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Timestep Stochastic Simulation of Computer Networks using Diffusion Approximation

A. Kochut, A.U. Shankar
14th IEEE International Symposium on Modeling, Analysis, and Simulation  
Timestep stochastic simulation (TSS) is a novel method for generating sample paths of computer networks, with low computation cost independent of packet rates.  ...  At each step, S(t+δ) is randomly chosen according to S(t) and the probability distribution P r[S(t + δ)|S(t)] obtained using the diffusion approximation.  ...  Conclusions and Future Work We presented a novel technique, called timestep stochastic simulation, for fast performance evaluation of computer networks.  ... 
doi:10.1109/mascots.2006.48 dblp:conf/mascots/KochutS06 fatcat:u4ee3v7jtffzljnazgtkb5g7qy

Local error estimates for adaptive simulation of the reaction–diffusion master equation via operator splitting

Andreas Hellander, Michael J. Lawson, Brian Drawert, Linda Petzold
2014 Journal of Computational Physics  
This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep.  ...  Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME.  ...  The timesteps are themselves stochastic variables and fluctuate during the course of the simulation.  ... 
doi:10.1016/j.jcp.2014.02.004 pmid:26865735 pmcid:PMC4746020 fatcat:wr6pz55thfch3ogqvmojtjdipa

Orchestral: a lightweight framework for parallel simulations of cell-cell communication [article]

Adrien Coulier, Andreas Hellander
2018 arXiv   pre-print
By the use of operator-splitting we decouple the simulation of reaction-diffusion kinetics inside the cells from the simulation of molecular cell-cell interactions occurring on the boundaries between cells  ...  We develop a modeling and simulation framework capable of massively parallel simulation of multicellular systems with spatially resolved stochastic kinetics in individual cells.  ...  Coulier for constructive criticism of the manuscript. This work has been funded by the Swedish research council (VR) under award no. 2015-03964 and by the eSSENCE strategic collaboration of eScience.  ... 
arXiv:1806.10889v1 fatcat:er646lgmqbf37p3gsiah2fewsa

Probability-based model of protein-protein interactions on biological timescales

Alexander L Tournier, Paul W Fitzjohn, Paul A Bates
2006 Algorithms for Molecular Biology  
Simulation methods can assist in describing and understanding complex networks of interacting proteins, providing fresh insights into the function and regulation of biological systems.  ...  In this study, a new model of bimolecular interactions is presented that uses a simple, probability-based description of the reaction process.  ...  Acknowledgements The authors thank Rafael Carazo-Salas and the members of the BMM Laboratory for useful discussions and insights.  ... 
doi:10.1186/1748-7188-1-25 pmid:17156482 pmcid:PMC1781080 fatcat:ezd3tufvqnfrrkyqyoxfklnbu4

An adaptive algorithm for simulation of stochastic reaction–diffusion processes

Lars Ferm, Andreas Hellander, Per Lötstedt
2010 Journal of Computational Physics  
For such systems, simulation of the diffusion requires the predominant part of the computing time.  ...  We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes.  ...  Financial support has been obtained from the Swedish Foundation for Strategic Research and the Swedish Graduate School in Mathematics and Computing at 26 Uppsala University.  ... 
doi:10.1016/j.jcp.2009.09.030 fatcat:lxowpoasbfajla7nkoqlgwd64q

Handling Multiscale Stochastic Differential Equations in Julia(If You Give a Mathematician a Compiler) [article]

Christopher Rackauckas
2020 figshare.com  
Handling Multiscale Stochastic Differential Equations in Julia Chris Rackauckas, University of California, Irvine, U.S.  ...  events Demonstration of RSwM1 Tim e X(t) W(t) Propose a timestep h Propose a timestep h Take a random number = (0, ℎ) ( + ℎ) = ( ) + Approximate the solution at t+h Approximate  ...  stack 1 2 Approximate the error at the new timestep Error is small enough.  ... 
doi:10.6084/m9.figshare.12752000.v1 fatcat:ijhnub2sc5ddrayowkiyoxpvdi

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

David M. Bianchi, Joseph R. Peterson, Tyler M. Earnest, Michael J. Hallock, Zaida Luthey-Schulten
2018 IET Systems Biology  
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  ...  using a 1 s timestep at an increase of simulation time from 45 min to ∼1 h.  ... 
doi:10.1049/iet-syb.2017.0070 pmid:33451183 pmcid:PMC8687183 fatcat:q6zx6edfxjafpp4nelfsysxboi

Learning reduced kinetic Monte Carlo models of complex chemistry from molecular dynamics

Qian Yang, Carlos A. Sing-Long, Evan J. Reed
2017 Chemical Science  
We propose a novel statistical learning framework for automatically and efficiently building reduced kinetic Monte Carlo (KMC) models of large-scale elementary reaction networks from data generated by  ...  a single or few molecular dynamics simulations (MD).  ...  This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0002007.  ... 
doi:10.1039/c7sc01052d pmid:28989618 pmcid:PMC5625287 fatcat:mhu7poof75g2rjuj3bvuw57u34

