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PubMed2006

Interval estimates for epidemic thresholds in two-sex network models.

Epidemic thresholds in network models of heterogeneous populations characterized by highly right-skewed contact distributions can be very small. When the population is above the threshold, an epidemic is inevitable and conventional control measures to reduce the transmissibility of a pathogen will fail to eradicate it. We consider a two-sex network model for a sexually transmitted disease which assumes random mixing conditional on the degree distribution. We derive expressions for the basic reproductive number (R(0)) for one and heterogeneous two-population in terms of characteristics of the degree distributions and transmissibility. We calculate interval estimates for the epidemic thresholds for stochastic process models in three human populations based on representative surveys of sexual behavior (Uganda, Sweden, USA). For Uganda and Sweden, the epidemic threshold is greater than zero with high confidence. For the USA, the interval includes zero. We discuss the implications of these findings along with the limitations of epidemic models which assume random mixing.

Acquired Immunodeficiency Syndrome↗

PubMed1995

Binocular rivalry is not chaotic.

Time series of the durations each eye was dominant during binocular rivalry were obtained psychophysically. The oscillations showed an adaptation effect with mean and standard deviations of rivalry dominance durations increasing as a square root function of time over the course of a trial. The data were corrected for this non-stationarity. Dominance durations had a log-normal probability distribution and the autocorrelation function revealed no short term correlations in the time series. In an attempt to distinguish whether the variability of durations was due to a deterministic, low-dimensional chaotic attractor or to a stochastic process, the data were subjected to two tests. The first was calculation of correlation dimensions and the second was nonlinear forecasting of the time series. Both tests included comparisons with randomized 'surrogate data' as controls. In neither case was there a large difference between test results for actual data and surrogate data. We conclude that chaos is not a major factor underlying variability in binocular rivalry.

Adaptation, Ocular↗

PubMed1988

Influence of the hypercycle on the error threshold: a stochastic approach.

The role of fluctuations on the error threshold of the hypercycle has been studied by a stochastic approach on a very simplified model. For this model, the master equation was derived and its unique steady state calculated. This state implies the extinction of the system. But the actual time necessary to reach the steady state may be astronomically long whereas for times of experimental interest the system could be near some quasi-stationary states. In order to explore this possibility a Gillespie simulation of the stochastic process has been carried out. These quasi-stationary states correspond to the deterministic steady states of the system. The error threshold shifts towards higher values of the quality factor Q. Moreover, information about the fluctuations around the quasi-stationary states is obtained. The results are discussed in relation to the deterministic states.

Animals↗

PubMed2000

Research into the effects of astronaut motion on the spacecraft: a review.

The paper reviews the research that has been undertaken to understand and quantify the disturbance effects of the astronaut's motion inside and outside the spacecraft on the vehicle's attitude and acceleratory environment. In early investigations, the dynamic interaction of astronauts, modeled as point masses, and the spacecraft, modelled as a rigid body, was analyzed. Through ground-based experiments and the modeling of astronaut-induced forces and moments as stochastic processes, it became possible to estimate the magnitude and energy content of the loads produced by the astronaut. The first experiment in space to measure the astronaut-induced disturbances was conducted on the Skylab orbital station. Loads generated while performing routine operations were measured on board the Space Shuttle in 1994 and on the space station Mir in 1996-1997.

Acceleration↗

PubMed2006

Propagation and control of stochastic signals through universal learning networks.

The way of propagating and control of stochastic signals through Universal Learning Networks (ULNs) and its applications are proposed. ULNs have been already developed to form a superset of neural networks and have been applied as a universal framework for modeling and control of non-linear large-scale complex systems. However, the ULNs cannot deal with stochastic variables. Deterministic signals can be propagated through a ULN, but the ULN does not provide any stochastic characteristics of the signals propagating through it. The proposed method named Probabilistic Universal Learning Networks (PrULNs) can process stochastic variables and can train network parameters so that the signals behave with the pre-specified stochastic properties. As examples of applications of the proposed method, control and identification of non-linear dynamic systems with noises are studied, and it is shown that the method are useful for dealing with the control and identification of the non-linear stochastic systems contaminated with noises.

Artificial Intelligence↗

PubMed1998

Regulation of IL-4 expression by activation of individual alleles.

