Stochastic Spread Research Articles

Stochastic epidemics and rumours on finite random networks

In this paper, we investigate the stochastic spread of epidemics and rumours on networks. We focus on the general stochastic (SIR) epidemic model and a recently proposed rumour model on networks in Nekovee et al. (2007) [3], and on networks with different random structures, taking into account the structure of the underlying network at the level of the degree–degree correlation function. Using embedded Markov chain techniques and ignoring density correlations between neighbouring nodes, we derive a set of equations for the final size of the epidemic/rumour on a homogeneous network that can be solved numerically, and compare the resulting distribution with the solution of the corresponding mean-field deterministic model. The final size distribution is found to switch from unimodal to bimodal form (indicating the possibility of substantial spread of the epidemic/rumour) at a threshold value that is higher than that for the deterministic model. However, the difference between the two thresholds decreases with the network size, n , following a n − 1 / 3 behaviour. We then compare results (obtained by Monte Carlo simulation) for the full stochastic model on a homogeneous network, including density correlations at neighbouring nodes, with those for the approximating stochastic model and show that the latter reproduces the exact simulation results with great accuracy. Finally, further Monte Carlo simulations of the full stochastic model are used to explore the effects on the final size distribution of network size and structure (using homogeneous networks, simple random graphs and the Barabasi–Albert scale-free networks).

Patterns and causes of species richness: a general simulation model for macroecology

Understanding the causes of spatial variation in species richness is a major research focus of biogeography and macroecology. Gridded environmental data and species richness maps have been used in increasingly sophisticated curve-fitting analyses, but these methods have not brought us much closer to a mechanistic understanding of the patterns. During the past two decades, macroecologists have successfully addressed technical problems posed by spatial autocorrelation, intercorrelation of predictor variables and non-linearity. However, curve-fitting approaches are problematic because most theoretical models in macroecology do not make quantitative predictions, and they do not incorporate interactions among multiple forces. As an alternative, we propose a mechanistic modelling approach. We describe computer simulation models of the stochastic origin, spread, and extinction of species' geographical ranges in an environmentally heterogeneous, gridded domain and describe progress to date regarding their implementation. The output from such a general simulation model (GSM) would, at a minimum, consist of the simulated distribution of species ranges on a map, yielding the predicted number of species in each grid cell of the domain. In contrast to curve-fitting analysis, simulation modelling explicitly incorporates the processes believed to be affecting the geographical ranges of species and generates a number of quantitative predictions that can be compared to empirical patterns. We describe three of the 'control knobs' for a GSM that specify simple rules for dispersal, evolutionary origins and environmental gradients. Binary combinations of different knob settings correspond to eight distinct simulation models, five of which are already represented in the literature of macroecology. The output from such a GSM will include the predicted species richness per grid cell, the range size frequency distribution, the simulated phylogeny and simulated geographical ranges of the component species, all of which can be compared to empirical patterns. Challenges to the development of the GSM include the measurement of goodness of fit (GOF) between observed data and model predictions, as well as the estimation, optimization and interpretation of the model parameters. The simulation approach offers new insights into the origin and maintenance of species richness patterns, and may provide a common framework for investigating the effects of contemporary climate, evolutionary history and geometric constraints on global biodiversity gradients. With further development, the GSM has the potential to provide a conceptual bridge between macroecology and historical biogeography.

Global Efficiency Assessment based on Component Composition of OEE Using AltaRica Data-Flow Language

We present in this article a method to assess a system efficiency based on modelling of the temporal and stochastic spread of faults. The OEE (Overall Equipment Effectiveness) has become through the NF E60-182 standard one of the major indicators of the effectiveness in piloting production systems. It includes 3 main concepts (Quality, Performance and Availability). If its evaluation can be easy for a single system, the modelling of its components for the global efficiency assessment is much more difficult (taking into account redundancies, temporal scale factors ...). In order to take in account the local contribution of each component of a complex system, a notion of OTE (Overall Throughput Effectiveness) is developed. The purpose of OTE is twofold: it measures factorylevel performance and factory-level diagnostics such as bottleneck detection. The expected result gives a formal contribution to the establishment a methodology for analysis, design, and decisionmaking. The results are discussed using a demonstrator based on AltaRica Data-Flow, language in both formal and graphic and real tool modelling / simulation

Modeling of the elongation and retraction of Escherichia coli P pili under strain by Monte Carlo simulations

