ARMA - filtering of evoked potentials.
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Electronic Data Processing↗
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Results for “Stochastic Processes”
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Additive-multiplicative stochastic models of financial mean-reverting processes.
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through an Itô-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.
Journal Article↗
A stochastic model for the development of an AIDS epidemic in a heterosexual population.
A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.
Acquired Immunodeficiency Syndrome↗
The irreducible uncertainty of the demography-environment interaction in ecology.
The interpretation of ecological data has been greatly improved by bridging the gap between ecological and statistical models. The major challenge is to separate competing hypotheses concerning demography, or other ecological relationships, and environmental variability (noise). In this paper we demonstrate that this may be an arduous, if not impossible, task. It is the lack of adequate ecological theory, rather than statistical sophistication, which leads to this problem. A reconstruction of underlying ecological processes can only be done if we are certain of either the demographic or the noise model, which is something that can only be achieved by an improved theory of stochastic ecological processes. Ignoring the fact that this is a real problem may mislead ecologists and result in erroneous conclusions about the relative importance of endogenous and exogenous factors in natural ecosystems. The lack of correct model identification may also have far-reaching consequences for population management and conservation.
Animals↗
[Study of the protective effects of phenothiazine derivatives on a stochastic model of brain compression edema-swelling].
Search for pathogenically substantiated drugs to treat and prevent brain edema-swelling (BES) is a topical problem of modern biology and medicine. It is possible to solve this challenging biomedical problem by using a method for devising a stochastic model of the tested process. The developed stochastic model of BES identifies the nerve tissue structural components involving in the anti-edematous mechanism of action of phenothiazine derivatives under the conditions of 7-day brain compression. Analyzing the results of this model application revealed the major governing structures in the morphofunctional complexes under study. The investigations made on the stochastic model yielded a quantitative assessment of the impact of morphofunctional structural relationships under the influence of disturbing factors.
Animals↗
Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach.
A stochastic model for single neuron's activity is constructed as the continuous limit of a birth-and-death process in the presence of a reversal hyperpolarization potential. The resulting process is a one dimensional diffusion with linear drift and infinitesimal variance, somewhat different from that proposed by Lánský and Lánská in a previous paper. A detailed study is performed for both the discrete process and its continuous approximation. In particular, the neuronal firing time problem is discussed and the moments of the firing time are explicitly obtained. Use of a new computation method is then made to obtain the firing p.d.f. The behaviour of mean, variance and coefficient of variation of the firing time and of its p.d.f. is analysed to pinpoint the role played by the parameters of the model. A mathematical description of the return process for this neuronal diffusion model is finally provided to obtain closed form expressions for the asymptotic moments and steady state p.d.f. of the neuron's membrane potential.
Membrane Potentials↗
Comments on lack of interference in the four strand model of crossing over.
Assuming a four strand model and no chromatid interference, lack of chiasma interference is known to be equivalent to the assumption that the formation of chiasmata follows a Poisson process. We prove the lack of chiasma interference is also equivalent to the assumption that a random gamete shows recombination on any given interval of a chromosome independently of recombination on all disjoint intervals. Both assumptions are sufficient, but not necessary, for Haldane's formula relating recombination to map distance to be true, as we demonstrate by specific counterexamples. These issues are discussed in the context of the theory of stochastic point processes.
Chromatids↗
A stochastic study on the concentration process of radioactive substances to aquatic organisms.
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Animals↗
From deterministic dynamics to probabilistic descriptions.
THE PRESENT WORK IS DEVOTED TO THE FOLLOWING QUESTION: What is the relationship between the deterministic laws of dynamics and probabilistic description of physical processes? It is generally accepted that probabilistic processes can arise from deterministic dynamics only through a process of "coarse graining" or "contraction of description" that inevitably involves a loss of information. In this work we present an alternative point of view toward the relationship between deterministic dynamics and probabilistic descriptions. Speaking in general terms, we demonstrate the possibility of obtaining (stochastic) Markov processes from deterministic dynamics simply through a "change of representation" that involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. The fundamental implications of this finding for statistical mechanics and other areas of physics are discussed. From a mathematical point of view, the theory we present is a theory of invertible, positivity-preserving, and necessarily nonunitary similarity transformations that convert the unitary groups associated with deterministic dynamics to contraction semigroups associated with stochastic Markov processes. We explicitly construct such similarity transformations for the so-called Bernoulli systems. This construction illustrates also the construction of the so-called Lyapounov variables and the operator of "internal time," which play an important role in our approach to the problem of irreversibility. The theory we present can also be viewed as a theory of entropy-increasing evolutions and their relationship to deterministic dynamics.
