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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↗
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↗
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↗
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↗
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↗
PubMed1992

Analyzing the dynamics of hand tremor time series.

We investigate physiological, essential and parkinsonian hand tremor measured by the acceleration of the stretched hand. Methods from the theory of dynamical systems and from stochastics are used. It turns out that the physiological tremor can be described as a linear stochastic process, and that the parkinsonian tremor is nonlinear and deterministic, even chaotic. The essential tremor adopts a middle position, it is nonlinear and stochastic.

Hand↗
PubMed1978

Mechanism of antigen-induced antibody biosynthesis from antibody precursors, the heavy and light immunoglobulin chains.

The immediate precursors of antibody molecules, the heavy (H) and light (L) peptide chains of the immunoglobulins, combine with each other by means of disulfide bonds formed by dehydrogenation of their cysteine residues. In the absence of an antigen this process yields the heterogeneous mixture of normal immunoglobulins. Antigens or their processed derivatives (Ag) interfere with this stochastic process by noncovalent combination with complementarily fitting H chains. The (Ag.H)(n) complexes thus formed, owing to the loss of rotational and translational freedom, combine preferentially with those L chains whose V(L) regions have some affinity for the determinants of the antigen molecule. Subsequent release of Ag from the (Ag.H.L)(n) complexes yields free antigen and antibody molecules. Each of the released Ag molecules can be used repeatedly for the same reaction cycle and thus can induce the biosynthesis of a large number of antibody molecules. Any macromolecule, natural or synthetic, that has at least a few polar groups and that can penetrate to the nascent H and L chains can thus act as an antigen. Whereas the structure of the H and L chains is genetically determined and transmitted through the germ line, the process induced by the antigen is a phenotypic phenomenon. The antigen acts in this process as a stereospecific cofactor or regulator of the thiol-disulfide transhydrogenation of the combining H and L chains of immunoglobulins.

Antibody Formation↗
PubMed1978

Eye movements of African chameleons: spontaneous saccade timing.

Despite asynchrony, saccades of left and right eyes of African chameleons had similar timing statistics. Prominent qualitative aspects of these statistics did not change if one or both eyes were masked. Evidently, an internal stochastic process regulated chameleon saccade generation.

Animals↗
PubMed1989

The propagation of uncertainty in human mortality processes operating in stochastic environments.

This paper presents a model describing how the uncertainty due to influential exogenous processes combines with stochasticity intrinsic to physiological aging processes and propagates through time to generate uncertainty about the future physiological state of the population. Variance expressions are derived for (a) the future values of the physiological variables under the assumption that external factors evolve under a linear stochastic diffusion process, and (b) the cohort survival functions and cohort life expectancies which reflect the uncertainty in the future values of the physiological variables. The model implies that a major component of uncertainty in forecasts of the physiological characteristics of a closed cohort is due to differential rates of survival associated with different realizations of the external process. This suggests that the limits to forecasting may be different in physiological systems subject to systematic mortality than in physical systems such as weather where the concepts of closed cohorts and of mortality selection have no simple analog.

Aging↗
PubMed1990

Non-stationary analysis of electromyographic activity prior to a ballistic voluntary contraction.

The electromyogram (EMG) in a ballistic voluntary action of muscle after a slight sustained contraction shows a short period of decrease or disappearance of the activity prior to the onset of phasic discharge. The EMG of elbow extensor (triceps brachii) prior to phasic discharge was analyzed as a non-stationary stochastic process. The distribution of the EMG amplitude began to change from 100 ms before the phasic discharge. The statistical test showed that the EMG activity became non-Gaussian from 30 to 50 ms before the phasic discharge. The standard deviation of the EMG showed a decreasing tendency from 80 to 100 ms prior to the phasic discharge. The statistical evidence for the EMG depression was also confirmed in fourth and sixth order coefficients of the orthogonal expansion of the probability density function. These results suggested that the EMG process profoundly changed its statistical characteristics just before the phasic discharge.

Action Potentials↗
PubMed2026

Climate and soil shape Daqu wheat quality and seed microbiome via rhizosphere taxa and microbial assembly.

The grain quality and seed microbiome of Daqu wheat are fundamental determinants of Daqu fermentation performance; however, the mechanisms by which cultivation environments influence these traits via rhizosphere microbial communities remain unclear. Bacterial and fungal communities across the bulk soil-rhizosphere-seed continuum of three wheat cultivars grown in four ecoregions were characterized using absolute quantitative amplicon sequencing. The rhizosphere microbiome was treated as a central intermediary, while the response variables were seed microbial diversity and grain-quality traits, including starch content, protein content, and grain hardness. Twelve physicochemical properties of soil and 11 climatic factors were integrated into a multidimensional association framework. Environmental conditions exerted stronger influences on both seed quality traits and microbial diversity than cultivar identity. Distinct regional signatures were also evident in rhizosphere microbiomes, with environmental gradients explaining community variation more effectively than geographic distance. Bacterial communities exhibited greater sensitivity to environmental fluctuations than fungi. Mantel analyses identified available nitrogen, precipitation, and atmospheric pressure as significant drivers of core rhizosphere taxa (P&#xa0;<&#xa0;0.05). iCAMP revealed that stochastic processes predominantly governed rhizosphere bacterial assembly, whereas stochastic and deterministic mechanisms jointly shaped fungal assembly. Partial least squares path modeling further uncovered a rhizosphere-mediated environment-seed cascade, wherein sunlight intensity and duration, atmospheric pressure, and soil nitrogen directly or indirectly affected seed wet gluten content, grain hardness, and seed microbial diversity through their influences on rhizosphere microbiota. Rhizosphere bacterial diversity was negatively associated with seed bacterial diversity (path coefficient&#xa0;=&#xa0;-0.118, P&#xa0;<&#xa0;0.05), indicating that rhizosphere communities may shape seed endophytic bacterial assemblages via environmental filtering and competitive interactions. Collectively, these findings elucidate how environments shape the quality and seed microbiomes of Daqu wheat, providing scientific guidance for optimal site selection and the standardized production of high-quality brewing wheat for industrial Baijiu.

Triticum↗
PubMed1989

Quantifying uncertainty in medical decisions.

Effective handling of uncertainty is one of the central problems in medical decision making. The sources and effects of uncertainty in medical decision making are examined and some new quantitative approaches for solving the associated problems are outlined. To handle uncertainty in the branching probabilities and node utilities for probability trees representing alternative treatment strategies, a public domain software package that can be used for the construction, analysis and comparison of probability trees with random parameters was developed. To facilitate specification of the random variables that arise in medical decision making problems, public domain software packages for both data-driven and subjective estimation of probability densities from the Johnson translation system of distributions have also been developed. For the analysis of complex problems that cannot be adequately represented by probability trees or by simple stochastic processes such as Markov chains, network simulation approaches that are oriented toward the sequence of activities seen by individual patients in the course of treatment are described.

Computer Simulation↗