A new upper bound for the critical probability of the frog model on homogeneous trees

We consider the interacting particle system on the homogeneous tree of degree $(d + 1)$, known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after a random number of jumps, with geometric distribution. We prove an upper bound for the critical parameter of survival of the model, which improves the previously known results. This upper bound was conjectured in a paper by Lebensztayn et al. ($J. Stat. Phys.$, 119(1-2), 331-345, 2005). We also give a closed formula for the upper bound

Frog model on biregular trees

Orientador: Elcio LebensztaynTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O {\emph{modelo dos sapos}} é um sistema de partículas, a tempo discreto, cujos agentes realizam passeios aleatórios simples em um grafo com probabilidade de desaparecimento $(1-p)$ antes de cada salto. Inicialmente, cada vértice do grafo contém um número aleatório de partículas. Aquelas posicionadas na raiz do grafo encontram-se acordadas, as demais adormecidas. Cada vez que uma partícula acordada visita uma partícula adormecida, a última é acordada. Resultados de transição de fase com respeito à sobrevivência e recorrência do modelo são apresentados para $(d_{1},d_{2})$-árvores birregulares. Para o modelo com configuração inicial de uma partícula por vértice, determinamos a correta ordem de magnitude da probabilidade crítica com respeito à sobrevivência do modelo quando $d_{1}$ e $d_{2}$ tendem para infinito. Provamos um novo limitante superior para a probabilidade crítica do modelo dos sapos em $d$-árvores homogêneas, que melhora os resultados previamente conhecidos. Esse limitante superior foi conjecturado em Lebensztayn et al. (\emph{J. Stat. Phys., 119(1-2), 331-345,2005}). Também damos uma fórmula explícita para o limitante superiorAbstract: The \emph{frog model} is a discrete time particle system whose agents perform simple random walks on a graph with probability of disappearance $(1-p)$ before each jump. Initially, each vertex of the graph contains a random number of particles. Those positioned at the root of the graph are awake, the others are sleeping. Each time an awakened particle visits a sleeping particle, the latter particle is awakened. Phase transition results with respect to survival and recurrence of the model are presented for $(d_{1}, d_{2})$-biregular trees. For the model with initial configuration of one particle per vertex, we determine the correct order of magnitude for the critical probability of survival of the model as $d_{1}$ and $d_{2}$ approaches infinity. We prove a new upper bound for the critical probability of the frog model on $d$-homogeneous trees, which improves the previously known results. This upper bound was conjectured in Lebensztayn et al. (\emph{J. Stat. Phys., 119 (1-2), 331-345, 2005}). We also give an explicit formula for the upper boundDoutoradoEstatisticaDoutor em Estatística140887/2017-2CNPQCAPE

A Novel Theoretical Probabilistic Model for Opportunistic Routing with Applications in Energy Consumption for WSNs

This paper proposes a new theoretical stochastic model based on an abstraction of the opportunistic model for opportunistic networks. The model is capable of systematically computing the network parameters, such as the number of possible routes, the probability of successful transmission, the expected number of broadcast transmissions, and the expected number of receptions. The usual theoretical stochastic model explored in the methodologies available in the literature is based on Markov chains, and the main novelty of this paper is the employment of a percolation stochastic model, whose main benefit is to obtain the network parameters directly. Additionally, the proposed approach is capable to deal with values of probability specified by bounded intervals or by a density function. The model is validated via Monte Carlo simulations, and a computational toolbox (R-packet) is provided to make the reproduction of the results presented in the paper easier. The technique is illustrated through a numerical example where the proposed model is applied to compute the energy consumption when transmitting a packet via an opportunistic network

Phase transition for a directed percolation model on homogeneous trees

Orientador: Élcio LebensztaynDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O Resumo poderá ser visualizado no texto completo da tese digitalAbstract: The Abstract is available with the full electronic digital documentMestradoEstatisticaMestre em Estatístic

Caracterización de los programas de tratamiento cognitivo-conductual para el manejo de problemas de comportamiento en niños y adolescentes realizados en Bogotá entre 2002 y 2008

El presente proyecto describe y analiza las características de los programas de tratamiento cognitivo-conductual de los problemas de comportamiento en niños y adolescentes realizados en Bogotá entre los años 2002 y 2008. Para tal fin se llevó a cabo una investigación de corte empírico-analítico, de tipo descriptivo con una metodología de carácter documental, la cual permitió identificar el estado actual de los diferentes programas objeto de este estudio en términos de los logros y avances, así como las limitaciones, dificultades y vacíos que presentan en el contexto local