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Queuing theory allows simulating scenarios applied to requirements of events of stochastic origin to solve problems in the attention service of electrical networks. Regarding emergency reactions, companies may experience response time delays due to incorrect sizing of the number of crew members, among other parameters. So is the case for a company in the Chilean energy sector called Enel, which is currently experiencing response delay issues. A complete formulation is presented, which can be easily used for planning the crews required for attention to the response to electrical distribution system faults. The formulation is applied to an electrical distribution company located in Chile. [ABSTRACT FROM AUTHOR]

The economy, society, and environment of the world are undergoing profound changes. Achieving sustainable development has become the common aspiration of the international communities. In recent years, sustainability issues are gaining increasing prominence for cities to formulate long-term development strategies. The Yangtze River Delta (YRD) urban agglomeration, one of China's most developed and densely populated industrial areas, has encountered environmental problems. Assessment of city sustainability of the YRD is a prominent issue in the process of urban construction. The paper used multi-criteria decision making (MCDM) framework to evaluate the sustainability level of 26 cities in the YRD by selecting 24 indicators from the economic, social, and environmental dimensions. In the weighting process, the paper proposed a new subjective and objective integrated weighting method based on stochastic simulation techniques. Relative results including pairwise priority matrix (PPM), comprehensive priority index (CPI), and the most likely ranking were obtained to reflect the superiority degree between two cities by adequate comparisons. The assessment results indicate that all the cities showed an upward trend from 2015 to 2019. Shanghai had overwhelming advantages over the other cities. The CPIs of Suzhou, Nanjing, Wuxi, Changzhou in Jiangsu province, and Hangzhou, Ningbo, Zhoushan in Zhejiang province were above 50 in 2015 and increased to over 85 in 2019. Additionally, most cities had unbalanced development on the three dimensions. Each city should firstly pay more attention to their own weak points, and then achieve balanced development and long-term sustainability. [ABSTRACT FROM AUTHOR]

This work considers the method of uniformization for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformization can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformization from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformization approach forms a computationally attractive choice. Furthermore, as a new application of the uniformization method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformization. [ABSTRACT FROM AUTHOR]

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates.We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Abstract We have developed a new algorithm which merges discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle based fluid dynamics simulation framework of smoothed dissipative particle dynamics (SDPD). This hybrid algorithm enables discrete stochastic simulation of spatially resolved chemically reacting systems on a mesh-free dynamic domain with a Lagrangian frame of reference. SDPD combines two popular mesoscopic techniques: smoothed particle hydrodynamics and dissipative particle dynamics (DPD), linking the macroscopic and mesoscopic hydrodynamics effects of these two methods. We have implemented discrete stochastic simulation using the reaction–diffusion master equations (RDME) formalism, and deterministic reaction–diffusion equations based on the SDPD method. We validate the new method by comparing our results to four canonical models, and demonstrate the versatility of our method by simulating a flow containing a chemical gradient past a yeast cell in a microfluidics chamber. Highlights • A hybrid spatial SSA and SDPD method is proposed. • It allows the simulation of stochastic advection–reaction–diffusion problems in a Lagrangian description. • Successful validation of the new method in several benchmark problems. • Method is tested on a problem where commercial CAE software and typical deterministic methods cannot capture all dynamics. [ABSTRACT FROM AUTHOR]

Summary DelaySSAToolkit.jl is a Julia package for modelling reaction systems with non-Markovian dynamics, specifically those with time delays. These delays implicitly capture multiple intermediate reaction steps and hence serve as an effective model reduction technique for complex systems in biology, chemistry, ecology and genetics. The package implements a variety of exact formulations of the delay stochastic simulation algorithm. Availability and implementation The source code and documentation of DelaySSAToolkit.jl are available at https://github.com/palmtree2013/DelaySSAToolkit.jl. [ABSTRACT FROM AUTHOR]

