6,583 research outputs found
Analytical results for a Fokker-Planck equation in the small noise limit
We present analytical results for the lowest cumulants of a stochastic
process described by a Fokker-Planck equation with nonlinear drift. We show
that, in the limit of small fluctuations, the mean, the variance and the
covariance of the process can be expressed in compact form with the help of the
Lambert W function. As an application, we discuss the interplay of noise and
nonlinearity far from equilibrium.Comment: 5 pages, 4 figure
The Stochastically Subordinated Log Normal Process Applied To Financial Time Series And Option Pricing
The method of stochastic subordination, or random time indexing, has been recently applied to Wiener process price processes to model financial returns. Previous emphasis in stochastic subordination models has involved explicitly identifying the subordinating process with an observable quantity such as number of trades. In contrast, the approach taken here does not depend on the specific identification of the subordinated time variable, but rather assumes a class of time models and estimates parameters from data. In addition, a simple Markov process is proposed for the characteristic parameter of the subordinating distribution to explain the significant autocorrelation of the squared returns. It is shown in particular, that the proposed model, while containing only a few more parameters than the commonly used Wiener process models, fits selected fmancial time series particularly well, characterising the autocorrelation structure and heavy tails, as well as preserving the desirable self-similarity structure present in popular chaos-theoretic models, and the existence of risk-neutral measures necessary for objective derivative valuation
Symmetry Relations for Trajectories of a Brownian Motor
A Brownian Motor is a nanoscale or molecular device that combines the effects
of thermal noise, spatial or temporal asymmetry, and directionless input energy
to drive directed motion. Because of the input energy, Brownian motors function
away from thermodynamic equilibrium and concepts such as linear response
theory, fluctuation dissipation relations, and detailed balance do not apply.
The {\em generalized} fluctuation-dissipation relation, however, states that
even under strongly thermodynamically non-equilibrium conditions the ratio of
the probability of a transition to the probability of the time-reverse of that
transition is the exponent of the change in the internal energy of the system
due to the transition. Here, we derive an extension of the generalized
fluctuation dissipation theorem for a Brownian motor for the ratio between the
probability for the motor to take a forward step and the probability to take a
backward step
Enhancement of the stability of genetic switches by overlapping upstream regulatory domains
We study genetic switches formed from pairs of mutually repressing operons.
The switch stability is characterised by a well defined lifetime which grows
sub-exponentially with the number of copies of the most-expressed transcription
factor, in the regime accessible by our numerical simulations. The stability
can be markedly enhanced by a suitable choice of overlap between the upstream
regulatory domains. Our results suggest that robustness against biochemical
noise can provide a selection pressure that drives operons, that regulate each
other, together in the course of evolution.Comment: 4 pages, 5 figures, RevTeX
A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics
We present a novel multiscale simulation approach for modeling stochasticity
in chemical reaction networks. The approach seamlessly integrates
exact-stochastic and "leaping" methodologies into a single "partitioned
leaping" algorithmic framework. The technique correctly accounts for stochastic
noise at significantly reduced computational cost, requires the definition of
only three model-independent parameters and is particularly well-suited for
simulating systems containing widely disparate species populations. We present
the theoretical foundations of partitioned leaping, discuss various options for
its practical implementation and demonstrate the utility of the method via
illustrative examples.Comment: v4: 12 pages, 5 figures, final accepted version. Error found and
fixed in Appendi
Stability Properties of Nonhyperbolic Chaotic Attractors under Noise
We study local and global stability of nonhyperbolic chaotic attractors
contaminated by noise. The former is given by the maximum distance of a noisy
trajectory from the noisefree attractor, while the latter is provided by the
minimal escape energy necessary to leave the basin of attraction, calculated
with the Hamiltonian theory of large fluctuations. We establish the important
and counterintuitive result that both concepts may be opposed to each other.
Even when one attractor is globally more stable than another one, it can be
locally less stable. Our results are exemplified with the Holmes map, for two
different sets of parameter, and with a juxtaposition of the Holmes and the
Ikeda maps. Finally, the experimental relevance of these findings is pointed
out.Comment: Phys.Rev. Lett., to be publishe
Robust Trapped-Ion Quantum Logic Gates by Continuous Dynamical Decoupling
We introduce a novel scheme that combines phonon-mediated quantum logic gates
in trapped ions with the benefits of continuous dynamical decoupling. We
demonstrate theoretically that a strong driving of the qubit decouples it from
external magnetic-field noise, enhancing the fidelity of two-qubit quantum
gates. Moreover, the scheme does not require ground-state cooling, and is
inherently robust to undesired ac-Stark shifts. The underlying mechanism can be
extended to a variety of other systems where a strong driving protects the
quantum coherence of the qubits without compromising the two-qubit couplings.Comment: Slightly longer than the published versio
Sampling rare switching events in biochemical networks
Bistable biochemical switches are ubiquitous in gene regulatory networks and
signal transduction pathways. Their switching dynamics, however, are difficult
to study directly in experiments or conventional computer simulations, because
switching events are rapid, yet infrequent. We present a simulation technique
that makes it possible to predict the rate and mechanism of flipping of
biochemical switches. The method uses a series of interfaces in phase space
between the two stable steady states of the switch to generate transition
trajectories in a ratchet-like manner. We demonstrate its use by calculating
the spontaneous flipping rate of a symmetric model of a genetic switch
consisting of two mutually repressing genes. The rate constant can be obtained
orders of magnitude more efficiently than using brute-force simulations. For
this model switch, we show that the switching mechanism, and consequently the
switching rate, depends crucially on whether the binding of one regulatory
protein to the DNA excludes the binding of the other one. Our technique could
also be used to study rare events and non-equilibrium processes in soft
condensed matter systems.Comment: 9 pages, 6 figures, last page contains supplementary informatio
Mechanical quality factor of a sapphire fiber at cryogenic temperatures
A mechanical quality factor of was obtained for the 199
Hz bending vibrational mode in a monocrystalline sapphire fiber at 6 K.
Consequently, we confirm that pendulum thermal noise of cryogenic mirrors used
for gravitational wave detectors can be reduced by the sapphire fiber
suspension.Comment: To be published to Physiscs Letters A. Number of pages: 10 Number of
figures: 5 Number of tables:
Simulation of the effects of increased truck size and weight. Final technical report
Notes: Report covers the period Sept 1977-Nov 1979. Contract amount $135,560Federal Highway Administration, Washington, D.C.http://deepblue.lib.umich.edu/bitstream/2027.42/499/2/43514.0001.001.pd
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