Life sciences could benefit immensely from the massive growth of HPC processing power occurred in the last ten years. Indeed, complex biological systems are described by sophisticated mathematical models, whose solution requires highly scalable solvers. In particular, for what concerns cardiac electrophysiology, the simulation of the electrical excitation of the heart muscle, and the subsequent contraction-relaxation process, represents a challenging computational task. In the present talk, we will describe the main mathematical model of the cardiac electrical and mechanical interactions, the so-called cardiac electro-mechanical coupling model. This model consists of a system of non-linear partial differential equations (PDEs), constituted by four sub-models: the anisotropic Bidomain model, i.e. a system of degenerate parabolic reaction-diffusion PDEs describing the electrical current flow through the tissue; the membrane model of the cardiac cell myocyte describing the ionic fluxes across the membrane, including stretch-activated channels; the active tension model describing the intracellular calcium dynamics and the consequent generation of the cellular force; the quasi-static anisotropic finite elasticity equations describing the deformation of the ventricular walls. The complex interaction between the cardiac bioelectrical and mechanical phenomena is modeled by a system of non-linear partial differential equations (PDEs), known as cardiac electromechanical coupling (EMC) model. Due to the extremely different spatial and temporal scales of the physical phenomena occurring during a single heartbeat, the discretization of the EMC model with finite elements in space and finite differences in time yields the solution of thousands of large scale linear systems, with O(106 - 108) degrees of freedom each. The effective solution of such linear systems requires the use of hundreds/thousands processors and, consequently, of highly scalable preconditioners. The numerical simulations are based on our finite element parallel solver, which employs Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton-Krylov-Algebraic Multigrid methods for the solution of the non-linear systems arising from the discretization of the finite elasticity equations.
Finally, the results of three-dimensional parallel simulations will demonstrate the effectiveness of the resulting algorithms.
contact: christian.vergara@polimi.it
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Life sciences could benefit immensely from the massive growth of HPC processing power occurred in the last ten years. Indeed, complex biological systems are described by sophisticated mathematical models, whose solution requires highly scalable solvers. In particular, for what concerns cardiac electrophysiology, the simulation of the electrical excitation of the heart muscle, and the subsequent contraction-relaxation process, represents a challenging computational task. In the present talk, we will describe the main mathematical model of the cardiac electrical and mechanical interactions, the so-called cardiac electro-mechanical coupling model. This model consists of a system of non-linear partial differential equations (PDEs), constituted by four sub-models: the anisotropic Bidomain model, i.e. a system of degenerate parabolic reaction-diffusion PDEs describing the electrical current flow through the tissue; the membrane model of the cardiac cell myocyte describing the ionic fluxes across the membrane, including stretch-activated channels; the active tension model describing the intracellular calcium dynamics and the consequent generation of the cellular force; the quasi-static anisotropic finite elasticity equations describing the deformation of the ventricular walls. The complex interaction between the cardiac bioelectrical and mechanical phenomena is modeled by a system of non-linear partial differential equations (PDEs), known as cardiac electromechanical coupling (EMC) model. Due to the extremely different spatial and temporal scales of the physical phenomena occurring during a single heartbeat, the discretization of the EMC model with finite elements in space and finite differences in time yields the solution of thousands of large scale linear systems, with O(106 - 108) degrees of freedom each. The effective solution of such linear systems requires the use of hundreds/thousands processors and, consequently, of highly scalable preconditioners. The numerical simulations are based on our finite element parallel solver, which employs Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton-Krylov-Algebraic Multigrid methods for the solution of the non-linear systems arising from the discretization of the finite elasticity equations.
Finally, the results of three-dimensional parallel simulations will demonstrate the effectiveness of the resulting algorithms.
contact: christian.vergara@polimi.it
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Proximal methods have gained much interest for solving large-scale possibly non smooth optimization problems. When dealing with complicated convex functions, the expression of the proximity operator is however often non explicit and it thus needs to be determined numerically. We show in this work how block-coordinate algorithms can be designed to perform this task. We deduce also distributed optimization strategies allowing us to implement our solutions on multicore architectures. Applications of these methods to video restoration of old TV sequences illustrate the good performance of the proposed algorithms.
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Regression analysis is an important tool for analysing the relationships between the response variable and known explanatory variables. When the response variables or explanatory variables are compositional, i.e. multivariate observations carrying only relative information (proportions, percentages), a special treatment in regression is necessary. Compositional data are characterized by the simplex sample space with the Aitchison geometry that forms the Euclidean structure. Proper statistical methodology for this kind of observations is the logratio methodology that enables to express the data isometrically in the real Euclidean space where it is possible to apply standard statistical tools (Aitchison, 1986; Pawlowsky-Glahn et al., 2015). The lecture is focused on three main regression tasks, where compositional data are involved: either regression with a compositional response variable, or regression with compositional explanatory variables, or regression between parts of a composition. The main methodological approach for dealing with compositional regression is based on orthonormal logratio coordinates. Although regression models in orthonormal logratio coordinates are theoretically well justified, both the normalizing constants to reach orthonormality and the natural logarithm itself result in quite a complex interpretation of the regression parameters. In the lecture, we will present new orthogonal logratio coordinates (Muller et al., 2017) in order to achieve better interpretability of regression parameters while preserving all important features of regression models for compositional data. Theoretical results will be applied to real-world examples.
