Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Metric properties of locally connected graphs.
Abstract: A set of n points in the plane which are not all collinear defines at least n distinct lines. In 2008, Chen and Chvátal conjectured that this property holds for all finite metric spaces. This conjecture is still open, even for metric spaces induced by graphs. In this talk, we show that locally connected graphs satisfy this property and an even stronger one.
Regret analysis for stochastic optimization problems under parametric models.
Abstract: In this talk, we analyze the growth rate of the regret -or optimality gap- when learning the optimal actions in stochastic optimization problems, formulated in a parametric setting. More precisely, we assume access to samples from random variables whose unknown distribution belongs to a parametric family. For both smooth and non-smooth problems, we describe the asymptotic behavior of the expected optimality gap, and use it to design appropriate estimators. Different examples will be given where explicit calculations are...
Optimizing Throughput and Makespan of Queuing Systems by Information Design.
Abstract: We study the optimal provision of information for two natural performance measures of queuing systems: throughput and makespan. A set of parallel links (queues) is equipped with deterministic capacities and stochastic travel times where the latter depend on a realized scenario, and the number of scenarios is assumed to be constant. A continuum of flow particles (users) arrives at the system at a constant rate. A system operator knows the realization of the scenario and may (partially) reveal this information via a public signaling...
Abstract: In this talk, we examine a concentration phenomenon for solutions to the constant Q-curvature equation, a critical fourth-order equation on a closed Riemannian manifold. The challenge of finding constant Q-curvature metrics is closely linked to the Yamabe problem and arises from the goal of identifying optimal metrics for a given compact, boundaryless manifold. In this work, we address the problem on a product Riemannian manifold. We will start by briefly introducing the concept of Q-curvature and then outline the main ideas for...
Aperiodic Wang tiles associated with metallic means.
RESUMEN: A Penrose tiling consists of two polygonal tiles whose frequency ratio is equal to the golden ratio. Similarly, tilings by the aperiodic monotile discovered in 2023 by David Smith are such that the ratio of the frequencies of the two orientations of the monotile is equal to the fourth power of the golden ratio. The structure of Jeandel-Rao tilings discovered in 2015 is also explained using the golden ratio. We know of aperiodic tilings that are not related to the golden ratio. However, the characterization of possible numbers for...
Reconstructing elastic strain fields from its Longitudinal Ray Transform.
RESUMEN: In the problem of Bragg-edge elastic strain tomography, measurements are obtained from energy resolved neutron transmission imaging, which provides information about the Longitudinal Ray Transform (LRT) of the elastic strain field. The goal is to recover the elastic strain field by inverting its LRT. The inversion of the ray transform for tensor fields is a well studied problem [1]. It is known that only the solenoidal part of symmetric tensor fields can be recovered from their LRT, there are inversion formulas available that...
Symmetries in Overparametrized Neural Networks: A Mean-Field View. & Feature Learning with a structured covariance
Orador: Javier Maass (CMM) 15:00 hrs Resumen: We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under distributional symmetries of the data w.r.t. the action of a general compact group G. We consider for this a class of generalized shallow NNs given by an ensemble of N multi-layer units, jointly trained using stochastic gradient descent (SGD) and possibly symmetry-leveraging (SL) techniques, such as Data Augmentation (DA), Feature Averaging (FA) or Equivariant Architectures (EA). We...
Manifold Learning, Diffusion-Maps and Applications.
Summary: We introduce the nonlinear dimensionality reduction problem known as Manifold Learning and present the diffusion maps algorithm (Coiffman and Lafon, 2006). Dif- fusion maps utilize the connectivity between data points through a diffusion process on the dataset. Additionally, we show some applications of this technique to 2D tomography reconstruction when the angles are unknown
Asymptotic stability of kinks in the odd energy space.
Abstract: In this talk I will first present a 10 years old result about the asymptotic stability of the kink in the classical φ^4 model under the assumption of oddness of the initial perturbations. I will explain how the problem can be decomposed into radiation and internal modes and how the components can be controlled through virial estimates. This result depends on some numerical approximations and its proof can be viewed as computer assisted. Recently, we were able to generalize the asymptotic stability result to one dimensional scalar...
