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Diffusion Approximation (diffusion + approximation)
Selected AbstractsBayesian Inference for Stochastic Kinetic Models Using a Diffusion ApproximationBIOMETRICS, Issue 3 2005A. Golightly Summary This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m, 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network. [source] Using Population Count Data to Assess the Effects of Changing River Flow on an Endangered Riparian PlantCONSERVATION BIOLOGY, Issue 4 2006DIANE M. THOMSON análisis de viabilidad poblacional; gestión ribereña; método de difusión; presas; riesgo de extinción Abstract:,Methods for using simple population count data to project extinction risk have been the focus of much recent theoretical work, but few researchers have used these approaches to address management questions. We analyzed 15 years of census data on the federally endangered endemic riparian plant Pityopsis ruthii (Small) with the diffusion approximation (DA). Our goals were to evaluate relative extinction risk among populations in two different watersheds (in Tennessee, U.S.A.) and potential effects of variation in managed river flow on population dynamics. Populations in both watersheds had high projected risks of extinction within 50 years, but the causes of this risk differed. Populations of P. ruthii on the Hiwassee River had higher initial population sizes but significantly lower average growth rates than those on the Ocoee River. The only populations with low predicted short-term extinction risk were on the Ocoee. Growth rates for populations on both rivers were significantly reduced during periods of lower river flow. We found only marginal evidence of a quadratic relationship between population performance and flow. These patterns are consistent with the idea that low flows affect P. ruthii due to growth of competing vegetation, but the degree to which very high flows may reduce population growth is still unclear. Simulations indicated that populations were most sensitive to growth rates in low-flow years, but small changes in the frequency of these periods did not strongly increase risk for most populations. Consistent with results of other studies, DA estimates of extinction risk had wide confidence limits. Still, our results yielded several valuable insights, including the need for greater monitoring of populations on the Hiwassee and the importance of low-flow years to population growth. Our work illustrates the potential value of simple methods for analyzing count data despite the challenges posed by uncertainty in estimates of extinction risk. Resumen:,Los métodos que utilizan datos de conteos simples de la población para proyectar el riesgo de extinción han sido el foco reciente de mucho trabajo teórico, pero pocos investigadores han utilizado estos métodos para responder preguntas de gestión. Analizamos 15 años de datos de censos de la planta ribereña, endémica y federalmente en peligro Pityopsis ruthii (Small) mediante el método de difusión. Nuestras metas fueron evaluar el riesgo de extinción de poblaciones en dos cuencas hidrológicas distintas y con dos efectos potenciales de la variación del flujo de agua sobre la dinámica de la población. Las poblaciones en ambas cuencas tenían alto riesgo de extinción proyectado a 50 años, pero las causas de este riesgo difirieron. Las poblaciones de P. ruthii en el Río Hiwassee tuvieron poblaciones iniciales más grandes, pero tasas de crecimiento significativamente menores, que las poblaciones en el Río Ocoee. Las únicas poblaciones con bajo riesgo de extinción pronosticado estaban en el Ocoee. Las tasas de crecimiento de las poblaciones en ambos ríos se redujeron significativamente durante períodos de bajo flujo en el río. Sólo encontramos evidencia marginal de la relación cuadrática entre el funcionamiento de la población y el flujo. Estos patrones son consistentes con la idea de que los bajos flujos afectan a P. ruthii debido al crecimiento de vegetación competitiva, pero aun no es claro el grado en que flujos muy grandes pueden reducir el crecimiento poblacional. Las simulaciones indicaron que las poblaciones son más sensibles a las tasas de crecimiento en años con bajo flujo en los ríos, pero pequeños cambios en la frecuencia de esos períodos no aumentaron el riesgo en la mayoría de las poblaciones. Consistentemente con los resultados de otros estudios, las estimaciones del riesgo de extinción mediante el método de difusión tienen amplios límites de confianza. Aun así, nuestros resultados aportaron varios conocimientos valiosos, incluyendo la necesidad de mayor monitoreo de las poblaciones en el Hiwassee y la importancia para el crecimiento poblacional de los años con bajo flujo. Nuestro trabajo ilustra el valor potencial de métodos sencillos de análisis de datos de conteo a pesar de los retos impuestos por la incertidumbre en las estimaciones del riesgo de extinción. [source] An EM-like reconstruction method for diffuse optical tomographyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2010*Article first published online: 28 JUN 2010, Caifang Wang Abstract Diffuse optical