57,585 research outputs found
Metastable states and quasicycles in a stochastic Wilson-Cowan\ud model of neuronal population dynamics
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N -> infinity, where N determines the size of each population, the dynamics is described by deterministic Wilson–Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady–state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise–induced transitions between the resulting metastable states using a Wentzel–Kramers–Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory/inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles)
Quasi-steady state reduction of molecular motor-based models of directed intermittent search
We present a quasi–steady state reduction of a linear reaction–hyperbolic master equation describing the directed intermittent search for a hidden target by a motor–driven particle moving on a one–dimensional filament track. The particle is injected at one end of the track and randomly switches between stationary search phases and mobile, non-search phases that are biased in the anterograde direction. There is a finite possibility that the particle fails to find the target due to an absorbing boundary at the other end of the track. Such a scenario is exemplified by the motor–driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker–Planck (FP) equation, which has an additional inhomogeneous decay term that takes into account absorption by the target. The FP equation is used to compute the probability of finding the hidden target (hitting probability) and the corresponding conditional mean first passage time (MFPT) in terms of the effective drift velocity V , diffusivity D and target absorption rate λ of the random search. The quasi–steady state reduction determines V, D and λ in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3–state model and show that our quasi–steady state reduction yields results that are in excellent agreement with Monte Carlo simulations of the full system under physiologically reasonable conditions. We then consider a more complex multiple motor model of bidirectional transport, in which opposing motors compete in a “tug-of-war,” and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets
A primer on noise-induced transitions in applied dynamical systems
Noise plays a fundamental role in a wide variety of physical and biological
dynamical systems. It can arise from an external forcing or due to random
dynamics internal to the system. It is well established that even weak noise
can result in large behavioral changes such as transitions between or escapes
from quasi-stable states. These transitions can correspond to critical events
such as failures or extinctions that make them essential phenomena to
understand and quantify, despite the fact that their occurrence is rare. This
article will provide an overview of the theory underlying the dynamics of rare
events for stochastic models along with some example applications
Universality of efficiency at maximum power
We investigate the efficiency of power generation by thermo-chemical engines.
For strong coupling between the particle and heat flows and in the presence of
a left-right symmetry in the system, we demonstrate that the efficiency at
maximum power displays universality up to quadratic order in the deviation from
equilibrium. A maser model is presented to illustrate our argument.Comment: 4 pages, 2 figure
Density functional calculations of nanoscale conductance
Density functional calculations for the electronic conductance of single
molecules are now common. We examine the methodology from a rigorous point of
view, discussing where it can be expected to work, and where it should fail.
When molecules are weakly coupled to leads, local and gradient-corrected
approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias
regime, XC corrections to the current are missed by the standard methodology.
For finite bias, a new methodology for performing calculations can be
rigorously derived using an extension of time-dependent current density
functional theory from the Schroedinger equation to a Master equation.Comment: topical review, 28 pages, updated version with some revision
Non-equilibrium steady states of ideal bosonic and fermionic quantum gases
We investigate non-equilibrium steady states of driven-dissipative ideal
quantum gases of both bosons and fermions. We focus on systems of sharp
particle number that are driven out of equilibrium either by the coupling to
several heat baths of different temperature or by time-periodic driving in
combination with the coupling to a heat bath. Within the framework of
(Floquet-)Born-Markov theory, several analytical and numerical methods are
described in detail. This includes a mean-field theory in terms of occupation
numbers, an augmented mean-field theory taking into account also non-trivial
two-particle correlations, and quantum-jump-type Monte-Carlo simulations. For
the case of the ideal Fermi gas, these methods are applied to simple lattice
models and the possibility of achieving exotic states via bath engineering is
pointed out. The largest part of this work is devoted to bosonic quantum gases
and the phenomenon of Bose selection, a non-equilibrium generalization of Bose
condensation, where multiple single-particle states are selected to acquire a
large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among
others, we provide a theory for transitions where the set of selected states
changes, describe an efficient algorithm for finding the set of selected
states, investigate beyond-mean-field effects, and identify the dominant
mechanisms for heat transport in the Bose selected state
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Steady-state fluctuations of a genetic feedback loop:an exact solution
Genetic feedback loops in cells break detailed balance and involve
bimolecular reactions; hence exact solutions revealing the nature of the
stochastic fluctuations in these loops are lacking. We here consider the master
equation for a gene regulatory feedback loop: a gene produces protein which
then binds to the promoter of the same gene and regulates its expression. The
protein degrades in its free and bound forms. This network breaks detailed
balance and involves a single bimolecular reaction step. We provide an exact
solution of the steady-state master equation for arbitrary values of the
parameters, and present simplified solutions for a number of special cases. The
full parametric dependence of the analytical non-equilibrium steady-state
probability distribution is verified by direct numerical solution of the master
equations. For the case where the degradation rate of bound and free protein is
the same, our solution is at variance with a previous claim of an exact
solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent
studies). We show explicitly that this is due to an unphysical formulation of
the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of
Chemical Physics (2012
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