Dipartimento di Matematica – Politecnico di Milano

Prossimi Seminari

The theory of quantum statistical comparison with some applications to quantum information science
Francesco Buscemi, Nagoya University
martedì 12 settembre 2017 alle ore 15:00, Aula Seminari III piano
ABSTRACT

ABSTRACT

In mathematical statistics a central role is played by the notion of statistical models (or, equivalently, statistical experiments). These objects, which can be imagined as families of probability distributions, are often used to describe the statistician’s state of knowledge about an unknown parameter. It is then natural to compare statistical models on the basis of their “information content.” This kind of problems led in the 1950s to the formulation of a whole new theory, sometimes named “statistical comparison theory,” which soon developed into a very deep field with many applications, ranging from mathematical statistics, to physics and economics. In this lecture I will present an overview of the basic ideas of statistical comparison, some possible generalizations to the quantum setting, and a few applications in quantum thermodynamics, entanglement theory, quantum measurement theory, and the theory of open quantum systems.
TBA
Santiago Badia, Universitat Politècnica de Catalunya, Barcelona
giovedì 14 settembre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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contact:christian.vergara@polimi.it
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Benoit Perthame, Laboratoire J.-L. Lions, Université Pierre et Marie Curie, Paris
giovedì 28 settembre 2017 alle ore 14:00, Sala Seminari Saleri VI Piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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contact: pasquale.ciarletta@polimi.it
Stabilized methods and inf-sup conditions
Tomas Chacon Rebollo, Instituto de Matematicas, Universidad de Sevilla
mercoledì 4 ottobre 2017 alle ore 14:00, Aula Seminari “F. Saleri”, MOX
ABSTRACT

ABSTRACT

Stabilized methods provide a procedure to stabilize the various sources of instabilities that arise in the numerical simulation of incompressible fluid flows with reduced computational cost. It consists in adding to the standard Galerkin formulation specific terms aiming at stabilizing the possible sources of instabilities (convection dominance, pressure discretization,…). We shall describe an analysis technique for Navier-Stokes equations, in which the stability of the pressure discretization is based upon the existence of an underlying inf-sup condition between an augmented velocity space and the pressure space. We will next apply this kind of techniques to the discretization of the Primitive Equations of the Ocean. We will end by presenting an application to reduced-order modeling of turbulence.
Contatto: luca.bonaventura@polimi.it
Use of Routine Databases in the Design and Analysis of Surgical Trials
Linda Sharples, London School of Hygiene and Tropical Medicine
giovedì 5 ottobre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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ABSTRACT

A number of features of surgical interventions make their evaluation in randomised trials more difficult. For example, new procedures may be technically difficult to deliver so that surgical performance takes time to stabilise and outcomes may vary over time and between different surgeons. Moreover, there is a lack of trials culture among surgeons, so that efficient designs that are acceptable to the community are required. This talk will review some of the practical and technical issues involved in evaluations of surgical interventions, focusing on our work on the use of routine databases to explore learning curves, clustering between surgeons and the multiple component nature of the interventions. Some implications for design and analysis will be discussed and the limitations will be illustrated through the AMAZE trial in cardiac surgery patients who have a history of atrial fibrillation (irregular heart rhythm).

Contact: francesca.ieva@polimi.it
Tettonica delle placche polarizzata e terremoti
Carlo Doglioni, Dipartimento di Scienze della Terra, Università La Sapienza, Roma
martedì 17 ottobre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

