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PubMed2004

Random dynamics of the Morris-Lecar neural model.

Determining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes. In both the transitions from excitable to oscillating regimes are associated with different bifurcation scenarios. This work examines how random perturbations affect these two bifurcation scenarios. It is first numerically shown that the Morris-Lecar model driven by white Gaussian noise current tends to have a unique stationary distribution in the phase space. Numerical evaluations also reveal quantitative and qualitative changes in this distribution in the vicinity of the bifurcations of the deterministic system. However, these changes notwithstanding, our numerical simulations show that the Lyapunov exponents of the system remain negative in these parameter regions, indicating that no dynamical stochastic bifurcations take place. Moreover, our numerical simulations confirm that, regardless of the asymptotic dynamics of the deterministic system, the random Morris-Lecar model stabilizes at a unique stationary stochastic process. In terms of random dynamical system theory, our analysis shows that additive noise destroys the above-mentioned bifurcation sequences that characterize class I and class II regimes in the Morris-Lecar model. The interpretation of this result in terms of neuronal coding is that, despite the differences in the deterministic dynamics of class I and class II membranes, their responses to noise-like stimuli present a reliable feature.

Animals↗
PubMed1986

The mathematical basis of population rhythms in nervous and neuromuscular systems.

The mechanism underlying rhythmical aggregate activity of a population of neural or neuromuscular elements is examined in this report. By making use of the spectral properties of stochastic processes (Papoulis, 1965), it is shown that such population rhythms are the inevitable effect of the rhythmical activities of the individual elements, irrespective of the phase relations of the latter. This result applies to both "discrete" signals, such as spike trains, and "continuous" ones, such as membrane potential fluctuations. It has implications regarding the generation of common physiological rhythms and the preservation of rhythms when converging activity of one of the above two types is transformed into activity of the other type.

Action Potentials↗
PubMed2004

Likelihood-based inference for stochastic models of sexual network formation.

Sexually-transmitted diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women's network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results suggest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership formation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally.

Databases as Topic↗
PubMed1992

Noise, sensitivity, and resolution of flow cytometers.

The sensitivity and resolution of flow cytometers are functions of the signal produced by a given particle as well as by the noise in the presence of which the signal is detected. The noise is primarily due to the fact that emission of light as well as its detection by photoelectric devises are stochastic processes. This fact leads to equations describing how resolution and sensitivity are limited by the magnitude of the signal, the background, and the photoelectron quantum yield of the detector. The equations are pointing to a method by which the signal and noise of a flow cytometer can be measured in absolute terms, as well as a way to determine fluorescence sensitivity without having to extrapolate to the noise level. The equations appear to be validated when applied to measuring data obtained with two different flow cytometers.

Calibration↗
PubMed2002

Stochastic versus stable transcriptional differences on Plasmodium falciparum DNA microarrays.

The recent availability of the Plasmodium falciparum genome sequence has opened up convenient, large-scale analysis of transcriptional products in malaria. Protocols for cDNA labelling, cDNA hybridisation, and fluorescent signal detection developed for other organisms can be applied directly to malaria. However, P. falciparum offers unique challenges in data analysis due to stochastic variability in expression of some gene products, such as variable erythrocyte surface proteins. Careful comparison of global transcriptional patterns in two well-studied clones of P. falciparum (Dd2 and HB3) indicates that reliable, stable transcriptional alterations in malaria can be readily distinguished from stochastic processes. To do this, we utilised a complex experimental design which involves a combination of self-hybridisations and cross-hybridisations between two independently grown parasite populations for each clone being examined (for short, we call this a '2x2 CombiScan'). While even a simple 2x2 CombiScan required 12 microarray hybridisations, the effort generated output that was highly interpretable. Reliable RNA transcriptional differences between Dd2 and HB3 could be readily visualised using public algorithms for data normalisation and clustering.

Animals↗
PubMed2003

Attenuation caused by infrequently updated covariates in survival analysis.

This paper deals with hazard regression models for survival data with time-dependent covariates consisting of updated quantitative measurements. The main emphasis is on the Cox proportional hazards model but also additive hazard models are discussed. Attenuation of regression coefficients caused by infrequent updating of covariates is evaluated using simulated data mimicking our main example, the CSL1 liver cirrhosis trial. We conclude that the degree of attenuation depends on the type of stochastic process describing the time-dependent covariate and that attenuation may be substantial for an Ornstein-Uhlenbeck process. Also trends in the covariate combined with non-synchronous updating may cause attenuation. Simple methods to adjust for infrequent updating of covariates are proposed and compared to existing techniques using both simulations and the CSL1 data. The comparison shows that while existing, more complicated methods may work well with frequent updating of covariates the simpler techniques may have advantages in larger data sets with infrequent updatings.

Computer Simulation↗
PubMed2005

Modelling the spread of penicillin-resistant Streptococcus pneumoniae in day-care and evaluation of intervention.

In 1995, a disease control and intervention project was initiated in Malmöhus county in southern Sweden to limit the spread of penicillin-resistant pneumococci. Since most of the carriers of pneumococci are preschool children, and since most of the spread is believed to take place in day-care, a mathematical model, in the form of a stochastic process, for the spread in a day-care group was constructed. Effects of seasonal variation and size of the day-care group were particularly considered. The model was then used for comparing results from computer simulations without and with intervention. Results indicate that intervention is highly effective in day-care groups with more than ten children during the second half of the year.

Biometry↗
PubMed2006

A relaxation of the gamma frailty (Burr) model.

Frailty models are used in univariate data to account for individual heterogeneity. In the popular gamma frailty model the marginal hazard has the form of a Burr model. Although the Burr model is very useful and can offer insight on the data, it is far from perfect. The estimation of the covariate effects is linked to the baseline hazard and this makes the model coefficients hard to interpret. At the same time, the frailties are assumed constant over time, while biological reasoning in some cases may indicate that frailties may be time dependent. In this paper we present a relaxation of the Burr model which is based on loosening the link between the estimation of the covariate effects and the baseline hazard. This can be achieved by replacing the cumulative baseline hazard in the Burr model by a set of time functions, and the frailty variance by a vector of coefficients directly estimated from the data using a partial likelihood. We illustrate the similarities of the model with the Burr model and a further extension of the latter, a model with an autoregressive stochastic process for the frailty. We compare the models on simulated data sets with constant and time-dependent frailties and show how the relaxed Burr models performs on two different real data sets. We show that the relaxed Burr model serves as a good approximation to the Burr model when the frailty is constant, and furthermore it gives better results when the frailty is time dependent.

Adolescent↗
PubMed1991

Subfreezing volumetric behavior and stochastic modeling of intracellular ice formation in Drosophila melanogaster embryos.

Cryomicroscopic observations were made of the volumetric behavior and kinetics of intracellular ice formation (IIF) in Drosophila melanogaster embryos in a modified cell culture medium (BD.20) or BD.20 + 2 M ethylene glycol. After rapid cooling to a given temperature, transient volumetric contraction of the embryos during the isothermal period was quantified by computerized video image analysis. Fitting these data to the numerical solution of the volume flux equation yielded estimates of the hydraulic permeability coefficient (Lp) for individual embryos at various subfreezing temperatures. Lp approximately followed an Arrhenius relation between -2 and -9 degrees C, with a value of 0.168 microns/(min-atm) extrapolated to 0 degrees C and an apparent activation energy delta E of 38.9 kcal/mol. IIF during an isothermal period occurred at random times whose characteristic temperature range and kinetics were affected by the presence of ethylene glycol. A stochastic process model developed to fit these data indicated the influence of both time-dependent and instantaneous components of IIF, presumed to be the result of seeding and heterogeneous nucleation, respectively. The presence of 2 M ethylene glycol depressed the characteristic temperature of instantaneous IIF by about 12 degrees C and reduced the rate constant for time-dependent IIF. Comparison with observed incidences of IIF yielded an estimate of the supercooling tolerance of 3 to 5 degrees C.

Animals↗
PubMed1990

A mathematical model for scheduling screening tests for progressive diseases.

In this paper, a mathematical model describing the stochastic process underlying the etiology of noncontagious, curable, progressive diseases is developed. In our previous study of progressive diseases, the reliabilities of screening tests were assumed to be constants, independent of how long the individual has had the disease. The purpose of this study is to develop more insight into modeling the disease process, and the interaction of screening tests with the natural behavior of the disease. To accomplish this task, more realistic screening parameters are selected, and optimum policies for mass screening programs under different reliabilities of screening tests are developed. These modifications make the model general enough to be applicable to a larger class of progressive diseases that includes breast cancer. Solutions to two simplified versions of the model for childhood neuroblastoma illustrate the use of our proposed procedure.

Catastrophic Illness↗
PubMed2005

A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization.

The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.

Algorithms↗
PubMed2002

Increased noise as an effect of haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 in vitro.

In human diseases related to tumor-suppressor genes, it is suggested that only the complete loss of the protein results in specific symptoms such as tumor formation, whereas simple reduction of protein quantity to 50%, called haploinsufficiency, essentially does not affect cellular behavior. Using a model of gene expression, it was presumed that haploinsufficiency is related to an increased noise in gene expression also in vivo [Cook, D. L., Gerber, A. N. & Tapscott, S. J. (1998) Proc. Natl. Acad. Sci. USA 95, 15641-15646]. Here, we demonstrate that haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 (NF1) results in an increased variation of dendrite formation in cultured NF1 melanocytes. These morphological differences between NF1 and control melanocytes can be described by a mathematical model in which the cell is considered to be a self-organized automaton. The model describes the adjustment of the cells to a set point and includes a noise term that allows for stochastic processes. It describes the experimental data of control and NF1 melanocytes. In the cells haploinsufficient for NF1 we found an altered signal-to-noise ratio detectable as increased variation in dendrite formation in two of three investigated morphological parameters. We also suggest that in vivo NF1 haploinsufficiency results in an increased noise in cellular regulation and that this effect of haploinsufficiency may be found also in other tumor suppressors.

Case-Control Studies↗
PubMed1992

Coloured noise or low-dimensional chaos?

Devising a method capable of distinguishing a low-dimensional chaotic signal that might be embedded in a noisy stochastic process has become a major challenge for those involved in time-series analysis. Here a null hypothesis approach is used in conjunction with a known nonlinear predictive test, to probe for the presence of chaos in epidemiological data. A probabilistic set of rules is used to stimulate a historic record of New York City measles outbreaks, generally understood to be governed by a chaotic attractor. The simulated runs of 'surrogate data' are carefully constructed so as to be free from any underlying low-dimensional chaotic process. They therefore serve as a useful null model against which to test the observed time series. However, despite the assumed differences between the dynamics of measles outbreaks and the null model, a nonlinear predictive scheme is found to be unable to differentiate between their characteristic time series. The methodology confirms that, if there is in fact a chaotic signal in the measles data, it is extremely difficult to detect in time series of such limited length. The results have general relevance to the analysis of physical, ecological and environmental time series.

Biometry↗
PubMed2001

Route of simian immunodeficiency virus inoculation determines the complexity but not the identity of viral variant populations that infect rhesus macaques.