P pili are fimbrial adhesion organelles expressed by uropathogenic Escherichia coli in the upper urinary tract. They constitute a stiff helix-like polymer consisting of a number of subunits joined by head-to-tail bonds. The elongation and retraction properties of individual P pili exposed to strain have been modeled by Monte Carlo (MC) simulations. The simulation model is based upon a three-state energy landscape that deforms under an applied force. Bond opening and closure are modeled by Bells theory while the elongation of the linearized part of the pilus is described by a worm-like chain model. The simulations are compared with measurements made by force measuring optical tweezers. It was found that the simulations can reproduce pili elongation as well as retraction, under both equilibrium and dynamic conditions, including entropic effects. It is shown that the simulations allow for an assessment of various model parameters, e.g. the unfolding force, energy barrier heights, and various distances in the energy landscape, including their stochastic spread that analytical models are unable to do. The results demonstrate that MC simulations are useful to model elongation and retraction properties of P pili, and therefore presumably also other types of pili, exposed to strain and/or stress. MC simulations are particularly suited for description of helix-like pili since these have an intricate self-regulating mechanical elongation behavior that makes analytical descriptions non-trivial when dynamic processes are studied, or if additional interactions in the rod or the behavior of the adhesion tip needs to be modeled.

Evolution of the energy distribution of ions moving in aluminum targets

The dynamics of ions moving in thin foils and underdense foams will play a key role in the design of future warm dense matter experiments. Using the SRIM code, we estimate that for initially mono-energetic 2.8 MeV Li + ions hitting a solid density Al foil, the induced energy spread due to stochastic effects is 10% at a depth of 3.4 μ m . In contrast, for 400 keV K + ions hitting an Al foam of 10% solid density, stochastic effects induce a nearly 100% energy spread. At these beam energies, the nuclear stopping effects are negligible for the Li beam, but not for the K beam. We estimate this stochastic energy spread leads to almost no change in uniformity of temperature for the target heated by the Li beam, but leads to a factor of two of non-uniformity in temperature of the target for the K beam over a depth of 3.4 μ m . One application of these new results for temperature profiles with realistic beam energy distributions is as input to hydrodynamic simulations of the evolution of the target.

Measuring the Ensemble Spread–Error Relationship with a Probabilistic Approach: Stochastic Ensemble Results

Abstract One widely accepted measure of the utility of ensemble prediction systems is the relationship between ensemble spread and deterministic forecast accuracy. Unfortunately, this relationship is often characterized by spread–error linear correlations, which oversimplify the true spread–error relationship and ignore the possibility that some end users have categorical sensitivities to forecast error. In the present paper, a simulation study is undertaken to estimate the idealized spread–error statistics for stochastic ensemble prediction systems of a finite size. Under a variety of spread–error metrics, the stochastic ensemble spread–error joint distributions are characterized by increasing scatter as the ensemble spread grows larger. A new method is introduced that recognizes the inherent nonlinearity of spread–error joint distributions and capitalizes on the fact that the probability of large forecast errors increases with ensemble spread. The ensemble spread–error relationship is measured by the skill of probability forecasts that are constructed from a history of ensemble-mean forecast errors using only cases with similar ensemble spread. Thus, the value of ensemble spread information is quantified by the ultimate benefit that is realized by end users of the probability forecasts based on these conditional-error climatologies. It is found that the skill of conditional-error-climatology forecasts based on stochastic ensemble spread is nearly equal to the skill of probability forecasts constructed directly from the raw ensemble statistics. The skill is largest for cases with anomalous spread and smallest for cases with near-normal spread. These results reinforce the findings of earlier studies and affirm that the temporal variability of ensemble spread controls its potential value as a predictor. Additionally, it is found that the skill of spread-based error probability forecasts is maximized when the chosen spread metric is consistent with the end user’s cost function.

Restoration algorithms for turbulence-degraded images based on optimized estimation of discrete values of overall point spread functions

For the problem of restoration of turbulence-degraded images, it is of utmost importance to make a correct estimation of the turbulence' s stochastic point spread function (PSF). A new method is presented for estimating the discrete values of overall PSFs of turbulence-degraded images. For this method, two short-exposure turbulence-degraded images are used as the inputs, for which the Fourier transforms are made and a series of equations for calculating the discrete values of the turbulence PSFs are developed. Some effective rules for selecting equations have been worked out to ensure a reliable solution for the PSFs. To overcome the interference of noise, two optimization algorithms for estimating the turbulence PSF values, based on quadratic and nonquadratic regularization that can be incorporated into the estimation process, are proposed, in which the constraints of the PSF values are non-negative and smooth [quadratic regularization non-negative and smooth (QRNNS) and nonquadratic regularization non-negative and smooth (NQRNNS)]. A series of experiments are performed to test the algorithms proposed, which show that the NQRNNS algorithm is both rational and highly effective.

