All Years Seminars
[INMA] 2015-10-27 (14:00) : Randomized iterative methods for linear systems
At Euler building (A002)
Speaker :
Peter RICHTARIK
( Cornell University
)
Abstract : We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random intersect, random linear solve, random update and random fixed point. By varying its two parametersa positive definite matrix (defining geometry), and a random matrix (sampled in an i.i.d. fashion in each iteration)we recover a comprehensive array of well known algorithms as special cases, including the randomized Kaczmarz method, randomized Newton method, randomized coordinate descent method and random Gaussian pursuit. We naturally also obtain variants of all these methods using blocks and importance sampling. However, our method allows for a much wider selection of these two parameters, which leads to a number of new specific methods. We prove exponential convergence of the expected norm of the error in a single theorem, from which existing complexity results for known variants can be obtained. However, we also give an exact formula for the evolution of the expected iterates, which allows us to give lower bounds on the convergence rate.
Joint work with Robert M. Gower (Edinburgh).
[INMA] 2015-10-20 (14.00) : SVD meets LS-SVM: a unifying picture
At Euler building (A002)
Speaker :
Johan Suykens (KU Leuven, ESAT)
Abstract : In a first introductory part of this talk, the role of primal and dual model representations for data-driven modelling is explained.
Its relevance is illustrated e.g. with respect to sparsity, large scale learning algorithms, optimization modelling, and networks. Within this context
one may view least-squares support vector machines (LS-SVMs) as a class of core models in supervised and unsupervised learning, and beyond.
In a second part it is revealed how the Singular Value Decomposition (SVD) can be obtained within the LS-SVM setting. This is done by connecting to the Lanczos
decomposition theorem and the shifted eigenvalue problem. Also nonlinear SVD extensions are proposed. This presentation is based on the recent results of [Suykens, 2015].
Related reference:
Suykens J.A.K., ``SVD revisited: a new variational principle, compatible feature maps and nonlinear extensions'', Applied and Computational Harmonic Analysis, 2015, in press.
[INMA] 2015-10-13 (14:00) : Revenge, apology and forgiveness as essential mechanisms for sustainable cooperation in social dilemmas
At Euler building (A002)
Speaker :
Tom Lenaerts (ULB)
Abstract : When starting a new collaborative endeavor, it pays to establish upfront how strongly your partner or partners plan to commit to the common goal and what compensation can be expected in case the collaboration is violated. Diverse examples in biological and social contexts have demonstrated the pervasiveness of making prior agreements on posterior compensations, suggesting that this behavior could have been shaped by natural selection. I will show using stochastic evolutionary dynamics that when the cost of arranging a commitment deal lies within certain limits, substantial levels of cooperation are attainable in the prisoners dilemma[1] and public goods games [2] . In addition I will show that behaviours like revenge, apology and forgiveness provide essential mechanisms for sustaining cooperation when long-term commitments fail in the Iterated Prisoners Dilemma [3]. The main conclusion from this work is that for apologies to work they need to be sincere as otherwise strategies emerge that lead to significantly reduced levels of cooperation.
[1] The Anh Han, Luis Moniz Pereira, Francisco C Santos and Tom Lenaerts (2013) Good agreements make good friends. Scientific Reports 3:2695.
[2] The Anh Han, Luis M Pereira and Tom Lenaerts (2015) Avoiding or restricting defectors in public goods games? Journal of the Royal Society Interface 12:20141203
[3] Luis A. Martinez-Vaquero, The Anh Han, Luís Moniz Pereira and Tom Lenaerts (2015) Apology and forgiveness evolve to resolve failures in cooperative agreements. Scientific Reports 5: 10639
[INMA] 2015-10-06 (14:00) : "Mathemagics" : when Mandelbrot sets win you big money at Poker
At Euler building (A002)
Speaker :
Vande Kerckhove, Corentin
Abstract : We have all been amazed, at some point, by a trick of cards performed by a magician. In this talk, we will investigate card tricks based on mathematical bases rather than on the agility of the performer. Perhaps the most common card tricks involve particular "shuffling" of a deck of cards. Magician, and some poker player, are interested in shuffles that conserve some structure, to be leveraged during the trick.
This talk focuses on one of the most common shuffles, known as the "riffle shuffle". We derive some properties known as the Gilbreath Principles, and highlight similarities between the deck structure after shuffling and the fractal pictures. As Arthur C. Clarke said "Any sufficiently advanced technology is indistinguishable from magic." We will apply the saying by showing how the concepts mentioned above allow to create a wonderful card trick, giving you or a friend a winning hand at poker.
Journal club based on the work of the two mathematicians Persi Diaconis and Ron Graham.
[INMA] 2015-09-29 (14:00) : Dual minimal bases and their use in the numerical stability of polynomial eigenvalue solvers
At Euler building (A002)
Speaker :
Van Dooren, Paul
Abstract : Joint work with Froilan Dopico (UC3M), Piers Lawrence (UCL) and Javier Perez (UManchester).
In this talk we give a new class of linearizations of a polynomial matrix $P(s) = P_0 + P_1s + \ldots + P_d s^d$ which could be called Fiedler-like linearizations of the polynomial
matrix $P(s)$. The class contains the pencils defined in the work of Fiedler, but also those in the work of Antonio and Vologiannidis. The new characterization of pencils is quite
straightforward and has a block structure that is much easier to describe than the derivations that were given in these earlier papers. Moreover, we show that applying the $QZ$ algorithm
to these pencils results in a backward error that can be mapped back to the coefficients $P_i, i = 0,\ldots, d$, and this in a backward stable manner. Our new approach is heavily based
on the concept of dual minimal polynomial bases, which we also discuss in this talk.
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