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17th International Conference on Computational Methods in Systems Biology (CMSB)

作者： Backenkoehler, Michael Bortolussi, Luca Wolf, Verena Saarland Univ Saarbrucken Germany Univ Trieste Trieste Italy

ISBN: (纸本)9783030313043;9783030313036

stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number of necessary runs, we propose a variance reduction technique based on control variates. We exploit constraints on the statistical moments of the stochastic process to reduce the estimators' variances. We develop an algorithm that selects appropriate control variates in an on-line fashion and demonstrate the efficiency of our approach on several case studies.

关键词： Chemical reaction network Chemical master equation stochastic simulation algorithm Moment equations Control variates Variance reduction

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Distributed simulation of Bio-interpreted (Coloured) stochastic Petri Nets 13

Distributed Simulation of Bio-interpreted (Coloured) Stochas...

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13th International Conference on Computer Engineering and Systems (ICCES)

作者： Badawy, Asmaa Herajy, Mostafa Awad, Wael Heiner, Monika Port Said Univ Dept Math & Comp Sci Fac Sci Port Said 42521 Egypt Brandenburg Tech Univ Cottbus Inst Comp Sci Postbox 10 13 44 D-03013 Cottbus Germany

ISBN: (纸本)9781538651117

To increase our understanding of the interactions between the different cellular and intercellular processes, it is imperative to construct accurate biological models. An important class of these models are usually used to predict the time evolution of the corresponding chemical species over a specified period of time. stochastic and coloured stochastic Petri nets can be adopted to construct graphical models that can be executed to simulate the firing of a set of reactions in a well-mixed chemical system. For the purpose of this specific application, (coloured) stochastic Petri nets employ internally the stochastic simulation algorithm (SSA) to perform the simulation. Although the result of the SSA is accurate in comparison with similar numerical simulation approaches (e.g., the systems of ordinary differential equations), it is empirically considered as a computationally expensive algorithm. In this paper, we propose an efficient parallel simulation algorithm for SSA to improve the execution of (coloured) stochastic Petri nets. We illustrate our proposal by applying it to a well-known model in the biological context: reaction diffusion. Furthermore, we evaluate the performance of the parallel algorithm and compare its runtime behaviour with the sequential one.

关键词： Coloured stochastic Petri Nets stochastic simulation algorithm Fine-grained Parallel simulation

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stochastic simulation of imperfect Mixing in Free Radical Polymerization

Stochastic Simulation of imperfect Mixing in Free Radical Po...

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Conference on Modelling, Monitoring and Control of Polymer Properties

作者： Hernandez, Hugo F. Tauer, Klaus Max Planck Inst Colloids & Interfaces D-14476 Golm Germany

A modified algorithm for the stochastic simulation of chemical reactions subject to mass transfer limitation (imperfect mixing) is presented. This algorithm takes into account the mixing by diffusion of the reacting species between two consecutive reactions. The method is used to simulate the effect of mass transfer limitation in free-radical polymerization. Since this is a stiff reaction network, a hybrid stochastic-deterministic approach is considered. The hybrid stochastic algorithm under imperfect mixing (HSSA-IM) is applied to the bulk polymerization of methyl methacrylate up to high conversions. The accuracy of the algorithm relies on the precise determination of diffusion coefficients during the reaction.

关键词： hybrid stochastic simulation imperfect mixing kinetic monte carlo simulation radical polymerization stochastic simulation algorithm trommsdorff effect

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Modeling and simulation of stochastic Neutron and Cumulative Deposited Fission Energy Distributions

Modeling and Simulation of Stochastic Neutron and Cumulative...

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作者： Patrick O'Rourke University of New Mexico

学位级别：博士

Methods of stochastic neutron transport are investigated and applied to novel formulations for the neutron number distribution and the cumulative fission energy deposition distribution. We utilize two Monte Carlo algorithms: the event-based Monte Carlo (EBMC) method and the stochastic simulation algorithm (SSA) to benchmark and analyze systems. We show that the SSA outperforms the EBMC for the parameter space we are interested in. We then utilize the SSA to analyze systems composed of multiple spherical regions with fast and thermal neutrons with time-dependent reactivity insertions and determine whether group-dependent number distributions approach a gamma distribution. We develop two methods for calculating the geometry-dependent transfer probabilities, the View Factor Approximation and the Sphere Point Picking Monte Carlo Method, and compare the parametric space for which the computationally superior VF approximation holds. We discuss several numerical solution methods that have been developed for solving the nonlinear adjoint transport equation satisfied by the neutron survival probability. We show the primary competitive direct solution referred to as the $\lambda$-Acceleration Method ($\lambda$AM), and introduce a new indirect solution method called the Eigenfunction Expansion Method (EFE). The space-angle shape of the solution in a nonhomogeneous planar medium equilibrate rapidly after the initiation of a chain and for practical purposes 3 modes are sufficient to accurately capture the time variation of the survival probability, with a full fission neutron multiplicity distribution, while just 1 mode gives acceptable accuracy in steady state. The order of the nonlinearity, correlated to the induced fission chain branching, has a larger effect on the solution than the number of modes retained in the expansion. In particular, the quadratic approximation, corresponding to truncation order 2 in the nonlinear fission branching terms, is accurate for near critical

