204 research outputs found
Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration
Analytical solutions for time-inhomogeneous linear birth-death processes with
immigration are derived. While time-inhomogeneous linear birth-death processes
without immigration have been studied by using a generating function approach,
the processes with immigration are here analyzed by Lie algebraic discussions.
As a result, a restriction for time-inhomogeneity of the birth-death process is
understood from the viewpoint of the finiteness of the dimensionality of the
Lie algebra.Comment: 12 page
Noncyclic geometric phase in counting statistics and its role as an excess contribution
We propose an application of fiber bundles to counting statistics. The
framework of the fiber bundles gives a splitting of a cumulant generating
function for current in a stochastic process, i.e., contributions from the
dynamical phase and the geometric phase. We will show that the introduced
noncyclic geometric phase is related to a kind of excess contributions, which
have been investigated a lot in nonequilibrium physics. Using a specific
nonequilibrium model, the characteristics of the noncyclic geometric phase are
discussed; especially, we reveal differences between a geometric contribution
for the entropy production and the `excess entropy production' which has been
used to discuss the second law of steady state thermodynamics.Comment: 15 pages, 2 figure
Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series data
A scheme is developed for estimating state-dependent drift and diffusion
coefficients in a stochastic differential equation from time-series data. The
scheme does not require to specify parametric forms for the drift and diffusion
coefficients in advance. In order to perform the nonparametric estimation, a
maximum likelihood method is combined with a concept based on a kernel density
estimation. In order to deal with discrete observation or sparsity of the
time-series data, a local linearization method is employed, which enables a
fast estimation.Comment: 10 pages, 4 figure
Karlin-McGregor-like formula in a simple time-inhomogeneous birth-death process
A novel approach is employed and developed to derive transition probabilities
for a simple time-inhomogeneous birth-death process. Algebraic probability
theory and Lie algebraic treatments make it easy to treat the
time-inhomogeneous cases. As a result, an expression based on the Charlier
polynomials is obtained, which can be considered as an extension of a famous
Karlin-KcGregor representation for a time-homogeneous birth-death process.Comment: 9 page
Counting statistics for genetic switches based on effective interaction approximation
Applicability of counting statistics for a system with an infinite number of
states is investigated. The counting statistics has been studied a lot for a
system with a finite number of states. While it is possible to use the scheme
in order to count specific transitions in a system with an infinite number of
states in principle, we have non-closed equations in general. A simple genetic
switch can be described by a master equation with an infinite number of states,
and we use the counting statistics in order to count the number of transitions
from inactive to active states in the gene. To avoid to have the non-closed
equations, an effective interaction approximation is employed. As a result, it
is shown that the switching problem can be treated as a simple two-state model
approximately, which immediately indicates that the switching obeys non-Poisson
statistics.Comment: 6 pages, 2 figure
- …