Simplest nonequilibrium phase transition into an absorbing state

We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur and a bulk where particles move diffusively. We study different versions of these models, and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display non-trivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a $(0+1)$-dimensional non-Markovian process is discussed.Comment: 9 pages, 7 figures, minor change

Entropy estimates of small data sets

Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator out-performs other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero. Otherwise, other well-known estimators remain a better choice. The potential range of applicability of this estimator is quite broad specially for biological and digital data series.Comment: 11 pages, 2 figure

Absorbing state phase transitions with a non-accessible vacuum

We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with creation processes of the form $A \to n A$ with $n \geq 2$. This class includes the (exactly solvable in one-dimension) {\it reversible} model $2 A \leftrightarrow A$ as a particular example, as well as many other {\it non-reversible} reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation-rate (in accordance with exact results), and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte-Carlo simulations, confirming all field theoretical predictions in one and two dimensions for various reversible and non-reversible models.Comment: 6 pages. 3 Figures. Final version as published in J.Stat.Mec

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Quasi-Neutral theory of epidemic outbreaks

Some epidemics have been empirically observed to exhibit outbreaks of all possible sizes, i.e., to be scalefree or scale-invariant. Different explanations for this finding have been put forward; among them there is a model for "accidental pathogens" which leads to power-law distributed outbreaks without apparent need of parameter fine tuning. This model has been claimed to be related to self-organized criticality, and its critical properties have been conjectured to be related to directed percolation. Instead, we show that this is a (quasi) neutral model, analogous to those used in Population Genetics and Ecology, with the same critical behavior as the voter-model, i.e. the theory of accidental pathogens is a (quasi)-neutral theory. This analogy allows us to explain all the system phenomenology, including generic scale invariance and the associated scaling exponents, in a parsimonious and simple way.Comment: 13 pages, 6 figures Accepted for publication in PLoS ONE the text have been modified in orden to improve the figure's resolutio