The Laoguanhe River is a major tributary of the Danjiang River, which is the source water for the Danjiangkou Reservoir (i.e., the source reservoir for the middle route of the South-to-North Water Diversion Project in China). This study was intended to provide scientific decision support to help manage the water environment in the Laoguanhe River and maintain high water quality levels for the water diversion project. Risk assessment based on water quality simulation was undertaken in this research. The QUAL2Kw model was used to improve the simulations of the water quality in the Laoguanhe River under sparse data conditions. Latin hypercube sampling (LHS) was used to improve flow inputs for QUAL2Kw. The model was used to calculate water quality risks under several scenarios based on a Markov stochastic process to reflect uncertainties. The simulation results indicated that water quality of the downstream sections of the Laoguanhe River could meet the basic requirements for exporting water to the Danjiangkou Reservoir. [ABSTRACT FROM AUTHOR]

Traffic noise is one of the leading causes of reductions in animal abundances near roads. Acoustic masking of conspecific signals and adventitious cues is one mechanism that likely causes animals to abandon loud areas. However, masking effects can be difficult to document in situ and the effects of infrequent noise events may be impractical to study. Here, we present the Soundscapes model, a stochastic individual-based model that dynamically models the listening areas of animals searching for acoustic resources ("searchers"). The model also studies the masking effects of noise for human detections of the searchers. The model is set in a landscape adjacent to a road. Noise produced by vehicles traveling on that road is represented by calibrated spectra that vary with speed. Noise propagation is implemented using ISO-9613 procedures. We present demonstration simulations that quantify declines in searcher efficiency and human detection of searchers at relatively low traffic volumes, fewer than 50 vehicles per hour. Traffic noise is pervasive, and the Soundscapes model offers an extensible tool to study the effects of noise on bioacoustics monitoring, point-count surveys, the restorative value of natural soundscapes, and auditory performance in an ecological context. [ABSTRACT FROM AUTHOR]

We have developed a method for modeling spatial stochastic biochemical reactions in complex, threedimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. We demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formation during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical. [ABSTRACT FROM AUTHOR]

In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compute the mean and covariance function from realizations of available stochastic models, e.g., from realizations of governing stochastic partial differential equations solutions. Such a constructed Gaussian process generally is nonstationary and does not assume a specific form of the covariance function. Our approach avoids the optimization step in data-driven GPR methods to identify the hyperparameters. More importantly, we prove that the physical constraints in the form of a deterministic linear operator are guaranteed in the resulting prediction. We also provide an error estimate in preserving the physical constraints when errors are included in the stochastic model realizations. To reduce the computational cost of obtaining stochastic model realizations, we propose a multilevel Monte Carlo estimate of the mean and covariance functions. Further, we present an active learning algorithm that guides the selection of additional observation locations. The efficiency and accuracy of PhIK are demonstrated for reconstructing a partially known modified Branin function, studying a three-dimensional heat transfer problem, and learning a conservative tracer distribution from sparse concentration measurements. [ABSTRACT FROM AUTHOR]

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. [ABSTRACT FROM AUTHOR]

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies. [ABSTRACT FROM AUTHOR]

To adapt their products to the durability requirements, car manufacturers must possess a suitable methodology to quantify the large variety of road induced fatigue loads that vehicles’ components undergo during their life. The load data acquisition process is generally based on long and costly measurement campaigns. Here an alternative load characterization methodology is proposed. It is based on stochastic modelling and simulation rather than purely on a collection of load measurements. Stochastic models, in the form of random processes, are proposed for vehicle- independent influential factors, namely road roughness and vehicle's speed. Random realizations are generated and used as inputs for multi-body simulations, describing the dynamics of any given vehicle. An arbitrarily large set of fatigue loads can therefore be obtained inexpensively, for any given elementary life situation, and subsequently, for the total life of the vehicle, using customer usage information. A study of the influence of a change in market region is performed as an illustration of the stochastic simulation methodology. For this study, existing measurements carried out by Renault within the considered market regions, are used as a source of statistical information. [ABSTRACT FROM AUTHOR]

