arXiv subjects

Gerardo Palafox-Castillo

Publications and source records attributed to Gerardo Palafox-Castillo.

4 recordsLinked to original sources

arXiv2025

A symbiotic SIR process

We study a symmetric two-disease SIR co-infection model on networks in which co-infected individuals recover at a rate distinct from that of single infections. The model explicitly represents all co-infection states and features absorbing recovered compartments for both diseases. Within a mean-field network approximation, we derive the basic reproduction number of the coupled system and show that invasion thresholds coincide with those of two independent SIR processes. Exploiting an exchange symmetry in the equal-transmission regime, we reduce the dynamics to a lower-dimensional invariant subsystem and analyze the impact of the co-infection recovery rate. We prove that slower recovery of co-infected individuals monotonically increases the co-infection burden and yields a lower bound on epidemic duration that grows as the co-infection recovery rate decreases. Numerical simulations further indicate that reduced co-infection recovery can increase the epidemic peak, an effect supported by a sensitivity-equation analysis. Together, these results highlight how co-infection-specific recovery dynamics can substantially alter transient epidemic behavior, even in the absence of endemic equilibria.

cond-mat.stat-mech↗

arXiv2025

On Convex Functions of Gaussian Variables

We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variable satisfying a ``Ehrhard-like'' property for its distribution function has a strictly convex normalized log moment generating function, unless the variable is Gaussian, in which case affine-ness is achieved. Moreover we characterize variables that satisfy the Ehrhard-like property as the convex images of Gaussians. As applications, we derive sharp comparisons between Rényi divergences for a Gaussian and a strongly log-concave variable, and characterize the equality case. We also demonstrate essentially optimal concentration bounds for the sequence of conic intrinsic volumes associated to convex cone and we obtain a reversal of McMullen's inequality between the sum of the (Euclidean) intrinsic volumes associated to a convex body and the body's mean width that generalizes and sharpens a result of Alonso-Hernandez-Yepes.

math.PR↗

arXiv2022

Stochastic epidemic model on a simplicial complex

Complex networks with pairwise connections have been vastly used for the modeling of interactions within systems. Although these type of models are capable to capture rich structures and different phases within a great variety of situations, their lack of explicit higher order interactions might result, in some contexts, limited. In this work a stochastic epidemic model on a simplicial complex is defined, generalizing the known Markovian SIR epidemic process on networks. By direct simulations and mean field analysis is shown that already by the introduction of third order interactions through a simplex, the SIR model can display important differences in its dynamics and stationary states with respect to the pairwise version of the model.

cond-mat.stat-mech↗

arXiv2021

A discrete complement of Lyapunov's inequality and its information theoretic consequences

We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also derive several information theoretic inequalities as consequences. In particular sharp bounds are derived for the varentropy, Rényi entropies, and the concentration of information of monotone log-concave random variables. Moreover, the majorization approach utilized in the proof of the main theorem, is applied to derive analogous information theoretic results in the symmetric setting, where the Lyapunov reversal is known to fail.

cs.IT↗