House of Graphs 2.0: A database of interesting graphs and more
status: accepted
A new variational discretization technique for initial value problems bypassing governing equations
Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs). It is based on an optimization (action) functional with doubled degrees of freedom, which is discretized using...
Simulation of Closed Timelike Curves in a Darwinian Approach to Quantum Mechanics
Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsc...
The intervention of Brain Gym in the mathematical abilities of high-school students: A pilot study
Published in Frontiers in Psychology
Introduction The learning process of Mathematics is a challenge in Latin America; therefore, it is of vital importance to conduct actions that improve the performance in this science. Methods This article is reporting on quasi-experimental research, where, through the use of Brain Gym, the objective is to improve: the definition of rational numbers...
An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data...
In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when es...
Nietzsche and Fractal Geometry: a philosophical continuity
The purpose of this work is to highlight the epistemological proximity between Nietzsche’s philosophy of science and the underlying philosophical principles of fractal geometry, as illustrated in the main work of its creator, French mathematician Benoit Mandelbrot.This work also aims to find the end of this philosophical continuity, finding an impo...
Understanding The Odds: Statistics in Public Health
Published in Frontiers for Young Minds
In the world of public health and medicine, researchers are often trying to discover new ways of understanding and preventing diseases and other negative health outcomes. When public health researchers want to examine the relationship between some sort of exposure, like smoking, and a disease, such as lung cancer, they will often start by calculati...
A skew-symmetric energy and entropy stable formulation of the compressible Euler equations
We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lea...
Analogues of Entropy in Bi-Free Probability Theory: Microstates
status: published
Sur les démonstrations du théorème de Borel-Lebesgue
Nous considérons ici le théorème de Borel-Lebesgue sur le plan historique. En particulier, nous présentons les démonstrations essentiellements dues à Cousin et Lebesgue. Finalement, nous donnons une démonstration permettant d’adapter la démonstration de Lebesgue au cas multidimensionnel sans faire appel à des outils sophistiqués tels que le théorèm...
