arXiv subjects

A. S. Martinez

Publications and source records attributed to A. S. Martinez.

5 recordsLinked to original sources

arXiv2021

Modeling cooperation and competition in biological communities

The far-reaching consequences of ecological interactions in the dynamics of biological communities remain an intriguing subject. For decades, competition has been a cornerstone in ecological processes, but mounting evidence shows that cooperation does also contribute to the structure of biological communities. Here, we propose a simple deterministic model for the study of the effects of facilitation and competition in the dynamics of such systems. The simultaneous inclusion of both effects produces rich dynamics and captures the context-dependence observed in the formation of ecological communities. The approach reproduces relevant aspects of primary and secondary plant succession, the effect invasive species, and the survival of rare species. The model also takes into account the role of the ecological priority effect and stress the crucial role of facilitation in conservation efforts and species coexistence.

q-bio.PE↗

arXiv2018

Cooperation risk and Nash equilibrium: quantitative description for realistic players

The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential games approach by taking into account the inherent risks of cooperation. We show the Public Goods game reduce to a Hamiltonian with one-body operators, with the correct Nash Equilibrium as the ground state. The inclusion of punishments to the Public Goods game reduces the cooperation risk, creating two-body interaction with a rich phase diagram, where phase transitions segregates the cooperative from competitive regimes.

cs.GT↗

arXiv2016

Scaling Analysis of Random Walks with Persistence Lengths: Application to Self-Avoiding Walks

We develop an approach for performing scaling analysis of $N$-step Random Walks (RWs). The mean square end-to-end distance, $\langle\vec{R}_{N}^{2}\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the ensemble averages of dot products between the walker's position and displacement vectors, at the $j$-th step. For RW models statistically invariant under orthogonal transformations, we analytically introduce a relation between $\langle\vec{R}_{N}^{2}\rangle$ and the persistence length, $λ_{N}$, which is defined as the mean end-to-end vector projection in the first step direction. For Self-Avoiding Walks (SAWs) on 2D and 3D lattices we introduce a series expansion for $λ_{N}$, and by Monte Carlo simulations we find that $λ_{\infty}$ is equal to a constant; the scaling corrections for $λ_{N}$ can be second and higher order corrections to scaling for $\langle\vec{R}_{N}^{2}\rangle$. Building SAWs with typically one hundred steps, we estimate the exponents $ν_{0}$ and $Δ_{1}$ from the IPL behavior as function of $j$. The obtained results are in excellent agreement with those in the literature. This shows that only an ensemble of paths with the same length is sufficient for determining the scaling behavior of $\langle\vec{R}_{N}^{2}\rangle$, being that the whole information needed is contained in the inner part of the paths.

cond-mat.stat-mech↗

arXiv2002

Risk aversion in economic transactions

Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once for ever for each operator) and the rules (e.g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.

cond-mat.stat-mech↗

arXiv2002

Deterministic walks in random networks: an application to thesaurus graphs

In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last τsteps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p. The tourist walk presents universal aspects with respect to τand can be done in a wide range of networks that can be viewed as ordinal neighborhood graphs. As an example, we show that graphs defined by thesaurus dictionaries share some of the statistical properties of low dimensional (d=2) Euclidean graphs and are easily distinguished from random graphs. This approach furnishes complementary information to the usual clustering coefficient and mean minimum separation length.

cond-mat.dis-nn↗