Computational social choice: between AI and Economics

Thursday 17 December 2015 h. 14:30, Room 2BC30
Andrea Loreggia (Padova, Dip. Mat.)
"Computational social choice: between AI and Economics"

During the last decades, the trend has been for disciplines to converge on common techniques to be used in similar problems, besides focusing on specific techniques to be used in narrow domains. AI is one of the best examples: the cross-fertilisation process leads to a very fascinating solutions. Consider for example genetic algorithms, which mimic evolutionary mechanisms to solve search and optimization problems. The individualistic approach of problem solving becomes insufficient: concepts, techniques and experts need to collaborate to get a better understanding of the problems they would like to solve. The techniques that AI makes available are being used by many other disciplines. AI nowadays inundates our everyday life with tools and methods that are hidden in our household electrical devices, smartphones and much more. Starting from the field of multi-agent systems, researchers in AI recently considered the use of models and problems from economics. Notable examples are voting systems used to aggregate the results of several search engines, game theoretic methods that analyse the complex interaction of autonomous agents, and matching procedures implemented on large-scale problems such as the coordination of kidneys transplants and the assignment of students to schools. In this scenario, a number of research lines federated under the name of computational social choice. The need for a computational study of collective decision procedures is clear. On the one hand, from crowdsourcing to university admission ranking, many real-life applications apply existing social choice methods to large scale problems. On the other hand, collective decision-making is not a prerogative of human societies, and multi-agent systems can use these methods to coordinate their actions when facing complex situations. In this talk, we would like to focus on two examples that highlight the impact of a computational approach to classical problems of collective choice. First, by studying repeated decisions (think of opinion polls that precede an election) to evaluate the quality of the result, and, second, by devising innovative procedures to predict the preferences of a collection of individuals.

A simple mathematical model for micro-swimmers

Wednesday 2 December 2015 h. 14:30, Room 2BC30
Marta Zoppello (Padova, Dip. Mat.)
"A simple mathematical model for micro-swimmers"

What does it mean swimming? How can mathematics treat this problem? What is the best strategy to move in a certain direction?
The study of the swimming strategies of micro-organisms is attracting increasing attention in the recent literature. One of the main difficulties is the complexity of the hydrodynamic forces exerted by the fluid on the swimmer as a reaction to its shape changes.
We show that there exists an optimal swimming strategy which leads to minimize the time to reach a desired target. Numerical simulations performed are in good agreement with theoretical predictions and suggest that the optimal strategy is periodic, i.e. composed of a sequence of identical strokes.

Learning with Kernels

Wednesday 18 November 2015 h. 14:30, Room 2BC30
Michele Donini (Padova, Dip. Mat.)
"Learning with Kernels"

To solve a problem on a computer, we need an algorithm, which is a sequence of instructions that should be carried out to transform the input into the output. For some tasks, we do not have an algorithm: we know what the input is, we know what the output should be but we do not know how to transform the input into the output. What we lack in knowledge, we make up for in data. We can exploit data to "learn" using a Machine Learning algorithm, that is able to extract automatically the algorithm for the task.
In this talk, we give an introduction to a family of Machine Learning algorithms called Kernel Methods, starting from a general introduction to the Machine Learning problems and its purposes. After building up the fundamental tools of learning with kernels, we will introduce the principal ideas behind this family of algorithms and its ability to learn automatically using data.

Doctoral School in Mathematical Science - Opening Day 2015/2016

The opening day of the Doctoral School in Mathematics will take place on October 7, 2015, at
in room 1BC45.

11:30: meeting, brief introduction of Seminario Dottorato 2015/16
11:30-12:30: talk of Daria Ghilli "Rare events in finance by PDE methods"
12:30-13-30: presentation of the activities/courses of PhD Programme 2015/16
13:30: refreshments at the common room of 7th floor

For further information feel free to contact Pierpaolo Soravia.