tomography (DOT) is an optical imaging modality which provides the spatial distributions of optical parameters inside an object. The forward model of DOT is described by the diffusion approximation of radiative transfer equation, while the DOT is to reconstruct the optical parameters from boundary measurements. In this paper, an EM-like iterative reconstruction method specifically for the steady state DOT problem is developed. Previous iterative reconstruction methods are mostly based on the assumption that the measurement noise is Gaussian, and are of least-squares type. In this paper, with the assumption that the boundary measurements have independent and identical Poisson distributions, the inverse problem of DOT is solved by maximizing a log-likelihood functional with inequality constraints, and then an EM-like reconstruction algorithm is developed according to the Kuhn,Tucker condition. The proposed algorithm is a variant of the well-known EM algorithm. The performance of the proposed algorithm is tested with three-dimensional numerical simulation. Copyright © 2010 John Wiley & Sons, Ltd. [source] Modelling of air drying of Hac,haliloglu-type apricotsJOURNAL OF THE SCIENCE OF FOOD AND AGRICULTURE, Issue 2 2006Hakan Okyay Menges Abstract In this study a laboratory dryer was used for the thin layer drying of sulfured and non-sulfured apricots. The moisture ratio values throughout the drying process were calculated by 14 different mathematical models, namely Newton, Page, modified Page, modified Page-II, Henderson and Pabis, logarithmic, two-term, two-term exponential, Wang and Singh, Thompson, diffusion approximation, modified Henderson and Papis, Verma et al. and Midilli et al. models. Root mean square error, reduced chi-square, mean bias error, adjusted R -square and modelling efficiency were used as statistical parameters to determine the most suitable model among them. According to the results, the Page model was chosen to explain the thin layer drying behaviour of sulfured and non-sulfured apricots. The effects of drying air temperature (T) and velocity (V) on the constants and coefficients of the best moisture ratio model were determined by multiple regression analysis. The moisture ratio (MR) could be predicted by the Page model equation MR = exp(,ktn) with constants and coefficients k = 0.470893 + 0.078775V and n = 0.017786 exp(0.051935T) for sulfured apricots and k = 4.578252 + 1.144643T and n = 0.888040 + 0.145559V for non-sulfured apricots. It is possible to predict the moisture content of the product with the generalised Page model incorporating the effects of drying air temperature and velocity on the model constants and coefficients in the ranges T = 70,80 °C and V = 1,3 m s,1. This developed model showed acceptable agreement with the experimental results, explained the drying behaviour of the product and could also be used for engineering applications. Copyright © 2005 Society of Chemical Industry [source] Mathematical modeling of 980-nm and 1320-nm endovenous laser treatmentLASERS IN SURGERY AND MEDICINE, Issue 3 2007Serge R. Mordon PhD Abstract Background and Objectives Endovenous laser treatment (ELT) has been proposed as an alternative in the treatment of reflux of the great saphenous vein (GSV) and small saphenous vein (SSV). Numerous studies have since demonstrated that this technique is both safe and efficacious. ELT was presented initially using diode lasers of 810 nm, 940 nm, and 980 nm. Recently, a 1,320-nm Nd:YAG laser was introduced for ELT. This study aims to provide mathematical modeling of ELT in order to compare 980 nm and 1,320 nm laser-induced damage of saphenous veins. Study Design/Materials and Methods The model is based on calculations describing light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation, and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma, Inc., Arlington, MA). Calculations were performed so as to determine the damage induced in the intima tunica, the externa tunica and inside the peri-venous tissue for 3 mm and 5 mm vessels (considered after tumescent anesthesia) and different linear endovenous energy densities (LEED) usually reported in the literature. Results Calculations were performed for two different vein diameters: 3 mm and 5 mm and with LEED typically reported in the literature. For 980 nm, LEED: 50 to 160 J/cm (CW mode, 2 mm/second pullback speed, power: 10 W to 32 W) and for 1,320 nm, LEED: 50 to 80 J/cm (pulsed mode, pulse duration 1.2 milliseconds, peak power: 135 W, repetition rate 30 Hz to 50 Hz). Discussion and Conclusion Numerical simulations are in agreement with LEED reported in clinical studies. Mathematical modeling shows clearly that 1,320 nm, with a better absorption by the vessel wall, requires less energy to achieve wall damage. In the 810,1,320-nm range, blood plays only a minor role. Consequently, the classification of these lasers into hemoglobin-specific laser wavelengths (810, 940, 980 nm) and water-specific laser wavelengths (1,320 nm) is inappropriate. In terms of closure rate, 980 nm and 1,320 nm can lead to similar results and, as reported by the literature, to