Centrality metrics and spectral properties of graphs.
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
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.
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.
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.
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