Low-jitter clock multiplication: a comparison between PLLs and DLLs

This paper shows that, for a given power budget, a practical phase-locked loop (PLL)-based clock multiplier generates less jitter than a delay-locked loop (DLL) equivalent. This is due to the fact that the delay cells in a PLL ring-oscillator can consume more power per cell than their counterparts in the DLL. We can show that this effect is stronger than the notorious jitter accumulation effect that occurs in the voltage-controlled oscillator (VCO) of a PLL. First, an analysis of the stochastic-output jitter of the architectures, due to the most important noise sources, is presented. Then, another important source of jitter in a DLL-based clock multiplier is treated, namely the stochastic mismatch in the delay cells which compose the DLL voltage-controlled delay line (VCDL). An analysis is presented that relates the stochastic spread of the delay of the cells to the output jitter of the clock multiplier. A circuit design technique, called impedance level scaling, is then presented which allows the designer to optimize the noise and mismatch behavior of a circuit, independently from other specifications such as speed and linearity. Applying this technique on a delay cell design yields a direct tradeoff between noise induced jitter and power usage, and between stochastic mismatch induced jitter and power usage.

Spatial autocorrelation and linkage of Mendelian RAPD markers in a population of Picea abies Karst.

The spatial clustering of single- and di-locus genotypes in a natural, continuous population of Norway spruce was investigated using 69 Mendelian Random Amplified Polymorphic DNA (RAPD) markers that covered about 15 of the species genome, and whose linkage relationships were known. Spatial autocorrelation techniques and randomization tests, applied to both single- and di-locus genotypes, revealed a weak, though significant, spatial structure at the scale 0-200 m (5 of single-locus and 7 of di-locus genotypes). To assess the relative importance of isolation by distance and linkage between markers on their spatial genetic structuring, we grouped joins between sampled trees into equivalence categories expected to show similar, specific patterns of spatial distribution under isolation by distance. Results from both single- and di-locus analyses were consistent with the existence of patches of like homozygotes (about 8 and 11 of loci at the single- and di-locus level, respectively) surrounded by a mix of like heterozygotes. Similar structuring has been predicted by simulation models under isolation by distance and selective neutrality. Overall, linkage between markers accounted for an increase of spatial clumping of di-locus genotypes involving tightly linked loci with recombination fractions up to 0.1, a consequence of limited, stochastic spread of single-locus genotypes in space. Our results support the hypothesis that isolation by distance and linkage have a small, though significant, effect even within continuous forest tree populations. In general, the spatial distribution of multilocus genotypes within populations should be interpreted with caution when linkage relationships among the markers used are unknown.

Microscopic recoil model for light-cone fluctuations in quantum gravity

We present a microscopic model for light-cone fluctuations in vacuo, which incorporates a treatment of quantum-gravitational recoil effects induced by energetic particles. Treating defects in space-time as solitons in string theory, we derive an energy-dependent refractive index and a stochastic spread in the arrival times of mono-energetic photons due to quantum diffusion through space-time foam, as found previously using an effective Born-Infeld action. Distant astrophysical sources provide sensitive tests of these possible quantum-gravitational phenomena.

Spatial structure of two-locus genotypes under isolation by distance.

Extensive Monte Carlo simulations are conducted of spatial distributions of two-locus genotypes in large, continuous populations under isolation by distance models. The results show that substantial patches of double homozygotes are present in the spatial structures, even when loci are unlinked. The stochastic spread of identical two-locus genotypes largely outpowers the tendency for recombination to decouple patterns for separate loci. A spatial patch is a large area containing mostly one double homozygous genotype in a highly contiguous constellation. This patch structure is reflected in high positive spatial autocorrelations and large excesses of pairs, or joins, of identical double homozygotes at short-to-intermediate distances of spatial separation. Although spatial patches of double homozygotes are the dominant spatial feature, and the major contributors to overall high levels of autocorrelations among two-locus genotypes, other substantial features include areas of concentrations of identical genotypes heterozygous at only one locus. One implication of the patch structure is the presence of high levels of linkage disequilibrium, caused by isolation by distance even for unlinked loci, at some spatial scales; yet the disequilibrium in the large total populations is near 0. Thus linkage disequilibrium produced by isolation by distance is highly dependent on spatial scale. Another implication is that high degrees of spatial structuring and autocorrelations are produced for genetic variation controlling quantitative traits, at least when the number of loci is relatively small, under a wide range of situations, even if the trait is selectively neutral. The significance of the results to field studies is also examined.

Restoration of stochastically blurred images by the geometrical mean filter

The restoration of images degraded by a stochastic point spread function and additive detection noise is examined. Previously, the optimization criterion of the Wiener technique was applied successfully to this problem. However, when the strengths ofthe noise sources are not small, the restoration results of this method become noisy, albeit the deblurring results are of good quality. First, to obtain smoother restoration, the constrained least squares deconvolution method was developed. The objective function chosen was the one which yields smooth restoration. The restoration results of this filter were very smooth, as expected, but the deblurring was not as effective as that of the Wiener technique. Then, a geometrical mean filter that combines both the Wiener and the constrained least squares criteria was developed. This resulted in restored pictures that were both smooth and deblurred. The two filters developed are computationally inexpensive since they both can be implemented in the Fourier domain using the circulant matrix approximation.