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PubMed2003

Stochastic cascade processes as a model of multi-stage concurrent information processing.

McClelland's (Psychol. Rev. 86 (1979) 287) influential cascade model of reaction time (RT) is often seen as an important explicitly formulated alternative to strictly serial models because some of its basic notions fit in with known characteristics of neural activation processes. A disadvantage is that it is an essentially deterministic model to which noise is added by across-trials parameter variability that is unrelated to the concept of cascaded activation propagation per se. We propose and analyze a general stochastic cascade model based on neural counting processes; within this framework we present a new process-oriented interpretation of McClelland's cascade activation equation. We then theoretically explain and numerically explore conditions under which the stochastic cascade model predicts additive vs. interactive mean RT effects, and compare them to known properties of McClelland's model. Some of these properties remain valid even within a stochastic neural counting formulation, while others reflect assumptions which are essentially unrelated to the concept of cascaded activation.

Brain↗

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↗

PubMed1998

Stochastic effects in a model of nematode infection in ruminants.

We illustrate the importance of stochastic effects in population models of biological systems and demonstrate a number of analytic and simulation-based approaches that can usefully be applied to such models. In so doing, we compare the stochastic approach to the more usual deterministic one. The model studied represents the gastrointestinal infection of ruminants by nematodes when the hosts maintain a fixed density. The incorporation of a feedback mechanism, which accounts for the immune response of the infected animals, results in a highly nonlinear model; similar forms of nonlinearity are a feature of many plausible models in population biology. In the absence of an analytic solution to the full stochastic model we explore a number of approximations and compare them to simulations of the full stochastic process. We explore three modes of behaviour of the system. In the endemic regime the stochastic system fluctuates widely around the non-zero fixed points of the deterministic model. In the managed regime, where the system is subject to external periodic perturbation, stochastic effects are negligible. Finally, we find that in a regime in which the deterministic model predicts the long-term persistence of oscillations the stochastic model shows that extinction can occur. Of the approximation procedures we consider, the Normal approximation to the full stochastic process is the most generally applicable, and it is also the most accurate in the light of simulation results. Local linearization provides reasonably accurate prediction of the variance-covariance structure, and a transfer function approach allows calculation of the time-lagged auto- and cross-correlations in the endemic regime. Linearization of the stochastic updates themselves results in poor prediction of the population variances.

Animals↗

PubMed2005

Coevolutionary dynamics: from finite to infinite populations.

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.

Animals↗

PubMed2004

Statistical characteristics of mechanical heart valve cavitation in accelerated testing.

BACKGROUND AND AIM OF THE STUDY: Cavitation damage has been observed on mechanical heart valves (MHVs) undergoing accelerated testing. Cavitation itself can be modeled as a stochastic process, as it varies from beat to beat of the testing machine. This in-vitro study was undertaken to investigate the statistical characteristics of MHV cavitation. METHODS: A 25-mm St. Jude Medical bileaflet MHV (SJM 25) was tested in an accelerated tester at various pulse rates, ranging from 300 to 1,000 bpm, with stepwise increments of 100 bpm. A miniature pressure transducer was placed near a leaflet tip on the inflow side of the valve, to monitor regional transient pressure fluctuations at instants of valve closure. The pressure trace associated with each beat was passed through a 70 kHz high-pass digital filter to extract the high-frequency oscillation (HFO) components resulting from the collapse of cavitation bubbles. Three intensity-related measures were calculated for each HFO burst: its time span; its local root-mean-square (LRMS) value; and the area enveloped by the absolute value of the HFO pressure trace and the time axis, referred to as cavitation impulse. These were treated as stochastic processes, of which the first-order probability density functions (PDFs) were estimated for each test rate. RESULTS: Both the LRMS value and cavitation impulse were log-normal distributed, and the time span was normal distributed. These distribution laws were consistent at different test rates. CONCLUSION: The present investigation was directed at understanding MHV cavitation as a stochastic process. The results provide a basis for establishing further the statistical relationship between cavitation intensity and time-evolving cavitation damage on MHV surfaces. These data are required to assess and compare the performance of MHVs of different designs.

Acceleration↗

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↗

PubMed1996

Stochastic comparison of processes generated by random interruptions of monotone functions and related results.

Many stochastic processes considered in applied probability models, and, in particular, in reliability theory, are processes of the following form: Shocks occur according to some point process, and each shock causes the process to have a random jump. Between shocks the process increases or decreases in some deterministic fashion. In this paper we study processes for which the rate of increase or decrease between shocks depends only on the height of the process. For such processes we find conditions under which the processes can be stochastically compared. We also study 'hybrid' processes in which periods of increase and periods of decrease alternate. A further result yields a stochastic comparison of processes that start with a random jump, rather than processes in which there is at the beginning some random delay time before the first jump.

Life Tables↗

PubMed1999

Maps for distributions and their time evolution.

Many dynamical stochastic processes occur "on top" of a deterministic process. We present a method which uses the trajectory of the deterministic process as basis functions for quasiarbitrary distributions. A map for the stochastic process can then be computed. This may have applications in electron storage rings or other devices perturbed by a small stochasticity. In this paper we will look only at the most elementary applications of the method.

Journal Article↗

PubMed2005

Roles of isoamylase and ADP-glucose pyrophosphorylase in starch granule synthesis in rice endosperm.