Gillespie’s direct method (DM) [D. Gillespie, J. Chem. Phys. 81, 2340 (1977)] for exact stochastic simulation of chemical reaction systems has been widely adopted. It is easy to implement but requires large computation for relatively large systems. Recently, two more efficient methods, next reaction method (NRM) [M. A. Gibson and J. Bruck, J. Phys. Chem. A 105, 1876 (2000)] and optimized DM (ODM) [Y. Cao et al., J. Chem. Phys. 121, 4059 (2004)], have been developed to improve simulation speed. It has been demonstrated that the ODM is the state-of-the-art most efficient method for exact stochastic simulation of most practical reaction systems. In this paper, we first develop an exact stochastic simulation algorithm named ODMK that is more efficient than the ODM. We then develop an approximate method named K-skip method to further accelerate simulation. Using two chemical reaction systems, we demonstrate that our ODMK and K-skip method can save 20%–30% and 70%–80% simulation time, respectively, comparing to the ODM. We also show that our ODMK and K-skip method provide almost the same simulation accuracy as the ODM. [ABSTRACT FROM AUTHOR]

Stochastic chemical kinetics more accurately describes the dynamics of “small” chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques. [ABSTRACT FROM AUTHOR]

In this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasi-steady-state type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result. [ABSTRACT FROM AUTHOR]

In recent years, computer simulations have become increasingly useful when trying to understand the complex dynamics of biochemical networks, particularly in stochastic systems. In such situations stochastic simulation is vital in gaining an understanding of the inherent stochasticity present, as these models are rarely analytically tractable. However, a stochastic approach can be computationally prohibitive for many models. A number of approximations have been proposed that aim to speed up stochastic simulations. However, the majority of these approaches are fundamentally serial in terms of central processing unit (CPU) usage. In this paper, we propose a novel simulation algorithm that utilises the potential of multi-core machines. This algorithm partitions the model into smaller sub-models. These sub-models are then simulated, in parallel, on separate CPUs. We demonstrate that this method is accurate and can speed-up the simulation by a factor proportional to the number of processors available. [ABSTRACT FROM AUTHOR]

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA-the state-dependent doubly weighted SSA (sdwSSA)-that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Typical multiscale biochemical models contain fast-scale and slow-scale reactions, where 'fast' reactions fire much more frequently than 'slow' ones. This feature often causes stiffness in discrete stochastic simulation methods such as Gillespie's algorithm and the Tau-Leaping method leading to inefficient simulation. This paper proposes a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. Numerical results on a stiff decaying dimerization model and a heat shock protein regulation model demonstrate the efficiency and accuracy of the proposed methods for multiscale biochemical systems. [ABSTRACT FROM AUTHOR]

Several real-world systems, such as gene expression networks in biological cells, contain coupled chemical reactions with a time delay between reaction initiation and completion. The non-Markovian kinetics of such reaction networks can be exactly simulated using the delay stochastic simulation algorithm (dSSA). The computational cost of dSSA scales with the total number of reactions in the network. We reduce this cost to scale at most with the smaller number of species by using the concept of partial reaction propensities. The resulting delay partial-propensity direct method (dPDM) is an exact dSSA formulation for well-stirred systems of coupled chemical reactions with delays. We detail dPDM and present a theoretical analysis of its computational cost. Furthermore, we demonstrate the implications of the theoretical cost analysis in two prototypical benchmark applications. The dPDM formulation is shown to be particularly efficient for strongly coupled reaction networks, where the number of reactions is much larger than the number of species. [ABSTRACT FROM AUTHOR]

The weighted stochastic simulation algorithm (wSSA) was developed by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness. [ABSTRACT FROM AUTHOR]

In robust biological systems, wide deviations from highly controlled normal behavior may be rare, yet they may result in catastrophic complications. While in silico analysis has gained an appreciation as a tool to offer insights into system-level properties of biological systems, analysis of such rare events provides a particularly challenging computational problem. This paper proposes an efficient stochastic simulation method to analyze rare events in biochemical systems. Our new approach can substantially increase the frequency of the rare events of interest by appropriately manipulating the underlying probability measure of the system, allowing high-precision results to be obtained with substantially fewer simulation runs than the conventional direct Monte Carlo simulation. Here, we show the algorithm of our new approach, and we apply it to the analysis of rare deviant transitions of two systems, resulting in several orders of magnitude speedup in generating high-precision estimates compared with the conventional Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The τ-leap method first developed by Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)] can significantly speed up stochastic simulation of certain chemically reacting systems with acceptable losses in accuracy. Recently, several improved τ-leap methods, including the binomial, multinomial, and modified τ-leap methods, have been developed. However, in all these τ-leap methods, the mean of the number of times, Km, that the mth reaction channel fires during a leap is not equal to the true mean. Therefore, all existing τ-leap methods produce biased simulation results, which limit the simulation accuracy and speed. In this paper, we analyze the mean of Km based on the chemical master equation. Using this analytical result, we develop unbiased Poisson and binomial τ-leap methods. Moreover, we analyze the variance of Km, and then develop an unbiased Poisson/Gaussian/binomial τ-leap method to correct the errors in both the mean and variance of Km. Simulation results demonstrate that our unbiased τ-leap method can significantly improve simulation accuracy without sacrificing speed. [ABSTRACT FROM AUTHOR]

