The influence of network structure in neuronal information transmission

Wednesday 31 May 2017 h.14:30, Room 2BC30
Giacomo Baggio (Padova, DEI)
“The influence of network structure in neuronal information transmission"

Understanding how neurons communicate is one of the most challenging open problems in neuroscience. In this talk, I will present some recent results aiming at formulating this problem from a mathematical and information-theoretic viewpoint. After an overview on neuronal network dynamical models, I will introduce a digital communication framework for studying the information transmission problem in a neuronal network driven by linear dynamics. Within this framework, a novel metric for measuring the information capacity of a neuronal network based on Shannon’s capacity and the notion of inter-symbol interference will be discussed. Finally, I will illustrate how the structure of the network matrix and, in particular, its departure from normality, affects the information capacity of a network.
The talk will be introductory in nature and it is intended for a general audience.

Variational Approaches in Shape Partitioning

Wednesday 3 May 2017 h.14:30, Room 2BC30
Martin Huska (Padova, Dip. Mat.)
“Variational Approaches in Shape Partitioning"

The rapid development of 3D scanning technology has incredibly increased the availability of digital models exploited for a wide range of applications varying from computer graphics and medical imaging up to industrial production. One fundamental procedure that processes the raw acquired data for further manipulation, e.g. in product design, animation, deformation and reverse engineering, is the shape partitioning. This process consists in the decomposition of an object into non-overlapping salient sub-parts determined by a shape attribute.
In this seminar, we will introduce the concept of Shape Partitioning together with the wide range of partitioning methods. Next, we will observe a few partitioning/segmentation models in the field providing some results. At last, if the time allows, we will introduce the concept of Convex-Nonconvex segmentation over surfaces.
The seminar will be held at introductory level, thus, general audience is welcome to participate.

An introduction to domain perturbation theory for elliptic eigenvalue problems

Wednesday 29 March 2017 h.14:30, Room 2BC30
Francesco Ferraresso (Padova, Dip. Mat.)
“An introduction to domain perturbation theory for elliptic eigenvalue problems”

How does the sound of a drum depend on its shape? This weak variant of the classical question “Can one hear the shape of a drum?” can be considered in the framework of domain perturbation theory for elliptic differential operators. Starting with easy examples we will see that the answer to this apparently harmless question is rather different in the case of regular perturbations and in the case of singular perturbations. We will focus on the singular case, where the geometry of the problem is deeply mixed with the differential structure, in particular with the boundary conditions. Finally, we will give an account of recent advances in the study of a specific singular perturbation (the dumbbell domain) for the Laplace operator and for the biharmonic operator.
The seminar is intended for a general audience and it aims to introduce basic concepts from spectral theory as well as more advanced research results.

Quantized option pricing in Mathematical Finance

Wednesday 15 March 2017 h.14:30, Room 2BC30
Lucio Fiorin (Padova, Dip. Mat.)
“Quantized option pricing in Mathematical Finance”

Quantization is a widely used tool in Signal Processing and Numerical Probability, and it has been recently applied to Mathematical Finance. The quantization of a continuous random variable consists in finding the “best” discrete version of it, i.e. minimizing the L^2 distance. It is possible, using this technique, to create new algorithms for the pricing of European options under different models of the underlying asset.
In this seminar we introduce the basic tools used in mathematical finance and we will present the most common results in the theory of option pricing. After a brief discussion on the existing models of the price of a financial asset, we will give the audience some ideas on how quantization can be a powerful tool able to overcome existing problems.

Topology, analysis and the Riemann-Hilbert correspondence

Wednesday 1 March 2017 h.14:30, Room 2BC30
Christopher Lazda (Padova, INdAM Marie Curie Fellow)
“Topology, analysis and the Riemann-Hilbert correspondence”

The Riemann-Hilbert correspondence gives a way of passing back and forth between topology and differential geometry, describing the behaviour of differential equations in terms of the monodromy of their local solutions. Starting with the example of the logarithm, I will give an introduction to the ideas behind this correspondence in a concrete and down to earth manner, concentrating on the case of Riemann surfaces. If there is time I will also explain how this gives a completely algebraic way to study topological invariants.