La tettonica delle placche e? il combinato di effetti secolari quali il raffreddamento della Terra e la dinamica astronomica. Quest’ultima appare il modulatore dei meccanismi e causa della polarizzazione del sistema caotico e auto-organizzato della geodinamica. Fenomeni di lungo periodo sia interni che esterni al pianeta determinano una deformazione stazionaria, intervallata da eventi semi-istantanei. Entrambe le tipologie di fenomeni rappresentano il rilascio di energia in zone dove si crea un gradiente, sia esso di pressione o temperatura. I margini di placca rappresentano l’espressione di gradienti di velocita? tra le placche, controllati da gradienti di viscosita? nel canale a bassa velocita? alla base della litosfera, a loro volta controllati da variazioni laterali della composizione chimica del mantello. Il canale a bassa velocita? e? il piano di scollamento fondamentale della tettonica delle placche e appare come la sede principale di sviluppo del magmatismo terrestre. La cinematica delle placche che possiamo ricostruire e? fortemente vincolata dalla profondita? del magmatismo. La parte pellicolare della litosfera, caratterizzata da una reologia fragile per fenomeni di alta frequenza, rilascia energia gravitazionale negli ambienti tettonici estensionali (gravimoti) e invece elastica negli ambienti trascorrenti e compressivi EelastomotiI. L’energia si accumula in volumi di crosta superiore e le faglie non sono altro che le guide d’onda lungo cui una parte di questa energia viene incanalata dai volumi e dissipata in forma elastica durante un terremoto.

Contact: edie.miglio@polimi.it
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Barry Simon, California Institute of Technology
lunedì 30 ottobre 2017 alle ore 16:30, Aula Chisini, via Saldini 50
RANDOMNESS IN PARTIAL DIFFERENTIAL EQUATIONS
Felix Otto, Max Plank Institute, Leipzig
lunedì 20 novembre 2017 alle ore 16:30, Aula Chisini, via Saldini 50
Multi-scale and multi-physics modeling of complex flow and transport processes for energy storage in the subsurface
Rainer Helmig, Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart
giovedì 23 novembre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

The subsurface is being increasingly utilised both as a resource and as an energy and waste repository. Historically, there have been few issues of concern related to competition between resources, with groundwater contamination being a notable exception. However, with increasing exploitation, resource conflicts are becoming increasingly common and complex. Current issues in this regard include, for example, the long-range impact of mechanical, chemical and thermal energy storage on groundwater resources, and the complex effects surrounding hydraulic fracturing in both geothermal and shale gas production.
To analyse and predict the mutual influence of subsurface projects and their impact on groundwater reservoirs, advanced numerical models are necessary. In general, these subsurface systems include processes of varying complexity occurring in different parts of the domain of interest. These processes mostly take place on different spatial and temporal scales. It is extremely challenging to model such systems in an adequate way, accounting for the spatially varying and scale-dependent character of these processes.
In this seminar, we will give an overview of possible utilisation conflicts in subsurface systems and of how the groundwater is affected and review several model coupling concepts with a focus on the lecturer’s work in this field. The concepts are divided into temporal and spatial coupling concepts, where the latter are sub-divided into multi-process, multi-scale, multi-dimensional, and multi-compartment coupling strategies. We will present a large-scale simulation showing the general applicability of the modelling concepts of such complicated natural systems, especially the impact on the groundwater of simultaneously using geothermal energy and storing chemical and thermal energy. At the same time, we will show that such real large-scale systems provide a good environment for balancing the efficiency potential and possible weaknesses of the approaches discussed.

Contact: anna.scotti@polimi.it
Numerical simulations of non-ideal compressible-fluid flows
Alberto Guardone, Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano
giovedì 30 novembre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

In the close proximity of the liquid-vapour saturation curve and critical point, well-known thermodynamic phenomena including large compressibility and critical point effects results in very unusual fluid dynamics features, including non-ideal or rarefaction shock waves, mixed and split waves. This unconventional behaviour, which cannot occur in the ideal flow of dilute gases, is referred to as Non-Ideal Compressible-Fluid Dynamics or NICFD. The focus of this short lecture is to review the theoretical background of NICFD and to discuss the impact of highly non-ideal conditions on the design and properties of numerical schemes for compressible flows. Exemplary flow fields will be presented and compared to available experimental data from the Test-Rig for Organic VApours (TROVA) of Politecnico di Milano, a unique facility in which supersonic flows in non-ideal conditions can be measured and observed. The present results are obtained within the framework of the ERC Consolidator Grant NSHOCK, of which the presenter is the PI.

