arXiv subjects

Sebastián Risau-Gusman

Publications and source records attributed to Sebastián Risau-Gusman.

6 recordsLinked to original sources

arXiv2026

Condensation Transition in Entropy-Constrained Probability Spaces

Probability spaces are known to undergo a concentration of measure in high dimensions. In particular, if a $K$-dimensional probability distribution is sampled from a $(K-1)$-dimensional simplex with uniform measure, with high probability its empirical distribution of components is logarithmic. Here, we extend this result to the subset of distributions populating level sets of de simplex defined by a fixed Shannon entropy $H_0$. We show that the empirical distribution of components of the large majority of sampled distributions undergoes a phase transition. A critical entropy $H_c \approx \log K - 1 + γ$ exists, below which the overwhelming majority of sampled distributions are found in a condensed state, in which a single component captures a macroscopic fraction of the total probability, while the remaining components form a homogeneous incompressible fluid background. We derive the magnitude of the critical entropy, as well as the empirical distribution of components both above and below threshold. These results provide insight into how the level sets of fixed entropy in the simplex are populated.

cond-mat.stat-mech↗

arXiv2024

Expansion of net correlations in terms of partial correlations

The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The underlying network of direct interactions can be captured by a weighted graphical model. The connection between two variables can be weighted by their partial correlation, defined as the residual correlation left after accounting for the linear effects of mediating variables. While matrix inversion can be used to obtain marginal correlations from partial correlations, in large systems this approach does not reveal how the former emerge from the latter. Here we present an expansion of marginal correlations in terms of partial correlations, which shows that the effect of mediating variables can be quantified by the weight of the paths in the graphical model that connect the original pair of variables. The expansion is proved to converge for arbitrary probability distributions. The graphical interpretation reveals a close connection between the topology of the graph and the marginal correlations. Moreover, the expansion shows how marginal correlations change when some variables are severed from the graph, and how partial correlations change when some variables are marginalised out from the description. It also establishes the minimum number of latent variables required to replicate the exact effect of a collection of variables that are marginalised out, ensuring that the partial and marginal correlations of the remaining variables remain unchanged. Notably, the number of latent variables may be significantly smaller than the number of variables that they effectively replicate. Finally, for Gaussian variables, marginal correlations are shown to be related to the efficacy with which information propagates along the paths in the graph.

stat.ME↗

arXiv2021

Sleep quality, chronotype and social jet lag of adolescents from a population with a very late chronotype

Sleep disorders can be a negative factor both for learning as for the mental and physical development of adolescents. It has been shown that, in many populations, adolescents tend to have a poor sleep quality, and a very late chronotype. Furthermore, these features peak at adolescence, in the sense that adults tend to sleep better and have an earlier chronotype. But what happens when we consider adolescents in a population where already adults have poor sleep quality and a very late chronotype? We have conducted two non-clinical studies in the city of Bariloche, Argentina aimed at measuring sleep quality, chronotype, and social jet lag, using the Pittsburgh and Munich questionnaires. These were administered individually to groups of high school students, as well as to smaller samples of adults and preadolescents, in order to study differences between adolescents and these groups. The results show that in this population sleep quality is much poorer than in most other healthy populations recorded elsewhere. Furthermore, sleep quality is consistently worse for adolescents than for the other groups. The difference with adults seems to be due mainly to increased daytime sleepiness and sleep latency, whereas the difference with preadolescents seems to be due mainly to shorter sleep duration. We also found that the chronotypes of all the groups are very late, with a peak at an age between 18 and 24 ys. Social jet lag and sleep onset latency are also large, and they peak at adolescence, which suggests that they might be closely related to the large prevalence of poor sleep quality that we find in adolescents.

q-bio.QM↗

arXiv2013

Intransitivity and coexistence in four species cyclic games

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.

q-bio.PE↗

arXiv2011

Of lice and math: using models to understand and control populations of head lice

In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose variables are compatible with what is given in the literature on real infestations. We analyze two scenarios: one where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ('superspreader'). For both cases we assess the impact of several collective strategies of treatment.

q-bio.PE↗

arXiv2007

Oscillations in two-species models: tying the stochastic and deterministic approaches

We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are governed by the parameters of the corresponding deterministic (macroscopic) model. We provide a quantitative criterion for the quality of the stochastic oscillation, using a dimensionless parameter that depends only on the deterministic model. When this parameter is small, the oscillations are clear, and the frequencies of the stochastic and deterministic oscillations are close, for all stochastic models compatible with the same deterministic one. On the other hand, when it is large, the oscillations cannot be distinguished from a noise.

q-bio.PE↗