Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

Dynamic behavior, stochasticity and enviromental heterogeneity in Tribolium castaneum

In this study we analyzed the influence of demographic parameters on the population dynamics of Tribolium castaneum, combining empiricism and population theory to analyze the different effects of environmental heterogeneity, by employing Ricker models, designed to study a two-patch system taking into account deterministic and stochastic analysis. Results were expressed by bifurcation diagrams and stochastic simulations. Dynamic equilibrium was widely investigated with results suggesting specific parametric spaces in response to environmental heterogeneity and migration. Population equilibrium patterns, synchrony and persistence in T. castaneum were discussed

Stochastic dynamics in exotic and native blowflies: an analysis combining laboratory experiments and a two-patch metapopulation model

In this study we explored the stochastic population dynamics of three exotic blowfly species, Chrysomya albiceps, Chrysomya megacephala and Chrysomya putoria, and two native species, Cochliomyia macellaria and Lucilia eximia, by combining a density-dependent growth model with a two-patch metapopulation model. Stochastic fecundity, survival and migration were investigated by permitting random variations between predetermined demographic boundary values based on experimental data. Lucilia eximia and Chrysomya albiceps were the species most susceptible to the risk of local extinction. Cochliomyia macellaria, C. megacephala and C. putoria exhibited lower risks of extinction when compared to the other species. The simultaneous analysis of stochastic fecundity and survival revealed an increase in the extinction risk for all species. When stochastic fecundity, survival and migration were simulated together, the coupled populations were synchronized in the five species. These results are discussed, emphasizing biological invasion and interspecific interaction dynamics.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Simulation and economic analysis of bovine sex selection

A simulation model implemented in the programming software Delphi XE® was applied to evaluate sex selection in bovine. The hypothesis under investigation was that a dynamic model with stochastic and deterministic elements could detect the sexed semen technique to minimize pregnancy cost and to determine the adequate number of recipients required for in vivo (ET) and in vitro embryo production (IVP) in the proposed scenarios. Sex selection was compared through semen sexed using flow cytometry (C1) and density gradient centrifugation techniques (C2) in ET and IVP. Sensibility analyses were used to identify the adequate number of recipients for each scenario. This number was reinserted into the model to determine the biological and financial values that maximized ET and IVP using sexed semen (C1M and C2M). New scenarios showed that the density gradient technique minimized pregnancy cost based on the proposed scenarios. In addition, the adequate number of recipients (ET - C1M - 115 and C2M - 105)/(IVP - C1M - 145 and C2M - 140) per donor used was determined to minimize the pregnancy cost in all scenarios.

Analysis of the topography of a Bragg grating in chalcogenide glass

Relief Bragg gratings were recorded on the surface of Ga-Ge-S glass samples by interference of two UV laser beams at 351 nm, Scanning force microscopy was used to perform a 3D image analysis of the resulting surface topography, which shows the superposition of an imprinted grating over the base topography of the glass. An important question regarding the efficiency of the grating is to determine to what extent the base topography reduces the intended coherent scattering of the grating because of its stochastic character. To answer this question we separated both base and grating structures by Fourier filtering, examined both spatial frequency and roughness, and determined the correlation. (C) 2001 Elsevier B.V. B.V. All rights reserved.

GEOGRAPHIC-VARIATION IN APIS-CERANA-INDICA F - A SPATIAL AUTOCORRELATION ANALYSIS OF MORPHOMETRIC PATTERNS

Spatial patterns of morphometric variation in Apis cerana indica were analysed. Factor and spatial autocorrelation analyses were applied to 29 characters, measured in 17 populations in India. Correlograms showed that 15 characters are patterned geographically, and 13 of them are related to overall size. These characters are distributed as a north-south cline, probably reflecting adaptations to environmental conditions. However, the great number of characteristics without geographical pattern suggests that part of the morphometric variability is due to local stochastic divergences.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

A Multi-Stage Stochastic Non-Linear Model for Reactive Power Planning Under Contingencies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimal Reactive Power Planning Using Risk Analysis

In this paper, the optimal reactive power planning problem under risk is presented. The classical mixed-integer nonlinear model for reactive power planning is expanded into two stage stochastic model considering risk. This new model considers uncertainty on the demand load. The risk is quantified by a factor introduced into the objective function and is identified as the variance of the random variables. Finally numerical results illustrate the performance of the proposed model, that is applied to IEEE 30-bus test system to determine optimal amount and location for reactive power expansion.