# Courses

## Complex Networks

Academic Year 2014 - 2015

### Advanced Topics of Complex Networks

- Abstract:
- This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on Natural Networks (Networks).
- Hours:
- 20
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca); Walter Quattrociocchi (IMT Lucca)
- Compulsory for:
- Complex Networks
- Also available for:
- Computational Mechanics; Computer Science; Image Analysis; Management Science; Control Systems

### Algorithmics

- Abstract:
- This course covers basic and advanced foundations, problems and solutions of algorithmic computation. A first part offer an overview of the fundamental notions of algorithm analysis and recalls algorithmic solutions (and their complexity) for some basic problems like sorting and searching. The second part of the course will focus on advanced algorithms which are essential in some of the research fields relevant to the different curriculum of the Computer Decision and System Science track.
- Hours:
- 20
- Professors/Lecturers:
- Walter Quattrociocchi (IMT Lucca)
- Available for:
- Complex Networks; Computer Science; Image Analysis

### Banking and Finance (long seminar with optional exam)

- Abstract:
- TBD
- Hours:
- 12
- Professors/Lecturers:
- Michele Bonollo (IASON ltd.)
- Available for:
- Complex Networks; Computer Science; Economics; Management Science; Control Systems

### Basic Numerical Linear Algebra

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

### 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)
- Compulsory for:
- Complex Networks; Management Science
- Also available for:
- Computational Mechanics; Computer Science; Economics; Image Analysis; Control Systems

### Convex Optimization

- Abstract:
- The course aims at giving a modern and thorough treatment of algorithms for solving convex, large-scale and nonsmooth optimization problems. Applications of convex optimization. Convex sets, functions and optimization problems. Optimality conditions. Basic algorithms for unconstrained optimization (gradient, fast gradient and Newton methods). Basic algorithms for constrained optimization (Interior point and active set methods). Subdifferential and conjugate of convex functions. Duality. Proximal mappings. Proximal minimization algorithm. Augmented Lagrangian Method. Forward-Backward and Douglas-Rachford splitting. Alternating Direction Method of Multipliers (ADMM). Coordinate descent.
- Hours:
- 20
- Professors/Lecturers:
- Stephen Boyd (Stanford University)
- Compulsory for:
- Computational Mechanics; Control Systems
- Also available for:
- Complex Networks; Computer Science; Image Analysis

### Data Science with Complex Networks

- Abstract:
- Complex Systems are everywhere and in the era of massive production of electronic data coming from all sort of devices it is of crucial importance to have the right tools to manage and extract from them all the valuable information. To this aim during this course we will develop both the basic theoretical tools and the practical coding technics to tackle all sort of complex systems, ranging from Trade and Financial Networks, to the World Wide Web and the Social Networks. In particular Complex Networks Theory proved to be successful in the process of handling this enormous quantity of data and in order to apply these concepts to the various cases it is crucial to define a clear strategy and guidelines to represent the system data in the shape of a network. Using the Python scripting language we will introduce state of the art methods and algorithms to cope with some reference dataset.
- Hours:
- 20
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca); Alessandro Chessa (IMT Lucca)
- Compulsory for:
- Complex Networks
- Also available for:
- Computational Mechanics; Computer Science; Economics; Image Analysis; Management Science; Control Systems

### Ethics and Research: Objectivity, Neutrality and Values in Science

- Abstract:
- The course has been cancelled
- Hours:
- 10
- Professors/Lecturers:
- Tbd
- Available for:
- Analysis and Management of Cultural Heritage; Computational Mechanics; Complex Networks; Computer Science; Economics; Image Analysis; Management Science; Control Systems

### Finance

- Abstract:
- The course covers important topics in modern quantitative finance and risk management: efficient market hypothesis and violations, financial markets micro-structure and types of arbitrage, general principles of modelling the price dynamics of financial assets, market risk and other types of financial risks, Value-at-Risk (VaR) approach and applications, modelling of extreme events and crisis, VaR analysis for financial derivatives, copula methods,modelling of trends in time series in connection with technical analysis, and the foundations of high-frequency arbitrage trading. This course will enable the students to develop both theoretical knowledge and practical skills to analyze modern financial markets.
- Hours:
- 20
- Professors/Lecturers:
- Roberto Renò (Università degli Studi di Siena)
- Compulsory for:
- Management Science
- Also available for:
- Complex Networks; Economics; Control Systems

### Foundations of Probability Theory and Statistical Inference

- Abstract:
- This course aims at introducing the fundamental concepts of probability theory and statistical

inference.