Collective periodic behavior in interacting particle systems

Wednesday 15 February 2017 h.14:30, Room 2BC30
Daniele Tovazzi (Padova, Dip. Mat.)
“Collective periodic behavior in interacting particle systems"

Interacting particle systems constitute a wide class of models, originally motivated by Statistical Mechanics, which in the last decades have become more and more popular, extending their applications to various fields of research such as Biology and Social Sciences. These models are important tools that may be used to study macroscopic behaviors observed in complex systems. Among these phenomena, a very interesting one is collective periodic behavior, in which the system exhibits the emergence of macroscopic rhythmic oscillations even though single components have no natural tendency to behave periodically.
This talk aims to introduce to a general audience some basic tools in the theory of interacting particle systems and some of the mechanisms which can enhance the appearance of self-sustained macroscopic rhythm. After recalling some notions of Probability, we present the classical Curie-Weiss model, which doesn't exhibit periodic behavior, and we show how we can modify it in order to create macroscopic oscillations. This is also the starting point for some recent developments that will be sketched in the last part of the talk.

Zeta functions associated to profinite groups

Wednesday 1 February 2017 h.14:30, Room 2BC30
Leone Cimetta (Padova, Dip. Mat.)
“Zeta functions associated to profinite groups”

In this seminar we will discuss the properties of some Dirichlet series associated to a group G satisfying specific topological properties. These series deal with two important problems arisen in the last century, which both had a great development over the last decades.
The first problem (the subgroup growth of a profinite group G) involves the behaviour of the function a_n(G), that is the number of subgroups of G of index n.
The second problem consists in determining the probability that, randomly choosing n elements of a group, we get a generating set for the whole group.
The second problem, in particular, arises from a famous work by P. Hall, which solved it in 1936 in the finite case.
After recalling some basic definitions, we will present the motivations for the problems; then, starting from some examples and classical results for finite groups, we will give some ideas to develop both problems in the profinite case and show some relations between the series involved.

Secure And Scalable Management of Internet of Things Deployments

Wednesday 18 January 2017 h.14:30, Room 2BC30
Moreno Ambrosin (Padova, Dip. Mat.)
“Secure And Scalable Management of Internet of Things Deployments”

In recent years, the advent of Internet of Things (IoT) is populating the world with billions of low cost heterogeneous interconnected devices. IoT devices are quickly penetrating in many aspects of our daily lives, and enabling new innovative services, ranging from fitness tracking, to factory automation. Unfortunately, their wide use, as well as their low-cost nature, makes IoT devices also an attractive target for cyber attackers, which may exploit them to perform various type of attacks, such as Denial of Service (DoS) attacks or privacy violation of end users. Furthermore, the potentially very large scale of IoT systems and deployments, makes the use of existing security solutions practically unfeasible.
In this talk I will give an overview of the problem of secure management, and present our research effort in defining secure and scalable solutions for managing large IoT deployments. Moreover, I will focus in particular on two important parts of the device management process: (1) software updates distribution; and (2) device's software integrity check.

Extension fields, and classes in the genus of a lattice

Wednesday 14 December 2016 h.14:30, Room 2BC30
Frances Odumodu (Padova, Dip. Mat.)
“Extension fields, and classes in the genus of a lattice“

In this talk, which will be accessible to a large audience, a first part will be devoted to a basic reminder on extension fields with examples, and a second part to the more specific framework of number fields, i.e. finite degree extensions of rational numbers. Concerning the latter part, the Hasse-Minkowski local-global theorem for quadratic forms fails in general at the integral level, hence there are two levels of classification, the genus (local) and the integral class (global): we shall focus on some results concerning the classes in the genus of a lattice and in particular the trace form.

Biologically inspired deduction of Optimal Transport Problems

Wednesday 30 November 2016 h.14:30, Room 2BC30
Enrico Facca (Padova, Dip. Mat.)
“Biologically inspired deduction of Optimal Transport Problems”

In this talk, after a brief introduction on the Optimal Transport Problems and some PDEs based formulation, we will present a recently developed approach, based on an extension of a model proposed by Tero et al (2007), for the simulation of the dynamics of Physarum Polycephalum, a unicellular slime mold showing surprising optimization ability, like finding the shortest path connecting two food sources in a maze.
We conjecture that this model is an original formulation of the PDE-based OT problems. We show some theoretical and numerical evidences supporting our thesis.

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