An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed. This new algorithm is quite general, and it amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA), also known as the Gillespie [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)] algorithm. The basic idea is to use an outer SSA to simulate the slow processes with rates computed from an inner SSA which simulates the fast reactions. Averaging theorems for Markov processes can be used to identify the fast and slow variables in the system as well as the effective dynamics over the slow time scale, even though the algorithm itself does not rely on such information. This nested SSA can be easily generalized to systems with more than two separated time scales. Convergence and efficiency of the algorithm are discussed using the established error estimates and illustrated through examples. [ABSTRACT FROM AUTHOR]

Reactions in real chemical systems often take place on vastly different time scales, with “fast” reaction channels firing very much more frequently than “slow” ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system’s evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we examine the different formulations of Gillespie’s stochastic simulation algorithm (SSA) [D. Gillespie, J. Phys. Chem. 81, 2340 (1977)] with respect to computational efficiency, and propose an optimization to improve the efficiency of the direct method. Based on careful timing studies and an analysis of the time-consuming operations, we conclude that for most practical problems the optimized direct method is the most efficient formulation of SSA. This is in contrast to the widely held belief that Gibson and Bruck’s next reaction method [M. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000)] is the best way to implement the SSA for large systems. Our analysis explains the source of the discrepancy. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The traditional method of installing underground utilities (e.g., water, sewer, gas pipes, electrical cables) by burying them under roads has been used for decades. However, the repeated excavations related to this method cause problems, such as traffic congestion and business disruption, which can significantly increase financial and social costs. Multi-purpose Utility Tunnels (MUTs) are a good alternative for buried utilities. Although the initial cost of MUTs is higher than that of the traditional method, social cost savings make them more feasible, especially in dense urban areas. Different factors, such as the specifications of utilities, the location of the MUTs, and the construction method, should be investigated to determine if MUTs can be an economical and practical alternative. The construction method is one of the most important factors to assess to have a successful MUT project and reduce its impact on the surrounding area. Simulation can be used to investigate the different construction methods of MUTs. In this paper, two Stochastic Discrete Event Simulation models depicting two MUT construction methods (i.e., microtunneling and cut-and-cover) are developed to analyze the duration and cost of the MUT projects. Also, 4D simulation models of these methods are developed for constructability assessment of these projects. [ABSTRACT FROM AUTHOR]

In this paper, we explore the interplay between tumor cells and the human immune system, based on a deterministic mathematical model of minimal interactions by transforming it to stochastic model using a continuous-time Markov chain, where time is continuous but the state space is discrete. Furthermore, we simulate the stochastic basin of attraction to verify the behavior of the three critical points of interest in the deterministic system. Moreover, the stochastic simulations exemplify the cancer immunoediting theory in its three phases of development: elimination, equilibrium and escape. We extend the minimum model proposed in [DeLisi & Rescigno, 1977] to include a term of immunotherapy by lymphocyte injection, and we simulate two treatment regimes, equilibrium and escape, under several schemes. [ABSTRACT FROM AUTHOR]

