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At least 19 recordsLinked to original sources
PubMed2000

Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes

Stochastic fractal signals can be characterized by the Hurst coefficient H, which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate H are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integral transform. Numerical simulations confirm this relationship for ideal synthesized fractal signals. Their performance as estimators of H is compared based on a mean square error criterion and found to be similar. DFA measures are derived for physiological signals of heartbeat R-R intervals through the integral transform of a spectral density estimate. These agree with directly calculated DFA estimates, indicating that the relationship holds for signals with nonideal fractal properties. It is concluded that DFA and spectral measures provide equivalent characterizations of stochastic signals with long-term correlation.

Journal Article↗
PubMed2006

Chromatography as Lévy stochastic process.

The Stochastic Theory of Chromatography has been revised in light of some of the most relevant Lévy's findings in Theory of Probability, including the so-called Lévy's distance, the characteristic function and the theory of infinitesimally divisible distributions. These concepts represent the key to exploit and understand, at a molecular basis, phenomena typical of chromatographic separations under linear conditions, such as peak tailing and splitting. In particular, Lévy's distance has been used to quantify the degree of convergence of real peaks towards an ideal Gaussian shape; the characteristic function properties, introduced by Lévy to deal with the problem of the addition of independent random variables, have been employed to solve a wide variety of chromatographic models (including adsorption on heterogeneous surfaces) and to interpret mobile phase dispersion from a probabilistic point of view. Finally, Lévy's studies concerning infinitesimally divisible distributions have allowed to introduce in the stochastic description of chromatography, effects associated to dispersion in mobile phase. It has been demonstrated that, according to Lévy's canonical representation of stochastic processes, the basis of chromatography is a mobile phase Poisson Process. Represented as a Lévy's process, the microscopic-probabilistic model of chromatography permits the establishment of a connection between single-molecule properties and their statistical fluctuations and shapes of real chromatographic peaks allowing, at the same time, for the constitution of a link between different branches of physical sciences.

Chromatography↗
PubMed2006

Neuronal growth: a bistable stochastic process.

The fundamentally stochastic nature of neuronal growth has hardly been addressed in neuroscience. We report on the stochastic fluctuations of a neuronal growth cone's leading edge movement, the basic step in neuronal growth. Describing the edge movement as a stochastic bistable process leads to an isotropic noise parameter that is successfully used to test the model. An analysis of growth cone motility confirms the model, and predicts that linear changes of the bistable potential, as known from stochastic filtering, result in directed growth cone translocation.

Actins↗
PubMed1989

Absence of effect in stochastic processes: its influence on test validation and test use.

Negativity in stochastic processes presents problems in interpretation because it is never possible to attain an absolutely adequate assurance of safety with such processes. Thus, it is extremely difficult to have complete confidence in the utility of validation studies of new methods in comparison to those that are accepted to be well established, especially when these processes are stochastic in the statistical sense of this term. The regulatory scientist who must make decisions on the basis of available evidence, therefore, has to make a number of assumptions in dealing with negativity. It is important to review the validity and usefulness of these assumptions from time to time to ensure that they cannot be replaced by improved methodology in the light of new scientific knowledge.

Animals↗
PubMed1997

Stochastic processes in postural center-of-pressure profiles.

The stochastic processes of postural center-of-pressure profiles were examined in 3- and 5-year-old children, young adult students (mean 20 years), and an elderly age group (mean 67 years). Subjects stood still in an upright bipedal stance on a force platform under vision and nonvision conditions. The time evolutionary properties of the center-of-pressure dynamic were examined using basic stochastic process models. The amount of motion of the center of pressure decreased with increments of age from 3 to 5 years to young adult but increased again in the elderly age group. The availability of vision decreased the amount of motion of the center of pressure in all groups except the 3-year-old group, where there was less motion of the center of pressure with no vision. The stochastic properties of the center-of-pressure dynamic were assessed using both a two-process, random-walk model of Collins and De Luca and an Ornstein-Uhlenbeck model that is linear and has displacement governed only by a single stiffness term in the random walk. The two-process open- and closed-loop model accounted for about 96% and the Ornstein-Uhlenbeck model 92% of the variance of the diffusion term. Diffusion parameters in both models showed that the data were correlated and that they varied with age in a fashion consistent with developmental accounts of the changing regulation of the degrees of freedom in action. The findings suggest that it is premature to consider the trajectory of the center-of-pressure as a two-process, open- and closed-loop random-walk model given that: (a) the linear Ornstein-Uhlenbeck dynamic equation with only two parameters accommodates almost as much of the variance of the random walk; and (b) the linkage of a discontinuity in the diffusion process with the transition of open- to closed-loop processes is poorly founded. It appears that the nature of the stochastic properties of the random walk of the center-of-pressure trajectory in quiet, upright standing remains to be elucidated.

