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 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.

Síndrome do X Frágil com variante de Dandy-Walker: estudo clínico das manifestações comunicativas orais e escritas

A síndrome do X Frágil é a causa mais frequente de deficiência intelectual hereditária. A variante de Dandy-Walker trata-se de uma constelação específica de achados neurorradiológicos. Este estudo relata achados da comunicação oral e escrita de um menino de 15 anos com diagnóstico clínico e molecular da síndrome do X-Frágil e achados de neuroimagem do encéfalo compatíveis com variante de Dandy-Walker. A avaliação fonoaudiológica foi realizada por meio da Observação do Comportamento Comunicativo, aplicação do ABFW - Teste de Linguagem Infantil - Fonologia, Perfil de Habilidades Fonológicas, Teste de Desempenho Escolar, Teste Illinois de Habilidades Psicolinguísticas, avaliação do sistema estomatognático e avaliação audiológica. Observou-se: alteração de linguagem oral quanto às habilidades fonológicas, semânticas, pragmáticas e morfossintáticas; déficits nas habilidades psicolinguísticas (recepção auditiva, expressão verbal, combinação de sons, memória sequencial auditiva e visual, closura auditiva, associação auditiva e visual); e alterações morfológicas e funcionais do sistema estomatognático. Na leitura verificou-se dificuldades na decodificação dos símbolos gráficos e na escrita havia omissões, aglutinações e representações múltiplas com o uso predominante de vogais e dificuldades na organização viso-espacial. Em matemática, apesar do reconhecimento numérico, não realizou operações aritméticas. Não foram observadas alterações na avaliação audiológica periférica. A constelação de sintomas comportamentais, cognitivos, linguísticos e perceptivos, previstos na síndrome do X-Frágil, somada às alterações estruturais do sistema nervoso central, pertencentes à variante de Dandy-Walker, trouxeram interferências marcantes no desenvolvimento das habilidades comunicativas, no aprendizado da leitura e escrita e na integração social do indivíduo.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

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.

Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

Deterministic mathematical model for the prediction of the as-cast macrostructure

A multiphase deterministic mathematical model was implemented to predict the formation of the grain macrostructure during unidirectional solidification. The model consists of macroscopic equations of energy, mass, and species conservation coupled with dendritic growth models. A grain nucleation model based on a Gaussian distribution of nucleation undercoolings was also adopted. At some solidification conditions, the cooling curves calculated with the model showed oscillations (""wiggles""), which prevented the correct prediction of the average grain size along the structure. Numerous simulations were carried out at nucleation conditions where the oscillations are absent, enabling an assessment of the effect of the heat transfer coefficient on the average grain size and columnar-to-equiaxed transition.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

TIME COURSE OF SKELETAL MUSCLE LOSS AND OXIDATIVE STRESS IN RATS WITH WALKER 256 SOLID TUMOR

Reactive oxygen species oxidize proteins and modulate the proteasomal system in muscle-wasting cancer cachexia. On day 5 (D5), day 10 (D10), and day 14 (D14) after tumor implantation, skeletal muscle was evaluated. Carbonylated proteins and thiobarbituric acid reactive substances were measured. Chemiluminescence was employed for lipid hydroperoxide estimation. Glutathione, superoxide dismutase, and total radical antioxidant capacity were evaluated. The proteasomal system was assessed by mRNA atrogin-1 expression. Increased muscle wasting, lipid hydroperoxide, and superoxide dismutase, and decreased glutathione levels and total radical antioxidant capacity, were found on D5 in accordance with increased mRNA atrogin-1 expression. All parameters were significantly modified in animals treated with alpha-tocopherol. The elevation in aldehylde levels and carbonylated proteins observed on D10 were reversed by cc-tocopherol treatment. Oxidative stress may trigger signal transduction of the proteasomal system and cause protein oxidation. These pathways may be associated with the mechanism of muscle wasting that occurs in cancer cachexia. Muscle Nerve 42: 950-958, 2010

Linkage to chromosome 2q36.1 in autosomal dominant Dandy-Walker malformation with occipital cephalocele and evidence for genetic heterogeneity

