31 Marzo, 2016 11:00

MOX Seminar

Splitting methods for the magnetic Schroedinger equation

Marco Caliari, Universita' di Verona - Dipartimento di Informatica

Aula Seminari VI PIANO Mox-Dipartimento di Matematica, Politecnico di Milano

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Abstract in italiano: In questo seminario si introduce un metodo di splitting per l’equazione di Schroedinger con campo elettromagnetico du/dt = (1/2) (i nabla + A)^2 u + V u, dove u e' la funzione d'onda, A il potenziale vettore e V il potenziale scalare. Dopo aver imposto il gauge di Coulomb, l’equazione pu`o essere suddivisa in una parte cinetica, una potenziale e una di trasporto puro. Per quest’ultima si analizzano vari metodi semilagrangiani basati sulle linee caratteristiche e li si confronta, in particolare, dal punto di vista della conservazione della massa. Il metodo basato sulla trasformata di Fourier non uniforme (NFFT) risulta essere molto efficiente, sia in termini di accuratezza che di costo computazionale.

Abstract in English: This talk is about splitting methods for the magnetic Schroedinger equation du/dt = (1/2) (i nabla + A)^2 u + V u, where u is the quantum mechanical wave function, A the vector potential and V the scalar potential. After imposing the Coulomb gauge, the equation can be split into the kinetic part, the potential part and a pure convection part. For the latter, different semi-Lagrangian methods, based on the method of characteristics, are analyzed and compared, in particular from the point of view of mass conservation. The method based on the Nonuniform Fast Fourier Transform (NFFT) turns out to be very effective, both in terms ofaccuracy and compu- tational time.

contact: carlo.defalco@polimi.it

30 Marzo, 2016 11:00

MOX Seminar

Morphomechanical approach to embryonic development

Lev V. Beloussov, Lab of Developmental Biophysics, Faculty of Biology, Moscow State University

Aula Seminari

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Morphogenesis, that is, creation of new forms and structures in development of organisms is the main but still poorly understood component of ontogenesis. By the modern criteria, it belongs to the processes of self-organization, which may be simulated by two kinds of models: chemo-diffusional and those based upon mechanical forces/stresses. Among the advantages of the latter ones are naturally arisen feedbacks with 3-dimensional geometry, permitting to reproduce the complication of shapes without introducing each time ad hoc taken interventions.
As a first step, a plausibility of mechanical models was supported by discovering the patterns of mechanical stresses (MS) in embryonic tissues, regularly arranged in space/time of development. The next step was to explore whether the already established MS can affect newly generated mechanical forces within cells creating thus the feedback loops able to drive forth morphogenesis. Experimental and model evidences on the existence of such feedbacks will be presented.
Recently, the interest to morphomechanical approaches was greatly enhanced by discovery of mechanosensitive genes participating in development of Drosophila, fishes and amphibians. Taken together, the data obtained during several last decades strongly argue for a fundamental role of mechanically based feedbacks in regulating development of organisms on different structural levels.

contact: pasquale.ciarletta@polimi.it

30 Marzo, 2016 16:00 in punto

Sezione di Finanza Quantitativa

The Parabolic Taylor Formula of the Implied Volatility

Stefano Pagliarani, Ecole Polytechnique, CMAP

Aula Seminari III piano

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We are concerned with the study of the asymptotic behavior of the implied volatility (IV) and its derivatives with respect to strike and maturity. We consider a multivariate model driven by a stochastic process that, locally, is a diffusion in the sense of Stroock and Varadhan (1979) and Friedman (1975, 1976). Our main result is a rigorous derivation of the exact Taylor formula of the IV in a parabolic region close to expiry and at the money (ATM).

