Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Texture analysis using graphs generated by deterministic partially self-avoiding walks

Texture is one of the most important visual attributes for image analysis. It has been widely used in image analysis and pattern recognition. A partially self-avoiding deterministic walk has recently been proposed as an approach for texture analysis with promising results. This approach uses walkers (called tourists) to exploit the gray scale image contexts in several levels. Here, we present an approach to generate graphs out of the trajectories produced by the tourist walks. The generated graphs embody important characteristics related to tourist transitivity in the image. Computed from these graphs, the statistical position (degree mean) and dispersion (entropy of two vertices with the same degree) measures are used as texture descriptors. A comparison with traditional texture analysis methods is performed to illustrate the high performance of this novel approach. (C) 2011 Elsevier Ltd. All rights reserved.

Texture analysis based on maximum contrast walker

Recently, the deterministic tourist walk has emerged as a novel approach for texture analysis. This method employs a traveler visiting image pixels using a deterministic walk rule. Resulting trajectories provide clues about pixel interaction in the image that can be used for image classification and identification tasks. This paper proposes a new walk rule for the tourist which is based on contrast direction of a neighborhood. The yielded results using this approach are comparable with those from traditional texture analysis methods in the classification of a set of Brodatz textures and their rotated versions, thus confirming the potential of the method as a feasible texture analysis methodology. (C) 2010 Elsevier B.V. All rights reserved.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last mu (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory mu(1) = log(2) N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

Texture analysis and classification using deterministic tourist walk

In this paper, we present a study on a deterministic partially self-avoiding walk (tourist walk), which provides a novel method for texture feature extraction. The method is able to explore an image on all scales simultaneously. Experiments were conducted using different dynamics concerning the tourist walk. A new strategy, based on histograms. to extract information from its joint probability distribution is presented. The promising results are discussed and compared to the best-known methods for texture description reported in the literature. (C) 2009 Elsevier Ltd. All rights reserved.

Random walks systems with killing on Z

We study random walks systems on Z whose general description follows. At time zero, there is a number N >= 1 of particles at each vertex of N, all being inactive, except for those placed at the vertex one. Each active particle performs a simple random walk on Z and, up to the time it dies, it activates all inactive particles that it meets along its way. An active particle dies at the instant it reaches a certain fixed total of jumps (L >= 1) without activating any particle, so that its lifetime depends strongly on the past of the process. We investigate how the probability of survival of the process depends on L and on the jumping probabilities of the active particles.

NONHOMOGENEOUS RANDOM WALKS SYSTEMS ON Z

We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on Z, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to I but not fast enough.

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

Effects of human trampling on a rocky shore fauna on the Sao Paulo coast, southeastern Brazil

Increased tourist activity in coastal regions demands management strategies to reduce impacts on rocky shores. The highly populated coastal areas in southeastern Brazil are an example of degradation caused by development of industry and tourism. Among different shore impacts, trampling has been intensively studied, and may represent a significant source of stress for intertidal fauna. A randomised blocks design was applied to experimentally study the effects of two different trampling intensities on richness, diversity, density and biomass of the rocky shore fauna of Obuseiro beach, Guarujá, southeastern Brazil. Blocks were distributed in two portions of the intertidal zone, dominated respectively by Chthamalus bisinuatus (Cirripedia) and Isognomon bicolor (Bivalvia). Blocks were trampled over three months, simulating the vacation period in Brazil and were monitored for the following nine months. Results indicate that Chthamalus bisinuatus is vulnerable to trampling impacts. Richness, diversity and turn-over index tended to be higher in trampled plots four months after trampling ceased. In general, results agree with previous trampling studies, suggesting that even low intensities of trampling may cause some impact on intertidal communities. Management strategies should include isolation of sensitive areas, construction of boardwalks, visitor education and monitoring programmes. In Brazil, additional data obtained from experimental studies are necessary in order to achieve a better understanding of trampling impacts on rocky shore communities.

Entre a ruína e a obra de arte: psicossociologia da percepção da cidade histórica turística

Este artigo objetiva discutir o processo de significação da cidade histórica turística de Ouro Preto. Desenvolve-se por meio de uma pesquisa em psicologia social baseada na fenomenologia e no estudo micro-histórico da percepção. O trabalho foi baseado em extensa pesquisa de artigos, livros e outras fontes sobre a cidade de Ouro Preto. Ao final, mostram-se os diferentes discursos concernentes a quatro campos perceptivos criados durante o século XX.

Scripts em cena: HIV e mercado sexual no contexto turístico

A atividade turística tem impacto também na saúde das populações de comunidades anfitriãs. Com base em estudo etnográfico e em 14 entrevistas com monitores(as) de turismo ambiental, o objetivo deste artigo é analisar como o cenário sexual no contexto do turismo e seus scripts sexuais constroem a vulnerabilidade de caiçaras às DSTs/HIV e ao mercado sexual. Scripts sexuais tradicionais operacionalizados num cenário de "curtição", "prazer", "desinibição sexual", evidenciaram desigualdades sociais entre caiçaras e turistas que ampliam a vulnerabilidade dos jovens às DSTs/HIV e à mercantilização de sua sexualidade. Os scripts sexuais femininos (passividade/ingenuidade) dificultavam a negociação do preservativo nas cenas sexuais coletadas; os "mais pró-ativos" eram interpretados como disponibilidade para "programas". Os scripts "não negar fogo", "catar as turistas" também ampliavam a vulnerabilidade dos rapazes. O contexto turístico constrói um cenário sexual singular e atravessa as trajetórias socioafetivas dos moradores. Seu impacto deve ser considerado por políticas e programas de saúde locais.

Fatores de risco para nascimentos pré-termo em Londrina, Paraná, Brasil

Objetivou-se identificar fatores de risco para nascimentos pré-termo por meio de estudo caso-controle populacional que envolve nascidos vivos hospitalares de mães residentes em Londrina, Paraná, Brasil. Os casos foram os 328 nascimentos pré-termo e os controles, uma amostra proporcional de 369 nascimentos com 37 semanas ou mais. Realizou-se análise de regressão logística múltipla hierarquizada. Verificou-se associação (p < 0,05) para as variáveis: sócio-econômicas - moradia em favela e baixa idade do chefe familiar; características maternas: IMC < 19 e > 30kg/m², com filho anterior pré-termo, com tratamento para engravidar; características maternas durante a gestação: com companheiro há no máximo dois anos, preocupações, bebida alcoólica semanal, pré-natal inadequado, prática de caminhada como proteção; agravos na gestação - sangramento, infecção do trato genital, volume alterado do líquido amniótico, hipertensão arterial e internação; gestação múltipla. A identificação de fatores de risco e a melhoria da qualidade da atenção pré-concepcional e pré-natal podem reduzir a prematuridade.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.