Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

FILTERING TECHNIQUES APPLIED ON RAW CARRIER PHASE FOR GPS DETECTING SMALL DYNAMIC DISPLACEMENTS

This work is part of a research under construction since 2000, in which the main objective is to measure small dynamic displacements by using L1 GPS receivers. A very sensible way to detect millimetric periodic displacements is based on the Phase Residual Method (PRM). This method is based on the frequency domain analysis of the phase residuals resulted from the L1 double difference static data processing of two satellites in almost orthogonal elevation angle. In this article, it is proposed to obtain the phase residuals directly from the raw phase observable collected in a short baseline during a limited time span, in lieu of obtaining the residual data file from regular GPS processing programs which not always allow the choice of the aimed satellites. In order to improve the ability to detect millimetric oscillations, two filtering techniques are introduced. One is auto-correlation which reduces the phase noise with random time behavior. The other is the running mean to separate low frequency from the high frequency phase sources. Two trials have been carried out to verify the proposed method and filtering techniques. One simulates a 2.5 millimeter vertical antenna displacement and the second uses the GPS data collected during a bridge load test. The results have shown a good consistency to detect millimetric oscillations.

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.

Spin filtering and disorder-induced magnetoresistance in carbon nanotubes: Ab initio calculations

Nitrogen-doped carbon nanotubes can provide reactive sites on the porphyrin-like defects. It is well known that many porphyrins have transition-metal atoms, and we have explored transition-metal atoms bonded to those porphyrin-like defects inN-doped carbon nanotubes. The electronic structure and transport are analyzed by means of a combination of density functional theory and recursive Green's function methods. The results determined the heme B-like defect (an iron atom bonded to four nitrogens) is the most stable and has a higher polarization current for a single defect. With randomly positioned heme B defects in nanotubes a few hundred nanometers long, the polarization reaches near 100%, meaning they are effective spin filters. A disorder-induced magnetoresistance effect is also observed in those long nanotubes, and values as high as 20 000% are calculated with nonmagnectic eletrodes.

Shared information in stationary states of stochastic processes

We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

LIMIT THEOREMS FOR A GENERAL STOCHASTIC RUMOUR MODEL

We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.

H(infinity) filtering for rectangular discrete-time descriptor systems

This paper deals with the H(infinity) recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified gamma-level if the resulting cost is positive. In order to present some computational alternatives to the H(infinity) filters developed, they are rewritten in information form along with the respective array algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

Noise reduction in biomedical speech signal processing based on time and frequency Kalman filtering combined with spectral subtraction

The goal of this paper is to study and propose a new technique for noise reduction used during the reconstruction of speech signals, particularly for biomedical applications. The proposed method is based on Kalman filtering in the time domain combined with spectral subtraction. Comparison with discrete Kalman filter in the frequency domain shows better performance of the proposed technique. The performance is evaluated by using the segmental signal-to-noise ratio and the Itakura-Saito`s distance. Results have shown that Kalman`s filter in time combined with spectral subtraction is more robust and efficient, improving the Itakura-Saito`s distance by up to four times. (C) 2007 Elsevier Ltd. All rights reserved.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.