To study the in vivo role of IL-4-expressing cells, we developed a strategy to tag these cells, by generating mice in which one IL-4 allele was replaced with a cDNA encoding the human CD2 (huCD2) cell-surface molecule. Expression of the huCD2 reporter was, like IL-4, restricted to the appropriately polarized T helper 2 cells. However, most of the cells expressed only the IL-4 or the targeted allele. Analysis of the frequency of monoallelic versus biallelic expression suggests that the activation of each individual allele is regulated by a stochastic process whose probability can be augmented by increasing the strength of signal delivered through the TCR. Allele-specific activation may be a general feature of cytokine regulation that contributes to the functional diversity within T helper cell subpopulations.

Alleles↗

PubMed1980

Optimal investigation policies under selected PSRO procedures.

This article presents a methodology for utilization review which aids the local Professional Standards Review Organization (PSRO) in selecting optimal timing of Concurrent Stay certification by diagnosis. This procedure is accomplished by modeling patients' admissions, inpatients stays and discharges for each diagnosis as a stochastic process which is audited under the PSRO by three utilization review techniques: preadmission, concurrent and retrospective review. The timing of concurrent stay certification is determined so that the maximum benefits are derived for the utilization review cost expanded. The methodology presented here is a tool to aid local PSRO management in determining the most cost-beneficial utilization review process to utilized in their jurisdiction. It is not an attempt to demonstrate the effectiveness of our utilization review policy over another in general. On the contrary, while the model is generalizable to every PSRO, the utilization review policies resulting from any application are situation-specific. The major contributions of this article are new insight into modeling the utilization review process and the provision of a methodology for which computer programs exist and are readily available to any PSRO that should desire to determine its utilization review procedure in this cost-benefit framework. In order to apply the model it is necessary that certain parameters specific to the application site be estimated or assumed. Exact procedures to aid the PSRO in parameter estimation is the subject of current investigation.

Concurrent Review↗

PubMed1988

Models of dispersal in biological systems.

In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that are observed in nature. In the first type of movement, which we call the position jump or kangaroo process, the process comprises a sequence of alternating pauses and jumps. The duration of a pause is governed by a waiting time distribution, and the direction and distance traveled during a jump is fixed by the kernel of an integral operator that governs the spatial redistribution. Under certain assumptions concerning the existence of limits as the mean step size goes to zero and the frequency of stepping goes to infinity the process is governed by a diffusion equation, but other partial differential equations may result under different assumptions. The second major type of movement leads to what we call a velocity jump process. In this case the motion consists of a sequence of "runs" separated by reorientations, during which a new velocity is chosen. We show that under certain assumptions this process leads to a damped wave equation called the telegrapher's equation. We derive explicit expressions for the mean squared displacement and other experimentally observable quantities. Several generalizations, including the incorporation of a resting time between movements, are also studied. The available data on the motion of cells and other organisms is reviewed, and it is shown how the analysis of such data within the framework provided here can be carried out.

Cell Movement↗

PubMed2000

A moment closure model for sexually transmitted disease transmission through a concurrent partnership network.

A moment closure model of sexually transmitted disease spread through a concurrent partnership network is developed. The model employs pair approximations of higher-order correlations to derive equations of motion in terms of numbers of pairs and singletons. The model is derived from an underlying stochastic process of partnership network formation and disease transmission. The model is analysed numerically; and the final size and time evolution are considered for various levels of concurrency, as measured by the concurrency index kappa3 of Kretzschmar and Morris. Additionally, a new way of calculating R0 for spatial network models is developed. It is found that concurrency significantly increases R0 and the final size of a sexually transmitted disease, with some interesting exceptions.

Humans↗

PubMed2005

A local coupling model and compass parameter for eukaryotic chemotaxis.

Chemotaxis is a cellular sensing mechanism that guides immune cells to sites of infection and leads fibroblasts to sites of injury. Here, we show in migrating primary dendritic cells and fibroblasts that the leading edge is not a uniform signaling entity, but instead consists of independent coupling units in which transient activation of PI3-kinase links to local lamellipod extension and small discrete turns in the direction of migration. These findings led to a model in which global cell polarization is independent from the chemotaxis mechanism. In this model, chemotaxis does not require spatial integration but is instead a stochastic process in which each receptor binding event within the leading edge triggers a local lamellipod extension and a small turn in the direction of migration. We show that this model and a derived "compass parameter" are sufficient to simulate the observed random migration, biased random walk, and persistent chemotactic behaviors of eukaryotic cells.

