12 Gennaio, 2018 09:30 in punto

Dipartimento di Matematica del Politecnico di Milano

Profile Evidence, Fairness and the Risks of Mistaken Verdicts

Marcello Di Bello, City University of New York

aula F. Saleri - 6° piano - edificio 14 - Nave

abstract

abstract

Profile evidence expresses a positive statistical correlation between membership in a group and crime. For example, statistics indicate that people who committed a burglary before are more likely to commit burglary compared to people in the general population. This profile evidence, if it is introduced at trial against a defendant charged with burglary and known to have committed burglary before, would be highly probative of guilt. But even when it is probative of guilt, many resist admitting profile evidence in a criminal trial for the purpose of helping to establish the guilt of the defendant. Coming up with a satisfactory account of the intuitive resistance to admitting profile evidence has proven difficult in the literature. The paper argues that concerns about admitting profile evidence can be vindicated by appeal to another fundamental legal value, equality before the law. In particular, equality before the law requires that innocent defendants be exposed to equal risks of mistaken conviction. As it turns out, profile evidence puts the innocent defendants who belong to the profiled groups at greater risk of mistaken conviction, relative to other innocent defendants who do not belong to profiled groups. This is the problem with admitting profile evidence at trial. This line of argument has a number of applications. For example, consider the debate among forensic scientists about the proper use of DNA profiling technology in cold-hit cases. Many have warned that in these cases a DNA match should have a weaker probative value than in standard DNA evidence cases. But others, especially Bayesian statisticians, have disagreed. The equal risk approach presented in this paper justifies, on fairness grounds, weakening the probative value of a DNA match in cold-hit cases, while also accommodating the dissenting arguments put forward by the Bayesian statisticians.

10 Gennaio, 2018 15:15

Sezione di Analisi

Sobolev-type inequalities on Cartan-Hadamard manifolds and applications to some nonlinear diffusions

Matteo Muratori, Politecnico di Milano

Sala del Consiglio, 7° piano

abstract

abstract

It is well known that the classical Sobolev inequality not only holds on Euclidean space, but also on any Cartan-Hadamard manifold, namely a complete and simply connected Riemannian manifold with everywhere nonpositive sectional curvatures. On the other hand, the Poincaré (or spectral gap) inequality fails on Euclidean space but holds on hyperbolic space or more in general on any Cartan-Hadamard manifold with sectional curvatures bounded from above by a negative constant. However, almost nothing seems to be known in between, that is when curvatures are negative but allowed to vanish at infinity. Here we show some partial results in this direction, mainly restricted to radial functions, and discuss related consequences concerning smoothing effects for certain nonlinear diffusions of porous medium type. This is a joint work with A. Roncoroni.

19 Dicembre, 2017 15:15

Sezione di Analisi

Long-range phase transitions and minimal surfaces

Serena Dipierro, Università degli Studi di Milano

Aula seminari 3° piano

abstract

abstract

We discuss some recent results on nonlocal minimal surfaces and discuss their connections with nonlocal phase transitions. In particular, we will consider the "genuinely nonlocal regime" in which the diffusion operator is of order less than 1 and present some rigidity and symmetry results.

15 Dicembre, 2017 14:30

Seminario Matematico e Fisico di Milano

TORI COMPATTI ASSOCIATI A VARIETA' IPERKAEHLER DI TIPO KUMMER

Kieran O'Grady, Università di Roma La Sapienza

Aula C Dipartimento di Matematica, Via Saldini 50

abstract

abstract

Se X e' una varieta' iperkaehler di tipo Kummer, il gruppo di coomologia H^3(X) ha dimensione 8, e quindi possiamo associare a X una Jacobiana intermedia J^3(X) (un toro complesso compatto di dimensione 4, proiettivo se X e' proiettiva). Faro' vedere come ricostruire esplicitamente J^3(X) a partire dalla struttura di Hodge su H^2(X). In particolare seguira' che, se X e' proiettiva, allora J^3(X) e' una varieta' abeliana di tipo Weil. Lo studio di J^3(X) suggerisce come (tentare di) costruire famiglie esplicite localmente complete di varieta' iperkaehler di tipo Kummer proiettive. of these results extend or not to non linear operators and to degenerate elliptic operators.

14 Dicembre, 2017 14:00

MOX Colloquia

Five Decades of Time Parallel Time Integration: Best Current Methods for Parabolic and Hyperbolic Problems

Martin Gander, Section de Mathématiques, Université de Geneve

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

Time parallel time integration methods have received renewed interest over the last decade because of the advent of massively parallel computers, due to the clock speed limit reached on today's processors. When solving time dependent partial differential equations, the time direction is usually not used for parallelization. But when parallelization in space saturates, the time direction offers itself as a further direction for parallelization. The time direction is however special, and for evolution problems there is a causality principle: the solution later in time is determined by the solution earlier in time, so the flow of information is just into the direction forward in time. Algorithms trying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account.

