Dipartimento di Matematica

Prossimi Seminari

• Working with compositional data in coordinates
  Eva Fiserova, Palacky University Olomouc, Czech Republic
  mercoledì 21 novembre 2018 alle ore 14:30, aula Saleri VI piano
  ABSTRACT
  ABSTRACT
  

  Compositional data are multivariate observations carrying only relative information, popularly expressed in percentages, proportions, mg/kg, etc. Because of features inherent to compositional data, such as scale invariance and the relative scale, the statistical analysis of raw compositional data often leads to spurious results. Natural principles of compositional data are followed by the Aitchison geometry on a simplex, the sample space of compositional data (Aitchison, 1986; Pawlowsky-Glahn et al., 2015). However, because most standard statistical methods rely on the Euclidean geometry in real space, compositional data need to be converted to this space prior to statistical processing. In the lecture, we will present the log ratio methodology for dealing with compositional data and several types of their coordinate representations, such as orthonormal log-ratio coordinates, pivot coordinates, weighted pivot coordinates (Hron et al., 2017), or symmetric balances (!
  Kynvclova et al., 2017). Their usage will be demonstrated on examples.
  
• Illuminazione, visione e opere d’arte: il punto di vista del fisico
  Farini Alessandro, Istituto Nazionale di Ottica, CNR, Firenze
  mercoledì 21 novembre 2018 alle ore 15:00, Sala Consiglio VII piano
  ABSTRACT
  ABSTRACT
  

  Quale è il legame tra le onde elettromagnetiche appartenenti a quella parte dello spettro che chiamiamo visibile e la nostra visione? L’interpretazione che il nostro occhio e il nostro cervello forniscono della realtà circostante è così complessa che è necessario tenere conto di tantissimi fattori per comprendere ad esempio perché vediamo alcuni colori o percepiamo il contrasto in un certo modo. Uno degli esempi più affascinanti è sicuramente quello delle opere pittoriche, dove spesso ci rendiamo conto che l’artista dimostra una comprensione, almeno
  implicita, del funzionamento della nostra percezione veramente interessante. Questi aspetti saranno mostrati con alcuni esperimenti dal vivo che vogliono rendere più chiari i concetti espressi.
• An overview of some mathematical and computational problems in Network Science
  Michele Benzi, Scuola Normale Superiore, Pisa
  giovedì 22 novembre 2018 alle ore 14:00,  Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  ABSTRACT
  

  Network Science is a rapidly growing interdisciplinary area at the intersection of mathematics, computer science, and a multitude of disciplines from the natural and life sciences to the social sciences and even the humanities. Network analysis methods are now widely used in proteomics, in the study of social networks (both human and animal), in finance, in ecology, in bibliometric studies, in archeology, and in a host of other fields. In this talk I will introduce the audience to some of the mathematical and computational problems and methods of complex networks, with an emphasis on the basic notions of centrality and communicability. More specifically, I will describe some of the problems in large-scale numerical linear algebra arising in this area, and how they differ from the corresponding problems encountered in more traditional applications of numerical analysis. The talk will be accessible to students, requiring only a modest background in linear algebra, numerical analysis and graph theory.
  
  Contacts: paola.antonietti@polimi.it, paolo.zunino@polimi.it
  
• BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES
  Shigefumi Mori, Kyoto University Institute of Advanced Study
  lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50
• The Quantitative Alexandrov Theorem in Space forms
  Luigi Vezzoni, Università degli Studi di Torino
  martedì 27 novembre 2018 alle ore 15:15, Aula seminari 3° piano
  ABSTRACT
  ABSTRACT
  

  The talk focuses on a recent generalization of a classical result of Alexandrov. The celebrated Alexandrov’s Soap Bubble Theorem states that the spheres are the only closed (i.e. compact and without boundary) constant mean curvature hypersurfaces embedded in the Euclidean space. The theorem has been generalized to the hyperbolic space and to the hemisphere and to a large class of curvature operators. The main result of the talk is a quantitative version of Alexandrov’s theorem which I’ve obtained in collaboration with Giulio Ciraolo and Alberto Roncoroni by using a quantitative study of the method of the moving planes. The theorem implies a new pinching Theorem for hypersurfaces in space forms.
• First Principles Determination of Reaction Rates
  Carlo Cavallotti, Dipartimento di Chimica, Materiali e Ingegneria Chimica, “G. Natta”, Politecnico di Milano
  martedì 27 novembre 2018 alle ore 10:30, aula Saleri VI piano
  ABSTRACT
  ABSTRACT
  

