Courses

Computational Mechanics

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

Advanced Topics of Computer Science

Abstract:
This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on System Modelling and Analisys (SysMA).
Hours:
40
Professors/Lecturers:
Rocco De Nicola (IMT Lucca); Mirco Tribastone (IMT Lucca); Stefania Gnesi (CNR); Marinella Petrocchi (CNR)
Available for:
Computational Mechanics; Computer Science; Image Analysis; Control Systems

Advanced Topics of Control Systems

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

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

(course topics and grading plan available at http://dysco.imtlucca.it/atcs/)
Hours:
20
Professors/Lecturers:
Alberto Bemporad (IMT Lucca); Pantelis Sopasakis (IMT Lucca)
Compulsory for:
Control Systems
Also available for:
Computational Mechanics; Computer Science

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

Computational Contact and Fracture Mechanics

Abstract:
This course provides a general overview on the theories of contact and fracture mechanics, relevant for a wide range of disciplines ranging from materials science to engineering and geophysics. Introducing their theoretical foundations, the physical aspects of the resulting nonlinearities induced by such phenomena are emphasized. Numerical methods for their approximate solution are also presented, together with a series of applications to real case studies. The course covers the following topics: I. Contact mechanics A. The Hertzian contact between smooth spheres B. The Cattaneo-Mindlin theory for frictional contact C. Numerical methods for the treatment of the unilateral contact constraint (the penalty method and Lagrange multipliers in FEM, the active set strategy in BEM) D. Contact between rough surfaces: statistical and numerical methods II. Fracture mechanics A. Fundamentals of linear elastic fracture mechanics (LEFM), stress-intensity factors B. Strength and toughness of materials, criteria for crack propagation C. Examples in LEFM solved with the use of the finite element method D. Nonlinear fracture mechanics (NLFM): the cohesive zone model (CZM) E. Numerical implementation of the CZM in the finite element method F. Applications of NLFM to materials science, retrofitting of civil/architectonic structures, composite materials.
Hours:
20
Professors/Lecturers:
Marco Paggi (IMT Lucca)
Compulsory for:
Computational Mechanics

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

Extended and Mesh Free Finite Element Methods for Boundary Value Problems with Discontinuities and Multiscale Methods for Fracture (long seminar without exam)

Abstract:
Over the past decades, finite element methods have been developed into one of the most general
and powerful class of techniques to solve boundary value problems governed by partial differential
equations in order to study, predict and model the behavior of structures, materials, processes and
fluids. Within this course, extended finite element and mesh free methods will be presented to handle
problems with arbitrary strong and weak discontinuities. In these methods, the approximation
space of the test and trial functions are modified such that arbitrary discontinuities can be handled.
Afterwards, details of atomistic models, continuum models and possible coupling techniques in
statics and dynamics are presented in relation to the problem of fracture of materials. Techniques
of adaptive adjustment of the atomistic region based on the propagation of defects at the nanoscale will be addressed.

In detail, the following topics will be covered:

• The partition of unity and its relation to completeness
• Lagrangian and Eulerian kernel functions
• Weak and strong form and weak and strong discontinuities
• PUFEM, EFG, RKPM and DRKPM and their shape functions
• Level sets and signed distance function
• Nodal, stress­point and cell­integration in a meshfree method
• Principles and implementation procedure of XFEM
• Principles of embedded and interface elements
• Modeling aspects of atomistic simulations in statics and dynamics
• Computer algorithms of atomistic simulations
• Modeling fracture in the continuum based on the phantom node method and virtual atom
cluster models
• Coupling techniques of continuum and atomistic regions
• Adaptive adjustment of the atomistic region
• Coarse graining and refinement techniques
• Applications to realistic materials
Hours:
10
Professors/Lecturers:
Pattabhi Ramaiah Budarapu (IMT Lucca)
Compulsory for:
Computational Mechanics

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

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

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)
Compulsory for:
Image Analysis
Also available for:
Computational Mechanics; 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

Principles of Concurrent and Distributed Programming

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

Software Engineering for Service-Oriented Systems and Autonomic Systems

Abstract:
Service-Oriented Computing is an emerging paradigm where services are understood as autonomous, platform-independent computational entities that can be described, published, categorised, discovered, and dynamically assembled for developing massively distributed, interoperable, evolvable systems and applications. In this course a model-driven approach to the development of service-oriented software systems is presented where foundational theories and techniques are integrated in a pragmatic software engineering approach. In particular, an introduction to modelling service-oriented systems in a diagrammatic style with UML is given and their formal foundations in terms of process algebra and automata are presented. It will be shown how mathematical models can be generated by model transformations and further used for qualitative and quantitative analysis of service-oriented software.
Hours:
20
Professors/Lecturers:
Francesco Tiezzi (Università degli Studi di Camerino); Martin Wirsing (Ludwig-Maximilians-Universität München)
Available for:
Computational Mechanics; Computer Science; Image Analysis; 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

Timed Automata and Logics for Real-Time Systems

Abstract:
TBD
Hours:
20
Professors/Lecturers:
Luca Aceto (Reykjavik University)
Available for:
Computational Mechanics; Computer Science; Control Systems