Noticias en español
A stroll through monotone inclusion problems and their splitting algorithms.
Abstract: Many situations in convex optimization can be modeled as the problem of finding a zero of a monotone operator, which can be regarded as a generalization of the gradient of a differentiable convex function. In order to numerically address this monotone inclusion problem it is vital to be able to exploit the inherent structure of the monotone operator defining it. The algorithms in the family of the splitting methods are able to do this by iteratively solving simpler subtasks which are defined by separately using some parts of the original problem. In this talk, we will introduce...
Read MoreAbstract: 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 finding solutions that concentrate around specific...
Read MoreAperiodic 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 such ratios is a question, posed as early as 1992 by...
Read MoreOptimizing 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 scheme to the flow particles. Upon arrival, the...
Read MoreRegret 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 possible.
Read MoreReconstructing 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 reconstruct such solenoidal component and there are...
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