30 Marzo, 2016 16:00 in punto

Sezione di Analisi

Flows of non-smooth vector fields and applications to PDEs

Maria Colombo, University of Zurich

Sala Consiglio 7° piano

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The classical Cauchy-Lipschitz theorem shows existence and uniqueness of the flow of any sufficiently smooth vector field in R^d. In 1989, Di Perna and Lions proved that Sobolev regularity for vector fields, with bounded divergence and a growth assumption, is sufficient to establish existence, uniqueness and stability of a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE. Their theory relies on a growth assumption on the vector field which prevents the trajectories from blowing up in finite time; in particular, it does not apply to fast-growing, smooth vector fields.
In this seminar we give an overview of the topic and we introduce a notion of maximal flow for non-smooth vector fields which allows for finite-time blow up of the trajectories. We show existence and uniqueness under only local assumptions on the vector field and we apply the result to a kinetic equation, the Vlasov-Poisson system, where we describe the solutions as transported by a suitable flow in the phase space. This allows, in turn, to prove existence of weak solutions for general initial data.


This seminar is organized within the PRIN 2012 Research project «Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni - Partial Differential Equations and Related Analytic-Geometric Inequalities» Grant Registration number 2012TC7588_003, funded by MIUR – Project coordinator Prof. Filippo Gazzola

23 Marzo, 2016 11:00

MOX Seminar

On a multidimensional free boundary problem governed by anomalous diffusion: analytical and numerical study

Nataliya Vasylyeva, Institute of Mathematics NAS of Ukraine

Aula Seminari

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Other the past few decades an intensive effort has been put into developing theoretical models for systems with diffusive motion that can not be modelled as standard Brownian motion. The signature of this anomalous di®usion is that the mean square displacement of the diffusing species scales as a nonlinear power law in time, i.e. behaves as t to the power alpha. If alpha belongs to (0,1), this is referred to as subdi®usion. In recent years the additional motivation for these studies has been stimulated by experimental measurements of subdi®usion in porous media, glass forming materials, biological media. The review paper by Klafter et al. provides numerous references to physical phenomena in which anomalous diffusion occurs. Here we analyze anomalous di®usion version of the quasistationary Stefan problem (the fractional Hele-Shaw problem) in the multidimensional case ¬Omega(t) in R^n, n greater or equal to 2. This free boundary problem in the case of zero surface tension of the moving boundary is a mathematical model of a solute drug release from a polymer matrix (n = 1; 3).
First we represent results related with a classical solvability of this moving boundary problem. Second we discuss a
numerical technique which has been applied to obtain numerical simulations of the solutions. The relevant mathematical models of drug release from a polymeric matrix are powerful tools in studies of controlled-release drug system. Therefore, the investigations of fractional calculus in moving boundary problems would be of great interest to both theoretical and experimental studies in the future.

contact: chritian.vergara@polimi.it

Brief CV: She has obtained her PhD degree in Mathematics in 2003 on free boundary problems with singular initial data. She is working as Senior Researcher at the Institute of Applied Mathematics and Mechanics of NAS of Ukraine. Her main research activities are in the field of free boundary problems, in the field of boundary value problems for elliptic and parabolic equations in domains with nonsmooth boundaries; in the field of fractional calculus and its application to boundary value problems. She is author more than 38 publications.
She has been the local coordinators of Marie Curie IRSES project (“EUMLS”) in FP7 and she is currently the local coordinator of Marie Curie RISE project (“AMMODIT”) in Horizon 2020.
She is a member of Editorial board in Universal Journal of Applied Mathematics”;“American Journal of Computational and Applied Mathematics”, “Fractional Differential Calculus”.

23 Marzo, 2016 15:00

MOX Seminar

Physical based VFX for cinema

Jean Claude Nouchy, Visual Cortex Lab

Aula Consiglio VII piano

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The seminar will introduce Houdini, professional software used to procedurally create contents for multimedia products, like video games, films, shorts and commercials.
There are several features, from polygonal modeling to particle simulations as well as all type of physical simulations for fluids, cloth or finite elements.
The presentation will also explore the mathematical and physical assets implied in the algorithms and solvers used by the software to generate the graphic assets, as well as their behavior in the virtual space.

