530 research outputs found
Simply Generated Trees, B-series and Wigner Processes
We consider simply generated trees and study multiplicative functions on
rooted plane trees. We show that the associated generating functions satisfy
differential equations or difference equations. Our approach considers B-series
from Butcher's theory, the generating functions are seen as generalized
Runge-Kutta methodsComment: 19 pages, 1 figur
Stationary distributions and condensation in autocatalytic CRN
We investigate a broad family of non weakly reversible stochastically modeled
reaction networks (CRN), by looking at their steady-state distributions. Most
known results on stationary distributions assume weak reversibility and zero
deficiency. We first give explicitly product-form steady-state distributions
for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency.
Examples of interest in statistical mechanics (inclusion process), life
sciences and robotics (collective decision making in ant and robot swarms) are
provided. The product-form nature of the steady-state then enables the study of
condensation in particle systems that are generalizations of the inclusion
process.Comment: 25 pages. Some typos corrected, shortened some part
Long time behavior of the solutions to non-linear Kraichnan equations
We consider the solution of a nonlinear Kraichnan equation with a covariance kernel
and boundary condition . We study the long time behaviour of
as the time parameters go to infinity, according to the asymptotic
behaviour of . This question appears in various subjects since it is related
with the analysis of the asymptotic behaviour of the trace of non-commutative
processes satisfying a linear differential equation, but also naturally shows
up in the study of the so-called response function and aging properties of the
dynamics of some disordered spin systems.Comment: 32 page
Phenotypic diversity and population growth in fluctuating environment: a MBPRE approach
Organisms adapt to fluctuating environments by regulating their dynamics, and
by adjusting their phenotypes to environmental changes. We model population
growth using multitype branching processes in random environments, where the
offspring distribution of some organism having trait t\in\cT in environment
e\in\cE is given by some (fixed) distribution on \bbN.
Then, the phenotypes are attributed using a distribution (strategy)
on the trait space \cT. We look for the optimal strategy ,
t\in\cT, e\in\cE maximizing the net growth rate or Lyapounov exponent, and
characterize the set of optimal strategies. This is considered for various
models of interest in biology: hereditary versus non-hereditary strategies and
strategies involving or not involving a sensing mechanism. Our main results are
obtained in the setting of non-hereditary strategies: thanks to a reduction to
simple branching processes in random environment, we derive an exact expression
for the net growth rate and a characterisation of optimal strategies. We also
focus on typical genealogies, that is, we consider the problem of finding the
typical lineage of a randomly chosen organism.Comment: 21 page
Ultrasensitivity and sharp threshold theorems for multisite systems
We study the ultrasensitivity of multisite binding processes where ligand
molecules can bind to several binding sites, considering more particularly
recent models involving complex chemical reactions in phosphorylation systems
such as allosteric phosphorylation processes, or substrate-catalyst chain
reactions and nucleosome mediated cooperativity. New statistics based formulas
for the Hill coefficient and the effective Hill coefficient are provided and
necessary conditions for a system to be ultrasensitive are exhibited. We then
assume that the binding process is described by a density dependent birth and
death process. We provide precise large deviation results for the steady state
distribution of the process, and show that switch-like ultrasensitive responses
are strongly related to the multi-stability of the associated dynamical system.
Ultrasensitivity occurs if and only if the entropy of the dynamical system has
more than one global minimum for some critical ligand concentration. In this
case, the Hill coefficient is proportional to the number of binding sites, and
the systems is highly ultrasensitive. We also discuss the interpretation of an
extension of the effective Hill coefficient for which we
recommend the computation of a broad range of values of instead of just the
standard one corresponding to the 10% to 90% variation in the dose-response. It
is shown that this single choice can sometimes mislead the conclusion by not
detecting ultrasensitivity. This new approach allows a better understanding of
multisite ultrasensitive systems and provides new tools for the design of such
systems
Strand separation in negatively supercoiled DNA
Abstract.: We consider Benham's model for strand separation in negatively supercoiled circular DNA, and study denaturation as function of the linking difference density κ<0. We propose a statistical version of this model, based on bayesian segmentation methods of current use in bioinformatics; this leads to new algorithms with priors adapted to supercoiled DNA, taking into account the random nature of the free energies needed to denature base pair
- …