Journal Article↗
An empirical Bayes approach to the estimation of the incidence curve of HIV infection.
A new approach is proposed for estimating the incidence curve of HIV infection and obtaining short term prediction of AIDS incidence. It is based on the method of back calculation which utilizes the fact that AIDS incidence is generated from HIV infection incidence by convolution with the incubation period distribution, but avoids the difficulties associated with approximating the infection incidence curve by a class of step functions. Instead, the infection incidence is modelled as a simple stochastic epidemic process which ensures smoothness of the estimate. We first derive the distribution of AIDS incidence knowing infection incidence. The best linear estimators of infection incidence as well as future AIDS incidence are given; a smoothed past AIDS incidence is also obtained. The parameters of the stochastic infection process can be estimated by maximum likelihood using a normal approximation to the marginal distribution of the AIDS incidence. This approach is applied to AIDS incidence data in the United States up to mid 1987. We find that the epidemic started in mid 1976, peaked at the end of 1983 and dropped afterwards.
Acquired Immunodeficiency Syndrome↗
Ageing of hamster embryo fibroblasts as the result of both differentiation and stochastic mechanisms.
Fibroblasts from hamster embryos were serially cultivated in vitro and their evolution followed from a morphological, physiological and biochemical point of view. After an exponential growth for about 20 passages, cells entered the ageing phase which ended up after 29-34 passages. From our observations, it seems that the arrest of growth results from two different phenomena: first, the typically fibroblastic cells may undergo a stochastic ageing process; second, some of these cells evolve into a terminal differentiation process, characterized by a different non-fibroblastic phenotype.
Aging↗
Stochastic modelling of landfill processes incorporating waste heterogeneity and data uncertainty.
A landfill is a very complex heterogeneous environment and as such it presents many modelling challenges. Attempts to develop models that reproduce these complexities generally involve the use of large numbers of spatially dependent parameters that cannot be properly characterised in the face of data uncertainty. An alternative method is presented, which couples a simplified microbial degradation model with a stochastic hydrological and contaminant transport model. This provides a framework for incorporating the complex effects of spatial heterogeneity within the landfill in a simplified manner, along with other key variables. A methodology for handling data uncertainty is also integrated into the model structure. Illustrative examples of the model's output are presented to demonstrate effects of data uncertainty on leachate composition and gas volume prediction.
Environmental Pollutants↗
Population bottlenecks in quasispecies dynamics.
The characteristics of natural populations result from different stochastic and deterministic processes that include reproduction with error, selection, and genetic drift. In particular, population fluctuations constitute a stochastic process that may play a very relevant role in shaping the structure of populations. For example, it is expected that small asexual populations will accumulate mutations at a higher rate than larger ones. As a consequence, in any population the fixation of mutations is accelerated when environmental conditions cause population bottlenecks. Bottlenecks have been relatively frequent in the history of life and it is generally accepted that they are highly relevant for speciation. Although population bottlenecks can occur in any species, their effects are more noticeable in organisms that form large and heterogeneous populations, such as RNA viral quasispecies. Bottlenecks can also positively select and isolate particles that still keep the ability to infect cells from a disorganized population created by crossing the error threshold.
Base Sequence↗
The stochastic diffusion models of nerve membrane depolarization and interspike interval generation.
The first step to make the theory of stochastic diffusion processes that arise in connection with single neuron description more understandable is reviewing the deterministic leaky-integrator model. After this step the general principles of simple stochastic models are summarized which clearly reveal that two different sources of noise, intrinsic and external, can be identified. Many possible strategies of neuronal coding exist and one of these, the rate coding, for which the stochastic modeling is relevant, is pursued further. The rate coding is reflected, in experimental as well as theoretical studies, by an input-output curve and its properties are reviewed for the most common stochastic diffusion models. The results for the simplest stochastic diffusion model, the Wiener process, are presented and from them strong limitations of this model can be understood. The most common diffusion model is the Ornstein-Uhlenbeck process, which is one substantial step closer to reality since the spontaneous changes of the membrane potential are included in the model. Both these models are characterized by an additive noise. Taking into account the state dependency of the changes caused by neuronal inputs, we derive models where the noise has a multiplicative effect on the membrane depolarization. Two of these models are compared with the Wiener and Ornstein-Uhlenbeck models. How to identify the parameters of the models, which is an unavoidable task for the models verification, is investigated. The time-variable input is taken into account in the last part of the paper. An intuitive approach is stressed throughout the review.