Some proofs are sketched or omitted in order to have more time for examples, applications and

exercises.

In particular, the course deals with the following topics:

• probability space, random variable, expectation, variance, cumulative distribution function, discrete and absolutely continuous distributions, random vector, joint and marginal distributions, joint cumulative distribution function, covariance,

• conditional probability, independent events, independent random variables, conditional probability density function, order statistics,

• multivariate Gaussian distribution,

• probability-generating function, Fourier transform/characteristic function,

• types of convergence and some related important results,

• point estimation, interval estimation, hypothesis testing, linear regression, introduction to Bayesian statistics. - Hours:
- 30
- Professors/Lecturers:
- Irene Crimaldi (IMT Lucca)
- Compulsory for:
- Complex Networks; Economics; Management Science
- Also available for:
- Computational Mechanics; Computer Science; Image Analysis; Control Systems

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

- Abstract:
- This 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 the proposal are given.
- Hours:
- 10
- Professors/Lecturers:
- Marco Paggi (IMT Lucca)
- Available for:
- Analysis and Management of Cultural Heritage; Computational Mechanics; Complex Networks; Computer Science; Economics; Image Analysis; Management 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.
- Hours:
- 40
- Professors/Lecturers:
- Nicola Dimitri (Università degli Studi di Siena)
- Compulsory for:
- Complex Networks; Economics; Management Science
- Also available for:
- Computer Science; Control Systems

### Introduction to Network Theory

- Abstract:
- TBD
- Hours:
- 10
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca)
- Compulsory for:
- Analysis and Management of Cultural Heritage; Complex Networks; Management Science
- Also available for:
- Computational Mechanics; Computer Science; Economics; Image Analysis; Control Systems

### Large Scale Image Analysis for Natural and Life Sciences

- Abstract:
- Principles of imaging modalities (optical microscopy, spectroscopy, CT, MRI, PET, SPECT) and their applications in natural and life sciences (Dharmakumar); Basics of image analysis (filtering, segmentation, detection) and basics of statistical mining; Designing robust image analysis methods; Large-scale analysis; Integration with databases and knowledge sharing platforms; Error testing and precision bound repetition studies for longitudonal and group studies (phenotyping); High performance computing for imaging (computer vision); Scientific and data visualization; Prerequisites: Probability and basic random processes, basic computer programming, statistics (or econometrics), databases.
- Hours:
- 20
- Professors/Lecturers:
- Sotirios Tsaftaris (The University of Edinburgh); Rohan Dharmakumar (Cedars-Sinai Medical Center)
- Compulsory for:
- Image Analysis
- Also available for:
- Computational Mechanics; Complex Networks; Computer Science

### Management and Corporate Finance

- Abstract:
- Applications of quantitative techniques to managerial decisions (data-driven decision making). Topics include applications of data mining, machine learning, statistical models, predictive analytics, econometrics, optimization, risk analysis, decision theory, data visualization and business communication in finance, marketing, operations, R&D, business intelligence and other business areas generating and consuming large amounts of data.
- Hours:
- 20
- Professors/Lecturers:
- Fabio Pammolli (Politecnico di Milano)
- Compulsory for:
- Analysis and Management of Cultural Heritage; Management Science
- Also available for:
- Complex Networks; Computer Science; Economics; Control Systems

### Management of Complex Systems: Approaches to Problem Solving

- Abstract:
- Methods and approach to problem solving. Problem analysis; analysis of complex systems (related to cultural heritage, such as a city of art organization, promotion, etc.). The course will include practical simulations. The course will be linked to a seminar on specific Case studies.
- Hours:
- 40
- Professors/Lecturers:
- Andrea Zocchi; Dario Cacciatore (Whirlpool Corporation)
- Compulsory for:
- Analysis and Management of Cultural Heritage
- Also available for:
- Complex Networks; Computer Science; Management Science; Control Systems

### Network Theory

- Abstract:
- Course description: Basic of Graph Theory: degree, clustering, connectivity, assortativity, communities. Analysis of Complex Networks, datasets and software. Community Detection, Modularity, Spectral Properties. Fractals, Self-Organised Criticality, Scale Invariance. Random Graph, Barabasi Albert Model, Fitness model, Small world. HITS Algorithm and PageRank. Real instances of Complex Networks in Biology and Social Sciences. Board of Directors, Ownership Networks, measures of Centrality and Control. World Trade Web, Minimal Spanning Trees, Competition and Products spaces. Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis.
- Hours:
- 10
- Professors/Lecturers:
- Guido Caldarelli (IMT Lucca); Antonio Scala (CNR - Istituto di Sistemi Complessi)
- Compulsory for:
- Complex Networks
- Also available for:
- Computational Mechanics; Computer Science; Image Analysis; Management Science; Control Systems