contact: nicola.parolini@polimi.it
TBA
Martin Gander, Section de Mathématiques, Université de Geneve
giovedì 14 dicembre 2017 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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contact: marco.verani@polimi.it
Combining in vitro and in silico approaches towards patient-specific cardiovascular investigations
Gabriele Dubini, Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano
giovedì 18 gennaio 2018 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT

ABSTRACT

This seminar will outline the workflow developed at the Laboratory of Biological Structure Mechanics – LaBS, Politecnico di Milano. (www.labsmech.polimi.it) for the investigation of cardiovascular devices. The combined in vitro and in silico approach will be applied to the study of stenting procedures of peripheral arteries in idealized and patient-specific models as well as to the study of percutaneous aortic valves, where fluid-structure interaction simulations are required. Such examples will demonstrate the extent to which performances of minimally-invasive devices are related to their design, the materials and the applied loads.

contact: christian.vergara@polimi.it
TBA
D. Nordsletten, Biomedical Engineering Department, King’s College London
giovedì 15 febbraio 2018 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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TBA

contact: christian.vergara@polimi.it
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Rolf Krause, Center for Computational Medicine in Cardiology, Università della Svizzera italiana,
giovedì 22 febbraio 2018 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
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Contact: christian.vergara@polimi.it

Seminari Matematici Politecnico di Milano

Seminari Matematici Milano e dintorni

Archivio Seminari

Multivariate Splines and Their Applications
Ming-Jun Lai, Dept. of Math. University of Georgia, Athens, GA, USA
giovedì 20 luglio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
Multivariate splines are piecewise polynomial or rational functions over a collection of polygons. We shall explain some approximation properties of these splines and construction of locally supported basis functions. Then I will explain how to use them for numerical solution of linear and nonlinear partial differential equations and data fitting for statistical analysis. Our approach is based on barycentric coordinates (BB form) and generalized barycentric coordinates (GBC). The smoothness conditions, boundary conditions or interpolatory conditions will be set up as linear constraints when we minimize energy functional associated with the PDE to be solved or data to be fitted. Our approach enables us to use higher order polynomials and the smoothness higher than continuity easily. Several numerical examples of PDE and data fitting will be shown.
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Doubly nonlocal Cahn-Hilliard equations
Ciprian G. Gal, Florida International University, Miami, USA
venerdì 14 luglio 2017 alle ore 11:00, Aula seminari 3° piano
ABSTRACT
We consider a doubly nonlocal nonlinear parabolic equation
which describes phase-segregation of a two-component material in a
bounded domain. This model is a more general version than the recent
nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz,
such that it reduces to the latter under certain conditions. It turns
out that there are four possible cases of double interaction in which
the nonlocality is reflected, we shall discuss some of them.
ABSTRACT
A Three-Field Formulation for Poroelasticity
Ricardo Ruiz Baier, Mathematical Institute, University of Oxford
mercoledì 12 luglio 2017 alle ore 11:30, MOX, Aula Saleri, Dipartimento di Matematica, VI piano
ABSTRACT
In this talk we present a stable and convergent conforming finite element method for the discretisation of the linear poroelasticity equations in a new formulation, where the volumetric contributions to the total stress are merged into an additional unknown. The resulting saddle point formulation can be analysed by means of a Fredholm alternative, after realizing that the problem is a compact perturbation of a Stokes-like invertible system. A generic Galerkin scheme is constructed, whose solvability properties follow closely those from the continuous variational form, and more importantly, given that specific finite dimensional spaces are chosen adequately, it is stable even in the incompressible limit.
Contatto: luca.formaggia@polimi.it
ABSTRACT
Quantum Markov Chains and Associated Open Quantum Random Walks
Ameur Dhahri, Chungbuk National University
martedì 11 luglio 2017 alle ore 14:00 precise, Aula Seminari III piano
ABSTRACT
We establish the connection between Open Quantum Random Walks and the Quantum Markov Chains. In particular, we construct tow kinds of Quantum Markov Chains associated with Open Quantum Random Walks. Finally, we study the recurrence, transience and the property of accessibility associated to these Quantum Markov Chains.
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Glauber Dynamics on the Cycles: Spectral Distribution of the Generator
Hyun Jae Yoo, Hankyong National University
martedì 11 luglio 2017 alle ore 15:00 precise, Aula Seminari III piano
ABSTRACT
We consider Glauber dynamics on finite cycles. By introducing a vacuum state we consider an algebraic probability space for the generator of the dynamics. We obtain a quantum decomposition of the generator and construct an interacting Fock space. As a result we obtain a distribution of the generator in the vacuum state.