The main objectives of this study were to model various scenarios of African swine fever (ASF) virus transmission among farms in Vietnam and to evaluate the impact of control strategies using North American Animal Disease Spread Model (NAADSM). A total of 7,882 pig farms in the Red River Delta (RRD) region were obtained from the General Statistics Office, and then, random points corresponding to the number of farms in each province were generated as exact farm locations were not available. A total of 10 models were developed, including movement control scenarios. In addition, we conducted sensitivity analysis to assess the impact of indirect contact transmission probability (TP). Overall, the indirect contact exhibited an important role in transmitting the ASF virus. In order to minimize ASF transmission between farms, we found that movement restriction needed to reach a certain level (approximately between 50% and 75%) and that the restriction had to be applied in a timely manner. This study offers valuable insight into how ASF virus can be transmitted via direct and indirect contact and controlled among farms under the various simulation scenarios. Our results suggest that the enforcement of movement restriction was an effective control measure as soon as the outbreaks were reported. In addition, this study provided evidence that high standards of biosecurity can contribute to the reduction of disease spread. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of selecting a Pareto set from among finite alternatives, where each alternative has multiple performance measures evaluated by stochastic simulations. Under limited simulation resources, we propose an efficient algorithm for solving this problem based on a statistical hypothesis test. Using the test, the proposed algorithm evaluates the uncertainty of each design based on the observed simulation results to identify whether the selected Pareto set is accurate. Based on the evaluated uncertainty, the algorithm assigns additional resources to the designs to maximize the accuracy of the selected Pareto set. Applying the sequential procedure, the algorithm increases the precision of the observed information selectively and gradually. Several experiments, including a practical case study, demonstrated its improved efficiency compared to the existing algorithms in the literature. This improved efficiency, along with low complexity and high robustness to noise, allows the proposed algorithm to be effectively applied to practical system designs. [ABSTRACT FROM AUTHOR]

A farm-level stochastic simulation model was modified to estimate the cost per case of 3 foot disorders (digital dermatitis, sole ulcer, and white line disease) by parity group and incidence timing. Disorder expenditures considered within the model included therapeutics, outside labor, and on-farm labor. Disorder losses considered within the model included discarded milk, reduced milk production, extended days open, an increased risk of culling, an increased risk of death (natural or euthanized), and disease recurrence. All estimates of expenditures and losses were defined using data from previously published research in stochastic distributions. Stochastic simulation was used to account for variation within the farm model; 1,000 iterations were run. Sensitivity of foot disorder costs to selected market prices (milk price, feed price, replacement heifer price, and slaughter price) and herd-specific performance variables (pregnancy rate) were analyzed. Using our model assumptions, the cost per disorder case over all combinations of parity group and incidence timing, regardless of incidence likelihood, was lowest for digital dermatitis ($64 ± 24; mean ± standard deviation), followed by white line disease ($152 ± 26) and sole ulcer ($178 ± 29). Disorder costs were greater in multiparous versus primiparous cows and were always highest at the beginning of lactation. The greatest contributing cost categories were decreased milk production, an increased risk of culling, and disease recurrence. The contribution of cost categories to the total cost of disorder varied by disorder type, parity group, and incidence timing. For all disorders, the cost per case increased as milk price or replacement heifer price increased and decreased as feed price, pregnancy rate, or slaughter price increased. Understanding how foot disorder costs change according to cow-specific conditions (i.e., disorder type, parity group, and days in milk at incidence) and herd-specific conditions (i.e., market prices and performance variables) can help improve on-farm decisions about treatment and prevention of foot disorders. [ABSTRACT FROM AUTHOR]

Abstract: For biochemical systems, when some chemical species are represented by small numbers of molecules, discrete and stochastic approaches are more appropriate than continuous and deterministic approaches. The stochastic simulation algorithm (SSA), proposed by Gillespie, is a cardinal simulation method for the chemical kinetics. Because the SSA simulates every reaction event, the amount of the computational time is huge when models have many reaction channels and species. Therefore there have been many alternative algorithms whose goal is to improve the computational efficiency of the SSA. In this paper we use stochastic Taylor expansions to propose implicit second order weak Taylor tau-leaping methods for the stochastic simulation of chemical kinetics. These methods are motivated by the theory of weakly convergent discretizations of stochastic differential equations. Three different schemes of the second order weak Taylor tau-leaping methods are numerically tested to demonstrate the performance with accuracy. [Copyright &y& Elsevier]

The article assesses the stochastic simulation of a reversible chemical reaction whose rate law is of the first-order, which was presented by J. Mart&ieacute;nez-Urreaga, J. Mira and C. González-Fernández. The researchers used a subclass Markovian processes and the Monte Carlo method, which is implemented by the time-driven approach. They validated the results of stochastic simulation by comparing them with available experimental data.

