5,770 research outputs found
Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations
Delay is an important and ubiquitous aspect of many biochemical processes.
For example, delay plays a central role in the dynamics of genetic regulatory
networks as it stems from the sequential assembly of first mRNA and then
protein. Genetic regulatory networks are therefore frequently modeled as
stochastic birth-death processes with delay. Here we examine the relationship
between delay birth-death processes and their appropriate approximating delay
chemical Langevin equations. We prove that the distance between these two
descriptions, as measured by expectations of functionals of the processes,
converges to zero with increasing system size. Further, we prove that the delay
birth-death process converges to the thermodynamic limit as system size tends
to infinity. Our results hold for both fixed delay and distributed delay.
Simulations demonstrate that the delay chemical Langevin approximation is
accurate even at moderate system sizes. It captures dynamical features such as
the spatial and temporal distributions of transition pathways in metastable
systems, oscillatory behavior in negative feedback circuits, and
cross-correlations between nodes in a network. Overall, these results provide a
foundation for using delay stochastic differential equations to approximate the
dynamics of birth-death processes with delay
N-Site approximations and CAM analysis for a stochastic sandpile
I develop n-site cluster approximations for a stochastic sandpile in one
dimension. A height restriction is imposed to limit the number of states: each
site can harbor at most two particles (height z_i \leq 2). (This yields a
considerable simplification over the unrestricted case, in which the number of
states per site is unbounded.) On the basis of results for n \leq 11 sites, I
estimate the critical particle density as zeta_c = 0.930(1), in good agreement
with simulations. A coherent anomaly analysis yields estimates for the order
parameter exponent [beta = 0.41(1)] and the relaxation time exponent (nu_||
\simeq 2.5).Comment: 12 pages, 7 figure
MCMC inference for Markov Jump Processes via the Linear Noise Approximation
Bayesian analysis for Markov jump processes is a non-trivial and challenging
problem. Although exact inference is theoretically possible, it is
computationally demanding thus its applicability is limited to a small class of
problems. In this paper we describe the application of Riemann manifold MCMC
methods using an approximation to the likelihood of the Markov jump process
which is valid when the system modelled is near its thermodynamic limit. The
proposed approach is both statistically and computationally efficient while the
convergence rate and mixing of the chains allows for fast MCMC inference. The
methodology is evaluated using numerical simulations on two problems from
chemical kinetics and one from systems biology
Glassy dynamics of kinetically constrained models
We review the use of kinetically constrained models (KCMs) for the study of
dynamics in glassy systems. The characteristic feature of KCMs is that they
have trivial, often non-interacting, equilibrium behaviour but interesting slow
dynamics due to restrictions on the allowed transitions between configurations.
The basic question which KCMs ask is therefore how much glassy physics can be
understood without an underlying ``equilibrium glass transition''. After a
brief review of glassy phenomenology, we describe the main model classes, which
include spin-facilitated (Ising) models, constrained lattice gases, models
inspired by cellular structures such as soap froths, models obtained via
mappings from interacting systems without constraints, and finally related
models such as urn, oscillator, tiling and needle models. We then describe the
broad range of techniques that have been applied to KCMs, including exact
solutions, adiabatic approximations, projection and mode-coupling techniques,
diagrammatic approaches and mappings to quantum systems or effective models.
Finally, we give a survey of the known results for the dynamics of KCMs both in
and out of equilibrium, including topics such as relaxation time divergences
and dynamical transitions, nonlinear relaxation, aging and effective
temperatures, cooperativity and dynamical heterogeneities, and finally
non-equilibrium stationary states generated by external driving. We conclude
with a discussion of open questions and possibilities for future work.Comment: 137 pages. Additions to section on dynamical heterogeneities (5.5,
new pages 110 and 112), otherwise minor corrections, additions and reference
updates. Version to be published in Advances in Physic
Birth, death and diffusion of interacting particles
Individual-based models of chemical or biological dynamics usually consider
individual entities diffusing in space and performing a birth-death type
dynamics. In this work we study the properties of a model in this class where
the birth dynamics is mediated by the local, within a given distance, density
of particles. Groups of individuals are formed in the system and in this paper
we concentrate on the study of the properties of these clusters (lifetime,
size, and collective diffusion). In particular, in the limit of the interaction
distance approaching the system size, a unique cluster appears which helps to
understand and characterize the clustering dynamics of the model.Comment: 15 pages, 6 figures, Iop style. To appear in Journal of Physics A:
Condensed matte
Macroscopic Quantum Phenomena from the Correlation, Coupling and Criticality Perspectives
In this sequel paper we explore how macroscopic quantum phenomena can be
measured or understood from the behavior of quantum correlations which exist in
a quantum system of many particles or components and how the interaction
strengths change with energy or scale, under ordinary situations and when the
system is near its critical point. We use the nPI (master) effective action
related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a
tool for systemizing the contributions of higher order correlation functions to
the dynamics of lower order correlation functions. Together with the large N
expansion discussed in our first paper(MQP1) we explore 1) the conditions
whereby an H-theorem is obtained, which can be viewed as a signifier of the
emergence of macroscopic behavior in the system. We give two more examples from
past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice
under the large (field components), 2PI and second order perturbative
expansions, illustrating how N and enter in these three aspects of
quantum correlations, coherence and coupling strength. 3) the behavior of an
interacting quantum system near its critical point, the effects of quantum and
thermal fluctuations and the conditions under which the system manifests
infrared dimensional reduction. We also discuss how the effective field theory
concept bears on macroscopic quantum phenomena: the running of the coupling
parameters with energy or scale imparts a dynamical-dependent and an
interaction-sensitive definition of `macroscopia'.Comment: For IARD 2010 meeting, Hualien, Taiwan. Proceedings to appear in J.
Physics (Conf. Series
Some Properties of the Speciation Model for Food-Web Structure - Mechanisms for Degree Distributions and Intervality
We present a mathematical analysis of the speciation model for food-web
structure, which had in previous work been shown to yield a good description of
empirical data of food-web topology. The degree distributions of the network
are derived. Properties of the speciation model are compared to those of other
models that successfully describe empirical data. It is argued that the
speciation model unifies the underlying ideas of previous theories. In
particular, it offers a mechanistic explanation for the success of the niche
model of Williams and Martinez and the frequent observation of intervality in
empirical food webs.Comment: 23 pages, 6 figures, minor rewrite
On the suppression of the diffusion and the quantum nature of a cavity mode. Optical bistability; forces and friction in driven cavities
A new analytical method is presented here, offering a physical view of driven
cavities where the external field cannot be neglected. We introduce a new
dimensionless complex parameter, intrinsically linked to the cooperativity
parameter of optical bistability, and analogous to the scaled Rabbi frequency
for driven systems where the field is classical. Classes of steady states are
iteratively constructed and expressions for the diffusion and friction
coefficients at lowest order also derived. They have in most cases the same
mathematical form as their free-space analog. The method offers a semiclassical
explanation for two recent experiments of one atom trapping in a high Q cavity
where the excited state is significantly saturated. Our results refute both
claims of atom trapping by a quantized cavity mode, single or not. Finally, it
is argued that the parameter newly constructed, as well as the groundwork of
this method, are at least companions of the cooperativity parameter and its
mother theory. In particular, we lay the stress on the apparently more
fundamental role of our structure parameter.Comment: 24 pages, 7 figures. Submitted to J. Phys. B: At. Mol. Opt. Phy
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