Adult↗
PubMed1999

Artificial neural networks as approximators of stochastic processes.

Artificial Neural Networks (ANNs) must be able to learn by experience from environment. This property can be considered as being closely related to the approximating capabilities of the networks. Unfortunately at present only the ability of ANNs in approximating deterministic input-output mappings has been exploited. In this article it has been shown that some classes of neural networks, named Stochastic Neural Networks, which are capable of using approximating stochastic processes are defined. As stochastic processes may also be viewed as random functions, they include deterministic (non-random) functions as a particular case. Thus the class of Stochastic Neural Networks can be considered as a generalisation of the usually defined neural networks. From an application point of view such a class of networks is more adherent to real world in which neural networks must work in an environment which is essentially stochastic. The theory presented in the article has been carried out starting from the so-called "canonical representation" for non-stationary stochastic processes. Finally, an application example showing in detail the validity of the proposed approach has been reported.

Journal Article↗
PubMed1981

Probability of neuronal spike initiation as a curve-crossing problem for Gaussian stochastic processes.

Probability of neuronal spike initiation was considered within the framework of a simple stochastic model. The time of spike occurrence was defined as the first time of crossing of a stochastic process and a determined time function. This problem has been investigated in the case of a stationary Gaussian stochastic process and a linear time function. An integral equation obtained for the probability density function of the first time crossing was numerically solved by means of computer calculations. The model was applied to the analysis of temporal pattern of spike activity evoked in the cat spinal motoneurones by depolarizing current injected through the recording microelectrode.

Animals↗
PubMed1986

A stochastic process determines the time at which cell division begins in Escherichia coli.

The theoretical distributions of cell masses in exponential cultures of bacteria were derived for both total cells and cells having formed a constriction in preparation for division. The parameters used for this derivation include the mass doubling time, tau, the T-period, and 3 statistical parameters (h, sigma 1, sigma 2) which describe the variability of the cell cycle. The theoretical distributions were compared with observed distributions from E. coli B/rA growing in glucose minimal medium (45 min doubling time) to determine whether a stochastic process in the division pathway affects the time of initiation of constriction or the duration of the constriction process. The results indicate that the stochastic process determines the onset rather than the completion of constriction and that the timing of this process is coupled (6% variability, = sigma 1) to a given cell mass. The values obtained for the duration of the T-period, T = 9.3 min, and for a half-life parameter associated with the stochastic process, h = 4.3 min, agree with previously reported data.

Cell Division↗
PubMed2000

Analysis of time series from stochastic processes

Analysis of time series from stochastic processes governed by a Langevin equation is discussed. Several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the Fokker-Planck equation. The coefficients are estimated directly from a time series. The applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting.

Journal Article↗
PubMed1991

Transient behavior of a stochastic process for screening progressive diseases.

This paper extends a mathematical model developed by the authors for describing the stochastic process underlying the etiology of non-contagious progressive diseases. For a population with no prior history of scheduled screening, the number of undetected and detected diseased individuals in the population under an established screening policy is used to calculate the expected total screening cost at any given time during the transient period of the associated stochastic process. A graphical representation of our model shows the status of different subgroups of a particular age group at any time T, and provides a clear summary of the expected number of individuals whose disease remains undetected.

Mass Screening↗
PubMed1985

Mortality and aging in a heterogeneous population: a stochastic process model with observed and unobserved variables.

Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of "failure" processes in heterogeneous populations are discussed.

Aging↗
PubMed1982

Model analysis of the frequency of neuronal action potentials in the case of Gaussian input stochastic processes.

The authors describe the effects of changes in excitatory and inhibitory synapse weight on the number of spikes generated in the presence of constant absolute refractory phase and threshold level values. Input stochastic processes with Gaussian distributions were presumed. The problem was resolved in a hybrid computer model of stochastic neuronal activity. The results are given in the form of "e-curves", "i-curves" and gradient fields. It was shown that, in a set of paired values of the two weights, zones could be found in which the number of generated spikes depended mainly on just one of them. It was also shown that, in a given neurone with a fixed synapse morphology, the effect of the individual synapses on the number of generated spikes altered with changes in input stochastic processes to the synapses.

Action Potentials↗
PubMed2001

Experimental evidence of tunneling as a stochastic process.

