27 Maggio, 2014 14:00 in punto

MOX Seminar

I fattori affettivi e l'apprendimento matematico: 25 anni di ricerca nel campo dell'affect in mathematics education

PIETRO DI MARTINO, universita' di Pisa

Aula Saleri 6° piano Dipartimento di Matematica - Mox - Politecnico di Milano

21 Maggio, 2014 12:15

Seminari di Cultura Matematica

Mobilità, classifiche, teatro: alcune facce della matematica

Alberto Colorni, Politecnico

Aula Rogers

20 Maggio, 2014 12:00

Sezione di Probabilità e Statistica Matematica

Is a discretely observed semimartingale of Ito type?

Jean Jacod, Université Pierre et Marie Curie, Paris

Aula Seminari Fausto Saleri , sesto piano

abstract

abstract

In high-frequency statistics, and among various hypotheses, the fact that the underlying observed process is an Ito semimartingale is always assumed. However, for financial data for example, prices should be semimartingales (because of the fundamental asset pricing theorem ), but there is no reason why it should be an Ito semimartingale.
So it is important to derive tests for checking whether this assumption is enforced, or not. The problem cannot be solved in full generality, but we will see that under some restrictive structural assumptions, plus the fact that the process is continuous, some tests can be constructed.
This is joint work with Yacine Ait-Sahalia.

19 Maggio, 2014 14:00 in punto

Sezione di Probabilità e Statistica Matematica

Mathematics meets chemistry: a new paradigm for implicit salvation models

BENJAMIN STAMM, Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie - France

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

abstract

abstract

Computational chemistry has attracted much attention since this years choice of the Nobel prize winners in chemistry for their contributions to multi-scale models such as the QM/MM method. The large majority of chemically interesting phenomena take place in condensed phase, where the environment (e.g., solvent) can play a crucial role in determining the structure, the properties and the dynamics of the system to be studied. In a practical context, accounting for all solvent molecules in a either Molecular Dynamics (MD) or even Quantum Mechanical (QM) computation is infeasible due to the complexity of the underlying equations. A particular choice of a multi-scale model is to model the solvent environment to be a conducting continuum medium (COSMO-model) and the resulting electrostatic energy contribution to the solvation energy can be computed by solving a Poisson equation in the Van der Waals cavity of the solute molecule.

The mathematical problem is therefore set (and well-posed) and we illustrate how to approximate its solution using Schwarz s domain decomposition method adapted to integral equations. In this manner, the problem can be solved iteratively and the coupling of the local problems is determined by the connectivity of the molecule (in contrast to fast multipole-based boundary element solvers). The resulting numerical scheme is extremely fast and a linear scaling of the computing resources with respect to the number of atoms of the solute molecule can be achieved. In numerical examples we show how this approach outperforms existing methods such as the fast multipole method by several orders of magnitude.

CONTACT: paola.antonietti@polimi.it; alfio.quarteroni@epfl.ch

14 Maggio, 2014 12:15

Seminari di Cultura Matematica

L'America dimenticata. I rapporti tra le civiltà e un errore di Tolomeo

Lucio Russo, Università degli Studi di Roma Tor Vergata

Aula Rogers

Computational chemistry has attracted much attention since this years choice of the Nobel prize winners in chemistry for their contributions to multi-scale models such as the QM/MM method. The large majority of chemically interesting phenomena take place in condensed phase, where the environment (e.g., solvent) can play a crucial role in determining the structure, the properties and the dynamics of the system to be studied. In a practical context, accounting for all solvent molecules in a either Molecular Dynamics (MD) or even Quantum Mechanical (QM) computation is infeasible due to the complexity of the underlying equations. A particular choice of a multi-scale model is to model the solvent environment to be a conducting continuum medium (COSMO-model) and the resulting electrostatic energy contribution to the solvation energy can be computed by solving a Poisson equation in the Van der Waals cavity of the solute molecule.

The mathematical problem is therefore set (and well-posed) and we illustrate how to approximate its solution using Schwarz s domain decomposition method adapted to integral equations. In this manner, the problem can be solved iteratively and the coupling of the local problems is determined by the connectivity of the molecule (in contrast to fast multipole-based boundary element solvers). The resulting numerical scheme is extremely fast and a linear scaling of the computing resources with respect to the number of atoms of the solute molecule can be achieved. In numerical examples we show how this approach outperforms existing methods such as the fast multipole method by several orders of magnitude.

CONTACT: paola.antonietti@polimi.it; alfio.quarteroni@epfl.ch

13 Maggio, 2014 16:30

Lezioni Leonardesche

BIRATIONAL INVARIANTS AND APPLICATIONS TO RATIONALITY PROBLEMS

Claire Voisin, Ecole Polytechnique, Palaiseau

Università di Milano, Dipartimento di Matematica, Via Saldini

Computational chemistry has attracted much attention since this years choice of the Nobel prize winners in chemistry for their contributions to multi-scale models such as the QM/MM method. The large majority of chemically interesting phenomena take place in condensed phase, where the environment (e.g., solvent) can play a crucial role in determining the structure, the properties and the dynamics of the system to be studied. In a practical context, accounting for all solvent molecules in a either Molecular Dynamics (MD) or even Quantum Mechanical (QM) computation is infeasible due to the complexity of the underlying equations. A particular choice of a multi-scale model is to model the solvent environment to be a conducting continuum medium (COSMO-model) and the resulting electrostatic energy contribution to the solvation energy can be computed by solving a Poisson equation in the Van der Waals cavity of the solute molecule.

