Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics

We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.Comment: 12 pages, 7 figure

Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on $X$ and obtain the existence of equilibrium states as additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states do not have a purely additive part. We then apply our results to the construction of invariant measures of time-homogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical Systems. 23 page

Environmental problems and opportunities of the peri-urban interface and their impact upon the poor

The objective of this document is to provide an overview of the problems and opportunities of the peri-urban interface (PUI) with regard to the broad concerns of environmentalsustainability and poverty

The Influence of oral environment on diet choices in goats: a focus on saliva protein composition

There is ample evidence that ruminants are capable of making choices between different foods that provide a more balanced diet that would be obtained by eating at random. In the particular case of goats, they occupy a diversity of habitats and different breeds present variability of feeding behaviors resultant from adaptations to the existent plant species. In their food search activity, individuals are faced with variable amounts of plant secondary metabolites (PSMs), which may present some toxic and anti-nutritional effects depending on the individual’s ability to deal with it. The oral cavity has a key role in the recognition and decision processes of ingestion or rejection. In this chapter we will first consider how goats identify foods and behave according to the food items available. Focus will be done on the importance of taste sense in this process and the information available on the main structures involved in taste detection and perception in goats will be reviewed. In a second section we will focus on the characteristics of goat’s saliva, particularly in terms of their protein composition, presenting results obtained by our research team