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.
Decremental tree sums.
Abstract: In this talk, I will discuss the following semi-dynamic graph problem: Maintain a vertex-weighted forest under the following operations: Delete an edge; change the weight of a vertex; and, given a vertex v, return the total weight of all vertices in the same tree as v. I’ll present the following results from joint work with Marek Sokołowski. * A data structure with O(m + n log* n) time for m operations; * a linear-time data structure for *unweighted* forests; * and a data structure with (conditionally) optimal, but unknown...
Expansion of random 0/1 polytopes and the Mihail and Vazirani conjecture.
Abstract: A 0/1 polytope is the convex hull of a set of 0/1 d-dimensional vectors. A conjecture of Milena Mihail and Umesh Vazirani says that the graph of vertices and edges of every 0/1 polytope is highly connected. Specifically, it states that the edge expansion of the graph of every 0/1 polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of...
Generalized Assignment and Knapsack Problems in the Random-Order Model
Abstract: We study different online optimization problems in the random-order model. There is a finite set of bins with known capacity and a finite set of items arriving in a random order. Upon arrival of an item, its size and its value for each of the bins is revealed and it has to be decided immediately and irrevocably to which bin the item is assigned, or to not assign the item at all. In this setting, an algorithm is $\alpha$-competitive if the total value of all items assigned to the bins is at least an $\alpha$-fraction of the...
Thermodynamics-informed Neural Networks (THINNs).
Abstract: Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than...
A Normality Conjecture on Rational Base Number Systems
RESUMEN: The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two interesting families of infinite words emerge, called minimal and maximal words. We formulate the conjecture that every minimal and maximal word is normal over an appropriate subalphabet. The aim of the talk is to convince the audience that the conjecture seems true and of considerable difficulty. In particular, we shall discuss its connections with...
Optimización del diseño minero considerando la sustentabilidad de la operación
Abstract: El diseño de una operación minera es una decisión estratégica que define la geometría de la explotación, condicionando el acceso al mineral, los costos e inversiones necesarios para esto. El diseño define el método de extracción, el manejo de materiales y por lo tanto los equipos. Más aún, el diseño minero incluye la infraestructura dentro y fuera de la mina, incluyendo plantas tratamiento, botaderos y relaves. Dada esta relevancia, son múltiples los esfuerzos que se han realizado para encontrar un diseño óptimo. Sin embargo, a...
Simultaneous identification of piecewise constant sound speed and initial data for the photoacoustic tomography problem
RESUMEN: Photoacoustic tomography is a biomedical imaging modality whose goal is to reconstruct a map of absorption in biological tissue in order to identify different structures, and in particular to determine whether they are healthy or not. This modality has multiple applications, including tumor detection, breast cancer diagnosis, imaging of blood vessel networks, and measuring blood oxygenation. In this talk, we will focus on acoustic inversion—one of the steps of photoacoustic tomography—in the case where the speed of sound is an...
Chen-Chvátal Conjecture in Graphs and Hypergraphs.
Abstract: It is well known that a set of n non-collinear points in the Euclidean plane determines at least n distinct lines. In 2008, Chen and Chvátal conjectured that this result extends to arbitrary finite metric spaces with an appropriate definition of line. In this talk, we present a survey of this conjecture, outlining known results in the contexts of metric spaces, hypergraphs, and graphs
Spectral Theory of Substitutions.
RESUMEN: Given a finite alphabet, a substitution is a rule that assigns to each letter a nontrivial word over the same alphabet. Although they are simple combinatorial objects, substitutions arise across a wide range of mathematical disciplines, including combinatorics on words, theoretical computer science (automata theory), number theory (Diophantine approximation, multiplicative functions), mathematical physics (quasicrystals), and ergodic theory (induced systems). In this talk, we will review recent work on the spectral properties of...
Drift parameter estimation for a fractional interacting particle system.
Resumen: We consider a system of interacting particles with Lipschitz continuous drift functions, driven by additive fractional Brownian motions with H in [1/2, 1). For this system, we address the drift parameter estimation problem from continuous observations over a fixed time interval, assuming that the drift depends linearly on an unknown parameter vector. We propose estimators inspired by the least squares approach, demonstrate their consistency and asymptotic normality as the number of particles tends to infinity, and present a...
