lecturers:
- Beatrice Manzoni (SDA Bocconi School of Management)
- Compulsory for:
- Analysis and Management of Cultural Heritage
- Also available for:
- Economics, Management and Data Science

### 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:

### States and Markets

- Abstract:
- This course has been cancelled.
- Hours:
- 30
- Specializing course for:
- Economics, Management and Data Science

### 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, Management and Data Science
- Also available for:
- Cognitive, Computational and Social Neurosciences; Computer Science and System Engineering