The results of stochastic simulations of growth and evaporation of small clusters in vapor are reported. Energy dependent growth rates are determined from the monomer-cluster collision rate and decay rates are found from a detailed balance, with the equilibrium size and energy distribution of clusters calculated using the capillarity approximation and the equilibrium vapor pressure. These rates are used in simulations of two-dimensional random walks in size and energy space to determine the fraction of clusters in supersaturated vapor of size (imin+1) that reach a size imax. By assuming that clusters of size imin are in equilibrium, this fraction can be related to the nonisothermal nucleation rate. The simulated rates show good agreement with the previously published analytical results. In the absence of an inert carrier gas, the nonisothermal nucleation rates are typically between 1% and 5% of the isothermal rates. [ABSTRACT FROM AUTHOR]

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques. [ABSTRACT FROM AUTHOR]

One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical postprocessing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moments of system responses and which enables more advanced statistical post-processing. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient ranking and selection algorithm for a stochastic simulation model. The proposed algorithm evaluates an uncertainty to assess whether the observed best design is truly optimal, based on hypothesis test. Then, it conservatively allocates additional simulation resources to reduce uncertainty with an intuitive allocation rule in each iteration of a sequential procedure. This conservative allocation provides a high robustness to noise for the algorithm. The results of several experiments demonstrated its improved performance compared to the other algorithms in the literature. The algorithm can be an efficient way to solve optimization problems in real-world systems where significant noise exists. [ABSTRACT FROM AUTHOR]

We discuss the use of stochastic simulation as a tool to learn about optimal behavior and Nash equilibria of a sequential voting model proposed by Osborne, related to Duverger’s law. We introduce a graphical Java applet, which implements such simulations and investigates its properties. We show that in an appropriate setup, the applet is guaranteed to eventually find behavior, which is within ε of being optimal. [ABSTRACT FROM AUTHOR]

Importance sampling has been used to improve the efficiency of simulations where the simulation output is uniquely determined, given a fixed input. We extend the theory of importance sampling to estimate a system’s reliability with stochastic simulations. Thanks to the advance of computing power, stochastic simulation models are employed in many applications to represent a complex system behavior. A stochastic simulation model generates stochastic outputs at the same input. Given a budget constraint on total simulation replications, we develop a new approach, which we call stochastic importance sampling, which efficiently uses stochastic simulations with unknown output distribution. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of an estimator. Application to a computationally intensive aeroelastic wind turbine simulation demonstrates the benefits of the proposed approach. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

To predict runoff under different annual precipitation and reflect the impact of annual precipitation and its inner-annual distribution on the runoff process, the soil and water assessment tool (SWAT) model is combined with the stochastic simulation of precipitation based on the torrential rain analysis. Taking the watershed above Wangkuai Reservoir in China as an example, the SWAT model is constructed. and the stochastic simulation models of precipitation under three annual precipitation states are established. Then, based on the torrential rain analysis, five precipitation scenarios with annual precipitation of 300, 600, and 900 mm are assumed, and the daily precipitation process of each scenario is generated as the input of the SWAT model. The results are as follows: the SWAT model has a very good performance for monthly runoff simulation; the maximum monthly runoffs of the five precipitation scenarios are 5.99, 7.09, 9.14, 17.48, and 23.71 m3/s , respectively, and the annual runoffs are 2.24, 3.02, 3.30, 4.75, and 5.08 m3/s , respectively. When the annual precipitation is about 600 mm, the influence of precipitation inner-annual distribution on the monthly runoff process is mainly reflected in July to October. When the annual precipitation is about 900 mm, the influence is mainly reflected in August. This study provides a new idea for runoff prediction and provides reference for the study of the rainfall–runoff uncertainty relationship. Moreover, the improved precipitation stochastic simulation and its combination with the SWAT model can be applied to the study of other basins for further discovery. [ABSTRACT FROM AUTHOR]

