PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Stochastic Processes”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4Linked to original sources
PubMed1992

On inherited fertility in biological systems: a model of correlated fluctuations in the stochastic branching process.

A new evolutionary model with hereditary modes considered as correlated fluctuations of fertility has been proposed. It has been demonstrated that the model allows the global statistical properties of the system to be evaluated, e.g. the ensemble average and the probability of extinction. The results obtained show the increase of instability of a population with the enhancement of inheritance efficiency. The existence of at least an exponential stratification in the population has also been shown. Possible applications of the present model are discussed.

Animals↗
PubMed1982

A hybrid computer model of stochastic activity of the neurone.

The authors describe a hybrid computer neurone model intended for the investigation of stochastic transformations effected by neurones in correlation to some of their physiological parameters. The model is designed so as to give the best possible characterization of the internal dynamics of a neurone with minimum limiting conditions. It allows the generation of suitable input stochastic processes or operates with input processes obtained experimentally in the living neurone and it carries out basic statistical tests of the output stochastic process.

Computers, Hybrid↗
PubMed1989

Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates.

Antigenic variation of African trypanosomes results from the periodic activation of a single new variant cell surface glycoprotein (VSG) gene out of a repertoire of about a 1000 VSG genes. In spite of the apparently random genetic basis of the process of antigenic variation, the relapsing parasitemias are characterized by an as yet unexplained order of appearance of major VSG variants. Here we mathematically test hypotheses concerning the blood-based parasitemia. In our model the antigenic switches occur at random at the DNA level. A variable proportion of the switches has a short intermediate phase in which two different VSGs simultaneously occur on the cell surface. We show that, in a theoretical population of 230 single expressor variants in an immunocompetent or in an immunodeficient host, it is not possible to explain the ordered appearance of variants by affecting the growth coefficients of single expressors or double expressors or by affecting the antigen switch probabilities. Rather, a realistic parasitemia can be obtained if the majority of switches has a double expressor switch-intermediate phase and if the double expressors have a differential susceptibility to the immune control. This study is significant in providing a theoretical basis for the ordered appearance of variants and in explaining previously unresolved discrepancies between the rate of appearance of new variants in culture and in vivo. In addition, testable predictions as to the development of the infections, switch rate of variants, fraction of double expressors, and parasite mortality coefficients are generated.

Animals↗
PubMed1985

Statistics and quantum bumps in arthropod photoreceptors.

Discrete waves of depolarizing membrane potential in arthropod photoreceptors, called quantum bumps, appear to result from single-photon absorptions of the visual pigment. Statistical analysis of bump records suggest a model for bump occurrence in dark-adapted receptors at low levels of illumination. This model assumes that a photon that isomerizes a visual pigment molecule can trigger a stochastic process that can produce no more than one bump under normal conditions, and that the stochastic processes triggered by different isomerized visual pigment molecules are independent of each other.

Animals↗
PubMed1986

Evidence that the process of murine melanoma metastasis is sequential and selective and contains stochastic elements.

Malignant neoplasms are heterogeneous for many different biological characteristics, including invasion and metastasis. The pathogenesis of metastasis involves a series of sequential steps which must be completed by metastatic cells. In the present study we examined the metastatic behavior of three highly metastatic and three nonmetastatic subpopulations isolated from the K-1735 melanoma syngeneic to the C3H/HeN mouse. Cells were labeled with [125I]iodo-2'-deoxyuridine, and their initial organ distribution, fate, and production of experimental metastases were determined. Highly metastatic cells survived in lung parenchyma to produce metastases, whereas nonmetastatic cells did not. However, even with the highly metastatic cells only 2% of the original inoculum was responsible for the final production of metastases. The results support the concept that the fate of tumor cells released into the bloodstream is determined by sequential and selective events and introduces a third regulatory factor. Cells endowed with metastatic properties have a higher probability of forming metastases than cells not so endowed, but this probability is not 100%. Hence, metastasis should be considered as a sequential, selective, and stochastic process.