Animals↗

PubMed2005

A gamma mixture model better accounts for among site rate heterogeneity.

MOTIVATION: Variation of substitution rates across nucleotide and amino acid sites has long been recognized as a characteristic of molecular sequence evolution. Evolutionary models that account for this rate heterogeneity usually use a gamma density function to model the rate distribution across sites. This density function, however, may not fit real datasets, especially when there is a multimodal distribution of rates. Here, we present a novel evolutionary model based on a mixture of gamma density functions. This model better describes the among-site rate variation characteristic of molecular sequence evolution. The use of this model may improve the accuracy of various phylogenetic methods, such as reconstructing phylogenetic trees, dating divergence events, inferring ancestral sequences and detecting conserved sites in proteins. RESULTS: Using diverse sets of protein sequences we show that the gamma mixture model better describes the stochastic process underlying protein evolution. We show that the proposed gamma mixture model fits protein datasets significantly better than the single-gamma model in 9 out of 10 datasets tested. We further show that using the gamma mixture model improves the accuracy of model-based prediction of conserved residues in proteins. AVAILABILITY: C++ source codes are available from the authors upon request.

Chromosome Mapping↗

PubMed2005

Analysis of interval-censored longitudinal data with application to onco-haematology.

The analysis of repeated measurements on a biomarker, either alone or jointly with the analysis of time to the event of interest, is an area of active research. Nevertheless, we are not yet able to deal in complete generality with these complex data, which frequently consist of error-prone, sparse and intermittent values. In many cancer studies, they arise in the framework of clinical trials and thus their relationship with prognosis is a primary focus. In such a setting, the Cox model is regarded as the standard technique for analysis. The aim of this work is to illustrate an alternative approach to the analysis of studies in which the biomarker values are complicated by interval censoring and an event occurs when the biomarker itself passes a certain threshold. We propose a linear mixed model with a Gaussian stochastic process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of event occurrence. It is developed within the classic approach to longitudinal data analysis that was previously adapted for left-censored data, only. We apply this method to a study on the minimal residual disease (MRD) in childhood leukaemia. MRD is an interval-censored measurement of residual leukaemic cells that was scheduled at 9 time-points during treatment. The aim is to investigate the relationship between MRD and the disease process. Relapse, the event of interest, may conveniently be represented as MRD over a pre-defined threshold. Our focus is on modelling the probability of relapse conditional on MRD observed prior to it. Results show that the approach is promising as it allows proper description of the data, while maintaining flexibility of modelling, feasibility of computations and interpretability of results.

Biomarkers↗

PubMed2005

A complex adaptive systems approach to the kinetic folding of RNA.

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence-to-structure mapping are discussed.

Genes, Bacterial↗

PubMed2006

A stochastic exposure assessment model to estimate vanadium intake by beef cattle used as sentinels for the South African vanadium mining industry.

This paper presents an environmental exposure assessment model for estimating chronic intake of vanadium (a transition metal) by cattle farmed extensively in areas contaminated by vanadium pollutants. The exposure model differs from most other models in several ways: (1) it does not rely heavily on extrapolating information from the point source (e.g. stack height, exit velocity, exit diameter) to the point of exposure. (2) It incorporates the physiological constraints of the species exposed. (3) It takes into account oral as well as inhalation exposure. (4) It addresses terrain, by using measurements at the point of exposure. (5) It accounts for existing background concentrations of pollutants and pollutants from multiple sources. (6) It uses a stochastic process with distribution functions to account for variability in the data over time. Environmental inputs into the model included aerial fall-out sample vanadium (n=566), unwashed grass sample vanadium (n=342) and soluble soil sample vanadium (n=342). Physiological cattle inputs were derived from two cohorts of Brahman-cross sentinel cattle (n=30). The model provided an estimate of the chronic external exposure dose of vanadium for two separate groups of cattle grazing over a 5-year period (1999-2004) immediately adjacent (median dose=2.14mg vanadium/kg body weight/day) and 2km away (median dose=1.07mg/kg/day) from a South African vanadium-processing plant, respectively. The final output of the model is a distribution curve of the probable vanadium intake based on the variability within the inputs over the 5-year period of the study. The model is adaptable enough for application to other transition metals and species (including man), and could be used as an alternative to plume-dispersion modelling.

Air Pollutants↗

PubMed2004

Rapid evolution in conformational space: a study of loop regions in a ubiquitous GTP binding domain.

The rapidly evolving subsets of a protein are often evident in multiple sequence alignments as poorly defined, gap-containing regions. We investigated the 3D context of these regions observed in 28 protein structures containing a GTP-binding domain assumed to be homologous to the transforming factor p21-RAS. The phylogenetic depth of this data set is such that it is possible to observe lineages sharing a common protein core that diverged early in the eukaryotic cell history. The sequence variability among these homolog proteins is directly linked to the structural variability of surface loops. We demonstrate that these regions are self-contained and thus mostly free of the evolutionary constraints imposed by the conserved core of the domain. These intraloop interactions have the property to create stem-like structures. Interestingly, these stem-like structures can be observed in loops of varying size, up to the size of small protein domains. We propose a model under which the diversity of protein topologies observed in these loops can be the product of a stochastic sampling of sequence and conformational space in a near-neutral fashion, while the proximity of the functional features of the domain core allows novel beneficial traits to be fixed. Our comparative observations, limited here to the proteins containing the RAS-like GTP-binding domain, suggest that a stochastic process of insertion/deletion analogous to "budding" of loops is a likely mechanism of structural innovation. Such a framework could be experimentally exploited to investigate the folding of increasingly complex model inserts.

Amino Acid Sequence↗

PubMed2002

Spatial heterogeneity and the stability of reaction states in autocatalysis.

The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is studied. In a nonspatial setting the reactive state of the system is found to be unstable in small volumes where internal fluctuations drive the system to the unreactive state. This phenomena is of potential importance to the stability of reactions in biological cells. A simple spatial model is constructed by linking N nonspatial models via migration of reactants controlled by a mixing rate lambda. Simulation of this stochastic process demonstrates the importance of such mixing in controlling the impact of internal fluctuations on the stability of the autocatalytic reaction. For high mixing rate the mean reactant levels in equilibrium correspond to the well-mixed deterministic system, although a significant degree of spatial heterogeneity remains. For intermediate mixing rates, mean reactant levels vary continuously with lambda, where the interaction of internal fluctuations with limited spatial mixing modifies the reactive states of the deterministic system. However, there is a threshold below which mixing is unable to control internal fluctuations which drive the system into the unreactive state. Thus a critical minimum level of communication between the cells is required to stabilize the reaction across the entire system. Approximate analytic results, obtained using moment-closure techniques, support these findings and demonstrate the relationship between the spatial stochastic and nonspatial deterministic models.

Biophysical Phenomena↗

PubMed2002

A stochastic model of multistable visual perception.

Multistability in vision is an intriguing phenomenon that is currently not well understood. In this paper, we present a new, stochastic model for multistable visual perception. It is based on results of time series analysis of experimental data, yielding evidence for it being a linear, stochastic process. This is the outcome of testing for unstable periodic orbits and comparing the correlation dimension of the data to that of white noise. In the model, all degrees of freedom but one can be determined by general knowledge, thus resulting in a high degree of parsimony. The remaining parameter is used to model the individual characteristics that vary between subjects. Fitting simulations to the experimental data proves the parameter to be in a physiologically highly plausible range.

Depth Perception↗

PubMed2001

Modeling heterogeneity of properties and random effects in drug dissolution.

PURPOSE: To investigate new models characterizing dissolution data obtained for heterogenous materials (model I) and under randomly time-varying conditions (model II). METHODS: In model I, the heterogeneity of the dissolving substance introduces variation of the fractional dissolution rate. In model II, the fractional dissolution rate evolves randomly, and thus the dissolution has the characteristics of a stochastic process. This situation is studied for the constant and time-dependent means of the dissolution rate. RESULTS: The time dynamics of the dissolved fraction is presented for model I. The standard characteristics of dissolution are derived under general conditions and for several examples. One of them is in accordance with a function found empirically (1). A duality between the time-dependency of the fractional dissolution rate and the heterogeneity of the substance is investigated. The mean and variance of the dissolved fraction are calculated for model II. A method for estimating the mean dissolution rate is proposed and illustrated using Monte-Carlo experiments. CONCLUSIONS: It follows from model I that the heterogeneity, with the same mean properties, slows down the dissolution with respect to the homogeneous case. The second approach permits predictions about the role of the stochastic fluctuations of the dissolution rate and to establish the boundaries for the dissolution profiles.

Models, Biological↗