  The central focus of chemical kinetics is the determination of the rate at which one or more molecules react to transform into new molecules through the rearrangements of chemical bonds.
  Theoretically, chemical kinetics lies at the interface between quantum and classical mechanics, with the explicit formulation of rate laws requiring an extensive use of statistical thermodynamics.
  In the last years a priori rate calculations for gas phase reactions have undergone a gradual but dramatic transformation, with current predictions often rivaling the accuracy of the best available experimental data.
  In this seminar I will talk about the current status of ab initio chemical kinetics and of the challenges that must still be met in order to transform this branch of physical chemistry from a qualitative to a quantitative predictive science. A few example of research areas were contributions are necessary are the following: 1) the efficient determination of absolute and relative minima as well as first order saddle points on multidimensional potential energy surfaces for which gradient and, if necessary, Hessian information is available; 2) the determination of the number of energy states for a collection of non harmonic quantum oscillators; 3) the determination of a large number of eigenvalues for the quantum Hamiltonian of multidimensional rotors; 4) efficient approaches for the integration of the energy and momentum resolved master equation for chemically reactive systems.
  
• Emodinamica della circolazione epatica: problemi e nuove acquisizioni
  Massimiliano Tuveri, Azienda Ospedaliera Universitaria Integrata, Verona, Italy
  giovedì 29 novembre 2018 alle ore 11:30, aula consiglio VII piano
  ABSTRACT
  ABSTRACT
  

  : Il fegato ha una vascolarizzazione peculiare comparata con gli altri organi. Ha infatti afferente vascolari di tipo arterioso (arteria epatica) e venoso (vena porta) che confluiscono nel sistema sinusoidale del fegato. Da qui si diparte una efferenza unica venosa rappresentata dalle vene sovraepatiche. La vascolarizzazione intraparenchimale ha una struttura complessa: si divide in due lobi distinti e autonomi ognuno dei quali presenta dei segmenti (8 in tutto) che sono perfusi indipendentemente. Questo riveste una particolare importanza dal punto di vista clinico, specialmente chirurgico, quando si tratta di rimuovere parte del fegato. La quantità di fegato necessaria per la sopravvivenza del paziente, quando per motivi oncologici debba essere asportata ampia parte del fegato, è difficile da predire. Il rischio di insufficienza epatica acuta è infatti molto alto. Il paziente inoltre sviluppa un particolare quadro emodinamico rappresentato da uno stato circolator!
  io ipercinetico con aumento della gittata cardiaca e basse pressioni periferiche, aumento delle resistenze intraparenchimali epatiche e aumento della pressione portale con sviluppo di vie collaterali portosistemiche. I meccanismi alla base della rigenerazione epatica, che permettono al restante parenchima di rimanere vitale e assicurare le funzioni vitali, sono fondamentalmente regolati dallo shear stress arterioso ma sopratutto venoso. Il severo aumento della shear stress è stato posto anche in relazione al danno sinusoidale per l’espressione patologica di sostanze vasoattive.
  Un fattore chiave appare la comprensione dell’entità e del comportamento dello shear stress nel sistema portale. Vi è come detto una correlazione diretta tra la variazione e il gradiente dello shear stress e la modificazione della microcircolazione epatica e la secrezione endoteliale di sostanze vasoattive. La modellazione del fegato e delle sue componenti emodinamiche appare quindi un fattore cruciale per comprendere il funzionamento e eventuali fattori correttivi da apportare in sede clinica. Un fegato computazionale paziente-specifico appare quindi uno strumento estremamente utile per predire le modificazioni emodinamiche e pianificare nel futuro possibili strategie terapeutiche.
  
• Characterization of Attraction Domains for Generic Quantum Semigroups
  Damiano Poletti, Politecnico di Milano
  giovedì 29 novembre 2018 alle ore 14:30 precise, Aula Seminari III piano
  ABSTRACT
  ABSTRACT
  

  In my talk I will present the topics covered during my theses work, concerning problems linked to decoherence and asymptotic evolution of Quantum Markov Semigroups. More precisely I will introduce the subclass of Generic Quantum Semigroups and show existing results characterizing their decoherence-free subalgebra and their invariant states. Eventually I will show the results we obtained regarding attraction domains of invariant states, a topic closely related to the asymptotic behaviour of any state undergoing system evolution.