关键词： stochastic simulation algorithm Master equations Monte Carlo methods Boltzmann Master equation neutron transport

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stochastic modeling and simulation of gene networks

Stochastic modeling and simulation of gene networks

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作者： Xu, Zhouyi University of Miami

学位级别：Ph.D.

Recent research in experimental and computational biology has revealed the necessity of using stochastic modeling and simulation to investigate the functionality and dynamics of gene networks. However, there is no sophisticated stochastic modeling techniques and efficient stochastic simulation algorithms (SSA) for analyzing and simulating gene networks. Therefore, the objective of this research is to design highly efficient and accurate SSAs, to develop stochastic models for certain real gene networks and to apply stochastic simulation to investigate such gene networks. To achieve this objective, we developed several novel efficient and accurate SSAs. We also proposed two stochastic models for the circadian system of Drosophila and simulated the dynamics of the system. The K-leap method constrains the total number of reactions in one leap to a properly chosen number thereby improving simulation accuracy. Since the exact SSA is a special case of the K-leap method when K=1, the K-leap method can naturally change from the exact SSA to an approximate leap method during simulation if necessary. The hybrid τ/K-leap and the modified K-leap methods are particularly suitable for simulating gene networks where certain reactant molecular species have a small number of molecules. Although the existing τ-leap methods can significantly speed up stochastic simulation of certain gene networks, the mean of the number of firings of each reaction channel is not equal to the true mean. Therefore, all existing τ-leap methods produce biased results, which limit simulation accuracy and speed. Our unbiased τ-leap methods remove the bias in simulation results that exist in all current leap SSAs and therefore significantly improve simulation accuracy without sacrificing speed. In order to efficiently estimate the probability of rare events in gene networks, we applied the importance sampling technique to the next reaction method (NRM) of the SSA and developed a weighted NRM (wNRM). We furthe

关键词： Circadian Rhythm Importance Sampling Weighted stochastic simulation algorithm Unbiased Tau-leap Method K-leap Method stochastic simulation algorithm

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Multiscale Hy3S: Hybrid stochastic simulation for supercomputers

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BMC BIOINFORMATICS 2006年第1期7卷 93-93页

作者： Salis, H Sotiropoulos, V Kaznessis, YN Univ Minnesota Dept Chem Engn & Mat Sci Minneapolis MN 55455 USA Univ Minnesota Digital Technol Ctr Minneapolis MN 55455 USA

Background: stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. Results: Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI;special discrete events, such as transcriptional and translation elongation and cell division;mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters;combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis;use of NetCDF optimized binary format to quickly read and write large datasets;and a simple graphical user interface, written in Matlab, to help users create biological systems and an

关键词： stochastic Differential Equation Biochemical Network stochastic simulation algorithm Biochemical Reaction Network Continuous Markov Process

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FERN - a Java framework for stochastic simulation and evaluation of reaction networks

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BMC BIOINFORMATICS 2008年第1期9卷 356-356页

作者： Erhard, Florian Friedel, Caroline C. Zimmer, Ralf Univ Munich Inst Informat LFE Bioinformat D-80333 Munich Germany

Background: stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. Results: In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. Conclusion: FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alo

关键词： stochastic simulation Reaction Network simulation algorithm stochastic simulation algorithm Molecule Number

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A HIERARCHY OF NETWORK MODELS GIVING BISTABILITY UNDER TRIADIC CLOSURE

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MULTISCALE MODELING & simulation 2022年第4期20卷 1394-1410页

作者： Di Giovacchino, Stefano Higham, Desmond J. Zygalakis, Konstantinos C. Univ Laquila Dept Engn & Comp Sci & Math I-67100 Laquila Italy Univ Edinburgh Sch Math Edinburgh EH9 3FD Scotland

Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of large-scale social interaction networks. Here, depending on the initial state and the transient dynamics, the system may evolve towards either of two long-time states. In this work, we propose and study a hierarchy of network evolution models that incorporate triadic closure, building on the work of Grindrod, Higham, and Parsons [Internet Math., 8 (2012), pp. 402-423]. We use a chemical kinetics framework, paying careful attention to the reaction rate scaling with respect to the system size. In a macroscale regime, we show rigorously that a bimodal steady state distribution is admitted. This behavior corresponds to the existence of two distinct stable fixed points in a deterministic mean-field ODE. The macroscale model is also seen to capture an apparent metastability property of the microscale system. Computational simulations are used to support the analysis.

关键词： birth and death processes graph Langevin equation mean field metastability stochastic simulation algorithm

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A modified uniformization method for the solution of the chemical master equation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第1期59卷 573-584页

作者： Zhang, Jingwei Watson, Layne T. Cao, Yang Virginia Polytech Inst & State Univ Dept Comp Sci Blacksburg VA 24061 USA Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA

The chemical master equation is considered an accurate description of general chemical systems, and especially so for gene regulatory networks and protein-protein interaction networks. However, solving chemical master equations directly is considered computationally intensive. This paper discusses an efficient way of solving the chemical master equation for some prototypical problems in systems biology. Comparisons between this new approach and some traditional approaches, especially Monte-Carlo algorithms, are also presented, and show that under certain conditions the new approach performs better than Monte-Carlo algorithms. (C) 2009 Published by Elsevier Ltd

关键词： Chemical master equation Systems biology External uniformization method stochastic simulation algorithm

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Hybrid CME-ODE method for efficient simulation of the galactose switch in yeast

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IET SYSTEMS BIOLOGY 2018年第4期12卷 170-176页

作者： Bianchi, David M. Peterson, Joseph R. Earnest, Tyler M. Hallock, Michael J. Luthey-Schulten, Zaida Univ Illinois Dept Chem 505 S Mathews Ave Urbana IL 61820 USA NSF Ctr Phys Living Cells 1110 W Green StMC-704320 Loomis Lab Urbana IL 61820 USA Univ Illinois Ctr Macromol Modeling & Bioinformat NIH 405 N Mathews Ave Urbana IL 61820 USA Univ Illinois Sch Chem Sci 505 S Mathews Ave Urbana IL USA Univ Illinois Ctr Biophys & Quantitat Biol 1110 W Green StMC-704 Urbana IL 61820 USA Univ Illinois Beckman Inst Adv Sci & Technol 405 N Mathews Ave Urbana IL 61820 USA Univ Illinois Dept Phys 1110 W Green StMC-704 Urbana IL 61820 USA

It is well known that stochasticity in gene expression is an important source of noise that can have profound effects on the fate of a living cell. In the galactose genetic switch in yeast, the unbinding of a transcription repressor is induced by high concentrations of sugar particles activating gene expression of sugar transporters. This response results in high propensity for all reactions involving interactions with the metabolite. The reactions for gene expression, feedback loops and transport are typically described by chemical master equations (CME). Sampling the CME using the stochastic simulation algorithm (SSA) results in large computational costs as each reaction event is evaluated explicitly. To improve the computational efficiency of cell simulations involving high particle number systems, the authors have implemented a hybrid stochastic-deterministic (CME-ODE) method into the publically available, GPU-based lattice microbes (LM) software suite and its python interface pyLM. LM and pyLM provide a convenient way to simulate complex cellular systems and interface with high-performance RDME/CME/ODE solvers. As a test of the implementation, the authors apply the hybrid CME-ODE method to the galactose switch in Saccharomyces cerevisiae, gaining a 10-50x speedup while yielding protein distributions and species traces similar to the pure SSA CME.

关键词： proteins biology computing reaction kinetics theory molecular biophysics cellular biophysics biochemistry microorganisms genetics master equation reaction-diffusion systems stochastic processes biological techniques galactose switch yeast stochasticity gene expression living cell genetic switches distinct phenotypes galactose genetic switch sugar particles sugar transporters feedback loops chemical master equations cell simulations high particle number systems lattice microbes software suite complex cellular systems stochastic simulation algorithm hybrid CME-ODE method hybrid stochastic-deterministic method high-performance reaction-diffusion master equations-CME-ODE solvers GPU-based lattice microbes Saccharomyces cerevisiae protein distributions

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