Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

A stochastic frontier production function with flexible risk properties

This paper considers a stochastic frontier production function which has additive, heteroscedastic error structure. The model allows for negative or positive marginal production risks of inputs, as originally proposed by Just and Pope (1978). The technical efficiencies of individual firms in the sample are a function of the levels of the input variables in the stochastic frontier, in addition to the technical inefficiency effects. These are two features of the model which are not exhibited by the commonly used stochastic frontiers with multiplicative error structures, An empirical application is presented using cross-sectional data on Ethiopian peasant farmers. The null hypothesis of no technical inefficiencies of production among these farmers is accepted. Further, the flexible risk models do not fit the data on peasant farmers as well as the traditional stochastic frontier model with multiplicative error structure.

The frontal assessment battery (FAB) reveals neurocognitive dysfunction in substance-dependent individuals in distinct executive domains: Abstract reasoning, motor programming, and cognitive flexibility

Substance-dependence is highly associated with executive cognitive function (ECF) impairments. However. considering that it is difficult to assess ECF clinically, the aim of the present study was to examine the feasibility of a brief neuropsychological tool (the Frontal Assessment Battery FAB) to detect specific ECF impairments in a sample of substance-dependent individuals (SDI). Sixty-two subjects participated in this study. Thirty DSM-IV-diagnosed SDI, after 2 weeks of abstinence, and 32 healthy individuals (control group) were evaluated with FAD and other ECF-related tasks: digits forward (DF), digits backward (DB), Stroop Color Word Test (SCWT), and Wisconsin Card Sorting Test (WCST). SDI did not differ from the control group on sociodemographic variables or IQ. However, SDI performed below the controls in OF, DB, and FAB. The SDI were cognitively impaired in 3 of the 6 cognitive domains assessed by the FAB: abstract reasoning, motor programming, and cognitive flexibility. The FAB correlated with DF, SCWT, and WCST. In addition, some neuropsychological measures were correlated with the amount of alcohol, cannabis, and cocaine use. In conclusion, SDI performed more poorly than the comparison group on the FAB and the FAB`s results were associated with other ECF-related tasks. The results suggested a negative impact of alcohol, cannabis, and cocaine use on the ECF. The FAB may be useful in assisting professionals as an instrument to screen for ECF-related deficits in SDI. (C) 2010 Elsevier Ltd. All rights reserved.

Recognition by toll-like receptor 2 induces antigen-presenting cell activation and Th1 programming during infection by Neospora caninum

Neospora caninum is an apicomplexan parasite responsible for major economic losses due to abortions in cattle. Toll-like receptors (TLRs) sense specific microbial products and direct downstream signaling pathways in immune cells, linking innate, and adaptive immunity. Here, we analyze the role of TLR2 on innate and adaptive immune responses during N. caninum infection. Inflammatory peritoneal macrophages and bone marrow-derived dendritic cells exposed to N. caninum-soluble antigens presented an upregulated expression of TLR2. Increased receptor expression was correlated to TLR2/MyD88-dependent antigen-presenting cell maturation and pro-inflammatory cytokine production after stimulation by antigens. Impaired innate responses observed after infection of mice genetically deficient for TLR2((-/-)) was followed by downregulation of adaptive T helper 1 (Th1) immunity, represented by diminished parasite-specific CD4(+) and CD8(+) T-cell proliferation, IFN-gamma:interleukin (IL)-10 ratio, and IgG subclass synthesis. In parallel, TLR2(-/-) mice presented higher parasite burden than wild-type (WT) mice at acute and chronic stages of infection. These results show that initial recognition of N. caninum by TLR2 participates in the generation of effector immune responses against N. caninum and imply that the receptor may be a target for future prophylactic strategies against neosporosis. Immunology and Cell Biology (2010) 88, 825-833; doi:10.1038/icb.2010.52; published online 20 April 2010

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

The effect of resource aggregation at different scales: Optimal foraging behavior of Cotesia rubecula

Resources can be aggregated both within and between patches. In this article, we examine how aggregation at these different scales influences the behavior and performance of foragers. We developed an optimal foraging model of the foraging behavior of the parasitoid wasp Cotesia rubecula parasitizing the larvae of the cabbage butterfly Pieris rapae. The optimal behavior was found using stochastic dynamic programming. The most interesting and novel result is that the effect of resource aggregation within and between patches depends on the degree of aggregation both within and between patches as well as on the local host density in the occupied patch, but lifetime reproductive success depends only on aggregation within patches. Our findings have profound implications for the way in which we measure heterogeneity at different scales and model the response of organisms to spatial heterogeneity.

MapScript: A map algebra programming language incorporating neighborhood analysis

Map algebra is a data model and simple functional notation to study the distribution and patterns of spatial phenomena. It uses a uniform representation of space as discrete grids, which are organized into layers. This paper discusses extensions to map algebra to handle neighborhood operations with a new data type called a template. Templates provide general windowing operations on grids to enable spatial models for cellular automata, mathematical morphology, and local spatial statistics. A programming language for map algebra that incorporates templates and special processing constructs is described. The programming language is called MapScript. Example program scripts are presented to perform diverse and interesting neighborhood analysis for descriptive, model-based and processed-based analysis.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

Stochastic Schrodinger equation approach to quantum noise in resonant tunneling current

We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrodinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.