Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges

We explore the challenges posed by the violation of Bell-like inequalities by d-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random perturbations on the state or on the measurement settings, also quantifying the efforts needed to certify the possible violations in case of complete ignorance on the system state at hand.

The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

On the conservatism of post-Jungian criticism: competing concepts of the symbol in Freud, Jung and Walter Benjamin

The renewed interest in analytical psychology by academics working in the humanities has led to the emergence of a post-Jungian field of cultural criticism, at the theoretical core of which stands Jung's theory of symbolism. This article examines the centrality of symbolism to both Freud and Jung's psychology and explains how the differing concepts of the symbol lead to their divergent theories of interpretation in psychology and art criticism. Acknowledging the advantages of Jung's more expansive account of the symbol, it argues that Walter Benjamin's critical engagement with Jung nonetheless provides a useful correction to the problematic conservatism inherent to his concept of the symbol and its contemporary application.

Evaluación de la condición de salud del transformador mediante análisis de vibraciones usando la transformada hilbert-huang.

Tesis (Maestro en Ingeniería Eléctrica con Orientación en Potencia) UANL, 2011.

La portée épistémique de l’axiomatisation de la physique chez Hilbert

L'objectif du présent texte est de discuter de la portée épistémique de la méthode axiomatique. Tout d'abord, il sera question du contexte à partir duquel la méthode axiomatique a émergé, ce qui sera suivi d'une discussion des motivations du programme de Hilbert et de ses objectifs. Ensuite, nous exposerons la méthode axiomatique dans un cadre plus moderne afin de mettre en lumière son utilité et sa portée théorique. Finalement, il s'agira d'explorer l'influence de la méthode axiomatique en physique, surtout en ce qui a trait à l'application de la méthode par Hilbert. Nous discuterons de ses objectifs et de l'épistémologie qui accompagnait sa vision du 6 e problème, ce qui nous amènera à discuter des limites épistémiques de la méthode axiomatique et de l'entreprise scientifique en général.

De Kronecker à Gödel via Hilbert. Les fondements arithmétiques et une crise sans fondement

La crise des fondements n’a pas affecté les fondements arithmétiques du constructivisme de Kronecker, Bien plutôt, c’est le finitisme kroneckerien de la théorie de l’arithmétique générale ou polynomiale qui a permis à Hilbert de surmonter la crise des fondements ensemblistes et qui a poussé Gödel, inspiré par Hilbert, à proposer une extension du point de vue finitiste pour obtenir une preuve constructive de la consistance de l’arithmétique dans son interprétation fonctionnelle « Dialectica ».

On the V(subscript gamma) Dimension for Regression in Reproducing Kernel Hilbert Spaces

This paper presents a computation of the $V_gamma$ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression $epsilon$-insensitive loss function, and general $L_p$ loss functions. Finiteness of the RV_gamma$ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the $L_epsilon$ or general $L_p$ loss functions. This paper presenta a novel proof of this result also for the case that a bias is added to the functions in the RKHS.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities