6 Ottobre, 2016 16:30

Seminario Matematico e Fisico di Milano

Constructing curves on surfaces

François Charles, Université Paris-Sud (Orsay)

Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50

abstract

abstract

A number of important questions in arithmetic and algebraic geometry, like the Hodge conjecture, deal with construction methods for subvarieties of algebraic varieties. These conjectures deal with complex-analytic questions, number-theoretic ones and questions regarding transcendental number theory. We will describe various aspects of these conjectures, and explain the geometric ideas underlying the proof of some of these in specific cases.

5 Ottobre, 2016 11:30

MOX Seminar

Polynomial Adaptivity in Discontinuous Galerkin Large Eddy Simulation

Matteo Tugnoli, Dip. Scienze e Tecnologie Aerospaziali, Politecnico di Milano

Aula Seminari "Saleri" VI Piano - Mox - Dipartimento di Matematica, Politecncio di Milano

abstract

abstract

In the context of Large Eddy Simulation (LES) of turbulent flows, only the more energetic scales of motions are represented while the effect of the smaller ones is modelled. For complex and unsteady flows, it is difficult to set a priori the numerical resolution corresponding to the scales that must be directly simulated. Adaptive (in the polynomial or grid sense) LES should overcome this problem allowing to locally adapt the discretization resolution to simulate a necessary amount of the turbulent scales. The present talk is focused on the polynomial degree adaptation in a discontinuous Galerkin method. The polynomial adaptivity procedure is quite established for non turbulent phenomena, and usually relies on a suitable local error estimation. In a turbulent flows this approach should lead to a convergence towards the direct numerical simulation (DNS), in contrast with the aim of a LES. In the present talk different approaches will be presented and discussed.

contact: christian.vergara@polimi.it

4 Ottobre, 2016 11:15

MOX Seminar

Some problems in geometry and additive combinatorics

Endre Szemeredi, Rutgers University, USA

AULA CONSIGLIO VII Piano del Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

We are going to talk about the so called Heilbronn's problems, some geometrical Ramsey problems and Sidon-type and sum-product problems from arithmetic combinatorics.

contact: pasquale.ciarletta@polimi.it

3 Ottobre, 2016 16:03

Lezioni Leonardesche

On the fundamental theorem of Freiman

Endre Szemerédi, Rutgers University

Aula Chisini, via Saldini 50

abstract

abstract

We are going to discuss many applications and generalizations of Freiman's theorem in discrete mathematics and elsewhere. No previous knowledge is assumed.

28 Settembre, 2016 14:30

MOX Seminar

Computational study of the risk of restenosis in coronary bypasses

Bruno Guerciotti, MOX - Dipartimento di Matematica, Politecnico di Milano

Aula Seminari Saleri, VI Piano, Mox Dipartimento di Matematica, Ed. 14-Politecnico di Milano

abstract

abstract

Coronary artery disease, which is one of the leading causes of death in the world, is caused by the build-up of atherosclerotic plaques in the vessel walls. The result is a reduction of oxygen supply to the heart, which increases the risk of myocardial infarction, stroke and unstable angina. For high-risk patients, coronary artery bypass graft (CABG) is the preferred treatment. In particular, the gold standard procedure for the surgical treatment
of the left anterior descending (LAD) coronary artery disease is the left internal mammary artery (LIMA) bypass. However, despite its excellent patency rates, LIMA bypass may fail due to restenosis. Specifically, the long-term patency of LIMA is thought to be related to the degree of stenosis in the native vessel.
In this context, we present a computational study of the fluid-dynamics in patient-specific geometries with the aim of investigating a possible relationship between coronary stenosis and LIMA graft failure. Firstly, we propose a strategy to prescribe realistic boundary conditions in absence of measured data, based on an extension of the well–known Murray’s law to provide the flow division at bifurcations in case of stenotic vessels and non-Newtonian blood rheology. With the aim of investigating the actual influence of non-Newtonian blood rheology on the hemodynamics of 3D patient-specific stenotic vessels, we also show some results regarding the comparison between Newtonian and non-Newtonian rheology. Then,
we show the results regarding numerical simulations in patients treated with grafts in which the degree of coronary stenosis is virtually varied, in order to compare the fluid-dynamics in terms of hemodynamic indices potentially involved in restenosis development. Finally, we present some preliminary results concerning fluid-structure interaction simulations in CABGs with the aim of better understanding the influence of the bypass mechanical properties on the risk of graft failure.

contatto: christian.vergara@polimi.it

27 Settembre, 2016 11:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Graph decompositions via integer compositions

Emanuele Brugnoli, Università di Palermo

Aula seminari III piano

abstract

abstract

A composition of a positive integer n is defined as a way of writing n as an ordered sum of positive integers (parts). The study of compositions has a long and rich history. The earliest publication on this subject is by Percy Alexander MacMahon in 1893, entitled Memoir on the Theory of Compositions of a Number and started with the words ``Compositions are merely partitions in which the order of occurrence of the parts is essential.'' MacMahon derived a number of results, for example the total number of compositions and the number of compositions with a given number of parts, using generating functions.

