19,812 research outputs found
Simulation-based model selection for dynamical systems in systems and population biology
Computer simulations have become an important tool across the biomedical
sciences and beyond. For many important problems several different models or
hypotheses exist and choosing which one best describes reality or observed data
is not straightforward. We therefore require suitable statistical tools that
allow us to choose rationally between different mechanistic models of e.g.
signal transduction or gene regulation networks. This is particularly
challenging in systems biology where only a small number of molecular species
can be assayed at any given time and all measurements are subject to
measurement uncertainty. Here we develop such a model selection framework based
on approximate Bayesian computation and employing sequential Monte Carlo
sampling. We show that our approach can be applied across a wide range of
biological scenarios, and we illustrate its use on real data describing
influenza dynamics and the JAK-STAT signalling pathway. Bayesian model
selection strikes a balance between the complexity of the simulation models and
their ability to describe observed data. The present approach enables us to
employ the whole formal apparatus to any system that can be (efficiently)
simulated, even when exact likelihoods are computationally intractable.Comment: This article is in press in Bioinformatics, 2009. Advance Access is
available on Bioinformatics webpag
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium
Ground state properties of condensed Helium are calculated using the Path
Integral Ground State (PIGS) method. A fourth-order approximation is used as
short (imaginary) time propagator. We compare our results with those obtained
with other Quantum Monte Carlo techniques and different propagators. For this
particular application, we find that the fourth-order propagator performs
comparably to the pair product approximation, and is far superior to the
primitive approximation. Results obtained for the equation of state of
condensed Helium show that PIGS compares favorably to other QMC methods
traditionally utilized for this type of calculation
Stochastic simulation algorithm for the quantum linear Boltzmann equation
We develop a Monte Carlo wave function algorithm for the quantum linear
Boltzmann equation, a Markovian master equation describing the quantum motion
of a test particle interacting with the particles of an environmental
background gas. The algorithm leads to a numerically efficient stochastic
simulation procedure for the most general form of this integro-differential
equation, which involves a five-dimensional integral over microscopically
defined scattering amplitudes that account for the gas interactions in a
non-perturbative fashion. The simulation technique is used to assess various
limiting forms of the quantum linear Boltzmann equation, such as the limits of
pure collisional decoherence and quantum Brownian motion, the Born
approximation and the classical limit. Moreover, we extend the method to allow
for the simulation of the dissipative and decohering dynamics of superpositions
of spatially localized wave packets, which enables the study of many physically
relevant quantum phenomena, occurring e.g. in the interferometry of massive
particles.Comment: 21 pages, 9 figures; v2: corresponds to published versio
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