22 Marzo, 2016 14:30

MOX Seminar

Mathematical models of self-assembling polypeptide nanoparticles

Giuliana Indelicato, Dipartimento di Matematica, Universita' degli Studi di Torino

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

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In this talk I will discuss a mathematical framework that allows to predict and classify the layout of polypeptidic building blocks in synthetized nanoparticles. I will focus on the *de-novo *system called SAPN (self-assembling polypeptide nanoparticles) which self assembles from multiple copies of a polypeptidic building block and has been designed to act as a repetitive antigen display system in a novel generation of vaccines. Clinical trials on a vaccine against malaria based on this technology are due to start soon.
The characterization of these particles by experimental methods only is not sufficient to completely elucidate the morphology of the assembled structure. Moreover, the classical theory of Caspar and Klug for the arrangements of protein clusters in viral capsids cannot be used because the SAPNs particles exhibit more than the twelve pentagonal clusters allowed in such classification. In this presentation I will show that graph-theoretical methods can provide important insights into the geometry of such nanoparticles. I will study and classify the topology of the protein networks using tools from planar graph theory. Special attention will be devoted to symmetric particles,which can be fully described and classified.

contact: davide.ambrosi@polimi.it

18 Marzo, 2016 14:30

MOX Seminar

NPinR4FUN - Nonparametrics for Inference and Robustification for Functional Data

Anna Maria Paganoni-Nicholas Tarabelloni, MOX Dipartimento di Matematica, Politecnico di Milano

ATTENZIONE: 3° piano Aula Seminari, Dipartimento di Matematica, Politecnico di Milano

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The aim of the talk is to shed some lights on the recent developments of robust and non-parametric methods for the analysis of functional data. First of all, we will present the extension to functional data of depth measures and epigraphic indexes enabling the introduction of ranks and rank-based inference in such infinite-dimensional context. Statistical depths are non-parametric tools to measure the centrality of an observation with respect to a distribution of functions, and naturally bring along the notion of amplitude outlier. For this reason, they are used to build an extension of the boxplot to functional data and therefore to robustify a sample of observations. In opposition to amplitude outliers, a completely new kind of outlyingness arises as specific to functional data, that is the shape outlyingness. Recently, a powerful diagnostic tools, called outliergram and based on the use of Modified Band Depth (MBD) and Epigraphic Index (EI), has been proposed to identify shape outliers. Then, in the context of functional data, we will present correlation measures and independence tests based on generalisation of Kendall's tau and Spearman's rho coefficients, which have been recently proposed and are currently under study. Also, nonparametric extensions of quantiles to FDA have been advanced recently, and we will make use of this framework to solve the problem of calibrating a numerical model with functional response, aimed at reproducing a physiological ECG trace, to a functional dataset of real measurements. Many of these methods are implemented in an R package of recent development (roahd), which we will describe.

contact: laura.sangalli@polimi.it

16 Marzo, 2016 11:15

Seminari di Cultura Matematica

Robot attorno a noi: dove sono e dove saranno

Andrea Bonarini, Politecnico di Milano

Aula Rogers, via Ampère 2, Milano

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Evento in collaborazione con il Pigreco Day; per gli studenti che hanno sovrapposizione di orario il seminario sarà reso disponibile in differita streaming

16 Marzo, 2016 15:00

Seminari FDS

Robot attorno a noi: dove sono e dove saranno

Andrea Bonarini, 

Aula Rogers – Via Ampere, 2 – Milano – In occasione del PIday 2016

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Dal 2005 i robot fuori dalle fabbriche sono di piu' di quelli industriali, con un mercato in crescita esponenziale. Abbiamo aspirapolveri e droni militari, robot pulitori e robot per applicazioni mediche; il numero di applicazioni possibili aumenta di giorno in giorno, con gli aggiornamenti tecnologici che permettono una sempre maggiore autonomia. Nei prossimi anni vedremo robot per assistenza agli anziani, auto autonome, robot con cui lavorare fianco a fianco e chissa' quanti altri.

Nel seminario verranno presentati alcuni dei robot di oggi e dell'immediato futuro e cercheremo di capire come sono fatti e di cosa han bisogno.