contatto: alessandra.menafoglio@polimi.it
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Since it was painted, in 1656, Las Meninas by Diego Rodríguez de Silva y Velázquez, has never stopped astonishing those who
face it as spectators, scholars, painters, semiologists, either for its fascinating beauty and imposing size (276 x 318 centimeters), or for its enigmatic set. Quite unusually, we see the painter at work in front of us on a huge canvas, attentively looking into our space and our eyes, together with other depicted characters including the shining Infanta Margarita, aging five at that time, daughter of Felipe IV and Mariana de Austria, the Royal couple appearing reflected in a mirror hung on the rear wall, while the widespread gloom pervading the big space, sometimes ripped by finite irruptions of sharp light further feeds the mysterious atmosphere of the scene, studded by series of big paintings appearing on the high walls and in between the bays.But what actually is the scene, and what does it mean? Art critics and the rich international literature available about Las Meninas have shown, over time, the many levels of meaning and the sophisticated symbolism of the composition, which will be part of our investigation, driving us at a very point of focus: the perspective structure of the representation as a crucial key to understand the enigma.Indeed, as the greatest poetry is intrinsically connected with the sublime use of the grammar, so this art masterpiece seems to be built on and substantiated by the masterly and thoughtful use of projective codes and perceptual refinement, what
makes it at the same time a visual representation and a geometrical demonstration.
Therefore, our work will mainly focus on the perspective reconstruction of the room, onthe location of the characters in the stage, and on the mirror reflection, in relation to the decentralized position of the sight point, by using modern homological procedures to show the relationships between the apparent perspective image and the conjectured real spatial set, combining drawings, digital models and animations.To make the enigma even more dense and intriguing, the room we see in the painting, which has been identified as the atelier of the painter located in the Galería de Mediodía of the Alcázar de Madrid, the castle of the King of Spain in Madrid, was burned during a devastating fire occurred in the night of Christmas Eve in 1734. The analysis of the painting has also been proposed as an educational case studio in the course of Geometrical Complements of Graphic Representation, an elective course of the Master Program in Architecture at the Politecnico di Milano in the Academic Year 2014/2015.
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Locating the optimal age (time) at which to purchase an irreversible life annuity is a problem that has received considerable attention in the literature over the past decade. As Hainaut and Deelstra noticed (J. Econ. Dyn. Control 44 (2014) 124-146), one might think that individuals should annuitize their wealth in case their financial investments performs poorly, due to the fear that the performance might become even worst. An alternative reasoning suggest that, in order to have an acceptable annuity payment, individuals should switch to annuities if the financial performance are high enough. The annuitization problem is formulated as a continuous time optimal stopping problem. The optimal time of the annuity purchases depends both on the individual's wealth and life expectancy. It is characterized as the first time the individual's wealth crosses an unknown boundary, that divides the time-wealth plane into the so called continuation and stopping regions (where it is optimal respectively to postpone or immediately purchase an annuity). The problem of finding the optimal stopping boundary is converted into a parabolic free boundary problem. From this free boundary set-up we deduce an integral equation for the boundary, which can be used to compute its values numerically. A variety of numerical examples are presented in case of Gompertz-Makeham mortality and proportional hazard rate models.
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Reduced basis (RB) methods represent a reliable and efficient approach for the numerical approximation of problems involving the repeated solution of differential equations arising from engineering and applied sciences. Noteworthy examples include partial differential equations (PDEs) depending on several parameters, PDE-constrained optimization,
data assimilation and uncertainty quantification problems. When dealing with more complex nonaffine and/or nonlinear problems, several challenges have to be faced to ensure accuracy and computational efficiency. These involve, among others, the need of (i) generating the reduced problem in non-intrusive and purely algebraic way; (ii) estimating the reduction errors or providing effective error surrogates; (iii) approximating manifolds of large intrinsic dimension with low-dimensional subspaces through possibly nonlinear or localized model order reduction algorithms.
In this talk I will show how to combine some recent reduction and hyper-reduction techniques to solve a variety of
computationally-intensive problems ranging, e.g., from fluid dynamics on domains with varying shape to cardiac electrophysiology and parameter estimation in a Bayesian setting.
contact: paola.antonietti@polimi.it
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Multivariate functional data is a frequently observed data type, however there is only little literature exists on methods for misaligned multivariate functional data. In this seminar we will present a class of generally applicable models for handling multivariate functional data without the need of pre-processing. Inference of warp and amplitude effects is done simultaneously in an iterative procedure using Laplace approximation. We will apply it to two different datasets on human movement and finally compare it to other methods in a classification setup.
contact: simone.vantini@polimi.it
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
We consider the linear third-order Moore-Gibson-Thompson equation arising in acoustics, together with its memory relaxation. We analyze the stability properties of the solutions in dependence of the structural parameters of the models, and we discuss some intrinsic connections with the equation of linear viscoelasticity
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
We consider the linear third-order Moore-Gibson-Thompson equation arising in acoustics, together with its memory relaxation. We analyze the stability properties of the solutions in dependence of the structural parameters of the models, and we discuss some intrinsic connections with the equation of linear viscoelasticity
The topic of his research are control problems, boundary integral methods, reaction-diffusion systems, Eikonal equations, homogenization. In the field of Mathematical Modeling and Scientific Computation applied to Electrocardiology is a renowned expert for his contributions in the Electrocardiographic inverse problem, in the propagation phenomena in excitable media and in large scale simulations of the myocardial activation
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica