			Home About us Contact

Random Perturbation (random + perturbation)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007
Chunyan Ji
Abstract This paper discusses a randomized logistic equation (1) with initial value x(0)=x0>0, where B(t) is a standard one-dimension Brownian motion, and ,,(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Darwinian fitness, evolutionary entropy and directionality theory

BIOESSAYS, Issue 11 2005
Klaus Dietz
Two recent articles1,2 provide computational and empirical validation of the following analytical fact: the outcome of competition between an invading genotype and that of a resident population is determined by the rate at which the population returns to its original size after a random perturbation. This phenomenon can be quantitatively described in terms of the demographic parameter termed "evolutionary entropy", a measure of the variability in the age at which individuals produce offspring and die. The two articles also validate certain predictions of directionality theory, an evolutionary model that integrates demography and ecology with population genetics. In particular, directionality theory predicts that in populations that spend the greater part of their life cycle in the stationary growth phase, evolution will result in an increase in entropy. These species will be described by a late age of sexual maturity, small progeny sets and a broad reproductive time-span. In populations that undergo large fluctuations in size, however, the evolutionary outcome will be different. When the average size is large, evolution will result in a decrease in entropy,these populations will be described by early age of sexual maturity, large numbers of offspring and narrow reproductive span but when the average size is small, the evolutionary outcome will be random and non-directional. BioEssays 27:1097,1101, 2005. © 2005 Wiley Periodicals, Inc. [source]

RANDOM APPROXIMATED GREEDY SEARCH FOR FEATURE SUBSET SELECTION

ASIAN JOURNAL OF CONTROL, Issue 3 2004
Feng Gao
ABSTRACT We propose a sequential approach called Random Approximated Greedy Search (RAGS) in this paper and apply it to the feature subset selection for regression. It is an extension of GRASP/Super-heuristics approach to complex stochastic combinatorial optimization problems, where performance estimation is very expensive. The key points of RAGS are from the methodology of Ordinal Optimization (OO). We soften the goal and define success as good enough but not necessarily optimal. In this way, we use more crude estimation model, and treat the performance estimation error as randomness, so it can provide random perturbations mandated by the GRASP/Super-heuristics approach directly and save a lot of computation effort at the same time. By the multiple independent running of RAGS, we show that we obtain better solutions than standard greedy search under the comparable computation effort. [source]

The geometric minimum action method: A least action principle on the space of curves

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2008
Matthias Heymann
Freidlin-Wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool. Specifically, a numerical algorithm is proposed to compute the quasi-potential in the theory, which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous: the equilibrium distribution of the system, the pathways of transition between metastable states and their rate, etc., can all be expressed in terms of the quasi-potential. We propose an algorithm to compute these quantities called the geometric minimum action method (gMAM), which is a blend of the original minimum action method (MAM) and the string method. It is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi-potential. The theoretical background of the gMAM in the context of large deviations theory is discussed in detail, as well as the algorithmic aspects of the method. The gMAM is then illustrated on several examples: a finite-dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation, an infinite-dimensional analogue of this system modeled by a stochastic partial differential equation, and an example of a bistable genetic switch modeled by a Markov jump process. © 2007 Wiley Periodicals, Inc. [source]