Seminari Passati

• Mixed finite elements for next-generation atmospheric models
  Tommaso Benacchio , MOX, Politecnico di Milano
  martedì 20 novembre 2018 alle ore 10:30, aula Saleri VI piano
  ABSTRACT
  

  The terrestrial atmosphere provides the arena for physical processes on multiple spatial and temporal scales. Numerical methods used to solve the governing hyperbolic models must simulate features of meteorological interest accurately while handling efficiently fast and less significant wavelike phenomena. Tight production constraints in operational numerical weather prediction (NWP) drive the development of scalable dynamical cores to keep up with computing architectures that increasingly rely on massively parallel systems for performance.
  While spectral transform and grid-point models have traditionally held sway in operational NWP and climate prediction, finite element methods have been gaining ground in recent years, due to their straightforward accuracy-tuning capabilities and flexibility towards unstructured grid arrangements in a context of deteriorating parallel performance of legacy codes. The seminar will present a mixed finite element-based dynamical core for the solution of the nonhydrostatic compressible equations under gravity. The mimetic spatial discretization reproduces continuous vector identities at the discrete level and ensures desirable properties such as pointwise mass conservation. Placement of the thermodynamic variable in a horizontally discontinuous, vertically continuous function space was recently shown to remove spurious buoyancy modes. Time discretization is handled by an iterative semi-implicit method. The numerical scheme is coded in object-oriented Fortran within a novel co-des!
  igned software framework using PSyClone, a Python-based domain-specific compiler. The new paradigm enables a clear separation of the scientific routines from the computational infrastructure, greatly facilitating portability across platforms and performance optimization.
  Results on two- and three-dimensional benchmarks of nonhydrostatic dynamics with idealized orography closely match those of existing models. Scaling scores will also be presented that highlight the model’s computational performance.
  
  ABSTRACT
• What about nutrient kinetics in a (gliomatous) brain
  Angelique Perrillat , Université de Poitiers
  martedì 20 novembre 2018 alle ore 14:00, aula Saleri VI piano
  ABSTRACT
  

  The brain is an organ with high energy needs. While it represents only 2% of the body
  weight it grabs at least 20% of its total energy needs. The consumed energy can come from many
  forms such as glutamate, glucose, oxygen and also lactate. Moreover energy is necessary to support
  neural activity. But because energy management in healthy and tumoral cells can be difficult to
  observe and explain experimentally, we use mathematical modeling to help to describe and
  understand cells energy changes. We present here a time-delayed system and two fast-slow systems
  describing the local mechanisms of interest. We will also compare simulations with MRS and
  litterature data and discuss our results.
  
  ABSTRACT
• Bayesian Dynamic Tensor Regression
  Matteo Iacopini , Università Ca’ Foscari di Venezia
  giovedì 8 novembre 2018 alle ore 11:30, aula Saleri VI piano
  ABSTRACT
  

  Multidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools.
  We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases.
  For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, we exploit a suitable parametrization based on the parallel factor (PARAFAC) decomposition which enables to achieve both parameter parsimony and to incorporate sparsity effects. Our contribution is twofold: first, we provide an extension of multivariate econometric models to account for both tensor-variate response and covariates; second, we show the effectiveness of proposed methodology in defining an autoregressive process for time-varying real economic networks.
  Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We show the efficiency of the MCMC procedure on simulated datasets, with different size of the response and independent variables, proving computational efficiency even with high-dimensions of the parameter space. Finally, we apply the model for studying the temporal evolution of real economic networks.
  
  ABSTRACT
• Predator-prey model with competition, the emergence of territoriality
  Alessandro Zilio, Université Paris Diderot
  martedì 30 ottobre 2018 alle ore 15:15, Aula seminari 3° piano
  ABSTRACT
  

  I will present a series of works in collaboration with Henri Berestycki (PSL), dealing with systems of predators interacting with a single prey. The system is linked to the Lotka-Volterra model of interaction with diffusion, but unlike more classic works, we are interested in studying the case where competition between predators is very strong: in this context, the original domain is partitioned in different sub-territories occupied by different predators. The question that we ask is under which conditions the predators segregate in packs and whether there is a benefit to the hostility between the packs. More specifically, we study the stationary states of the system, the stability of the solutions and the bifurcation diagram, and the asymptotic properties of the system when the intensity of the competition becomes infinite.
  ABSTRACT
• Material constitutive modeling and parameter calibration: towards identification of representative material properties
  Vladimir Buljak, Department of Strength of Materials, University of Belgrade
  lunedì 29 ottobre 2018 alle ore 14:00, aula Saleri VI piano
  ABSTRACT
  

