198,567 research outputs found

    Parallel Load Balancing Strategies for Ensembles of Stochastic Biochemical Simulations

    Get PDF
    The evolution of biochemical systems where some chemical species are present with only a small number of molecules, is strongly influenced by discrete and stochastic effects that cannot be accurately captured by continuous and deterministic models. The budding yeast cell cycle provides an excellent example of the need to account for stochastic effects in biochemical reactions. To obtain statistics of the cell cycle progression, a stochastic simulation algorithm must be run thousands of times with different initial conditions and parameter values. In order to manage the computational expense involved, the large ensemble of runs needs to be executed in parallel. The CPU time for each individual task is unknown before execution, so a simple strategy of assigning an equal number of tasks per processor can lead to considerable work imbalances and loss of parallel efficiency. Moreover, deterministic analysis approaches are ill suited for assessing the effectiveness of load balancing algorithms in this context. Biological models often require stochastic simulation. Since generating an ensemble of simulation results is computationally intensive, it is important to make efficient use of computer resources. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms when applied to large ensembles of stochastic biochemical simulations. Two particular load balancing strategies (point-to-point and all-redistribution) are discussed in detail. Simulation results with a stochastic budding yeast cell cycle model confirm the theoretical analysis. While this work is motivated by cell cycle modeling, the proposed analysis framework is general and can be directly applied to any ensemble simulation of biological systems where many tasks are mapped onto each processor, and where the individual compute times vary considerably among tasks

    Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics

    Full text link
    In this paper we provide two representations for stochastic ion channel kinetics, and compare the performance of exact simulation with a commonly used numerical approximation strategy. The first representation we present is a random time change representation, popularized by Thomas Kurtz, with the second being analogous to a "Gillespie" representation. Exact stochastic algorithms are provided for the different representations, which are preferable to either (a) fixed time step or (b) piecewise constant propensity algorithms, which still appear in the literature. As examples, we provide versions of the exact algorithms for the Morris-Lecar conductance based model, and detail the error induced, both in a weak and a strong sense, by the use of approximate algorithms on this model. We include ready-to-use implementations of the random time change algorithm in both XPP and Matlab. Finally, through the consideration of parametric sensitivity analysis, we show how the representations presented here are useful in the development of further computational methods. The general representations and simulation strategies provided here are known in other parts of the sciences, but less so in the present setting.Comment: 39 pages, 6 figures, appendix with XPP and Matlab cod

    Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques

    Get PDF
    Process variations are a major concern in today's chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit's performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014. arXiv admin note: text overlap with arXiv:1407.302

    Coarse Grained Computations for a Micellar System

    Full text link
    We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the MC simulation, and on (computational) time scale separation between these and the remaining "slaved", fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse-grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g. equations of state) may provide a computational bridge between direct atomistic / stochastic simulation and the analysis of its macroscopic, system-level consequences

    Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

    Get PDF
    The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.Bayesian methodology, stochastic volatility, durations, non-centred in location, non-centred in scale, inefficiency factors.

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

    Get PDF
    <p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>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-alone program and within new systems biology applications. Finally, complex scenarios requiring intervention during the simulation progress can be modelled easily with FERN.</p
    corecore