Animals↗
PubMed1992

Graphical representation of survival curves associated with a binary non-reversible time dependent covariate.

The use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non-reversible (for example, heart transplant, initial response to chemotherapy). We can represent this type of intervening event as a three-state stochastic process with a starting state (S), an intervening state (I), and an absorbing state (D), which usually represents death. In this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate. The first method compares survival from baseline for the two possible paths through the stochastic process; the second method compares overall survival to survival with state I removed from the process; and, the third method compares survival for those already in state I at a landmark time x to those in state S at time x who will never enter state I. We develop discrete hazard estimates for the survival curves associated with the three methods. Two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods. Extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested.

Data Interpretation, Statistical↗
PubMed1987

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation.

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.

Genetics, Population↗
PubMed1967

Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains.

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected-if dependence is attributed to the trains-the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.

Action Potentials↗
PubMed1991

Stochastic differential equations, their interpretation and application.

The work is recommended to readers with some, maybe heuristic, imagine about stochastic processes that want to meet the notion stochastic differential equation and its interpretation. The notions like Brownian motion and stochastic integral with interpretations in concrete situations in areas of biology and medicine are discussed. The questions are related to mathematical modelling and they may be interpreted in connection with stochastic signal filtering and optimal queuing theory.

Stochastic Processes↗
PubMed1983

Statistical analysis of ongoing activity of neurones in the substantia gelatinosa and in lamina III of cat spinal cord.

Intracellular recordings from substantia gelatinosa (s.g.) neurones in chloralose-anaesthetized cats and in decerebrate preparations revealed the existence of ongoing synaptic activity. 59% of s.g. neurones showed ongoing spiking activity at rates of more than one per second. The ongoing activity of twenty s.g. neurones was subjected to statistical analysis. Stationarity was established for the activity of each neurone, the interspike interval (i.s.i.) distributions were bell-shaped, and no evidence of dependency of the length of an interval on the one preceding it was found. The mechanism of spike generation in these neurones is therefore an example of a renewal stochastic process. The pattern of ongoing discharge of twelve neurones recorded in lamina III was markedly different, and generated in each case a unimodal asymmetric i.s.i. histogram with a sharp rise to mode after a short dead time and a slow decay. The activity was stationary only in the long term, and there was strong evidence of dependency of intervals. The spike generating mechanism was therefore an example of a non-renewal stochastic process. The different patterns of activity are discussed in relation to differences in cutaneous input, and it is suggested that the pattern of activity in the s.g. neurones is the result of convergence on the neurones of a large number of small independent excitatory influences, whereas that of the neurones in lamina III is the result of excitation by powerful synchronous synaptic inputs. It is re-emphasized that statistical analysis of neural impulse sequences is a valuable technique in investigation of the function of a neurone within its network.

Anesthesia, General↗
PubMed2024

Seasonal hydrological dynamics affected the diversity and assembly process of the antibiotic resistome in a canal network.

The significant threat of antibiotic resistance genes (ARGs) to aquatic environments health has been widely acknowledged. To date, several studies have focused on the distribution and diversity of ARGs in a single river while their profiles in complex river networks are largely known. Here, the spatiotemporal dynamics of ARG profiles in a canal network were examined using high-throughput quantitative PCR, and the underlying assembly processes and its main environmental influencing factors were elucidated using multiple statistical analyses. The results demonstrated significant seasonal dynamics with greater richness and relative abundance of ARGs observed during the dry season compared to the wet season. ARG profiles exhibited a pronounced distance-decay pattern in the dry season, whereas no such pattern was evident in the wet season. Null model analysis indicated that deterministic processes, in contrast to stochastic processes, had a significant impact on shaping the ARG profiles. Furthermore, it was found that Firmicutes and pH emerged as the foremost factors influencing these profiles. This study enhanced our comprehension of the variations in ARG profiles within canal networks, which may contribute to the design of efficient management approaches aimed at restraining the propagation of ARGs.

Seasons↗
PubMed1989

An illness-death process with time-dependent covariates.

