12 Novembre, 2013 15:00 oclock

Multivariate functional halfspace depth, with applications to the classification of multivariate curves

Mia Hubert, Department of Mathematic KU Leuven

Aula Seminari F. Saleri 6° piano MOX-Dipartimento di Matematica del Politecnico di Milano

abstract

abstract

First, we describe multivariate functional halfspace depth (MFHD), which has recently been proposed as a new tool to study multivariate functional data. This depth function allows to estimate the central tendency and the variability of multiple sets of curves, and to detect outlying curves. The multivariate sample of curves may include warping functions, derivatives and integrals of the original curves for a better overall representation of the functional data via the depth. Next, we present the application of this depth function to supervised classification. We compare several existing and new classifiers on real and simulated data. In particular, their behavior is studied in the presence of outlying curves.

Reference:
Claeskens, G., Hubert, M., Slaets, L., Vakili, K. (2013).

Multivariate functional halfspace depth. Journal of the American Statistical Association, in press.


contact: anna.paganoni@polimi.it

6 Novembre, 2013 14:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Numerical shape optimization using the Method of Fundamental Solutions

Pedro Antunes, Group of Mathematical Physics - University of Lisbon

Aula seminari III piano

abstract

abstract

In this talk we consider some shape optimization problems for eigenvalues of the Laplacian and Bilaplacian (clamped plate and buckled plate eigenvalue problems).
The solution of these problems has been studied by using several numerical methods.
We address the use of a gradient type method with the Method of Fundamental Solutions (MFS) as forward solver. The MFS is a meshless method that allows the solution of the eigenvalue problems with high accuracy, even with small dimension matrices.
This feature allows to consider also the shape optimization with 3D and 4D domains.
Several examples are presented to illustrate the good performance of the method.

5 Novembre, 2013 15:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

The role of soil processes parameterization in numerical modelling of the atmosphere

Davide Cesari, Servizio Idrometeo dell ARPA Emilia Romagna

Aula Semianri F. Saleri - 6° piano Dipartimento di Matematica Politecnico di Milano

abstract

abstract

A correct representation of the state of the soil, mainly in terms of temperature and moisture content, is getting more and more important
in state of the art numerical models for weather prediction and climate. The physical processes taking place in the soil and having an impact on
atmospheric dynamics will be described, together with their mechanisms of interaction with the atmospheric surface layer. The equations
decribing processes in the soil, in the form usually applied in numerical models of the atmosphere, will be presented along with their
typical discretization and their coupling with the numerical representation of the atmosphere and of other surface processes.
Finally, the most common techniques for defining the initial state of the soil for numerical weather prediction purposes will be introduced,
showing the advantages and drawbacks of each of them.

28 Ottobre, 2013 16:30

Lezioni Leonardesche

ARITHMETIC OF SOME INTEGRABLE SYSTEM

NGÔ BẢO CHÂU, The University of Chicago

Università di Milano, Dipartimento di Matematica, Via Saldini

A correct representation of the state of the soil, mainly in terms of temperature and moisture content, is getting more and more important
in state of the art numerical models for weather prediction and climate. The physical processes taking place in the soil and having an impact on
atmospheric dynamics will be described, together with their mechanisms of interaction with the atmospheric surface layer. The equations
decribing processes in the soil, in the form usually applied in numerical models of the atmosphere, will be presented along with their
typical discretization and their coupling with the numerical representation of the atmosphere and of other surface processes.
Finally, the most common techniques for defining the initial state of the soil for numerical weather prediction purposes will be introduced,
showing the advantages and drawbacks of each of them.

23 Ottobre, 2013 15:00

Seminari FDS

La modellazione numerica di fenomeni naturali: supporto alla prevenzione

Luca Formaggia, Politecnico di Milano

Dipartimento di Matematica Aula Consiglio - VII piano Ed. 14 Nave – Via Bonardi, 9 -Milano

abstract

abstract

Fenomeni naturali, quali sismi, eruzioni vulcaniche, esondazioni, possono venire
descritte da modelli matematici e simulati al calcolatore utilizzando modelli numerici appropriati.
Seppure l incertezza dei dati e le inevitabili approssimazioni modellistiche rendono queste
simulazioni affette da incertezza, esse possono comunque fornire un valido supporto per disegnare
scenari e guidare le strategie di prevenzione e di protezione ambientale.

