16 Novembre, 2011 10:15 in punto

Atoms in motion: investigating the molecular bases of biology by multi-resolution computer simulations

Michele Cascella, University of Berne, Switzerland

Sala Consiglio, VII Piano, Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Thanks to the continuous growth of computational power, it is today possible to investigate
the real time-evolution of molecular systems in their environment with both qualitative and
quantitative accuracy. Different computational approaches, from ab-initio methods to coarse-grained models, can be used to address different problems at different time- and size- resolutions. Successful examples and perspectives on the application of these techniques in biophysics and molecular biology are presented during the talk.

9 Novembre, 2011 15:00 in punto

Seminari FDS

Dalle quantità alle strutture

Renato Betti, Dip. Matematica Politecnico di Milano

Aula Consiglio VII piano, edificio Nave via Bonardi, 9

abstract

abstract

Una ricostruzione concettuale degli sviluppi che hanno condotto all'idea di Galois sulla risolubilità per radicali delle equazioni algebriche.

28 Ottobre, 2011 11:00

Sezione di Geometria, Algebra e loro applicazioni

Combinatorial structures with regular automorphism groups.

Tatiana Jajayacova, Comenius University and Rose-Hulman Institute of Technology

Aula seminari III piano

abstract

abstract

The concept of an automorphism group of a combinatorial structure is a fundamental concept in the cross-section of Combinatorics and Group Theory.
Finding the automorphism group of a specific structure is a notoriously hard problem whose
general complexity has not been resolved but it is believed to be exponential.
In the
talk, I will address the opposite problem of constructing a combinatorial structure
for a given automorphism group.
The left (or right) regular action of a group on itself is one of the most natural group
actions to consider. The focus of our talk will be on combinatorial structures whose
full automorphism groups act regularly on their sets of vertices. Equivalently, we
discuss finite groups whose element sets admit the introduction of a combinatorial
structure whose full automorphism group consists solely of the automorphisms induced by the multiplication by the elements of the underlying group.
Such structures can be thought of as combinatorial representations of the corresponding groups.
Previous results on this topic include the
classification of graphical regular representations (graphs with regular automorphism groups), classification of digraphical regular representations (directed graphs with regular automorphism groups), as well as
the classification of general combinatorial structures (incidence structures) with regular automorphism groups. We generalize these results to the class of k-hypergraphs
which are incidence structures with all blocks of size k.

27 Ottobre, 2011 15:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Direct, inverse and reduced modeling in cardiac electrophysiology

Jean-Frederic Gerbeau, INRIA Paris-Rocquencourt

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

abstract

abstract

We will present some results in computational cardiac electrophysiology.
We will first address the forward problem, i.e. the direct simulation of an electrocardiogram.
Then we will show first results about the inverse problem: we will show how reduced order modeling
can be combined with evolutionary algorithms in order to estimate, from an electrocardiogram,
some parameters of a model of the electrical activity of the heart.

[1] M. Boulakia, S. Cazeau, M.A. Fernández, J.-F. Gerbeau, N. Zemzemi Mathematical modeling of electrocardiograms: a numerical study, Ann. Biomed. Eng., Vol. 38, Num. 3, pp. 1071-1097, 2010.

[2] M. Boulakia, E. Schenone, J.-F. Gerbeau, Reduced-order modeling for cardiac electrophysiology. Application to parameter identification, to appear in Int. J. Num. Meth. Bioengng.

27 Ottobre, 2011 15:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Depth Measures for Multivariate Functional Data: an application to ECG signals

Francesca Ieva, Politecnico di Milano, MOX - Dipartimento di Matematica,

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

abstract

abstract

The statistical analysis of functional data is a ever growing interest research area.
In biomedical context examples of complex output to be studied with suitable statistical techniques are more and more frequently appearing. The seminar is focused on the analysis of ECG signal (both arising from real clinical observation and numerical simulations) as multivariate functional data.

Two are the main focus of the analysis: the application of new multivariate functional indexes of depth to outlier detection, and classification of these signals in unsupervised classification framework in order to get a semiautomatic diagnostic tool for cardiovascular diseases like Bundle Brunch Block.