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates in order to make an appropriate adjustment for the transition and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown. The method developed is illustrated with data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach with which the effectiveness of the treatment can be compared between the placebo and propranolol treatment groups with respect to fatal and nonfatal events simultaneously.

Biometry↗
PubMed1978

Compartment model approach to the estimation of tumor incidence and growth: investigation of a model of cancer latency.

Consideration is made of the problems involved in determining the effects of a chronic disease process, such as stomach cancer, on the observed mortality of the U.S. population. Specifically, since the time of initiation of tumor growth is unknown and the tumor becomes clinically manifest only after reaching considerable size, the early rate and pattern of tumor growth is unobserved. As a possible solution to the analysis of such problems, it is proposed to use stochastic compartment modelling techniques which deal with the problems of estimating the transition probabilities of a partially observed stochastic process. Implementation of the stochastic compartment techniques in this case depends on the selection of certain mathematical expressions from theories of carcinogenesis, epidemiologic studies and animal studies which allow the calculation of transition probabilities to unobserved states by making them explicit functions of time or age. Though the selection of the specific functions might be subject to debate, the general strategy of explicitly selecting such functions, and thereby exposing them for review in terms of biologic reasonableness and consistency with the data, seems to be a valid and useful methodology. Furthermore, various ways of viewing the model results (say from its internal behavior, e.g., from implied distributions of waiting times in various disease states) yield different insights into the various factors in carcinogenesis. The model, with parameters representing tumor incidence, time to tumor death given onset, genetic susceptibility to tumor growth and the effects of competing forces of mortality, is fitted to data on deaths due to stomach cancer for male U.S. residents age 25 and over in 1969. Two basic forms of the model, one with a waiting time distribution for occupants of the latent state and another with a single latency time, achieved excellent fits to the data. Examination of parameter estimates and compartment waiting time distributions are consistent with theoretical expectations and intuition. It is concluded that such strategies, involving the integration of clinical, experimental and vital statistics data into a comprehensive model of population carcinogenesis, are potentially powerful tools for investigation of the temporal dimensions of disease development in a human population.

Adult↗
PubMed1991

Segmentation of speckle images based on level-crossing statistics.

When imaging is performed by using a coherent signal, the result is frequently a realization of the stochastic process known as speckle. The information sought from this process is often the mean value of its envelope or intensity at each point in the image plane. When only a single realization of the process is available, ergodicity is required within a sufficiently large region for accurate estimation of the mean. The identification of these regions is the segmentation problem that is addressed. The approach presented clips the speckle image at a constant threshold level and analyzes the resulting bilevel image based on the level-crossing statistics of the speckle process. An analysis of the level-crossing process leads to a decision rule for identifying or segmenting distinct regions of the image based on the sizes of the fades and the excursions in the clipped speckle. The measurement of these sizes is accomplished by using the morphological transformations of opening and closing. This new approach has been applied to computer-generated speckle images and may prove useful in laser, ultrasound, and radar imaging, in which speckle phenomena are manifest.

Image Processing, Computer-Assisted↗
PubMed1991

Comparing functional (PET) images: the assessment of significant change.

Statistical parametric maps (SPMs) are potentially powerful ways of localizing differences in regional cerebral activity. This potential is limited by uncertainties in assessing the significance of these maps. In this report, we describe an approach that may partially resolve this issue. A distinction is made between using SPMs as images of change significance and using them to identify foci of significant change. In the first case, the SPM can be reported nonselectively as a single mathematical object with its omnibus significance. Alternatively, the SPM constitutes a large number of repeated measures over the brain. To reject the null hypothesis, that no change has occurred at a specific location, a threshold adjustment must be made that accounts for the large number of comparisons made. This adjustment is shown to depend on the SPM's smoothness. Smoothness can be determined empirically and be used to calculate a threshold required to identify significant foci. The approach models the SPM as a stationary stochastic process. The theory and applications are illustrated using uniform phantom images and data from a verbal fluency activation study of four normal subjects.

Adult↗