16 Ottobre, 2013 14:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Comportamento asintotico del p-Laplaciano

Hynek Kovarik, Università di Brescia

Aula seminari III piano

abstract

abstract

Consideriamo il primo autovalore dell operatore dato dalla somma del p-Laplaciano e di un potenziale V in R^n.
Studiamo il comportamento asintotico di questo autovalore per V che tende a zero.
Mostreremo, in particolare, come lo
sviluppo asintotico dipende da p e dalla dimensione dello spazio.

14 Ottobre, 2013 16:30

Lezioni Leonardesche

A NEW LOOK AT THE JONES POLYNOMIAL OF A KNOT

EDWARD WITTEN, Institute for Advanced Study, Princeton

Università di Milano, Dipartimento di Matematica, Via Saldini

Consideriamo il primo autovalore dell operatore dato dalla somma del p-Laplaciano e di un potenziale V in R^n.
Studiamo il comportamento asintotico di questo autovalore per V che tende a zero.
Mostreremo, in particolare, come lo
sviluppo asintotico dipende da p e dalla dimensione dello spazio.

4 Ottobre, 2013 15:00 oclock

Lezioni Leonardesche

Stochastic optimization methods for health care delivery: the home care example

Ettore Lanzarone, CNR-IMATI Milan, Italy

Aula Saleri - 6° Piano MOX-Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Uncertainty is inherent in many health care optimization problems and cannot be neglected,
as it may have a significant impact on the problem solution.
For instance, uncertainty is associated to the availability of ambulances in
locating emergency vehicles, and related to the duration of surgery in planning and scheduling operating room theaters. Uncertainty also occurs in managing Home Care (HC) services: the most critical and frequent random event is a sudden variation in the amount of service required by
HC patients, which is in general highly variable. In this talk, I discuss how to manage uncertain demands while planning the activities of a HC provider, with particular reference to the nurse-to-patient assignment problem under continuity of care. I present three different optimization techniques that include demand uncertainty, i.e., a stochastic programming approach, a robust cardinality-constrained optimization model,
and an analytical policy. In addition, since all these approaches require an estimation of the future patients demands, I briefly discuss two possible stochastic models to predict a patient s care pathway and his/her demands for visits over time. Finally, the application to a relevant real case is described, and the benefits deriving
from implementing the proposed approaches are shown.

2 Ottobre, 2013 14:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Existence results for a fourth order equation arising in the theory of non-equilibrium phase transitions

Carlos Escudero, Universidad Autonoma de Madrid

aula seminari VI piano

abstract

abstract

In this talk we will introduce a model that arises in the
theory of non-equilibrium phase transitions, in particular in the
description of self-affine surfaces. We will briefly comment on the
role that this model is meant to play in this physical theory.
Furthermore, we will mention some open questions of physical nature
related to it. Subsequently we will start with the rigorous analysis
of our model, which is a fourth order partial differential equation. We
will describe our progress in building an existence theory for the
full model, which is a parabolic equation, and for its stationary
counterpart. For the latter case existence and multiplicity results
are provided, and for the former one we will show local in time
existence of the solution, that can be made global for small enough
data, and cannot if these are large enough. We will show how these
results fit into the physical theory, and what open questions are left
for the future.

27 Settembre, 2013 14:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Evolution equations as Wasserstein gradient flows

A. Takatsu, Nagoya University

Aula seminari III piano

abstract

abstract

In this talk, I study a certain evolution equation on a weighted Riemannian manifold as the gradient flow of a generalized relative entropy with respect to the Wasserstein metric. The Wasserstein metric is a metric on the space of probability measures. For example, it is known that the porous medium equation is the Wasserstein gradient flow of the Tsallis entropy. I give a criterion for generalized relative entropies to be convex. From the convexity of generalized relative entropies, I derive appropriate variants of the Poincaré and the logarithmic Sobolev inequalities, also the contraction propety of its gradient flow. This is a joint work with Shin-ichi Ohta.