2 citations · 3 across the 8 of their papers we have counts for
9 papers
Telegraph Processes with Extrinsic Fluctuations: Burst Dynamics and an Application to Domestic Cat Activity
Manuel Eduardo Hernández-García, Monica S. López-Castaños
Animal activity often consists of intermittent bursts separated by prolonged periods of inactivity. Here, we describe this behavior using a two-state telegraph process with extrins…
Oscillations and Spatial Patterns in Large-Scale Stochastic Gene Regulatory Networks
Manuel Eduardo Hernández-García, Jorge Velázquez-Castro
Gene regulatory networks (GRNs) are fundamental to cellular growth and tissue formation, orchestrating spatially and temporally regulated gene expression during development. These…
Oscillation Criteria in Large-Scale Gene Regulatory Networks with Intrinsic Fluctuations
Manuel Eduardo Hernández-García, Jorge Velázquez-Castro
Gene Regulatory Networks(GRNs) with feedback are essential components of many cellular processes and may exhibit oscillatory behavior. Analyzing such systems becomes increasingly c…
An Exact Moment-Based Approach for Chemical Reaction-Diffusion Networks: From Mass Action to Hill Functions
Manuel Eduardo Hernández-García, Eduardo Moreno-Barbosa, Jorge Velázquez-Castro
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the incl…
Extrinsic Fluctuations in the p53 Cycle
Manuel Eduardo Hernández-García, Mariana Gómez-Schiavon, Jorge Velázquez-Castro
Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robu…
Exact Solutions for Small Systems: Urns Models
Manuel Eduardo Hernández-García, Jorge Velázquez-Castro
In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, suc…
Relationship between Decimal Hill Coefficient, Intermediate Processes and Mesoscopic Fluctuations
Manuel Eduardo Hernández-García, Jorge Velázquez-Castro
The Hill function is relevant for describing enzyme binding and other processes in gene regulatory networks. Despite its theoretical foundation, it is often empirically used as a u…
Corrected Hill Function in Stochastic Gene Regulatory Networks
Manuel Eduardo Hernández-García, Jorge Velázquez-Castro
Describing reaction rates in stochastic bio-circuits is commonly done by directly introducing the deterministically deduced Hill function into the master equation. However, when fl…
The Hamilton-Jacobi characteristic equations for three dimensional Ashtekar gravity
Alberto Escalante, M. Eduardo Hernández-García
The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton…