arXiv subjects

Hugo Flores-Arguedas

Publications and source records attributed to Hugo Flores-Arguedas.

3 recordsLinked to original sources

arXiv2021

Bayesian Analysis of Glucose Dynamics during the Oral Glucose Tolerance Test (OGTT)

In this paper, we propose a model of the dynamics of the blood glucose level during an Oral Glucose Tolerance Test (OGTT). This dynamic includes the action of insulin and glucagon in the glucose homeostasis process as the reaction of an oral stimulus. We propose a Bayesian approach in the inference of five parameters related to insulin secretion, glucagon secretion, gastrointestinal emptying, and basal glucose level. Two insulin indicators related to the glucose level in blood and in the gastrointestinal tract allow us to suggest a classification for patients with impaired insulin sensitivity.

stat.AP↗

arXiv2021

Estimating the impact of non-pharmaceutical interventions and vaccination on the progress of the COVID-19 epidemic in Mexico: a mathematical approach

Non-pharmaceutical interventions have been critical in the fight against the COVID-19 pandemic. However, these sanitary measures have been partially lifted due to socioeconomic factors causing a worrisome rebound of the epidemic in several countries. In this work, we assess the effectiveness of the mitigation implemented to constrain the spread of SARS-CoV-2 in the Mexican territory during 2020. We also investigate to what extent the initial deployment of the vaccine will help to mitigate the pandemic and reduce the need for social distancing and other mobility restrictions. Our modeling approach is based on a simple mechanistic Kermack-McKendrick-type model. To quantify the effect of NPIs, we perform a monthly Bayesian inference using officially published data. The results suggest that in the absence of the sanitary measures, the cumulative number of infections, hospitalizations, and deaths would have been at least twice the official number. Moreover, for low vaccine coverage levels, relaxing NPIs may dramatically increase the disease burden; therefore, safety measures are of critical importance at the early stages of vaccination. The simulations also suggest that it may be more desirable to employ a vaccine with low efficacy but reach a high coverage than a vaccine with high effectiveness but low coverage levels. This supports the hypothesis that single doses to more individuals will be more effective than two doses for every person.

q-bio.PE↗

arXiv2019

Bregman dynamics, contact transformations and convex optimization

Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations, especially into the geometric structure of those dynamical systems and their structure--preserving discretizations. In this work, we introduce dynamical systems defined through a contact geometry which are not only naturally suited to the optimization goal but also subsume all previous methods based on geometric dynamical systems. As a consequence, all the deterministic flows used in optimization share an extremely interesting geometric property: they are invariant under contact transformations. In our main result, we exploit this observation to show that the celebrated Bregman Hamiltonian system can always be transformed into an equivalent but separable Hamiltonian by means of a contact transformation. This in turn enables the development of fast and robust discretizations through geometric contact splitting integrators. As an illustration, we propose the Relativistic Bregman algorithm, and show in some paradigmatic examples that it compares favorably with respect to standard optimization algorithms such as classical momentum and Nesterov's accelerated gradient.

math.OC↗