92 research outputs found
On the stability of stochastic jump kinetics
Motivated by the lack of a suitable constructive framework for analyzing
popular stochastic models of Systems Biology, we devise conditions for
existence and uniqueness of solutions to certain jump stochastic differential
equations (SDEs). Working from simple examples we find reasonable and explicit
assumptions on the driving coefficients for the SDE representation to make
sense. By `reasonable' we mean that stronger assumptions generally do not hold
for systems of practical interest. In particular, we argue against the
traditional use of global Lipschitz conditions and certain common growth
restrictions. By `explicit', finally, we like to highlight the fact that the
various constants occurring among our assumptions all can be determined once
the model is fixed.
We show how basic long time estimates and some limit results for
perturbations can be derived in this setting such that these can be contrasted
with the corresponding estimates from deterministic dynamics. The main
complication is that the natural path-wise representation is generated by a
counting measure with an intensity that depends nonlinearly on the state
Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues
In this paper we propose a new method for approximating the nonstationary
moment dynamics of one dimensional Markovian birth-death processes. By
expanding the transition probabilities of the Markov process in terms of
Poisson-Charlier polynomials, we are able to estimate any moment of the Markov
process even though the system of moment equations may not be closed. Using new
weighted discrete Sobolev spaces, we derive explicit error bounds of the
transition probabilities and new weak a priori estimates for approximating the
moments of the Markov processs using a truncated form of the expansion. Using
our error bounds and estimates, we are able to show that our approximations
converge to the true stochastic process as we add more terms to the expansion
and give explicit bounds on the truncation error. As a result, we are the first
paper in the queueing literature to provide error bounds and estimates on the
performance of a moment closure approximation. Lastly, we perform several
numerical experiments for some important models in the queueing theory
literature and show that our expansion techniques are accurate at estimating
the moment dynamics of these Markov process with only a few terms of the
expansion
Fast Matlab compatible sparse assembly on multicore computers
We develop and implement in this paper a fast sparse assembly algorithm, the
fundamental operation which creates a compressed matrix from raw index data.
Since it is often a quite demanding and sometimes critical operation, it is of
interest to design a highly efficient implementation. We show how to do this,
and moreover, we show how our implementation can be parallelized to utilize the
power of modern multicore computers. Our freely available code, fully Matlab
compatible, achieves about a factor of 5 times in speedup on a typical 6-core
machine and 10 times on a dual-socket 16 core machine compared to the built-in
serial implementation
SimInf: An R package for Data-driven Stochastic Disease Spread Simulations
We present the R package SimInf which provides an efficient and very flexible
framework to conduct data-driven epidemiological modeling in realistic large
scale disease spread simulations. The framework integrates infection dynamics
in subpopulations as continuous-time Markov chains using the Gillespie
stochastic simulation algorithm and incorporates available data such as births,
deaths and movements as scheduled events at predefined time-points. Using C
code for the numerical solvers and OpenMP to divide work over multiple
processors ensures high performance when simulating a sample outcome. One of
our design goal was to make SimInf extendable and enable usage of the numerical
solvers from other R extension packages in order to facilitate complex
epidemiological research. In this paper, we provide a technical description of
the framework and demonstrate its use on some basic examples. We also discuss
how to specify and extend the framework with user-defined models.Comment: The manual has been updated to the latest version of SimInf (v6.0.0).
41 pages, 16 figure
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