The probabilistic programming paradigm is gaining popularity due to the possibility of easily representing probabilistic systems and running a number of off-the-shelf inference algorithms on them. This paper explores ...
详细信息
ISBN:
(纸本)9783031737084;9783031737091
The probabilistic programming paradigm is gaining popularity due to the possibility of easily representing probabilistic systems and running a number of off-the-shelf inference algorithms on them. This paper explores how this paradigm can be used to analyse collective systems, in the form of Markov Population Processes (MPPs). MPPs have been extensively used to represent systems of interacting agents, but their analysis is challenging due to the high computational cost required to perform exact simulations of the systems. We represent MPPs as runs of the approximate variant of the stochastic simulation algorithm (SSA), known as tau-leaping, which can be seen as a probabilistic program. We apply Gaussian Semantics, a recently proposed inference method for probabilistic programs, to analyse it. We show that tau-leaping runs can be effectively analysed using a tailored version of Second Order Gaussian Approximation in which we use a Gaussian Mixture encoding of Poisson distributions. In the resulting analysis, the state of the system is approximated by a multivariate Gaussian Mixture generalizing other common Gaussian approximations such as the Linear Noise Approximation and the Langevin Method. Preliminary numerical experiments show that this approach is able to analyse MPPs with reasonable accuracy on the significant statistics while avoiding expensive numerical simulations.
Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled proce...
详细信息
Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochasticsimulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.
In this paper, we develop a modified accelerated stochasticsimulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all spec...
详细信息
In this paper, we develop a modified accelerated stochasticsimulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.
Presented here is an L-leap method for accelerating stochasticsimulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity funct...
详细信息
Presented here is an L-leap method for accelerating stochasticsimulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.
The spatial stochasticsimulation of biochemical systems requires significant calculation efforts. Parallel discrete-event simulation is a promising approach to accelerate the execution of simulation runs. However, ac...
详细信息
The spatial stochasticsimulation of biochemical systems requires significant calculation efforts. Parallel discrete-event simulation is a promising approach to accelerate the execution of simulation runs. However, achievable speedup depends on the parallelism inherent in the model. One of our goals is to explore this degree of parallelism in the Next Subvolume Method type simulations. Therefore we introduce the Abstract Next Subvolume Method, in which we decouple the model representation from the sequential simulationalgorithms, and prove that state trajectories generated by its executions statistically accord with those generated by the Next Subvolume Method. The experimental performance analysis shows that optimistic synchronization algorithms, together with careful controls over the speculative execution, are necessary to achieve considerable speedup and scalability in parallel spatial stochasticsimulation of chemical reactions. Our proposed method facilitates a flexible incorporation of different synchronization algorithms, and can be used to select the proper synchronization algorithm to achieve the efficient parallel simulation of chemical reactions. (C) 2011 Elsevier Ltd. All rights reserved.
We investigate the computational challenge of improving the accuracy of the stochasticsimulation estimation by inducing negative correlation through the anticorrelated variance reduction technique. A direct applicati...
详细信息
We investigate the computational challenge of improving the accuracy of the stochasticsimulation estimation by inducing negative correlation through the anticorrelated variance reduction technique. A direct application of the technique to the stochastic simulation algorithm (SSA), employing the inverse transformation, is not efficient for simulating large networks because its computational cost is similar to the sum of independent simulation runs. We propose in this study a new algorithm that employs the propensity bounds of reactions, introduced recently in their rejection-based SSA, to correlate and synchronise the trajectories during the simulation. The selection of reaction firings by our approach is exact due to the rejection-based mechanism. In addition, by applying the anticorrelated variance technique to select reaction firings, our approach can induce substantial correlation between realisations, hence reducing the variance of the estimator. The computational advantage of our rejection-based approach in comparison with the traditional inverse transformation is that it only needs to maintain a single data structure storing propensity bounds of reactions, which is updated infrequently, hence achieving better performance.
stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficie...
详细信息
stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochasticsimulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods.
stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulat...
详细信息
stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.
Computational modeling has become a widespread approach for studying real-world phenomena by using different modeling perspectives, in particular, the microscopic point of view concentrates on the behavior of the sing...
详细信息
Computational modeling has become a widespread approach for studying real-world phenomena by using different modeling perspectives, in particular, the microscopic point of view concentrates on the behavior of the single components and their interactions from which the global system evolution emerges, while the macroscopic point of view represents the system's overall behavior abstracting as much as possible from that of the single components. The preferred point of view depends on the effort required to develop the model, on the detail level of the available information about the system to be modeled, and on the type of measures that are of interest to the modeler;each point of view may lead to a different modeling language and simulation paradigm. An approach adequate for the microscopic point of view is Agent-Based Modeling and simulation, which has gained popularity in the last few decades but lacks a formal definition common to the different tools supporting it. This may lead to modeling mistakes and wrong interpretation of the results, especially when comparing models of the same system developed according to different points of view. The aim of the work described in this paper is to provide a common compositional modeling language from which both a macro and a micro simulation model can be automatically derived: these models are coherent by construction and may be studied through different simulation approaches and tools. A framework is thus proposed in which a model can be composed using a Petri Net formalism and then studied through both an Agent-Based simulation and a classical stochastic simulation algorithm, depending on the study goal.
We use the recently proposed Nested stochastic simulation algorithm(Nested SSA)to simulate the cell cycle model for budding *** results show that Nested SSA is able to significantly reduce the computational cost while...
详细信息
We use the recently proposed Nested stochastic simulation algorithm(Nested SSA)to simulate the cell cycle model for budding *** results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.
暂无评论