53,792 research outputs found
Optimal first-passage time in gene regulatory networks
The inherent probabilistic nature of the biochemical reactions, and low copy
number of species can lead to stochasticity in gene expression across identical
cells. As a result, after induction of gene expression, the time at which a
specific protein count is reached is stochastic as well. Therefore events
taking place at a critical protein level will see stochasticity in their
timing. First-passage time (FPT), the time at which a stochastic process hits a
critical threshold, provides a framework to model such events. Here, we
investigate stochasticity in FPT. Particularly, we consider events for which
controlling stochasticity is advantageous. As a possible regulatory mechanism,
we also investigate effect of auto-regulation, where the transcription rate of
gene depends on protein count, on stochasticity of FPT. Specifically, we
investigate for an optimal auto-regulation which minimizes stochasticity in
FPT, given fixed mean FPT and threshold.
For this purpose, we model the gene expression at a single cell level. We
find analytic formulas for statistical moments of the FPT in terms of model
parameters. Moreover, we examine the gene expression model with
auto-regulation. Interestingly, our results show that the stochasticity in FPT,
for a fixed mean, is minimized when the transcription rate is independent of
protein count. Further, we discuss the results in context of lysis time of an
\textit{E. coli} cell infected by a phage virus. An optimal lysis
time provides evolutionary advantage to the phage, suggesting a
possible regulation to minimize its stochasticity. Our results indicate that
there is no auto-regulation of the protein responsible for lysis. Moreover,
congruent to experimental evidences, our analysis predicts that the expression
of the lysis protein should have a small burst size.Comment: 8 pages, 3 figures, Submitted to Conference on Decision and Control
201
Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales
If one wants to represent the galaxy number density at some point in terms of
only the mass density at the same point, there appears the stochasticity in
such a relation, which is referred to as ``stochastic bias''. The stochasticity
is there because the galaxy number density is not merely a local function of a
mass density field, but it is a nonlocal functional, instead. Thus, the
phenomenological stochasticity of the bias should be accounted for by nonlocal
features of galaxy formation processes. Based on mathematical arguments, we
show that there are simple relations between biasing and nonlocality on linear
scales of density fluctuations, and that the stochasticity in Fourier space
does not exist on linear scales under a certain condition, even if the galaxy
formation itself is a complex nonlinear and nonlocal precess. The stochasticity
in real space, however, arise from the scale-dependence of bias parameter, .
As examples, we derive the stochastic bias parameters of simple nonlocal models
of galaxy formation, i.e., the local Lagrangian bias models, the cooperative
model, and the peak model. We show that the stochasticity in real space is also
weak, except on the scales of nonlocality of the galaxy formation. Therefore,
we do not have to worry too much about the stochasticity on linear scales,
especially in Fourier space, even if we do not know the details of galaxy
formation process.Comment: 24 pages, latex, including 2 figures, ApJ, in pres
Halo stochasticity in global clustering analysis
In the present work we study the statistics of haloes, which in the halo
model determines the distribution of galaxies. Haloes are known to be biased
tracer of dark matter, and at large scales it is usually assumed there is no
intrinsic stochasticity between the two fields. Following the work of Seljak &
Warren (2004), we explore how correct this assumption is and, moving a step
further, we try to qualify the nature of stochasticity. We use Principal
Component Analysis applied to the outputs of a cosmological N-body simulation
to: (1) explore the behaviour of stochasticity in the correlation between
haloes of different masses; (2) explore the behaviour of stochasticity in the
correlation between haloes and dark matter. We show results obtained using a
catalogue with 2.1 million haloes, from a PMFAST simulation with box size of
1000h^{-1}Mpc. In the relation between different populations of haloes we find
that stochasticity is not-negligible even at large scales. In agreement with
the conclusions of Tegmark & Bromley (1999) who studied the correlations of
different galaxy populations, we found that the shot-noise subtracted
stochasticity is qualitatively different from `enhanced' shot noise and,
specifically, it is dominated by a single stochastic eigenvalue. We call this
the `minimally stochastic' scenario, as opposed to shot noise which is
`maximally stochastic'. In the correlation between haloes and dark matter, we
find that stochasticity is minimized, as expected, near the dark matter peak (k
~ 0.02 h Mpc^{-1} for a LambdaCDM cosmology) and, even at large scales, it is
of the order of 15 per cent above the shot noise. Moreover, we find that the
reconstruction of the dark matter distribution is improved when we use
eigenvectors as tracers of the bias. [Abridged]Comment: 9 pages, 12 figures. Submitted to MNRA
On stochasticity in nearly-elastic systems
Nearly-elastic model systems with one or two degrees of freedom are
considered: the system is undergoing a small loss of energy in each collision
with the "wall". We show that instabilities in this purely deterministic system
lead to stochasticity of its long-time behavior. Various ways to give a
rigorous meaning to the last statement are considered. All of them, if
applicable, lead to the same stochasticity which is described explicitly. So
that the stochasticity of the long-time behavior is an intrinsic property of
the deterministic systems.Comment: 35 pages, 12 figures, already online at Stochastics and Dynamic
Wave Propagation in Stochastic Spacetimes: Localization, Amplification and Particle Creation
Here we study novel effects associated with electromagnetic wave propagation
in a Robertson-Walker universe and the Schwarzschild spacetime with a small
amount of metric stochasticity. We find that localization of electromagnetic
waves occurs in a Robertson-Walker universe with time-independent metric
stochasticity, while time-dependent metric stochasticity induces exponential
instability in the particle production rate. For the Schwarzschild metric,
time-independent randomness can decrease the total luminosity of Hawking
radiation due to multiple scattering of waves outside the black hole and gives
rise to event horizon fluctuations and thus fluctuations in the Hawking
temperature.Comment: 26 pages, 1 Postscript figure, submitted to Phys. Rev. D on July 29,
199
Stochasticity and evolutionary stability
In stochastic dynamical systems, different concepts of stability can be
obtained in different limits. A particularly interesting example is
evolutionary game theory, which is traditionally based on infinite populations,
where strict Nash equilibria correspond to stable fixed points that are always
evolutionarily stable. However, in finite populations stochastic effects can
drive the system away from strict Nash equilibria, which gives rise to a new
concept for evolutionary stability. The conventional and the new stability
concepts may apparently contradict each other leading to conflicting
predictions in large yet finite populations. We show that the two concepts can
be derived from the frequency dependent Moran process in different limits. Our
results help to determine the appropriate stability concept in large finite
populations. The general validity of our findings is demonstrated showing that
the same results are valid employing vastly different co-evolutionary
processes
- …