A model for tunneling based on stochastic processes proves to be capable of interpreting the results of two experiments at the microwave scale. The first of these consisted of measuring the penetration time in a subcutoff waveguide; the second one, in measuring the shift of a beam in a frustrated total reflection. Said shift which is a measurement of the traversal time of the barrier. In both cases, a peak in the real-time component was evidenced, as predicted by the theoretical model.

Journal Article↗
PubMed2004

Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions.

We consider stochastic processes where randomly chosen particles with positive quantities x,y (>0) interact and exchange the quantities asymmetrically by the rule x(') =c [(1-a) x+by] , y(') =d [ax+(1-b) y] (x> or =y) , where (0< or =) a,b (< or =1) and c,d (>0) are interaction parameters. Noninteger power-law tails in the probability distribution function of scaled quantities are analyzed in a similar way as in inelastic Maxwell models. A transcendental equation to determine the growth rate gamma of the processes and the exponent s of the tails is derived formally from moment equations in Fourier space. In the case c=d or a+b=1 (a not = 0, 1) , the first-order moment equation admits a closed form solution and gamma and s are calculated analytically from the transcendental equation. It becomes evident that at c=d , exchange rate b of small quantities is irrelevant to power-law tails. In the case c not = d and a+b not = 1 , a closed form solution of the first-order moment equation cannot be obtained because of asymmetry of interactions. However, the moment equation for a singular term formally forms a closed solution and possibility for the presence of power-law tails is shown. Continuity of the exponent s with respect to parameters a,b,c,d is discussed. Then numerical simulations are carried out and compared with the theory. Good agreement is achieved for both gamma and s.

Journal Article↗
PubMed1984

[Carcinogenesis, embryogenesis and aging from the view point of the assessment of cell proliferation and differentiation as a stochastic process].

An approach to cell proliferation and differentiation as to stochastic processes is described. The rate constants of cell population transitions to subsequent epigenetic states are interpreted as indicating instability of initial states. The duration of embryogenesis, the rate of loss of the ability to proliferation (a result of final differentiation) by the initial cell cultures, the error accumulation rate in the genetic cell apparatus (including both the genome itself and its interactions with the chromatin components) which determines the rate of ageing and the rate of the tumour incidence rise in particular, are all connected via the level of instability of the epigenetic states of cells. It is supposed that the differentiation mechanism of multicellular organisms originated from mechanisms of intragenome recombinational rearrangements of unicellular ones. A hypothetic scheme for basic processes occurring during cell differentiation is proposed accounting for the dual character of oncogenes necessary for differentiation but able to block it under definite conditions.

Aging↗
PubMed2003

Discrete stochastic process underlying perceptual rivalry.

In perceptual rivalry such as ambiguous figure perception and binocular rivalry, the conscious percept spontaneously alternates between two stable interpretations of an unchanging stimulus. It is well known that the time intervals of the perceptual alternation follow a gamma distribution (GD), but its implication for the alternation mechanism has not been clarified. We examined quantitatively GDs fitted to alternation intervals, and found that the shape-determining parameter alpha of the GDs took natural numbers. Because a GD determined by a natural number alpha is mathematically obtained from a discrete stochastic process (Poisson process), our result indicates that such a stochastic process underlies perceptual rivalry and that the alpha-time accumulation of the discrete events causes a perceptual alternation.

Adult↗
PubMed2002

Stochastic processes in the causation of rheumatic disease.

OBJECTIVE: Rheumatic disorders arise in certain individuals depending on the interaction of genetic and environmental factors, the contribution for each varying with the specific rheumatic disorder. However, a third variable, i.e., random or stochastic processes, may be important, but this has been poorly studied. We examined 3 rheumatic disorders to determine whether a simple stochastic process might be consistent with the incidence data. METHODS: A questionnaire and clinical survey of patients with ankylosing spondylitis, rheumatoid arthritis, and systemic sclerosis was performed to determine age at onset of first symptom. Population data were obtained from the Australian Bureau of Statistics. Computer modeling of the equation dN/dt = kP0 tr-1exp(-ktr/r) was performed, where dN/dt is the age-specific incidence rate, P0 is the proportion of population at risk, t is the age at onset, k is a constant, and r is the number of random events that must occur before the disease manifests. RESULTS: Analysis of the age-specific incidence for each of these 3 rheumatic disorders was consistent with the stochastic model, where r varied from 4 to 9. CONCLUSION: An examination of the age-specific incidence suggests that only a small number of random events need to occur in a predisposed population to allow the emergence of the rheumatic disorder. These random events might be environmental (e.g., infections or exposure to toxins) or due to acquired genetic changes (e.g., somatic mutations involving pivotal immune or growth/repair genes).

Adolescent↗