Rare events in finance by PDE methods

Wednesday 7 October 2015 h.11:30, Room 1BC45
Daria Ghilli (Padova, Dip. Mat.)
“Rare events in finance by PDE methods"

Rare events, or tails events, are events which happen only “rarely", in other words, they are situated in the tails of the distribution. Take for example the well-known experiment of tossing a coin: our experience (and also the law of large numbers) says that, after a big enough number of tosses, the most probable value for the empirical mean of the outcomes is 1/2. But what about the probability of being far from 1/2? This is a typical rare event.
The theory who deals with the estimation of tails events is called "large deviations theory" and has many applications, for example, in risk management and finance.
After an introduction to the theory, we consider applications to financial mathematics, concerning the estimation of price of particular type of options (out-of the money) near their maturity. These are typical financial objects whose value deteriorates quickly in time and then are considered, in this context, as rare events.
Our approach - mainly of analytical nature - is different from the classical probabilistic ones.

This seminar will be held as a special event during the OPENING DAY OF THE DOCTORAL SCHOOL.

Concorso pubblico per l'ammissione al Corso di Dottorato in Scienze Matematiche (XXXI ciclo) (Curriculi: Matematica, Matematica Computazionale) - A.A. 2015/2016

Concorso Pubblico per l’ammissione al
Corso di Dottorato in SCIENZE MATEMATICHE (XXXI ciclo)
(Curriculi: Matematica, Matematica Computazionale) – A.A. 2015/2016

Pubblicazione esito “valutazione titoli”
Si ricorda che la presente graduatoria ha carattere provvisorio. La graduatoria definitiva verrà pubblicata, come da bando di concorso (art. 8) dal 3 agosto 2015 mediante:

ValutazioneTitoli.pdf (Username: risultati2015, Password comunicata privatamente)

Why should people in approximation theory care about (pluri-)potential theory?

Wednesday 24 June 2015 h. 15:00, room 2BC30
Federico Piazzon (Padova, Dip. Mat.)
"Why should people in approximation theory care about (pluri-)potential theory?"

We give an introductory summary of results in (pluri-)potential theory that naturally come into play when considering classical approximation theory issues both in one and (very concisely) in several complex variables. We focus on Fekete points and the asymptotic of orthonormal polynomials for certain $L^2$ counterpart of Fekete measures. No specific knowledge on the topic is assumed.

An introduction to derived categories

Wednesday 10 June 2015 h. 14:30, room 2BC30
Francesco Mattiello (Padova, Dip. Mat.)
"An introduction to derived categories"

Derived categories were introduced in the sixties by Grothendieck and Verdier and have proved to be of fundamental importance in Mathematics.
Starting with a short review of the basic language of category theory, we will first introduce the notion of abelian category with the help of several examples. Then we will spend some time giving a thorough motivation for the construction of the derived category of an abelian category. Finally, we will look at a way to break a derived category into two pieces that permit (among other things) to recover the original abelian category.

Controllability and the numerical approximation of the minimum time function

Wednesday 27 May 2015 h. 14:30, room 2BC30
Thien Thuy Le Thi (Padova, Dip. Mat.)
"Controllability and the numerical approximation of the minimum time function"

In optimal control theory, minimum time problems are of interest since they appear in many applications such as robotics, automotive, car industry, etc.. The scope of this talk is to give a brief introduction of these problems. Controllability conditions under various settings are considered. Such conditions play a vital role in studying the regularity of the minimum time function T(x). Moreover, we will also introduce the HJB equation associated with a minimum time problem and approaches to computing T(x) approximately.

Variational methods in nonlinear elasticity: an introduction

Wednesday 6 May 2015 h. 14:30, room 2BC30
Alice Fiaschi (Padova, Dip. Mat.)
"Variational methods in nonlinear elasticity: an introduction"

After a brief introduction of the variational formulation for the standard model in nonlinear elasticity, we will consider the problem of finding the "right" space to describe the equilibrium configurations of an elastic body, from the point of view of the Calculus of Variations. In this framework, I will introduce the space of Young measures as a suitable space to describe materials exhibiting microstructures.

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