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At least 757 records · Page 42Linked to original sources
PubMed1991

Synaptic noise and the cross-correlation between motoneuron discharges and stimuli.

Theoretical analysis of motoneuron models predicts that the cross-correlogram between motoneuron discharges and stimuli should reflect the derivative of the post-synaptic potential (PSP) in the absence of synaptic noise. The cross-correlogram peaks become wider if the amplitude of the noise is significant. To deal with this case, the linear combination of the PSP and its first derivative has been proposed as an approximation. The synaptic noise was regarded as a Gaussian stochastic process (its diffusion approximation), and the estimation of the cross-correlation function for this case is presented. The results were found to be in agreement with reported experimental data. A comparison was made with the linear combination approximation and with the reported computer simulation.

Animals↗
PubMed2000

Modeling contact networks and infection transmission in geographic and social space using GERMS.

BACKGROUND: Stochastic models of discrete individuals and deterministic models of continuous populations may give different answers to questions about infectious diseases. GOAL: Discrete individual model formulations are sought that extend deterministic models of infection transmission systems so that both model forms contribute cooperatively to model-based decision making. STUDY DESIGN: GERMS models are defined as stochastic processes in continuous time with parameters analogous to those in deterministic models. A GERMS model simulator was developed that insured that the rate of events depended only on the current state of model. RESULTS: The confidence intervals of long-term averages of infection level in simulated GERMS models were shown to contain the deterministic model means. CONCLUSION: GERMS models provide a convenient framework for testing the sensitivity of model-based decisions to a variety of unrealistic assumptions that are characteristic of differential equation models. GERMS especially facilitates making more realistic assumptions about contact patterns in geographic and social space.

Humans↗
PubMedDate not supplied

Statistical correlation between transient pressure drop and cavitation at closure of a mechanical heart valve.

Cavitation on a mechanical heart valve (MHV) is attributable to transient regional pressure drop at the instant of valve closure. As a cavitation bubble collapses, it emits shock waves, which have the characteristics of high frequency oscillations (HFO) on a pressure time trace. The potential for such HFO bursts to cause material damage on an MHV can be measured by the cavitation impulse I, which is defined as the area under the trace of the HFO bursts. In the present study, experiments were conducted on a bileaflet MHV in a durability tester, operated at pulse rates from 300-1,000 bpm. In each case, the transient pressure near an occluder was monitored for 60,000 beats via a transducer. The peak pressure drop Pm and the corresponding cavitation impulse I obtained for the 60,000 beat sequence are found to resemble sample records of two stationary stochastic processes, each of which follows a log normal distribution. Their first order probability density functions are estimated from the records. The correlation is investigated between I and Pm associated with each beat, which is found to be of statistical significance.

Biomedical Engineering↗
PubMed2003

The phenomenology of niche evolution via quantitative traits in a 'black-hole' sink.

Previous studies of adaptive evolution in sink habitats (in which isolated populations of a species cannot persist deterministically) have highlighted the importance of demographic constraints in slowing such evolution, and of immigration in facilitating adaptation. These studies have relied upon either single-locus models or deterministic quantitative genetic formulations. We use individual-based simulations to examine adaptive evolution in a 'black-hole' sink environment where fitness is governed by a polygenic character. The simulations track both the number of individuals and their multi-locus genotypes, and incorporate, in a natural manner, both demographic and genetic stochastic processes. In agreement with previous studies, our findings reveal the central parts played by demographic constraints and immigration in adaptation within a sink (adaptation is more difficult in environments with low absolute fitness, and higher immigration can accelerate adaptation). A novel finding is that there is a 'punctuational' pattern in adaptive evolution in sink environments. Populations typically stay maladapted for a long time, and then rapidly shift into a relatively adapted state, in which persistence no longer depends upon recurrent immigration.

Animals↗
PubMed2006

Physical conditions on the early Earth.

The formation of the Earth as a planet was a large stochastic process in which the rapid assembly of asteroidal-to-Mars-sized bodies was followed by a more extended period of growth through collisions of these objects, facilitated by the gravitational perturbations associated with Jupiter. The Earth's inventory of water and organic molecules may have come from diverse sources, not more than 10% roughly from comets, the rest from asteroidal precursors to chondritic bodies and possibly objects near Earth's orbit for which no representative class of meteorites exists today in laboratory collections. The final assembly of the Earth included a catastrophic impact with a Mars-sized body, ejecting mantle and crustal material to form the Moon, and also devolatilizing part of the Earth. A magma ocean and steam atmosphere (possibly with silica vapour) existed briefly in this period, but terrestrial surface waters were below the critical point within 100 million years after Earth's formation, and liquid water existed continuously on the surface within a few hundred million years. Organic material delivered by comets and asteroids would have survived, in part, this violent early period, but frequent impacts of remaining debris probably prevented the continuous habitability of the Earth for one to several hundred million years. Planetary analogues to or records of this early time when life began include Io (heat flow), Titan (organic chemistry) and Venus (remnant early granites).

Biological Evolution↗
PubMed1990

Virus and host cell-dependent variation in transcription of the mumps virus genome.

Evidence has been presented that generation of polycistronic readthrough RNAs in mumps virus-infected cells is not a simple stochastic process with strain-dependent variations in the generation of certain readthrough products, but that this process is affected by host as well as viral factors. RNAs extracted from infected Vero cells or chicken embryo fibroblast (CEF) cells have been analysed by Northern blotting with virus-specific probes for the nucleocapsid (N), phosphoprotein (P), matrix (M), fusion (F), small hydrophobic (SH) and haemagglutinin-neuraminidase (HN) genes. Vero cells infected with tissue culture cell-adapted virus strains generate monocistronic as well as polycistronic RNAs. Transcription analysis of Vero cells infected with an egg-adapted strain reveal the absence of monocistronic M and F transcripts, with a concomitant increase in readthrough transcripts involving these genes. When the same virus infects CEF cells monocistronic RNAs accumulate. The presence of viral proteins in the various virus/host cell combinations assessed by immunofluorescence with mumps virus-specific monoclonal antibodies for the N, P, M, F and HN proteins correlates well with the patterns of transcription.

Animals↗
PubMed2005

A genetic-algorithm approach to simulating human immunodeficiency virus evolution reveals the strong impact of multiply infected cells and recombination.

It has been previously shown that the majority of human immunodeficiency virus type 1 (HIV-1)-infected splenocytes can harbour multiple, divergent proviruses with a copy number ranging from one to eight. This implies that, besides point mutations, recombination should be considered as an important mechanism in the evolution of HIV within an infected host. To explore in detail the possible contributions of multi-infection and recombination to HIV evolution, the effects of major microscopic parameters of HIV replication (i.e. the point-mutation rate, the crossover number, the recombination rate and the provirus copy number) on macroscopic characteristics (such as the Hamming distance and the abundance of n-point mutants) have been simulated in silico. Simulations predict that multiple provirus copies per infected cell and recombination act in synergy to speed up the development of sequence diversity. Point mutations can be fixed for some time without fitness selection. The time needed for the selection of multiple mutations with increased fitness is highly variable, supporting the view that stochastic processes may contribute substantially to the kinetics of HIV variation in vivo.

Algorithms↗
PubMed1999

Monte Carlo simulation of an antiferromagnetic Ising model at two competing temperatures.

We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.

Journal Article↗
PubMed1999

Randomly amplified discrete Langevin systems.

A discrete stochastic process involving random amplification with additive noise is studied analytically. If the non-negative random amplification factor b is such that =1, where beta is any positive noninteger, then the steady state probability density function for the process will have power law tails of the form p(x) approximately 1/x(beta+1). This is a generalization of recent results for 0<beta<2 obtained by Takayasu, Sato, and Takayasu [Phys. Rev. Lett. 79, 966 (1997)]. It is shown that the power spectrum of the time series x becomes Lorentzian, even when 1<beta<2, i.e., in the case of divergent variance.

Journal Article↗
PubMed1999

Fractal behavior in quantum statistical physics.

The properties of an ideal gas of spinless particles are investigated by using the path integral formalism. It is shown that the quantum paths exhibit a fractal character which remains unchanged in the relativistic domain provided the creation of new particles is avoided, and the Brownian motion remains the stochastic process associated with the quantum paths. These results are obtained by using a special representation of the Klein-Gordon wave equation. On the quantum paths the relation between velocity and momentum is not the usual one. The mean square value of the velocity depends on the time needed to define the velocity and its value shows the interplay between pure quantum effects and thermodynamics. The fractal character is also investigated starting from wave equations by analyzing the evolution of a Gaussian wave packet via the Hausdorff dimension. Both approaches give the same fractal character in the same limit. It is shown that the time that appears in the path integral behaves like an ordinary time, and the key quantity is the time interval needed for the thermostat to give to the particles a thermal action equal to the quantum of action. Thus, the partition function calculated via the path integral formalism also describes the dynamics of the system for short time intervals. For low temperatures, it is shown that a time-energy uncertainty relation is verified at the end of the calculations. The energy involved in this relation has not a thermodynamic meaning but results from the fact that the particles do not follow the equations of motion along the paths. The results suggest that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route.