A better understanding of the host and viral factors associated with human immunodeficiency virus (HIV) transmission is essential to developing effective strategies to curb the global HIV epidemic. Here we used the rhesus macaque-simian immunodeficiency virus (SIV) animal model of HIV infection to study the range of viral genotypes that are transmitted by different routes of inoculation and by different types of viral inocula. Analysis of transmitted variants was undertaken in outbred rhesus macaques inoculated intravenously (IV) or intravaginally (IVAG) with a genetically heterogeneous SIVmac251 stock derived from a well-characterized rhesus macaque viral isolate. In addition, we performed serial IV and IVAG passage experiments using plasma from SIV-infected macaques as the inoculum. We analyzed the V1-V2 region of the SIV envelope gene from virion-associated RNA in plasma from infected animals by the heteroduplex mobility assay (HMA) and by DNA sequence analysis. We found that a more diverse population of SIV genetic variants was present in the earliest virus-positive plasma samples from all five IV SIVmac251-inoculated monkeys and from two of five IVAG SIVmac251-inoculated monkeys. In contrast, we found a relatively homogeneous population of SIV envelope variants in three of five monkeys inoculated IVAG with SIVmac251 stock and in two monkeys infected after IVAG inoculation with plasma from an SIV-infected animal. In some IVAG-inoculated animals, the transmitted SIV variant was the most common variant in the inoculum. However, a specific viral variant in the SIVmac251 stock was not consistently transmitted by IVAG inoculation. Thus, it is likely that host factors or stochastic processes determine the specific viral variants that infect an animal after IVAG SIV exposure. In addition, our results clearly demonstrate that the route of inoculation is associated with the extent and breadth of the genetic complexity of the viral variant population in the earliest stages of systemic infection.

Administration, Intravaginal↗
PubMed1999

A random walk model of oligodendrocyte generation in vitro and associated estimation problems.

A branching stochastic process proposed earlier to model oligodendrocyte generation by O-2A progenitor cells under in vitro conditions does not allow invoking the maximum likelihood techniques for estimation purposes. To overcome this difficulty, we propose a partial likelihood function based on an embedded random walk model of clonal growth and differentiation of O-2A progenitor cells. Under certain conditions, the partial likelihood function yields consistent estimates of model parameters. The usefulness of this approach is illustrated with computer simulations and data analyses.

Algorithms↗
PubMed1998

A stochastic model of schistosomiasis immuno-epidemiology.

Schistosomiasis is a helminth (worm) infection with approximately 200 million people infected worldwide. There is still controversy on whether differing worm burdens between individuals is a result of differing contact rates or of acquired immunity. In this paper, we present a stochastic modelling framework to address these issues. By using appropriate approximations for the higher moments of the joint distributions, differential equations for the means, variances and co-variances of infection and immunity can be obtained. Numerical solutions of these equations to obtain age profiles of the above properties were compared with Monte Carlo simulations of the stochastic process. Simulations showed that the results depended on whether between host heterogeneity was generated by differing contact rates or differing immune responses. Heterogeneity in contact rates produced a highly aggregated distribution of parasites with a large variance/mean ratio. Heterogeneity in the immune response had very little effect on the overall dynamics. This agrees with the predominant field evidence which would suggest that infection is mainly determined by ecology with a smaller contribution of immunity.

Age Factors↗
PubMed1983

A stochastic model of malaria transition rates from longitudinal data: considering the risk of "lost to follow-up".

A model, using stochastic processes, is developed to estimate some epidemiological parameters of malaria in a homogeneous population from longitudinal data. Assessments of transition probabilities from one state of health to the other are made taking "lost to follow-up" as a competing risk. The model is based on the assumptions that individuals are transferred at constant rate between states, and only one transition is possible between two consecutive surveys. It shows a good fit to the observed data; the model is simple to understand and can easily be used if computer facilities are not available.

Epidemiologic Methods↗
PubMed2002

A measure of continuity of care based on the multiplicative intensity model.

Continuity of care is a concept that is frequently used to measure patient satisfaction and other benefits provided by the health care system. Although several measures of continuity of care are used, most are built on unrealistic assumptions about random visits to providers and do not utilize all available information. In this paper we advocate stochastic processes to model continuity of care, and we propose a new measure of provider continuity based on the multiplicative intensity model. Using data on hypertensive patients in the province of Alberta, Canada, we demonstrate the utility of our method that incorporates ways to accommodate covariate information. Compared to the currently popular method, the proposed method in this paper is shown to assess both concentration of care aspects and other visit-based characteristics of the care being provided.

Adult↗