Efficient molecular dynamics using geodesic integration and solvent–solute splitting

Benedict Leimkuhler, Charles Matthews
2016 Proceedings of the Royal Society A  
The methods described in this article are easily implemented using the standard apparatus of modern simulation codes.  ...  and without substantially altering diffusion rates, approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems.  ...  This work was completed in part with resources provided by the University of Chicago Research Computing Center.  ... 
doi:10.1098/rspa.2016.0138 pmid:27279779 pmcid:PMC4893190 fatcat:pxmx2cxh6rgwpi3r5hl5rendd4

Radionuclide Gas Transport through Nuclear Explosion-Generated Fracture Networks

Amy B. Jordan, Philip H. Stauffer, Earl E. Knight, Esteban Rougier, Dale N. Anderson
2015 Scientific Reports  
the importance of accurately simulating the fracture network.  ...  From stochastic simulations using randomly generated hydrogeologic parameters, normalized detection curves are presented to show differences in optimal sampling time for granite and tuff simulations.  ...  The authors would like to thank Carl Gable of LANL for help with numerical meshes using LaGriT.  ... 
doi:10.1038/srep18383 pmid:26676058 pmcid:PMC4682097 fatcat:jh4fdinoaneqrntjosqhovz2vu

A Parallel Modelling Algorithm for Simulating Calcium Release in Cells

Jeremy G. Stoddard, James S. Welsh, Derek R. Laver
2016 IFAC-PapersOnLine  
Abstract: Using a spatially discretised model structure to represent the behaviour of calcium release sites in a cell, this paper presents a parallel solution algorithm which treats each release site as  ...  'A parallel modelling algorithm for simulating calcium release in cells'.  ...  The simulation was repeated for each parallel method using COMPUTATION TIME The calcium release model considered in this paper is constructed from a 3-dimensional network of interconnected voxels,  ... 
doi:10.1016/j.ifacol.2016.12.107 fatcat:uo7isygalnbptntnsd6axro3se

Fractional diffusion emulates a human mobility network during a simulated disease outbreak [article]

Kyle B Gustafson, Basil S. Bayati, Philip A. Eckhoff
2016 arXiv   pre-print
We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network.  ...  In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk.  ...  Figure 3 One dimensional spatial network SIS simulations with R 0 = 4 using fractional diffusion.  ... 
arXiv:1601.07655v1 fatcat:apfxsdjxijf5hhood5u4dvoopq

Hybrid Modeling of Cell Signaling and Transcriptional Reprogramming and Its Application in C. elegans Development

Elana J. Fertig, Ludmila V. Danilova, Alexander V. Favorov, Michael F. Ochs
2011 Frontiers in Genetics  
We present a mechanistic hybrid model, GESSA, which integrates a novel pooled probabilistic Boolean network model of cell signaling and a stochastic simulation of transcription and translation responding  ...  to a diffusion model of extracellular signals.  ...  We thank NIH-NLM for support of Elana J. Fertig, Alexander V. Favorov, and Michael F. Ochs (grants LM009382 and LM008932).  ... 
doi:10.3389/fgene.2011.00077 pmid:22303372 pmcid:PMC3268630 fatcat:qrs24aoc45b4jdqx3qrswwsxw4

Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces

Rex A. Kerr, Thomas M. Bartol, Boris Kaminsky, Markus Dittrich, Jen-Chien Jack Chang, Scott B. Baden, Terrence J. Sejnowski, Joel R. Stiles
2008 SIAM Journal on Scientific Computing  
We describe and validate new tools and algorithms developed for a new version of the MCell simulation program (MCell3), which supports generalized Monte Carlo modeling of diffusion and chemical reaction  ...  Many important physiological processes operate at time and space scales far beyond those accessible to atom-realistic simulations, and yet discrete stochastic rather than continuum methods may best represent  ...  Spatially realistic stochastic simulations of cellular networks therefore require new computational tools, and in this paper we introduce unique new MCell algorithms that allow one to model reactions between  ... 
doi:10.1137/070692017 pmid:20151023 pmcid:PMC2819163 fatcat:cklf3a3afbhnjb2nx5cbrxehwa

Markov Chain Abstractions of Electrochemical Reaction-Diffusion in Synaptic Transmission for Neuromorphic Computing

Margot Wagner, Thomas M. Bartol, Terrence J. Sejnowski, Gert Cauwenberghs
2021 Frontiers in Neuroscience  
and the dimensionality of network dynamics across the brain covering a vast range of spatial and temporal scales.  ...  Progress in computational neuroscience toward understanding brain function is challenged both by the complexity of molecular-scale electrochemical interactions at the level of individual neurons and synapses  ...  , and the next timestep could be predicted solely using the current timestep.  ... 
doi:10.3389/fnins.2021.698635 pmid:34912188 pmcid:PMC8667025 fatcat:2fxtmjsyhjai7ofqrxzpxgpgg4
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