Journal Article↗
PubMed1999

Test your surrogate data before you test for nonlinearity.

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT, which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies, we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.

Journal Article↗
PubMed1999

Canonical phase-space approach to the noisy Burgers equation.

Presenting a general phase-space approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short-time regime we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica model and asymmetric exclusion model results.

Journal Article↗
PubMed1999

Competitive dynamics in a three-dimensional Ising model.

We consider a three-dimensional ferromagnetic Ising model on a cubic lattice in contact with a heat bath at temperature T. The states of the system evolve in time according to two stochastic processes: the one-spin-flip Glauber dynamics where the order parameter is not conserved, and the two-spin-exchange Kawasaki kinetics, which conserves the order parameter. The former process mimics an input of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model, and the corresponding critical exponents. Similarly to the observed for the related two-dimensional ferromagnetic Ising model, the phase diagram obtained exhibits the phenomenon of self-organization. Although the stationary states are mainly ferromagnetic at low temperatures, an antiferromagnetic phase appears for extremely high values of the flux of energy. Unlike the ferromagnetic case, the region of the phase diagram occupied by the antiferromagnetic phase is now larger. The determined critical exponents for this nonequilibrium model are in agreement with the well-known accepted values for the three-dimensional equilibrium Ising model.

Journal Article↗
PubMed1999

Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals.

We report a crossover from chaotic to self-organized critical dynamics in the Portevin-Le Chatelier effect in single crystals of Cu-10% Al in tension as a function of the applied strain rate. For low and intermediate strain rates, we provide an unambiguous support for the existence of chaotic stress drops by showing the existence of a finite correlation dimension and a stable positive Lyapunov exponent. A surrogate data analysis rules out the possibility that the time series is due to a power law stochastic process. As the strain rate is increased, the distributions of stress drops and the time intervals between the stress drops change from peaked to power law type with an exponent close to unity reminiscent of self-organized critical state. A scaling relation compatible with self-organized criticality relates the various exponents. The absence of a finite correlation dimension and a stable positive Lyapunov exponent at the highest strain rate also supports the evidence of crossover.

Journal Article↗
PubMed1999

Pair dispersion in synthetic fully developed turbulence.

The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a two-dimensional velocity field by means of a stochastic process with prescribed statistics and of a dynamical model (shell model) with fluctuating characteristic times. When the velocity field obeys Kolmogorov similarity, the Lagrangian statistics is self similar and agrees with Richardson's predictions [Proc. R. Soc. London Ser. A 110, 709 (1926)]. For intermittent velocity fields the scaling laws for the Lagrangian statistics are found to depend on the Eulerian intermittency in agreement with the multifractal description. As a consequence of the Kolmogorov law the Richardson law for the variance of pair separation is, however, not affected by intermittency corrections. Moreover, Lagrangian exponents do not depend on the particular Eulerian dynamics. A method of data analysis, based on fixed scale statistics rather than usual fixed time statistics, is shown to give much wider scaling range, and should be preferred for the analysis of experimental data.

Journal Article↗
PubMed1999

Universal equivalence of mean first-passage time and Kramers rate.

We prove that for an arbitrary time-homogeneous stochastic process, Kramers's flux-over-population rate is identical to the inverse of the associated mean first-passage time. In this way the mean first-passage time problem can be treated without making use of the adjoint equation in conjunction with cumbersome boundary conditions.

Journal Article↗
PubMed2000

Integrated approach to the assessment of long range correlation in time series data

To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach which requires the use of both methods in a consistent fashion. We provide the theoretical foundation of this approach and illustrate the main ideas using examples. The second objective relates to the observation of long range anticorrelation (Hurst exponent H < 1/2) in real world time series data. The very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur. Using examples, we discuss the possible factors that could contribute to the false claim of long range anticorrelations, and demonstrate the particular importance of the integrated approach in this case.

Journal Article↗
PubMed2000

Variety and volatility in financial markets

We study the price dynamics of stocks traded in a financial market by considering the statistical properties of both a single time series and an ensemble of stocks traded simultaneously. We use the n stocks traded on the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days following these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments fluctuate in time and are stochastic processes, themselves. We characterize the statistical properties of ensemble return distribution central moments by investigating their probability density functions and temporal correlation properties. In general, time-averaged and portfolio-averaged price returns have different statistical properties. We infer from these differences information about the relative strength of correlation between stocks and between different trading days. Last, we compare our empirical results with those predicted by the single-index model and we conclude that this simple model cannot explain the statistical properties of the second moment of the ensemble return distribution.

Journal Article↗