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On emergence and complexity of ergodic decompositions
(Academic Press Inc., 2021)
© 2021 Elsevier Inc.A concept of emergence was recently introduced in [5] in order to quantify the richness of possible statistical behaviors of orbits of a given dynamical system. In this paper, we develop this concept ...
A hybrid variational principle for the Keller-Segel system in R-2
(EDP Sciences, 2015)
We construct weak global in time solutions to the classical Keller-Segel system describing cell movement by chemotaxis in two dimensions when the total mass is below the established critical value. Our construction takes ...
Statistical properties of the quantile normalization method for density curve alignment
(ElsevierEstados Unidos, 2017)
On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
(Publicaciones académicas Ltd., 2016)
We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely ...
Contributions to bayesian machine learning via transport maps
(Universidad de Chile, 2020)
The uncertainty is intrinsic in machine learning since it is present in data, models, parameters,
and prediction. The Bayesian approach to machine learning considers all the uncertainty
under the same point of view, and ...
Invariant probabilities for discrete time linear dynamics via thermodynamic formalism
(2021-12-01)
We show the existence of invariant ergodic σ-additive probability measures with full support on X for a class of linear operators L : X → X, where L is a weighted shift operator and X either is the Banach space c0(ℝ) or ...
Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
(Universidad de los AndesDoctorado en MatemáticasFacultad de CienciasDepartamento de Matemáticas, 2023-04-14)
This Ph.D. thesis explores stochastic optimization from a Distributionally Robust perspective, focusing on two significant themes: the innovative use of decision variable-dependent ambiguity sets in Distributionally Robust ...
MEASURABILITY OF OPTIMAL TRANSPORTATION AND STRONG COUPLING OF MARTINGALE MEASURES
(2010)
We consider the optimal mass transportation problem in Rd with measurably parameterized marginals
under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability
result for this ...
Operadores no-expansivos y transporte óptimo: cadenas de Markov con curvatura de Ricci discreta nula
(Universidad de Chile, 2019)
En la presente memoria se revisan aspectos relativos al \textit{fen{\'o}meno de concentración de la medida}. En particular, se estudia la curvatura de Ricci discreta introducida por Yann Ollivier y su relación con la ...
Cadenas de Markov controladas : robustez distribucional y aplicaciones al control de posición de un drone de 4 hélices
(UniandesMatemáticasFacultad de CienciasDepartamento de Matemáticas, 2019)
En el presente documento, se estudia el concepto de procesos de decisión de Markov dentro de un contexto de optimización y de control. Por un lado, se estudian problemas de optimización estocástica. En particular, se ...