similar side effects. This model should serve as a useful tool to simulate and better understand the mechanism of action of the ELT. Lasers Surg. Med. 39:256,265, 2007. © 2007 Wiley-Liss, Inc. [source] The role of thermodynamics in disc fragmentationMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2009Dimitris Stamatellos ABSTRACT Thermodynamics play an important role in determining the way a protostellar disc fragments to form planets, brown dwarfs and low-mass stars. We explore the effect that different treatments of radiative transfer have in simulations of fragmenting discs. Three prescriptions for the radiative transfer are used: (i) the diffusion approximation of Stamatellos et al.; (ii) the barotropic equation of state (EOS) of Goodwin et al. and (iii) the barotropic EOS of Bate et al. The barotropic approximations capture the general evolution of the density and temperature at the centre of each proto-fragment but (i) they do not make any adjustments for particular circumstances of a proto-fragment forming in the disc and (ii) they do not take into account thermal inertia effects that are important for fast-forming proto-fragments in the outer disc region. As a result, the number of fragments formed in the disc and their properties are different, when a barotropic EOS is used. This is important not only for disc studies but also for simulations of collapsing turbulent clouds, as in many cases in such simulations stars form with discs that subsequently fragment. We also examine the difference in the way proto-fragments condense out in the disc at different distances from the central star using the diffusion approximation and following the collapse of each proto-fragment until the formation of the second core (,, 10,3 g cm,3). We find that proto-fragments forming closer to the central star tend to form earlier and evolve faster from the first to the second core than proto-fragments forming in the outer disc region. The former have a large pool of material in the inner disc region that they can accrete from and grow in mass. The latter accrete more slowly and they are hotter because they generally form in a quick abrupt event. [source] A new risk model based on policy entrance process and its weak convergence propertiesAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2007Zehui Li Abstract In this paper, we construct a new risk model based on the policy entrance process. The model is concerned with n kinds of independent policies, and each policy is allowed to claim more than once before it expires. As each kind of policy is issued according to a non-homogeneous Poisson process, the long run behaviour of the new risk process is investigated. When the tail of the claim size distribution is regularly varying, the standardized risk process is proved to converge to a stable law. When each kind of policy is issued according to a homogeneous Poisson process, we also give a diffusion approximation of the new risk process. Copyright © 2007 John Wiley & Sons, Ltd. [source] Ancestral Inference in Population Genetics Models with Selection (with Discussion)AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2003Matthew Stephens Summary A new algorithm is presented for exact simulation from the conditional distribution of the genealogical history of a sample, given the composition of the sample, for population genetics models with general diploid selection. The method applies to the usual diffusion approximation of evolution at a single locus, in a randomly mating population of constant size, for mutation models in which the distribution of the type of a mutant does not depend on the type of the progenitor allele; this includes any model with only two alleles. The new method is applied to ancestral inference for the two-allele case, both with genic selection and heterozygote advantage and disadvantage, where one of the alleles is assumed to have resulted from a unique mutation event. The paper describes how the method could be used for inference when data are also available at neutral markers linked to the locus under selection. It also informally describes and constructs the non-neutral Fleming,Viot measure-valued diffusion. [source] Bayesian Inference for Stochastic Kinetic Models Using a Diffusion ApproximationBIOMETRICS, Issue 3 2005A. Golightly Summary This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m, 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network. [source] EFFECTS OF GENETIC DRIFT ON VARIANCE COMPONENTS UNDER A GENERAL MODEL OF EPISTASISEVOLUTION, Issue 10 2004N.H. Barton Abstract We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(,z,) =where n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(,z,); (V*A) (1 ,F)Thus, epistasis inflates the expected additive variance above VA(1 ,F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 ,F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(,z,)==1 (2F) kVA(k) and (V*A) = (1 ,F)k(2F)k-1VA(k) With dominance (and even without epistasis), var(,z,)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 ,F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases. [source] | |||||||||||||