We previously reported a Vietnamese-American family with isolated autosomal dominant occipital cephalocele. Upon further neuroimaging studies, we have recharacterized this condition as autosomal dominant Dandy-Walker with occipital cephalocele (ADDWOC). A similar ADDWOC family from Brazil was also recently described. To determine the genetic etiology of ADDWOC, we performed genome-wide linkage analysis on members of the Vietnamese-American and Brazilian pedigrees. Linkage analysis of the Vietnamese-American family identified the ADDWOC causative locus on chromosome 2q36.1 with a multipoint parametric LOD score of 3.3, while haplotype analysis refined the locus to 1.1 Mb. Sequencing of the five known genes in this locus did not identify any protein-altering mutations. However, a terminal deletion of chromosome 2 in a patient with an isolated case of Dandy-Walker malformation also encompassed the 2q36.1 chromosomal region. The Brazilian pedigree did not show linkage to this 2q36.1 region. Taken together, these results demonstrate a locus for ADDWOC on 2q36.1 and also suggest locus heterogeneity for ADDWOC.

Effect of Fish Oil Supplementation for Two Generations on Changes of Lymphocyte Function Induced by Walker 256 Cancer Cachexia in Rats

Fish oil supplementation has been shown to improve the cachectic state of tumor-bearing animals and humans. Our previous study showed that fish oil supplementation (1 g per kg body weight per day) for 2 generations had anticancer and anticachetic effects in Walker 256 tumor-bearing rats as demonstrated by reduced tumor growth and body weight loss and increased food intake and survival. In this study, the effect of fish oil supplementation for 2 generations on membrane integrity, proliferation capacity, and CD4/CD8 ratio of lymphocytes isolated from mesenteric lymph nodes, spleen, and thymus of Walker 256 tumor-bearing animals was investigated. We also determined fish oil effect on plasma concentration and ex vivo production of cytokines [tumor necrosis factor-alpha (TNF-alpha), interferon-gamma (IFN-gamma), interleukin-4 (IL-4), IL-6, and IL-10]. Lymphocytes from thymus of tumor-bearing rats presented lower viability, but this change was abolished by fish oil supplementation. Tumor growth increased proliferation of lymphocytes from all lymphoid organs, and fish oil supplementation abolished this effect. Ex vivo production of TNF-alpha and IL-6 was reduced in supplemented animals, but IL-4 and IL-10 secretion was stimulated in both nontumor and tumor-bearing rats. IL-10 and IFN-gamma plasma levels was also decreased in supplemented animals. These results suggest that the anticachetic effects of fish oil supplementation for a long period of time (2 generations) in Walker 256 tumor-bearing rats may be associated to a decrease in lymphocyte function as demonstrated by reduced viability, proliferation capacity, and cytokine production.

Glucose metabolism by lymphocytes, macrophages, and tumor cells from Walker 256 tumor-bearing rats supplemented with fish oil for one generation

Here we investigated the effect of lifelong supplementation of the diet with coconut fat (CO, rich in saturated fatty acids) or fish oil (170, rich in n-3 polyunsaturated fatty acids) on tumor growth and lactate production from glucose in Walker 256 tumor cells, peritoneal macrophages, spleen, and gut-associated lymphocytes. Female Wistar rats were supplemented with CO or FO prior to mating and then throughout pregnancy and gestation and then the male offspring were supplemented from weaning until 90 days of age. Then they were inoculated subcutaneously with Walker 256 tumor cells. Tumor weight at 14 days in control rats (those fed standard chow) and CO supplemented was approximately 30 g. Supplementation of the diet with FO significantly reduced tumor growth by 76%. Lactate production (nmol h(-1) mg(-1) protein) from glucose by Walker 256 cells in the group fed regular chow (W) was 381.8 +/- 14.9. Supplementation with coconut fat (WCO) caused a significant reduction in lactate production by 1.6-fold and with fish oil (WFO) by 3.8-fold. Spleen lymphocytes obtained from W and WCO groups had markedly increased lactate production (553 +/- 70 and 635 +/- 150) when compared to non-tumor-bearing rats (similar to 260 +/- 30). FO supplementation reduced significantly the lactate production (297 +/- 50). Gut-associated lymphocytes obtained from W and WCO groups increased lactate production markedly (280 +/- 31 and 276 +/- 25) when compared to non-tumor-bearing rats (similar to 90 +/- 18). FO supplementation reduced significantly the lactate production (168 +/- 14). Lactate production by peritoneal macrophages was increased by tumor burden but there was no difference between the groups fed the various diets. Lifelong consumption of FO protects against tumor growth and modifies glucose metabolism in Walker tumor cells and lymphocytes but not in macrophages. Copyright (C) 2008 John Wiley & Sons, Ltd.