23 Novembre, 2012 14:00

Seminari PhD di Equazioni Differenziali

Damped KdV Equations

JEAN-PAUL CHEHAB, Université de Picardie

Aula seminari F.Saleri VI piano

abstract

abstract

We study numerically the long time behavior of a family of weakly damped and forced KdV equation on the Torus. In particular, we point out non trivial dynamics, Sobolev regularization effects.
We also focus on the damping rate for different damping models and introduce a simple function that allows to make a hierarchy between the models. Also, in some cases, we propose a way to rebuild a posteriori the damping operator using samples of the solution.

23 Novembre, 2012 12:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Fibrati di parti principali su spazi proiettivi e rappresentazioni di quiver

Riccardo Re, Università di Catania

Aula Seminari F. Saleri VI Piano

abstract

abstract

I fasci di parti principali associati a fasci di moduli su schemi sono stati introdotti da Grothendieck nell ambito della geometria algebrica,
ed essi costituiscono in questo contesto una generalizzazione dei jet bundles della geometria differenziale.
Nonostante la loro ormai datata introduzione, fino a tempi molto recenti la struttura dei fibrati di parti principali associati ad un line bundle O(d) su uno spazio proiettivo,
decisamente il caso più semplice dell intera teoria, non era stata ancora pienamente compresa.
Il lavoro di cui parlerò colma questa lacuna, dando una descrizione di tali fibrati usando la loro omogeneità e la teoria delle rappresentazioni di quiver associate a fibrati omogenei.

21 Novembre, 2012 11:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Bayesian Methods for Assessment of Health Care Fraud

Refik Soyer, The George Washington University

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Health care fraud costs a significant amount to the US healthcare system. According to FBI the fraud cost to US is about $80 billion a year. Detection and prevention of fraud are of interest to many parties including government, medical community and insurance industry. Due to complexities involved in defining fraudulent behavior and detecting fraud, the need for more sophisticated data mining tools and statistical methods have been recognized in the health care industry. As a result, methodologies such as neural networks, decision trees, association rules, link analysis and genetic algorithms have been used in for fraud detection. However, use of Bayesian methods has been quite limited with the exception of some recent work using Bayes networks.
In this talk we consider Bayesian methods for fraud detection. In so doing, we focus on co-clustering models for analysis of dyadic data connecting two entities such as providers and beneficiaries. These models can be used to identify billing patterns of potentially fraudulent providers who submit a large number of high-dollar claims to insurance programs. An important issue pertinent to dyadic data is to identify the cluster membership of each entity. We discuss how Bayesian inference can be developed for assessment of cluster memberships and illustrate what additional insights can be obtained from Bayesian analysis of the dyadic data. We consider different forms of dyadic data and estimation of cluster sizes and discuss potential extensions such as dynamic cluster membership.

16 Novembre, 2012 14:00 in punto

Seminari PhD di Equazioni Differenziali

Exponential and polynomial stability of linear semigroups and applications.

FILIPPO DELL'ORO, Politecnico di Milano

Aula seminari III piano

abstract

abstract

We present some abstract results
for the analysis of exponential and polynomial stability of linear semigroups in Hilbert spaces, and we discuss some applications to PDEs

15 Novembre, 2012 11:00

Sezione di Probabilità e Statistica Matematica

Stochastic calculus via regularizations in Banach spaces and applications

Francesco Russo, ENSTA-ParisTech

Aula Seminari III piano

We present some abstract results
for the analysis of exponential and polynomial stability of linear semigroups in Hilbert spaces, and we discuss some applications to PDEs

14 Novembre, 2012 

Seminari FDS

L'infanzia di Gödel e altri algoritmi

Vincenzo Della Mea, Dept. of Mathematics and Computer Science University of Udine, Italy

Educafè - Campus Leonardo - Piazza Leonardo da Vinci 32

abstract

abstract

Computer, reti, programmazione, i loro fondamenti teorici, Gödel, Turing, Chomsky: temi e personaggi che, in versi, diventano scuse per parlare di ciò che di solito si trova nella poesia. E la poesia diventa una scusa per parlare di come è nata e di come funziona l'informatica.

5 Novembre, 2012 17:00

Seminario Matematico e Fisico di Milano

A FRACTIONAL FRAMEWORK FOR PERIMETERS AND PHASE TRANSITIONS

ENRICO VALDINOCI, Università di Milano

Dipartimento di Matematica del Politecnico, Aula Consiglio

abstract

abstract

We review some recent results on minimisers of a non-local perimeter functional, in connection with some phase coexistence models whose diffusion term is given by the fractional Laplacian.

26 Ottobre, 2012 14:30 in punto

Seminario Matematico e Fisico di Milano

A generalised smoother for linear ordinary differential equations

Michelle Carey, University of Limerick

Aula Seminari III Piano Dipartimento di Matematica Politecnico di Milano

abstract

abstract

This paper introduces an o-the shelf smoother for linear ordinary differential equations.
This smoother is obtained by enhancing the functional data analysis estimation procedure for approximating discrete data by a function when the data is assumed to adhere to a specified linear ordinary differential equation (ODE) motivated from domain specific information. The estimate of the functional object is obtained minimising a penalised residual sum of squares where the roughness penalty is the L2 norm of the differential operator which contains the linear ODE. The almost universal approach to evaluating this roughness penalty involves using numerical integration techniques. Carey et al. (2012) developed a recursive algorithm that identifies the coefficients of the piecewise polynomials that comprise the B-spline basis function. In this paper, we propose utilising this alternative expression for the B-spline basis functions in order to produce an exact expression for the roughness penalty. Explicit expressions are derived for each of the estimated parameters that minimise the penalised residual sum of squares and for the
uncertainty quantification for these estimates.

Carey, M., G. G. E. Gath, and K. Hayes (2012). A universal matrix algorithm for the computation of the coecients of the polynomials comprising b–spline basis functions. Submitted. (ref. Dott. Laura Sangalli)

22 Ottobre, 2012 15:00 in punto

Seminario Matematico e Fisico di Milano

Domain Decomposition Algorithms for Problems with Two Sets of Material Parameters

Olof B. Widlund, Courant Institute of Mathematical Sciences, NYU, USA

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

One of the successes of domain decomposition theory has been in the construction of coarse
global components of the preconditioner, which allow for an iteration count that is independent
of the number of subdomains as well as growing quite slowly with the number of degrees of
freedom in individual subdomains. It has also been possible to establish bounds which are
independent of jumps in the material parameters across the interface formed by the boundaries
of the subdomains. (rif. Prof. Alfio Quarteroni)

19 Ottobre, 2012 14:30 in punto

Seminario Matematico e Fisico di Milano

Statistical characterizations of genome dynamics

Francesca Chiaromonte, Pennsylvania State University

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Recent studies of sequenced genomes have shown that the rates of different types of mutations tend to vary and co-vary along the nuclear
DNA. In order to provide a statistical characterization of this variation structure and of its association with features of the local genomic landscape, we have used a number of multivariate techniques on data from primate alignments (these include regression, linear and non-linear Principal Components, linear and non-linear Canonical Correlations). Most
recently we have used multivariate Hidden Markov Models to identify distinct mutational patterns and segment the human genome accordingly. Our
results provide crucial insights into genome dynamics, and the mutagenic role of various molecular mechanisms such as replication, recombination, repair and local chromatin environment. Moreover, we identify regions with
distinct mutational signatures whose locations, lengths and landscapes are evolutionarily meaningful.

This is joint work with Guru Ananda, Prabhani Kuruppummullage Don and Kateryna Makova of The Pennsylvania State University.