NumPI November 2018

numpi@lists.dm.unipi.it

4 participants
6 discussions

Annuncio di seminario
by Leonardo Robol 29 Nov '18

29 Nov '18

Buongiorno, allego l'annuncio del seminario per la settimana prossima, che sarà tenuto da Stefano Massei (EPF Lausanne). L'appuntamento è giovedì 6 dicembre alle 10:00 presso il Dipartimento di Informatica, Sala Seminari Ovest. -- Leonardo Robol. ==== Speaker: Stefano Massei Affiliation: EPF Lausanne Time: Thursday, 6 December 2018, h. 10:00 Place: Sala Seminari Ovest, Dipartimento di Informatica. Title: A low-rank technique for computing the quasi stationary distribution of Galton-Watson processes Branching processes describe the dynamics of a population of individuals which reproduce and die independently, according to some specific probability distributions. More precisely, we assume that any individual has a unit lifetime, at the end of which it might give birth to one or more offsprings simultaneously. This is encoded into the probability generating function P(z):=\sum p_j z^j where p_j is the probability of generating j individuals. These kind of processes are known in the literature as Galton-Watson processes. We consider populations that are certain to become extinct, yet appear to be stationary over any reasonable time scale. More precisely, we are interested in characterizing the quasi-stationary distribution of the process, i.e., the asymptotic distribution of the population size, conditional on its survival. Yaglom proved that if m:=P'(1)<1 then the quasi stationary distribution exists and its probability generating function G(z):=\sum g_j z^j solves the Schroeder functional equation G(P(z))= mG(z)+1-m, z in [0,1]. (*) We study the link between the regularity of P(z) and that of G(z) and we propose a strategy for solving (*) in the case where P(z) and G(z) are analytic on a disc of radius r>1. We see that the discretization of (*) leads to a numerical method that is capable to find arbitrary accurate approximations of the coefficients of G(z). Moreover, we point out the (numerical) low-rank structure that appears in the discretized problem, and we show how to exploit it in the proposed procedure.

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Annuncio di seminario
by Leonardo Robol 26 Nov '18

26 Nov '18

Buongiorno, allego l'annuncio del seminario di Marcus Carlsson, programmato per la prossima settimana. Il seminario si terrà in SNS, e sarà di martedì e non di giovedì. -- Leonardo Robol. ==== Speaker: Marcus Carlsson Affiliation: Lund University Time: Tuesday, 27 November 2018, h. 11:00 Place: Aula Bianchi scienze, SNS Title: Perturbation theory for the spectral decomposition of matrices Consider a Hermitian matrix and a small perturbation. We will consider how the eigenvalues and eigenvectors change with the perturbation. Typical theorems concerning this either consider a perturbation along a line or provide general estimates valid for all perturbations (such as Weyl’s inequalities). We first give an overview of the field and then provide new results which are global in the sense that the perturbation is not restricted to a line, but local in the sense that the estimates are valid modulo certain ordo terms. We apply this to the functional calculus of the matrix square root and matrix modulus. In the kernel-free case the corresponding result follows from the so called Daleskii-Krein theorem.

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Avviso di seminario (e reminder)
by Leonardo Robol 22 Nov '18

22 Nov '18

Buongiorno, allego l'annuncio del secondo seminario nella serie NumPI, e con l'occasione vi ricordo l'appuntamento di domani alle 10:00 per quello di Giovanni Barbarino (Sala Seminari Est, Dipartimento di Informatica). ==== Speaker: Jie Meng Affiliation: Pusan National University Time: Thursday, 22 November 2018, h. 10:00 Place: Sala Seminari, Dipartimento di Matematica, Università di Pisa Title: On the positive definite solution of the nonlinear matrix equation X^p=A+M^T(X#B)M The nonlinear matrix equation X^p = A + M^T (X # B)M is considered, where p ≥ 1 is a positive integer, M is an n × n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix. We call C # D the geometric mean of positive definite matrices C and D. Some properties of the positive definite solution of the nonlinear matrix equation is investigated, including the existence and uniqueness of the solution, a lower and an upper bound. Iteration method for finding the numerical solution is proposed. Perturbation bounds with respect to small perturbations on the coefficient matrices are obtained. -- Leonardo Robol

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Fwd: [dynlist] Dyn.Sys - C. Wormell @ Centro De Giorgi 14, 00h - 14th Nov.
by Federico Poloni 13 Nov '18