The mathematical problem is therefore set (and well-posed) and we illustrate how to approximate its solution using Schwarz s domain decomposition method adapted to integral equations. In this manner, the problem can be solved iteratively and the coupling of the local problems is determined by the connectivity of the molecule (in contrast to fast multipole-based boundary element solvers). The resulting numerical scheme is extremely fast and a linear scaling of the computing resources with respect to the number of atoms of the solute molecule can be achieved. In numerical examples we show how this approach outperforms existing methods such as the fast multipole method by several orders of magnitude.

CONTACT: paola.antonietti@polimi.it; alfio.quarteroni@epfl.ch

8 Maggio, 2014 11:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Il grado di massima verosimiglianza delle ipersuperfici di Fermat

Paolo Lella, Dipartimento di Matematica, Università di Torino

Aula seminari III piano

abstract

abstract

Uno degli strumenti classici per affrontare problemi di ottimizzazione statistica è il metodo di massima verosimiglianza.
Nel caso di modelli statistici algebrici, cioè di modelli nei quali le relazioni tra le variabili aleatorie sono polinomiali, applicare questo metodo significa studiare i punti critici della funzione di massima verosimiglianza che appartengono al luogo di annullamento dei polinomi. Il numero di punti critici risulta essere un invariante topologico della varietà e viene detto grado di massima verosimiglianza. Nel seminario studierò il grado di massima verosimiglianza delle ipersuperfici di Fermat. Le ipersuperfici di Fermat non hanno un chiaro significato statistico, ma il loro studio rappresenta un significativo esempio delle potenzialità dell applicazione di strumenti tipici della geometria algebrica al campo della statistica algebrica.
Si tratta di risultati ottenuti in collaborazione con D. Agostini, D. Alberelli e F. Grande.

7 Maggio, 2014 11:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues

Hugo Tavares, Instituto Superior Tecnico, Universidade de Lisboa

Aula seminari III piano

abstract

abstract

In this talk we consider a wide class of optimal partition problems involving Dirichlet eigenvalues of elliptic operators, with monotone cost functions. We prove the existence of an open optimal partition proving as well its regularity in the sense that the common boundary is, up to a residual set, locally a regular hypersurface. The proof involves a careful study of an associate Schrodinger system with competition terms, as well as several free boundary techniques (joint work with M. Ramos and S. Terracini).

16 Aprile, 2014 14:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

A surface-based model for cardiac electrophysiology and related inverse problems

ANNABELLE COLLIN, Inria Saclay Ile-de-France, France

Aula Seminari Saleri del VI Piano MOX- Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Cardiac electrophysiology describes and models chemical and electrical phenomena taking place in the cardiac tissue. Given the large number of related pathologies, there is an important need for understanding these phenomena. The electric wave propagating in the cardiac tissue can be represented by a nonlinear reaction-diusion partial dierential equation, coupled with an ordinary dierential
equation representing cellular activity. In this work, we propose a presentation of the bidomain model. Furthermore, the atria have very thin walls, mainly apparent as a thick surface in medical imaging. Our objective is to derive a surface bidomain model dened over the midsurface of the geometry, and able to take into account the anisotropy resulting from the preferred conduction direction along the muscle bers, which direction rapidly varies across the thickness. We propose a mathematically justied model using an asymptotic analysis in the spirit of thin structural models { such as shells { in mechanics.Various assessments and simulations including a pathological case are proposed in order to validate our model. Then, we present realistic physiological simulations - with an anatomical surface mesh representing the mid-surface of the two atria - which allow us to produce complete electrocardiograms. In the last part of this presentation, we are interested in associated estimation problems. The complex bidomain model must be adapted to each individual case in order to produce predictive simulations for a given patient. In this context, we can use the abundant available medical data, especially the patient electrical activation maps in order to adapt the bidomain model. We have proposed novel observer methods specically formulated for this combination of model and data.

contact: christian.vergara@unibg.it - davide.ambrosi@polimi.it - luca formaggia@polimi.it

16 Aprile, 2014 12:15 in punto

Seminari di Cultura Matematica

Indagini intorno al Cristo morto del Mantegna. (Convergenza di dati storici, documentari, stilistici, prospettici e tecnici intorno a un'opera paradigmatica del Rinascimento italiano)

Sandrina Bandera, Soprintendente per i Beni artistici, storici ed etnoantropologici di Milano

Aula Rogers

Cardiac electrophysiology describes and models chemical and electrical phenomena taking place in the cardiac tissue. Given the large number of related pathologies, there is an important need for understanding these phenomena. The electric wave propagating in the cardiac tissue can be represented by a nonlinear reaction-diusion partial dierential equation, coupled with an ordinary dierential
equation representing cellular activity. In this work, we propose a presentation of the bidomain model. Furthermore, the atria have very thin walls, mainly apparent as a thick surface in medical imaging. Our objective is to derive a surface bidomain model dened over the midsurface of the geometry, and able to take into account the anisotropy resulting from the preferred conduction direction along the muscle bers, which direction rapidly varies across the thickness. We propose a mathematically justied model using an asymptotic analysis in the spirit of thin structural models { such as shells { in mechanics.Various assessments and simulations including a pathological case are proposed in order to validate our model. Then, we present realistic physiological simulations - with an anatomical surface mesh representing the mid-surface of the two atria - which allow us to produce complete electrocardiograms. In the last part of this presentation, we are interested in associated estimation problems. The complex bidomain model must be adapted to each individual case in order to produce predictive simulations for a given patient. In this context, we can use the abundant available medical data, especially the patient electrical activation maps in order to adapt the bidomain model. We have proposed novel observer methods specically formulated for this combination of model and data.

contact: christian.vergara@unibg.it - davide.ambrosi@polimi.it - luca formaggia@polimi.it