Since the second half of 20th century, several groups of authors developed new research directions studying compositions restricted in some way, as also certain characteristics of these compositions.

In this talk, the strict connection between integer compositions and graph decompositions into Hamiltonian cycles is shown. Denoting, as usual, with K_v the complete graph on v vertices, a Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of K_v whose edges partition the edge-set of K_v. The earliest example of a HCS(2n+1) is attributed to Walecki; its vertex-set is V_{2n+1} := Z_{2n} U { ? } and it consists of all cycles belonging to the orbit of the starter cycle

( ?, 0, 1, -1, 2, -2, …, i, -i, …, n-1, -(n-1), n )

under the natural action of Z_{2n} on V_{2n+1}.

By means of a slight modification of the HCS(4n+1) of Walecki, we obtain 2^n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this result can be achieved by counting the inequivalent compositions of n under the action of D_n, the dihedral group of order 2n.

This seminar is organized within the PRIN 2012 Research project «Geometric Structures, Combinatorics and their Applications» Grant Registration number 2012XZE22K, funded by MIUR - Project coordinator Prof.ssa Norma Zagaglia

23 Settembre, 2016 11:15

MOX Seminar

On the Optimal Reconstruction of Partially Observed Functional Data

Alois Kneip, Universitat Bonn

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

abstract

abstract

If only fragments of functions are observable and none of these fragments cover the total domain, then it is impossible to estimate the covariance function over its total support. We propose a new functional PCA based prediction procedure that allows to reconstruct functional data from their fragmental observations under this challenging setup. By contrast to functional prediction models in the literature, we can proof the optimality of our prediction model without making use of the crucial, but unverifiable,orthogonality assumption on the prediction error. This also allows us to
identify situations under which our prediction procedure leads to a perfect reconstruction of the fragmental observations, i.e., without any prediction error. Finite sample properties are investigated through simulations and a
real data application.

contact: laura.sangalli@polimi.it

21 Settembre, 2016 16:30 in punto

Seminario Matematico e Fisico di Milano

Vortex filament dynamics

Walter Craig, McMaster University

Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50

abstract

abstract

The evolution of vortex filaments in three dimensions is an important problem in mathematical hydrodynamics. It appears in questions on solutions of the Euler equations as well as in the fine structure of vortex filamentation in a superfluid. It is also a setting in the analysis of partial differential equations with a compelling analogy to Hamiltonian dynamical systems. I will give an analysis of a system of model equations for the dynamics of near-parallel vortex filaments in a three dimensional fluid. These equations can be formulated as a Hamiltonian system of partial differential equations, and the talk will describe some aspects of a phase space analysis of solutions, including the construction of periodic and quasi-periodic orbits via a version of KAM theory for PDEs, and a topological principle to count multiplicity of solutions. This is ongoing joint work with L. Corsi (McMaster and Georgia Tech), C. Garcia (UNAM) and C.-R. Yang (McMaster and Shantou Univ.)

13 Luglio, 2016 16:15 in punto

Sezione di Analisi

Global stability for an inverse problem in soil-structure interaction

Edi Rosset, Università di Trieste

Aula seminari III piano

abstract

abstract

An important issue in structural building design is the soil–structure interaction. We make reference to the Winkler model and consider the inverse problem of determining the Winkler subgrade reaction coefficient k(x) of a slab foundation modelled as a thin elastic plate clamped at the boundary and loaded by a concentrated force. We investigate whether the coefficient k(x) depends continuously on the transversal deflection taken at the interior points. We prove a global Hölder stability estimate under some reasonable regularity assumptions on the unknown Winkler coefficient.

11 Luglio, 2016 11:30

MOX Seminar

Design and optimisation of non-smooth Imaging models via Partial Differential Equations (PDEs)

Luca Calatroni, Camelot Biomedical systems, Genova and MIDA group, Università degli studi di Genova

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

abstract

abstract

Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational principles are often considered. In their general form these models combine a regularisation and a data fitting term, balancing one against the other appropriately. Typically, Total variation (TV) regularisation is used due to its edge-preserving and smoothing properties. In this talk, we focus on the use of PDEs for the optimal design of several Imaging models. Starting from the use of higher-order and non-smooth variants of classical heat-type diffusion models often employed to counteract well-known TV reconstruction drawbacks (such as staircasing), we focus in particular on the use of non-smooth optimisation approaches with PDE constraints in the context of optimal parameter estimation for some non-standard image denoising problems. Finally, we consider some TV-based models recently reinterpreted in the framework of graphs and applied to some image segmentation problems.

contact:laura.sangalli@polimi.it