We also discuss the monotonicity of the moments of spectral measure as the couplings increase.

In particular, when the couplings are assumed to be uniform, as the cycle grows to an infinite chain, we show that the distribution (under suitable dilation and translation) converges to a Kesten distribution.
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Debt overhang and sovereign debt restructuring
Mattia Picarelli, Università di Roma 1
martedì 4 luglio 2017 alle ore 14:00 precise, Aula Seminari Terzo Piano
ABSTRACT
Debt overhang is defined as a situation where a large amount of debt distorts the optimal investment decisions and discourages the government’s efforts of the debtor country to undertake the necessary “adjustment policies”. In this paper, I study some different strategies that can be used to solve a sovereign debt overhang problem. In particular, I consider two strategies based on a debt restructuring process, via haircut or rescheduling, and a third one based on conditional-additional lending. This strategy relies on the idea that the debtor country can get new lending from the existing creditors, in order to undertake investments that can affect the productivity shock distribution in a positive way (or reduce the probability of default). The aim is to study the consequences, deriving from the three strategies described, on the incentives to invest in a “troubled country”. According to these consequences and under some specific conditions, I am able to build a ranking for these three strategies in order to see which is the most effective one. In particular, I find that if the change in investments due to the conditional-additional lending makes the probability of default low in this scenario, the conditional lending strategy will be the most effective one.
ABSTRACT
Dynamical low rank approximation of random time dependent PDEs
Fabio Nobile, Mathematics Institute, CSQI, Ecole Polytechnique Fédérale de Lausanne, Switzerland
giovedì 29 giugno 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
Partial differential equations with random coefficients and input data (random PDEs in short) arise in many applications in which the data of the PDE need to be described in terms of random variables/fields due either to a lack of knowledge of the system or to its inherent variability. The numerical approximation of statistics of the solution poses several challenges when the number of random parameters is large and/or the parameter-to-solution map is complex, and effective surrogate or reduced models are of great need in this context.
In this talk we consider time dependent PDEs with few random parameters and seek for an approximate solution in separable form that can be written at each time instant as a linear combination of linearly independent spatial functions multiplied by linearly independent random variables (low rank approximation) in the spirit of a truncated Karhunen-Loève expansion. Since the optimal deterministic and stochastic modes can significantly change over time, we consider here a dynamical approach where those modes are computed on the fly as solutions of suitable evolution equations. From a geometrical point of view, this corresponds to constraining the original dynamics to the manifold of fixed rank functions, i.e. functions that can be written in separable form with a fixed number of terms. Equivalently, the original equations are projected onto the tangent space to the manifold of fixed rank functions along the approximate trajectory, similarly to the Dirac-Frenkel variational principle in quantum mechanics.
We discuss the construction of the method as well as practical numerical aspects for several time dependent PDEs with random parameters, including the heat equation with a random diffusion coefficient; the incompressible Navier-Stokes equations with random Dirichlet boundary conditions; the wave equation with random wave speed. In the latter case, we propose a dynamical low rank approximation that preserves the symplectic structure of the equations.
ABSTRACT
Imaging the brain microstructure with diffusion-weighted MRI
Maxime Taquet, University of Louvain and Harvard Medical School
lunedì 26 giugno 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
The brain microstructure is the complex organization of axons, neurons and other cells that support the neural functions. Its mapping at the whole-brain level holds promise to the identification and characterization of neurological and psychiatric disorders as well as the assessment of response to treatment. Diffusion-weighted imaging has been at the forefront of developments of brain microstructure imaging. It is based on the recording of movements of pools of water molecules as they hit the cellular barriers in the brain. In this talk, I will provide a gentle introduction to DWI and microstructure imaging, present some recent developments and outline exciting challenges that the field is currently facing.
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