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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 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.
Computing systems are becoming increasingly sophisticated and control key aspects of our lives. In light of the increasing complexity of such computing devices, one of the key scientific challenges in computer science is to design and develop computing systems that do what they were expected to do, and do so reliably. The aim of this course is to introduce models for the formal description of computing systems, with emphasis on parallel, reactive and possibly real-time systems, and the techniques for system verification and validation that accompany them.
Model Predictive Control (MPC) is a well-established technique for controlling multivariable systems subject to constraints on manipulated variables and outputs in an optimized way. Following a long history of success in the process industries, in recent years MPC is rapidly expanding in several other domains, such as in the automotive and aerospace industries, smart energy grids, and financial engineering.
The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour.
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.
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.
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
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.