13 Nov '18

Mi hanno segnalato questo seminario domani al Centro De Giorgi --- non è uno della nostra serie, ma è comunque un argomento che può essere interessante per alcuni. Cordialmente, >> Begin forwarded message: >> >> *From: *Paolo Giulietti <paologiulietti.math(a)gmail.com >> <mailto:paologiulietti.math@gmail.com>> >> *Subject: **[dynlist] Dyn.Sys - C. Wormell @ Centro De Giorgi 14,00h - >> 14th Nov.* >> *Date: *November 12, 2018 at 5:35:20 PM GMT+1 >> *To: *dynlist-pisa(a)googlegroups.com <mailto:dynlist-pisa@googlegroups.com> >> >> Dear Dynamical Friends, >> >> this week, on Wednesday 14th of November at 14:00h at the Centro de >> Giorgi, ground floor, C. Wormell from the University of Sydney will >> talk about "Chebyshev Galerkin methods for transfer operators in >> uniformly-expanding dynamics" (abstract below). >> >> Let me Remind you that at 15:00h at Palazzo della Carovana there will >> be the monthly science colloquium of the SNS. >> >> Moreover, if you are using the GoogleCalendar, check it out to see >> latest additions to the January/February schedule! >> >> Cheers! >> P&J >> >> ----------------------------------------------------------------------------------------------------------------------------------- >> >> Abstract: Full-branched expanding maps, a class of simple chaotic >> systems, are >> commonly used as models for chaotic dynamics, as well as being of >> number-theoretical interest. However, nonspecialised numerical methods >> to calculate long-time statistical quantities such as invariant measures >> have a poor trade-off between computational effort and accuracy. >> >> In this talk I will present a rigorous method to calculate statistics of >> these maps by discretising the transfer operator in a Chebyshev >> polynomial basis. This is a highly efficient discretisation: I will show >> that, for analytic maps, numerical estimates obtained with this method >> converge exponentially quickly in the order of the discretisation. >> Finally, I will discuss some implementations of these algorithms for >> exploration and rigorous proof: in particular, in only a fraction of a >> second on a personal computer one can produce estimates of most >> statistical properties accurate to 14 decimal places. >> >> >> -- >> ------------------------------------------------------------------------- >> "NO! Try not. Do, or do not. There is no try." >> >> "Much to learn, you still have." >> >> \\Yoda\\ <smb://Yoda//> >> >> -- >> Hai ricevuto questo messaggio perché sei iscritto al gruppo >> "dynlist-pisa" di Google Gruppi. >> Per annullare l'iscrizione a questo gruppo e non ricevere più le sue >> email, invia un'email a dynlist-pisa+unsubscribe(a)googlegroups.com >> <mailto:dynlist-pisa+unsubscribe@googlegroups.com>. >> Per postare in questo gruppo, invia un'email a >> dynlist-pisa(a)googlegroups.com <mailto:dynlist-pisa@googlegroups.com>. >> Visita questo gruppo all'indirizzo >> https://groups.google.com/group/dynlist-pisa. >> Per altre opzioni visita https://groups.google.com/d/optout. > -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Fwd: 2 open PhD positions, TU Eindhoven with industry in Milano
by Gianna M. Del Corso 06 Nov '18

06 Nov '18

Michiel Hochstenbach mi chiede di diffondere questa call per 2 posizioni di PhD a Eindhoven/Milano. Gianna > Inizio messaggio inoltrato: > > Da: "Hochstenbach, M.E." <M.E.Hochstenbach(a)tue.nl> > Oggetto: 2 open PhD positions, TU Eindhoven with industry in Milano > Data: 6 novembre 2018 15:10:43 CET > A: "delcorso(a)di.unipi.it" <delcorso(a)di.unipi.it> > > Dear Gianna, > > I hope you are fine! > > This email is to let you know that we have 2 open 4-year PhD positions at TU Eindhoven per March 1, 2019 in the "BIGMATH" project; I will be the main academic advisor. > These are 2 Marie Curie EID (European Industrial Doctorate) positions, together with industry in Milano (AcomeA and SDG). > The PhD students will spend ca 28 months in Eindhoven and 20 months in Milano. > > Your friend Alessandra Micheletti is also involved in this project. > > All information is available at http://www.win.tue.nl/~hochsten/bigmath.html. > The project descriptions can be found there; the topics might include numerical linear algebra, big data, large-scale optimization, modeling, probability and statistics, model reduction. > The deadline is December 5. > > Could you please forward this info to potentially interested students? > > Thank you very much in advance! All the very best and kind regards, > > Michiel Hochstenbach > > PS: There are also 2 positions at the University of Milano (please see http://itn-bigmath.unimi.it/); for those positions the restriction is a presence of <= 12 months in Italy over the last 3 years (this is not a restriction for the Eindhoven positions). Moreover, there are 2 positions in Lisbon and 1 in Novi Sad. >

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Avviso di seminario
by Leonardo Robol 01 Nov '18

01 Nov '18

Speaker: Giovanni Barbarino Affiliation: Scuola Normale Superiore, Pisa Time: Thursday, 15 November 2018, h. 10:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: Higher order spectral symbols and eigenvalues approximation for Toeplitz matrices When modeling natural phenomena with linear partial differential equations, the discretized system of equations is generally represented by a sequence of matrices, often coupled with a function called spectral symbol that enclosures asymptotic spectral information of the sequence. In fact, when sampling the symbol, we obtain an approximation of the spectrum of the matrices, with an error having magnitude inversely proportional with respect to the matrix size. Under particular hypothesis, the sequence presents an higher-order asymptotic formula for the eigenvalues, that let us precisely compute the eigenvalues of large matrices with a technique of interpolation-extrapolation at a low computational cost and that is also parallelizable. This algorithm seems also to work on different kind of matrices, but with irregularities on the extreme eigenvalues, for which a more accurate analysis is needed. -- Leonardo Robol

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NumPI November 2018