I will show in this talk how time parallel time integration methods were invented over the past five decades, and give a classification into four different groups: methods based on multiple shooting,
space-time multigrid methods, methods based on domain decomposition and waveform relaxation, and direct time parallel methods. The performance of these methods depends on the nature of the underlying evolution problem, and it turns out that for the first two classes of methods, time parallelization is only really possible for parabolic problems, while the last two classes can also be used to parallelize
hyperbolic problems in time. I will also explain in more detail one of the methods from each class: the parareal algorithm and a space-time multigrid method, which are currently among the most promising methods for parabolic problems, and a Schwarz waveform relaxation method related to tent-pitching and a direct time parallel method based on diagonalization of the time stepping matrix, which are very effective for hyperbolic problems.

Contact: marco.verani@polimi.it

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.

13 Dicembre, 2017 15:15 in punto

Sezione di Fisica Matematica

Validity of the Boltzmann equation: how to incorporate long-range effects into a collisional dynamics

Chiara Saffirio, Universita' di Zurigo

Aula seminari MOX, VI piano

abstract

abstract

After the paper of Lanford in 1975, the short time rigorous derivation of the Boltzmann equation from a system of N particles interacting through a hard-core potential has been fully understood. In recent years, the validity of the Boltzmann equation for short-range interaction potentials has been addressed, while the long-range case is still an open problem. In this talk we will review the known results on the validity of the Boltzmann equation and discuss the instability arising from taking into account the long-range effects in the collisional dynamics by presenting a new approach to this problem.

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.

13 Dicembre, 2017 16:15

Sezione di Fisica Matematica

Homoenergetic solutions for the Boltzmann equation

Alessia Nota, Universita' di Bonn

Aula seminari MOX, VI piano

abstract

abstract

We consider a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which are useful to
describe the dynamics of Boltzmann gases under shear, expansion or compression in nonequilibrium situations.
While their well posedness theory has many similarities with the theory of homogeneous solutions of the Boltzmann equation, their
long time asymptotics differs completely, due to the fact that these solutions describe far from equilibrium phenomena. Indeed,
the long time asymptotics cannot always be described by Maxwellian distributions. For several collision kernels the asymptotics of
homoenergetic solutions is given by particle distributions which do not satisfy the detailed balance condition.
In this talk I will describe different possible long time asymptotics of homoenergetic solutions of the Boltzmann equation, as
well as some open problems in this direction. (This is a joint work with R.D.James and J.J.L.Velázquez).

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.

12 Dicembre, 2017 14:00

Sezione di Finanza Quantitativa

The uncertainty of value

Luca Del Viva, ESADE Business School

Aula Seminari del Terzo Piano

We consider a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which are useful to
describe the dynamics of Boltzmann gases under shear, expansion or compression in nonequilibrium situations.
While their well posedness theory has many similarities with the theory of homogeneous solutions of the Boltzmann equation, their
long time asymptotics differs completely, due to the fact that these solutions describe far from equilibrium phenomena. Indeed,
the long time asymptotics cannot always be described by Maxwellian distributions. For several collision kernels the asymptotics of
homoenergetic solutions is given by particle distributions which do not satisfy the detailed balance condition.
In this talk I will describe different possible long time asymptotics of homoenergetic solutions of the Boltzmann equation, as
well as some open problems in this direction. (This is a joint work with R.D.James and J.J.L.Velázquez).

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.

5 Dicembre, 2017 15:15

Sezione di Analisi

A sharp Bernstein-type theorem for entire minimal graphs

Alberto Farina, Université de Picardie

Sala Consiglio 7° piano

abstract

abstract

We consider entire solutions $u$ to the minimal surface equation in $R^N$, with $N\ge8$, and we prove the following sharp result : if $N-7$ partial derivatives $ \frac{\partial u }{\partial {x_j}}$ are bounded on one side (not necessarily the same), then $u$ is necessarily an affine function.

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.

5 Dicembre, 2017 14:30

MOX Seminar

Testing for a significance in spatial regression with functional response

Veronika Rímalová, Palacký University Olomouc, Czech Republic - Department of Mathematical Analysis and Applications

Aula Saleri VI Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

In this talk we present a problem consisting of modelling and testing for spatial functional data in the context of regression analysis. The motivating data set includes monthly measurements of 5 chemical elements taken from 5 different sites near Brno, Czech Republic. Sampling locations were selected with the purpose of testing if the sites can be divided in two parts, agricultural and forest soil, according to their chemical properties. We propose to treat the measurements taken from each sampling point as functions of time distributed in space. To test for the difference according to the soil type, we develop an interval-wise testing procedure, in a geostatistical framework. We propose to perform the tests on residuals of a spatial linear model with a functional response. We apply the proposed method to the available data and discuss the results from the geological viewpoint.
(joint work with A. Menafoglio, A. Pini, E. Fišerová)

Contact: alessandra.menafoglio@polimi.it

Martin J. Gander obtained his undergraduate degree from ETH Zürich in 1993, and his PhD from Stanford University in 1997. He then spent two years as a postdoctoral fellow at Ecole Polytechnique in Paris, before becoming professor of Mathematics at McGill University in 1999. In 2004, he followed the call by the University of Geneva for a full professorship in Mathematics. His main interests are numerical analysis, in particular parallel iterative methods for space-time problems.