Abstract: This study analyzed the ‘pressing with one finger’ technique for wrist pulse-taking and explored the identification of internal organs according to the resonance theory in the circulatory system. A five-section discretized-transmission-line model of the distal upper limb was proposed considering the radial artery, the distal positions chi–guan–cun, and the hand vasculature. The transfer function of the model was parameterized in terms of its resonance frequency and respective amplification factor. Rheological and geometrical parameters of the modeled arterial system were used to simulate a sample of 1000 healthy volunteers subjected to wrist pulse-taking examination. The ‘pressing with one finger’ technique was simulated individually at each position by varying the vertical (minor) diameter of the elliptical cross-sectional radial artery from 0% to 99%. The pulse waveform harmonics were calculated in the frequency domain and had their internal organs assigned according to the resonance theory. Compressions in range 0–70% resulted in resonance frequencies around 3–6Hz (related to the spleen) and amplification factors>1. Compression in range 70–85% shifted up the resonance frequency of the majority of cases up to 6–8Hz (related to the heart) and a minority of cases was shifted down to 0–2Hz. A large decrease in the amplification factor occurred with module values <1. Compressions in range 85–99% increased the resonance frequency to 7–10Hz (related to the gallbladder) with an even decent amplification factor. These effects were more pronounced in the proximal to distal sequence of positions. Therefore, pressing with one finger amplified specific pulse wave harmonics as a function of depth in all three positions, but it did not explore all harmonics described by the resonance theory. [Copyright &y& Elsevier]

Respondent-driven detection is a chain recruitment method used to sample contact persons of infected persons in order to enhance case finding. It starts with initial individuals, so-called seeds, who are invited for participation. Afterwards, seeds receive a fixed number of coupons to invite individuals with whom they had contact during a specific time period. Recruitees are then asked to do the same, resulting in successive waves of contact persons who are connected in one recruitment tree. However, often the majority of participants fail to invite others, or invitees do not accept an invitation, and recruitment stops after several waves. A mathematical model can help to analyse how various factors influence peer recruitment and to understand under which circumstances sustainable recruitment is possible. We implemented a stochastic simulation model, where parameters were suggested by empirical data from an online survey, to determine the thresholds for obtaining large recruitment trees and the number of waves needed to reach a steady state in the sample composition for individual characteristics. We also examined the relationship between mean and variance of the number of invitations sent out by participants and the probability of obtaining a large recruitment tree. Our main finding is that a situation where participants send out any number of coupons between one and the maximum number is more effective in reaching large recruitment trees, compared to a situation where the majority of participants does not send out any invitations and a smaller group sends out the maximum number of invitations. The presented model is a helpful tool that can assist public health professionals in preparing research and contact tracing using online respondent-driven detection. In particular, it can provide information on the required minimum number of successfully sent invitations to reach large recruitment trees, a certain sample composition or certain number of waves. [ABSTRACT FROM AUTHOR]

Computational simulation is a widely employed methodology to study the dynamic behavior of complex systems. Although common approaches are based either on ordinary differential equations or stochastic differential equations, these techniques make several assumptions which, when it comes to biological processes, could often lead to unrealistic models. Among others, model approaches based on differential equations entangle kinetics and causality, failing when complexity increases, separating knowledge from models, and assuming that the average behavior of the population encompasses any individual deviation. To overcome these limitations, simulations based on the Stochastic Simulation Algorithm (SSA) appear as a suitable approach to model complex biological systems. In this work, we review three different models executed in PISKaS: a rule-based framework to produce multiscale stochastic simulations of complex systems. These models span multiple time and spatial scales ranging from gene regulation up to Game Theory. In the first example, we describe a model of the core regulatory network of gene expression in Escherichia coli highlighting the continuous model improvement capacities of PISKaS. The second example describes a hypothetical outbreak of the Ebola virus occurring in a compartmentalized environment resembling cities and highways. Finally, in the last example, we illustrate a stochastic model for the prisoner's dilemma; a common approach from social sciences describing complex interactions involving trust within human populations. As whole, these models demonstrate the capabilities of PISKaS providing fertile scenarios where to explore the dynamics of complex systems. [ABSTRACT FROM AUTHOR]

