5,485 research outputs found
Synchronisation of stochastic oscillators in biochemical systems
A formalism is developed which describes the extent to which stochastic
oscillations in biochemical models are synchronised. It is based on the
calculation of the complex coherence function within the linear noise
approximation. The method is illustrated on a simple example and then applied
to study the synchronisation of chemical concentrations in social amoeba. The
degree to which variation of rate constants in different cells and the volume
of the cells affects synchronisation of the oscillations is explored, and the
phase lag calculated. In all cases the analytical results are shown to be in
good agreement with those obtained through numerical simulations
Phase lag in epidemics on a network of cities
We study the synchronisation and phase-lag of fluctuations in the number of
infected individuals in a network of cities between which individuals commute.
The frequency and amplitude of these oscillations is known to be very well
captured by the van Kampen system-size expansion, and we use this approximation
to compute the complex coherence function that describes their correlation. We
find that, if the infection rate differs from city to city and the coupling
between them is not too strong, these oscillations are synchronised with a well
defined phase lag between cities. The analytic description of the effect is
shown to be in good agreement with the results of stochastic simulations for
realistic population sizes.Comment: 10 pages, 6 figure
Statistical Mechanics of Recurrent Neural Networks I. Statics
A lecture notes style review of the equilibrium statistical mechanics of
recurrent neural networks with discrete and continuous neurons (e.g. Ising,
coupled-oscillators). To be published in the Handbook of Biological Physics
(North-Holland). Accompanied by a similar review (part II) dealing with the
dynamics.Comment: 49 pages, LaTe
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Overcoming controllability problems with fewest channels between testers
When testing a system that has multiple physically distributed
ports/interfaces it is normal to place a tester at each port. Each
tester observes only the events at its port and it is known that
this can lead to additional controllability problems. While such
controllability problems can be overcome by the exchange of
external coordination messages between the testers, this requires
the deployment of an external network and may thus increase the
costs of testing. The problem studied in this paper is finding a
minimum number of coordination channels to overcome
controllability problems in distributed testing. Three instances
of this problem are considered. The first problem is to find a
minimum number of channels between testers in order to overcome
the controllability problems in a given test sequence to be
applied in testing. The second problem is finding a minimal set of
channels that allow us to overcome controllability problems in any
test sequence that may be selected from the specification of the
system under test. The last problem is to find a test sequence
that achieves a particular test objective and in doing so allows
fewest channels to be used
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
HYPE with stochastic events
The process algebra HYPE was recently proposed as a fine-grained modelling
approach for capturing the behaviour of hybrid systems. In the original
proposal, each flow or influence affecting a variable is modelled separately
and the overall behaviour of the system then emerges as the composition of
these flows. The discrete behaviour of the system is captured by instantaneous
actions which might be urgent, taking effect as soon as some activation
condition is satisfied, or non-urgent meaning that they can tolerate some
(unknown) delay before happening. In this paper we refine the notion of
non-urgent actions, to make such actions governed by a probability
distribution. As a consequence of this we now give HYPE a semantics in terms of
Transition-Driven Stochastic Hybrid Automata, which are a subset of a general
class of stochastic processes termed Piecewise Deterministic Markov Processes.Comment: In Proceedings QAPL 2011, arXiv:1107.074
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