### Optimal Control

- Abstract:
- Discrete-time optimal control: dynamic programming for finite/infinite horizon and deterministic/stochastic optimization problems. LQ and LQG problems, Riccati equations, Kalman filter. Deterministic continuous-time optimal control: the Hamilton-Jacobi-Bellman equation and the Pontryagin’s principle. Examples of optimal control problems in economics.
- Hours:
- 20
- Professors/Lecturers:
- Giorgio Stefano Gnecco (IMT Lucca)
- Compulsory for:
- Complex Networks; Economics; Management Science
- Also available for:
- Computational Mechanics; Computer Science; Image Analysis; Control Systems

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

- Abstract:
- TBD
- Hours:
- 8
- Professors/Lecturers:
- Luca Aceto (Reykjavik University)
- Available for:
- Analysis and Management of Cultural Heritage; Computational Mechanics; Complex Networks; Computer Science; Economics; Image Analysis; Management Science; Control Systems

### Socio-Economic Networks

- Abstract:
- TBD
- Hours:
- 10
- Professors/Lecturers:
- Massimo Riccaboni (IMT Lucca); Giorgio Fagiolo (Scuola Superiore Sant’Anna, Pisa)
- Compulsory for:
- Complex Networks; Management Science
- Also available for:
- Computer Science; Economics; Control Systems

### Statistics Lab.

- Abstract:
- - Brief introduction to R (http://www.r-project.org/)

- Creating random variables.

- Applications to the central limit theorem and the law of large numbers

- Descriptive statistics: (i) Representing probability and cumulative distribution functions in discrete and continuous cases; (ii) calculating mean, variance, concentration indexes, covariance and correlation coeff.

- Statistical inference: (i) Point estimation and properties; (ii) interval estimation and properties; (iii) hypothesis testing and properties.

- Theory and applications of simple regression model (model, assumptions, estimation methods, residual diagnostics).

- If time permits:

Theory and applications of Bootstrap and Jacknife elements for simple parameters and for the regression model parameters.

Prerequisites: The topics of “Foundations of Probability Theory and Statistical inference” are

supposed known. - Hours:
- 10
- Professors/Lecturers:
- Irene Crimaldi (IMT Lucca); Rodolfo Metulini (IMT Lucca)
- Available for:
- Computational Mechanics; Complex Networks; Computer Science; Economics; Image Analysis; Management Science; Control Systems

### Stochastic Processes and Stochastic Calculus

- Abstract:
- This course aims at introducing some important stochastic processes (Markov chains, martingales,

Poisson process, Wiener process) and Ito 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,

- 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,

- Markov processes,

- Wiener process and Ito calculus,

- Ornstein-Uhlenbeck process.

Prerequisites: The topics of “Foundations of Probability Theory and Statistical Inference” are supposed to be known. - Hours:
- 30
- Professors/Lecturers:
- Irene Crimaldi (IMT Lucca); Andrea Gabrielli ( Istituto dei Sistemi Complessi (ISC) - CNR, UOS "Sapienza")
- Compulsory for:
- Complex Networks
- Also available for:
- Computational Mechanics; Computer Science; Economics; Image Analysis; Management Science; Control Systems

### Theory and Numerics of Ordinary and Partial Differential Equations

- Abstract:
- The first lesson of the course will provide a primer on complex variables. Using this mathematical formalism, the focus of the remaining first part of the course will be to introduce linear ordinary and linear partial differential equations, and the "cheap" methods to solve them using Fourier and Laplace transforms. The ordinary and partial differential equations will be placed into a context of applied mathematics (e.g. classic deterministic and stochastic systems) saving the theoretical approach for advanced lectures. The lecture notes will be provided in Mathematica computable document format, with an emphasis on graphical in-class demonstration.

The second part of the course will introduce PhD students to numerical techniques for the approximate treatment of linear partial differential equations (PDEs) governing physical, engineering and financial problems. The theoretical fundamentals 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. Special attention is given to the finite element technology and to the implementation of the weak forms into a research code for fast intensive computations. - Hours:
- 40
- Professors/Lecturers:
- Alexander Petersen (IMT Lucca); Marco Paggi (IMT Lucca)
- Compulsory for:
- Computational Mechanics; Complex Networks; Economics
- Also available for:
- Computer Science; Image Analysis; Management Science; Control Systems