27 Ottobre, 2011 10:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Model reduction approaches for simulation of cardiovascular stents and pulmonary valve

Alfonso Caiazzo,  Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany

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

abstract

abstract

The talk focuses on two particular approaches to reduce complexity of cardiovascular devices modeling, a key issue to achieve realistic
simulations in clinically relevant time. First, I will discuss a (Chorin-Temam) projection scheme for an incompressible fluid through a thin porous interface, modelled as a surface resistance term in the Navier-Stokes equations. The approach can be used as a reduced model of multilayer stents (thin-wired tubular devices) and pulmonary
valves. A finite element formulation will be described, which, treating the interface conditions with a Nitsche penalization method,
yields unconditional stability for any non-negative value of the interface resistance.
As next, a geometrical-based model order reduction for the simulation of the pulmonary artery will be described, motivated by pre-operative studies of artificial valve implantation. Given a set of patient geometries, we created an atlas (i.e. a representative template of the patient set), extracting then a reduced basis (POD) of the fluid numerical solution on this domain. By considering the patient geometries as small deformations of the atlas, the pre-computed POD basis will be mapped on individual meshes, allowing fast
patient-specific simulations to investigate rest/exercise flow conditions and different artificial valve properties.

21 Ottobre, 2011 14:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Asymptotic behavior of Caginalp phase-field systems

Alain Miranville, Universite de Poitiers

Aula seminari III piano

The talk focuses on two particular approaches to reduce complexity of cardiovascular devices modeling, a key issue to achieve realistic
simulations in clinically relevant time. First, I will discuss a (Chorin-Temam) projection scheme for an incompressible fluid through a thin porous interface, modelled as a surface resistance term in the Navier-Stokes equations. The approach can be used as a reduced model of multilayer stents (thin-wired tubular devices) and pulmonary
valves. A finite element formulation will be described, which, treating the interface conditions with a Nitsche penalization method,
yields unconditional stability for any non-negative value of the interface resistance.
As next, a geometrical-based model order reduction for the simulation of the pulmonary artery will be described, motivated by pre-operative studies of artificial valve implantation. Given a set of patient geometries, we created an atlas (i.e. a representative template of the patient set), extracting then a reduced basis (POD) of the fluid numerical solution on this domain. By considering the patient geometries as small deformations of the atlas, the pre-computed POD basis will be mapped on individual meshes, allowing fast
patient-specific simulations to investigate rest/exercise flow conditions and different artificial valve properties.

20 Ottobre, 2011 15:00 in punto

Seminari FDS

Statistica & Salute

Anna Maria Paganoni, Dip. Matematica Politecnico di Milano

Sala Consiglio 7° piano, edificio Nave via Bonardi, 9

abstract

abstract

Attualmente è in sempre maggiore crescita l'utilizzo della modellizzazione statistica per analizzare dati ad alta complessità con lo scopo di comprendere, spiegare e prevedere la realtà.In questo seminario verranno esposti alcuni esempi di tale uso,legati a progetti in collaborazione con la Direzione Sanità di Regione Lombardia e la Centrale Operativa del 118.

19 Ottobre, 2011 14:30 in punto

Seminari FDS

Energy minimizing coarse spaces with functional constraints

Ludmil Zikatanov, Department of Mathematics, The Pennsylvania State University, (USA)

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

abstract

abstract

We will report on the construction of energy minimizing coarse spaces built by patching solutions to appropriate saddle point problems. We first set an abstract framework for such constructions, and then we give an example of constructing coarse space and stable interpolation operator for the two level Schwarz method. We apply the theoretical results in the design of coarse spaces for discretizations of PDE with large varying coefficients. The stability and approximation bounds of the constructed interpolant are in a weighted norm and are independent of the variations in the coefficients. Such spaces can be used in for numerical upscaling and for two level overlapping Schwarz algorithms for elliptic PDEs with large coefficient jumps generally not resolved by a standard coarse grid. This is a joint work with Robert Scheichl (University of Bath, UK) and Panayot S. Vassilevski (Lawrence Livermore National Lab).

17 Ottobre, 2011 16:30

Lezioni Leonardesche

NEW DIRECTIONS IN REPRESENTATION THEORY

CHARLES W. CURTIS, University of Oregon

Luogo: Dipartimento di Matematica, V. Saldini, 50, Aula Chisini

We will report on the construction of energy minimizing coarse spaces built by patching solutions to appropriate saddle point problems. We first set an abstract framework for such constructions, and then we give an example of constructing coarse space and stable interpolation operator for the two level Schwarz method. We apply the theoretical results in the design of coarse spaces for discretizations of PDE with large varying coefficients. The stability and approximation bounds of the constructed interpolant are in a weighted norm and are independent of the variations in the coefficients. Such spaces can be used in for numerical upscaling and for two level overlapping Schwarz algorithms for elliptic PDEs with large coefficient jumps generally not resolved by a standard coarse grid. This is a joint work with Robert Scheichl (University of Bath, UK) and Panayot S. Vassilevski (Lawrence Livermore National Lab).