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Results for “stochastic processes”

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At least 73 records · Page 4Linked to original sources
PubMed2005

Non-Markovian stochastic processes: colored noise.

We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.

Artifacts↗
PubMed2005

Brownian motion and diffusion: from stochastic processes to chaos and beyond.

One century after Einstein's work, Brownian motion still remains both a fundamental open issue and a continuous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian motion and more general diffusive behaviors. Then, we focus on the problems concerning the determination of the microscopic nature of diffusion by means of data analysis. Finally, we discuss the general conditions required for the onset of large scale diffusive motion.

Biophysics↗
PubMed2002

The distribution of species range size: a stochastic process.

The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date.

Animals↗
PubMed1994

Quantum dynamics as a stochastic process.

The quantum Liouville equation is solved in the Wigner representation using generalized Monte Carlo techniques. For small increments of time, the solution is represented as a sequential classical evolution in phase space followed by a quantum "jump" distribution in momentum space, with the latter simulated via a stochastic method. Extending the work initiated by John and Remler [Ann Phys. (N.Y.) 180, 152 (1987)] the technique is developed and validated for higher dimensions. Also, an alternative algorithm is developed and applied to study motion of a quantum system in an anharmonic quartic potential well, with significantly improved results.

Algorithms↗
PubMedDate not supplied

[Protein folding with molecular chaperones:stochastic process under control].

Protein folding in a living cell occurs with the participation of specialized proteins, molecular shaperons. The functional role and molecular mechanism of action of shaperons are discussed. It is shown that shaperons can be considered as proteins that, upon interaction with the folding peptide chain, transform the spontaneous folding to a process controlled and regulated by cellular factors. Models describing these controlled phenomena are discussed.

Animals↗
PubMed1998

Phase- and density-dependent population dynamics in Norwegian lemmings: interaction between deterministic and stochastic processes.

We analysed two 26-year long (1970-1995) time-series on annual population growth rates of Norwegian lemmings (Lemmus lemmus) from Finse, south Norway, using a threshold autoregressive (TAR) approach. We demonstrate that the population dynamics is both phase- and density-dependent. The phase-dependence accounts for the observed nonlinearity. We used the deduced stochastic model structure as a basis for evaluating the dynamic properties of this system. The dynamics is characterized either by limit cycles or chaos (the latter with a strong semi-periodic component). Stochasticity is seen to play an important role in the determination of the periodicity. The ecological implications of these statistical and mathematical results are discussed.

Animals↗
PubMed1998

Stochastic processes strongly influence HIV-1 evolution during suboptimal protease-inhibitor therapy.

It has long been assumed that HIV-1 evolution is best described by deterministic evolutionary models because of the large population size. Recently, however, it was suggested that the effective population size (Ne) may be rather small, thereby allowing chance to influence evolution, a situation best described by a stochastic evolutionary model. To gain experimental evidence supporting one of the evolutionary models, we investigated whether the development of resistance to the protease inhibitor ritonavir affected the evolution of the env gene. Sequential serum samples from five patients treated with ritonavir were used for analysis of the protease gene and the V3 domain of the env gene. Multiple reverse transcription-PCR products were cloned, sequenced, and used to construct phylogenetic trees and to calculate the genetic variation and Ne. Genotypic resistance to ritonavir developed in all five patients, but each patient displayed a unique combination of mutations, indicating a stochastic element in the development of ritonavir resistance. Furthermore, development of resistance induced clear bottleneck effects in the env gene. The mean intrasample genetic variation, which ranged from 1.2% to 5.7% before treatment, decreased significantly (P < 0.025) during treatment. In agreement with these findings, Ne was estimated to be very small (500-15,000) compared with the total HIV-1 RNA copy number. This study combines three independent observations, strong population bottlenecking, small Ne, and selection of different combinations of protease-resistance mutations, all of which indicate that HIV-1 evolution is best described by a stochastic evolutionary model.

Acquired Immunodeficiency Syndrome↗