Action Potentials↗
Limits to forecasting precision for outbreaks of directly transmitted diseases.
BACKGROUND: Early warning systems for outbreaks of infectious diseases are an important application of the ecological theory of epidemics. A key variable predicted by early warning systems is the final outbreak size. However, for directly transmitted diseases, the stochastic contact process by which outbreaks develop entails fundamental limits to the precision with which the final size can be predicted. METHODS AND FINDINGS: I studied how the expected final outbreak size and the coefficient of variation in the final size of outbreaks scale with control effectiveness and the rate of infectious contacts in the simple stochastic epidemic. As examples, I parameterized this model with data on observed ranges for the basic reproductive ratio (R0) of nine directly transmitted diseases. I also present results from a new model, the simple stochastic epidemic with delayed-onset intervention, in which an initially supercritical outbreak (R0 > 1) is brought under control after a delay. CONCLUSION: The coefficient of variation of final outbreak size in the subcritical case (R0 < 1) will be greater than one for any outbreak in which the removal rate is less than approximately 2.41 times the rate of infectious contacts, implying that for many transmissible diseases precise forecasts of the final outbreak size will be unattainable. In the delayed-onset model, the coefficient of variation (CV) was generally large (CV > 1) and increased with the delay between the start of the epidemic and intervention, and with the average outbreak size. These results suggest that early warning systems for infectious diseases should not focus exclusively on predicting outbreak size but should consider other characteristics of outbreaks such as the timing of disease emergence.
Communicable Disease Control↗
Genetic and evolutionary fitness.
The advantages and disadvantages of evolutionary fitness (probability that a single mutant line will not become extinct) and genetic fitness (mean fecundity) are compared. For deterministic processes the two are equivalent, but for stochastic branching processes they may be totally unrelated except that an absolute genetic fitness of unity or less implies an evolutionary fitness of zero. To know the variance as well as the mean family size does not in general uniquely determine the evolutionary fitness. Except where genetic fitness is close to unity, the impact of selection is shown to be rapid for the binomial, Poisson, negative binomial, and truncated negative binomial distributions. Evolutionary fitness, though somewhat cumbersome, has greater relevance to evolution, genetic counseling, and voluntary population control; but genetic fitness which is much easier to handle is the more appropriate measure where a large number of mutants is involved. Some empirical data on the transmission of various types of characters from parent to child are analyzed to allow comparison of genetic fitness, Crow's index, and a Malthusian parameter, with evolutionary fitness. There is a fair, but far from perfect, agreement among them. Multiple correlation of evolutionary fitness with mean and variance of family size taken jointly suggests a much more satisfactory approximation. It thus appears that, at the least, the population geneticist cannot afford to ignore the variance (which is not adequately represented in Crow's index). These relationships, based on two sets of data only may be accidental and should be invoked with caution. It seems more than likely that other aspects of the distribution of family size (eg, even higher moments) may contain relevant information in certain cases.
Biological Evolution↗
Simple jumping process with memory: transport equation and diffusion.
We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.
Journal Article↗
Amplification of electromagnetic signals by ion channels.
Cells may respond to the exposure of low-frequency electromagnetic fields with changes in cell division, ion influx, chemical reaction rates, etc. The chain of events leading to such responses is difficult to study, mainly because of extremely small energies associated with low-frequency fields, usually much smaller than the thermal noise level. However, the presence of stochastic systems (for instance, ion channels) provides a basis for signal amplification, and could therefore, despite the low signal-to-noise ratio of the primary response, lead to the transmission of weak signals along the signaling pathways of cells. We have explored this possibility for an ion channel model, and we present a theory, based on the formalism of stochastically driven processes, that relates the time averages of the ion channel currents to the amplitude and frequency of the applied signal. It is concluded from this theory that the signal-to-noise ratio increases with the number of channels, the magnitude of the rate constants, and the frequency response of the intracellular sensing system (for instance, a calcium oscillator). The amplification properties of the stochastic system are further deduced from numerical simulations carried out on the model, which consists of multiple identical two-state channels, and the behavior for different parameters is examined. Numerical estimates of the parameters show that under optimum conditions, even very weak low-frequency electromagnetic signals (<100 Hz and down to 100 microT) may be detected in a cellular system with a large number of ion channels.
Biophysical Phenomena↗