2,791 research outputs found
Long delay times in reaction rates increase intrinsic fluctuations
In spatially distributed cellular systems, it is often convenient to
represent complicated auxiliary pathways and spatial transport by time-delayed
reaction rates. Furthermore, many of the reactants appear in low numbers
necessitating a probabilistic description. The coupling of delayed rates with
stochastic dynamics leads to a probability conservation equation characterizing
a non-Markovian process. A systematic approximation is derived that
incorporates the effect of delayed rates on the characterization of molecular
noise, valid in the limit of long delay time. By way of a simple example, we
show that delayed reaction dynamics can only increase intrinsic fluctuations
about the steady-state. The method is general enough to accommodate nonlinear
transition rates, allowing characterization of fluctuations around a
delay-induced limit cycle.Comment: 8 pages, 3 figures, to be published in Physical Review
A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model
As well known, cumulant expansion is an alternative way to moment expansion
to fully characterize probability distributions provided all the moments exist.
If this is not the case, the so called escort mean values (or q-moments) have
been proposed to characterize probability densities with divergent moments [C.
Tsallis et al, J. Math. Phys 50, 043303 (2009)]. We introduce here a new
mathematical object, namely the q-cumulants, which, in analogy to the
cumulants, provide an alternative characterization to that of the q-moments for
the probability densities. We illustrate this new scheme on a recently proposed
family of scale-invariant discrete probabilistic models [A. Rodriguez et al, J.
Stat. Mech. (2008) P09006; R. Hanel et al, Eur. Phys. J. B 72, 263268 (2009)]
having q-Gaussians as limiting probability distributions
Sub-Poissonian atom number fluctuations by three-body loss in mesoscopic ensembles
We show that three-body loss of trapped atoms leads to sub-Poissonian atom
number fluctuations. We prepare hundreds of dense ultracold ensembles in an
array of magnetic microtraps which undergo rapid three-body decay. The
shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian,
for ensembles comprising 50--300 atoms. The measured relative variance or Fano
factor agrees very well with the prediction by an analytic
theory () and numerical calculations. These results will facilitate
studies of quantum information science with mesoscopic ensembles.Comment: 4 pages, 3 figure
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Non-Gaussian fluctuations in stochastic models with absorbing barriers
The dynamics of a one-dimensional stochastic model is studied in presence of
an absorbing boundary. The distribution of fluctuations is analytically
characterized within the generalized van Kampen expansion, accounting for
higher order corrections beyond the conventional Gaussian approximation. The
theory is shown to successfully capture the non Gaussian traits of the sought
distribution returning an excellent agreement with the simulations, for {\it
all times} and arbitrarily {\it close} to the absorbing barrier. At large
times, a compact analytical solution for the distribution of fluctuations is
also obtained, bridging the gap with previous investigations, within the van
Kampen picture and without resorting to alternative strategies, as elsewhere
hypothesized.Comment: 2 figures, submitted to Phys. Rev. Let
Framework for state and unknown input estimation of linear time-varying systems
The design of unknown-input decoupled observers and filters requires the
assumption of an existence condition in the literature. This paper addresses an
unknown input filtering problem where the existence condition is not satisfied.
Instead of designing a traditional unknown input decoupled filter, a
Double-Model Adaptive Estimation approach is extended to solve the unknown
input filtering problem. It is proved that the state and the unknown inputs can
be estimated and decoupled using the extended Double-Model Adaptive Estimation
approach without satisfying the existence condition. Numerical examples are
presented in which the performance of the proposed approach is compared to
methods from literature.Comment: This paper has been accepted by Automatica. It considers unknown
input estimation or fault and disturbances estimation. Existing approaches
considers the case where the effects of fault and disturbance can be
decoupled. In our paper, we consider the case where the effects of fault and
disturbance are coupled. This approach can be easily extended to nonlinear
system
Predicting rare events in chemical reactions: application to skin cell proliferation
In a well-stirred system undergoing chemical reactions, fluctuations in the
reaction propensities are approximately captured by the corresponding chemical
Langevin equation. Within this context, we discuss in this work how the Kramers
escape theory can be used to predict rare events in chemical reactions. As an
example, we apply our approach to a recently proposed model on cell
proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {\bf
80}, 030903 (2009)]. In particular, we provide an analytical explanation for
the form of the exponential exponent observed in the onset rate of uncontrolled
cell proliferation.Comment: New materials and references added. To appear in Physical Review
Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction
On the elementary level, electronic current consists of individual electron
tunnelling events that are separated by random time intervals. The waiting time
distribution is a probability to observe the electron transfer in the detector
electrode at time given that an electron was detected in the same
electrode at earlier time . We study waiting time distribution for quantum
transport in a vibrating molecular junction. By treating the electron-vibration
interaction exactly and molecule-electrode coupling perturbatively, we obtain
master equation and compute the distribution of waiting times for electron
transport. The details of waiting time distributions are used to elucidate
microscopic mechanism of electron transport and the role of electron-vibration
interactions. We find that as nonequilibrium develops in molecular junction,
the skewness and dispersion of the waiting time distribution experience
stepwise drops with the increase of the electric current. These steps are
associated with the excitations of vibrational states by tunnelling electrons.
In the strong electron-vibration coupling regime, the dispersion decrease
dominates over all other changes in the waiting time distribution as the
molecular junction departs far away from the equilibrium
Stochastic Turing Patterns on a Network
The process of stochastic Turing instability on a network is discussed for a
specific case study, the stochastic Brusselator model. The system is shown to
spontaneously differentiate into activator-rich and activator-poor nodes,
outside the region of parameters classically deputed to the deterministic
Turing instability. This phenomenon, as revealed by direct stochastic
simulations, is explained analytically, and eventually traced back to the
finite size corrections stemming from the inherent graininess of the
scrutinized medium.Comment: The movies referred to in the paper are provided upon request. Please
send your requests to Duccio Fanelli ([email protected]) or Francesca
Di Patti ([email protected]
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