  Numerical simulations are used with growing popularity in diverse sectors of engineering. The most important applications are those which attempt to replace expensive experiments on real structures that involve material mechanical behavior beyond their elastic limit. Such circumstance makes strong requirement for formulating material constitutive models with appropriate numerical implementation and for defining protocols for their calibration. Both problems are rather challenging when dealing with advanced materials.
  In order to describe mechanical behavior of materials through an appropriate constitute model experiments are needed, but the transition from measurable quantities to sought parameters cannot always be directly established. Additional difficulty is encountered when dealing with complex constitutive models which tend to capture most of the physical processes taking place during material deforming, resulting in constitutive models with elevated number of parameters. Calibration of such models on the basis of too simple experiments, risks to identify particular solutions only, managing to fit a single experiment, thus not to be treated as material representative properties. A systematic way of resolving these difficulty is through the application of inverse analysis, centered on the minimization of a discrepancy function designed to quantify the difference between measured quantities and their counter parts, computed as a function of sought material parameters. This approach is!
  more and more frequently adopted despite common mathematical difficulties, such as ill-posedness, non-uniqueness of the solution and non-convex function minimization.
  Within this lecture some recent research contributions achieved by our team to the methodology of inverse analysis apt for calibration of complex constitutive models will be given. Results are presented with reference to real life engineering problems, related to diverse industrial environments. The first group of problems considers diagnostic analysis of structures based on instrumented indentation test. Results concern the development of reduced basis model for the acceleration of non-linear elasto-plastic simulations. The second group of problems concerns compaction of ceramic powders and the development of phenomenological constitutive models together with protocols for their calibration. The last group of problems, discussed within the lecture, is related to applications of porous ceramics for diesel particulate filters and catalytic substrates. Some innovative modeling techniques regarding thermally induced cracking and crack healing, observed in these materials will b!e shown.
  
  ABSTRACT
• Modelli statistici per comprendere dai dati la complessità del reale
  Alessandra Menafoglio, Dipartimento di Matematica, Politecnico di Milano
  mercoledì 24 ottobre 2018 alle ore 15:00, Aula B.2.4
• Strategic Use of Seller Information in Private-Value First-Price Auctions
  Shmuel Zamir, The Hebrew University
  lunedì 22 ottobre 2018 alle ore 11:00, Politecnico di Milano, Dipartimento di Matematica, Sala del Consiglio 7° piano
  ABSTRACT
  

  In the framework of a private-value-first-price auction, we consider the seller as a player in a game with the buyers in which he has private information about their realized valuations. We ask whether the seller can benefit by using his private information strategically. We find that in fact, depending upon his information, set of signals, and commitment power the seller may indeed increase his revenue by strategic transmission of his information. For example, in the case of two buyers with values distributed independently and uniformly on [0,1], a seller informed of the private values of the buyers, can achieve a revenue close to 1/2 by sending verifiable messages (compared to 1/3 in the standard auction), and this is the largest revenue that can be obtained with any signalling strategy.
  ABSTRACT
• Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation
  Michel Destrade, Chair of Applied Mathematics at NUI Galway
  giovedì 18 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
  ABSTRACT
  

  Biological soft tissues and soft gels are difficult to study and model mathematically. Bioengineers often see them as engineering materials and try to evaluate their mechanical properties with standard testing protocols, such as tensile testing, simple shear, torsion, etc. These processes are destructive for tissues, as a sample is taken out of the body and placed in a device. The resulting measured parameters and models are expected to be very different from their in vivo counterparts. To test soft tissues properly, non¬-destructively, and non¬-invasively, we can rely on elastic waves. We can study the influence of pre¬stress on their speed and obtain the nonlinear elastic parameter by inverse analysis. This idea forms the basis of the theory of acousto-¬elasticity, which can be dated back to early works of Brillouin, and has been used successfully in the past for “hard” elastic solids such as rocks and metals. With this talk, we will explore the extension of acousto-¬elasticity to “soft” elastic solids, which can be subjected to large deformations in service. We will look at theoretical, numerical, experimental, and even clinical results, generated in particular on gels, brain, breast, and skin.
  
  Contact: pasquale.ciarletta@polimi.it
  
  ABSTRACT

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