Abstract: The African wild dog (Lycaon pictus) is one of Africa''s most endangered species and therefore classified as endangered by IUCN. Earlier distributions included most of Africa but currently the African wild dog only has populations larger than 300 individuals in three countries (Botswana, Tanzania and South Africa). In 1998, a plan was launched in South Africa to manage sub-populations of the African wild dog in several small, geographically isolated, conservation areas. This management program involved the reintroduction of wild dogs into suitable conservation areas and periodic translocations among them. We used the stochastic population simulation model VORTEX to evaluate the Limpopo Valley Conservancy in the north of South Africa, as a possible reintroduction site for African wild dogs. The simulations showed that the size of the initial population released only had a small effect on the population dynamics. However, when individuals were supplemented and harvested over a longer period the probability of persistence increased. Number of females breeding, male mortality, and carrying capacity were key factors in the population dynamics, but according to VORTEX the severity of natural catastrophes had the greatest influence on the extinction risk and inbreeding. We suggest that the reintroduction program may be successful, if areas are properly secured, the dogs are held in a boma before release, wild animals or at least a mix of wild and captive animals are used for the release and the animals are vaccinated against rabies. It is, however, essential to continue monitoring followed by modelling efforts to re-evaluate the success of the reintroduction program. [Copyright &y& Elsevier]

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. [ABSTRACT FROM AUTHOR]

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms. [ABSTRACT FROM AUTHOR]

To investigate the behavior of biochemical systems, many runs of Gillespie's Stochastic Simulation Algorithm (SSA) are generally needed, causing excessive computational costs on Central Processing Units (CPUs). Since all SSA runs are independent, the Intel Xeon Phi coprocessors based on the Many Integrated Core (MIC) architecture can be exploited to distribute the workload. We considered two execution modalities on MIC: one consisted in running exactly the same CPU code of SSA, while the other exploited MIC's vector instructions to reuse the CPU code with only few modifications. MIC performance was compared with Graphics Processing Units (GPUs), specifically implemented in CUDA to optimize the use of memory hierarchy. Our results show that GPU largely outperforms MIC and CPU, but required a complete redesign of SSA. MIC allows a relevant speedup, especially when vector instructions are used, with the additional advantage of requiring minimal modifications to CPU code. [ABSTRACT FROM AUTHOR]

The interactions between point defects such as vacancies and self-interstitial atoms with solute atoms plays an important role in the evolution of the radiation damage microstructure. Alloys can suffer less void swelling, and exhibit reduced prismatic loop growth, compared with elemental metals, and this can be attributed to the solute atoms inhibiting point defect mobility. However, the microstructural evolution takes place on timescales inaccessible to electronic or atomistic methods, and high temperatures increase the complexity of Monte Carlo simulations, as more transitions become available, and more rates must be calculated. Here we present a combined analytical–numerical approach to model the stochastic evolution of the microstructure, focussing on the interactions between 〈 1 1 1 〉 crowdions and solute atoms in tungsten. [ABSTRACT FROM AUTHOR]

Shortening or omitting the dry period of dairy cows improves metabolic health in early lactation and reduces management transitions for dairy cows. The success of implementation of these strategies depends on their impact on milk yield and farm profitability. Insight in these impacts is valuable for informed decision-making by farmers. The aim of this study was to investigate how shortening or omitting the dry period of dairy cows affects production and cash flows at the herd level, and greenhouse gas emissions per unit of milk, using a dynamic stochastic simulation model. The effects of dry period length on milk yield and calving interval assumed in this model were derived from actual performance of commercial dairy cows over multiple lactations. The model simulated lactations, and calving and culling events of individual cows for herds of 100 cows. Herds were simulated for 5 years with a dry period of 56 (conventional), 28 or 0 days (n = 50 herds each). Partial cash flows were computed from revenues from sold milk, calves, and culled cows, and costs from feed and rearing youngstock. Greenhouse gas emissions were computed using a life cycle approach. A dry period of 28 days reduced milk production of the herd by 3.0% in years 2 through 5, compared with a dry period of 56 days. A dry period of 0 days reduced milk production by 3.5% in years 3 through 5, after a dip in milk production of 6.9% in year 2. On average, dry periods of 28 and 0 days reduced partial cash flows by €1,249 and €1,632 per herd per year, and increased greenhouse gas emissions by 0.7% and 0.5%, respectively. Considering the potential for enhancing cow welfare, these negative impacts of shortening or omitting the dry period seem justifiable, and they might even be offset by improved health. [ABSTRACT FROM AUTHOR]