Amyloplast-targeted green fluorescent protein (GFP) was used to monitor amyloplast division and starch granule synthesis in the developing endosperm of transgenic rice. Two classical starch mutants, sugary and shrunken, contain reduced activities of isoamylase1 (ISA1) and cytosolic ADP-glucose pyrophosphorylase, respectively. Dividing amyloplasts in the wild-type and shrunken endosperms contained starch granules, whereas those in sugary endosperm did not contain detectable granules, suggesting that ISA1 plays a role in granule synthesis at the initiation step. The transition from phytoglycogen to sugary-amylopectin was gradual in the boundary region between the inner and outer endosperms of sugary. These results suggest that the synthesis of sugary-amylopectin and phytoglycogen involved a stochastic process and that ISA1 activity plays a critical role in the stochastic process in starch synthesis in rice endosperm. The reduction of cytosolic ADP-glucose pyrophosphorylase activity in shrunken endosperm did not inhibit granule initiation but severely restrained the subsequent enlargement of granules. The shrunken endosperm often developed pleomorphic amyloplasts containing a large number of underdeveloped granules or a large cluster of small grains of amyloplasts, each containing a simple-type starch granule. Although constriction-type divisions of amyloplasts were much more frequent, budding-type divisions were also found in the shrunken endosperm. We show that monitoring GFP in developing amyloplasts was an effective means of evaluating the roles of enzymes involved in starch granule synthesis in the rice endosperm.

Glucans↗

PubMed2005

An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise.

Synaptically generated subthreshold membrane potential (Vm) fluctuations can be characterized within the framework of stochastic calculus. It is possible to obtain analytic expressions for the steady-state Vm distribution, even in the case of conductance-based synaptic currents. However, as we show here, the analytic expressions obtained may substantially deviate from numerical solutions if the stochastic membrane equations are solved exclusively based on expectation values of differentials of the stochastic variables, hence neglecting the spectral properties of the underlying stochastic processes. We suggest a simple solution that corrects these deviations, leading to extended analytic expressions of the Vm distribution valid for a parameter regime that covers several orders of magnitude around physiologically realistic values. These extended expressions should enable finer characterization of the stochasticity of synaptic currents by analyzing experimentally recorded Vm distributions and may be applicable to other classes of stochastic processes as well.

Animals↗

PubMed1997

A stochastic model for the analysis of bivariate longitudinal AIDS data.

We present a model for multivariate repeated measures that incorporates random effects, correlated stochastic processes, and measurement errors. The model is a multivariate generalization of the model for univariate longitudinal data given by Taylor, Cumberland, and Sy (1994, Journal of the American Statistical Association 89, 727-736). The stochastic process used in this paper is the multivariate integrated Ornstein-Uhlenbeck (OU) process, which includes Brownian motion and a random effects model as special limiting cases. This process is an underlying continuous-time autoregressive order [AR(1)] process for the derivatives of the multivariate observations. The model allows unequally spaced observations and missing values for some of the variables. We analyze CD4 T-cell and beta-2-microglobulin measurements of the seroconverters at multiple time points from the Los Angeles section of the Multicenter AIDS Cohort Study. The model allows us to investigate the relationship between CD4 and beta-2-microglobulin through the correlations between their random effects and their serial correlation. The data suggest that CD4 and beta-2-microglobulin follow a bivariate Brownian motion process. The fit of the model implies that an increase in beta-2-microglobulin is associated with a decrease in future CD4 but not vice versa, agreeing with immunologic postulates about the relationship between these two variables.

Acquired Immunodeficiency Syndrome↗

PubMed2004

SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks.

SmartCell has been developed to be a general framework for modelling and simulation of diffusion-reaction networks in a whole-cell context. It supports localisation and diffusion by using a mesoscopic stochastic reaction model. The SmartCell package can handle any cell geometry, considers different cell compartments, allows localisation of species, supports DNA transcription and translation, membrane diffusion and multistep reactions, as well as cell growth. Moreover, different temporal and spatial constraints can be applied to the model. A GUI interface that facilitates model making is also available. In this work we discuss limitations and advantages arising from the approach used in SmartCell and determine the impact of localisation on the behaviour of simple well-defined networks, previously analysed with differential equations. Our results show that this factor might play an important role in the response of networks and cannot be neglected in cell simulations.

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↗

PubMedDate not supplied

[Connection of the tangents of the regression slope of the heart rate graph with linear and nonlinear dynamics in stationary short-time series].

The connection of the regression slope of heart rate graph (b1) with linear and nonlinear dynamics in stationary short-time series (256 points) was studied. A new index for the estimation of nonlinear dynamics in stationary short-time series was used, which is based on the correlation dimension. The results of the study indicated that the dynamics of heart rate in stationary short-time series can be represented as the sum of linear (periodic) and nonlinear (stochastic) processes. A relation of b1 with both linear and nonlinear dynamics of heart rate was found. The formulas for the calculation of absolute and relative (to the amplitude of periodic fluctuations) noise levels in heart rate dynamics were derived. A comparative analysis of nonlinear dynamics of heart rate in stationary short-time series for different functional states of humans was performed. The increase in the relative noise level in heart rate dynamics with increasing breathing frequency is related not only to a decrease in control breathing amplitude but also to an increase in the noise amplitude. The decrease in the absolute noise level for nervous excitation, fatigue, and mental stress were found. The predominance of nonlinear (stochastic) processes over linear (periodic) processes in the relaxed state was established.

Heart↗

PubMed2004

Scaling of prediction error does not confirm chaotic dynamics underlying irregular firing using interspike intervals from midbrain dopamine neurons.

Dopamine neurons in the substantia nigra pars compacta often fire in an irregular, single spike mode in vivo, and a similar firing pattern can be observed in vitro when small conductance calcium-activated potassium channel blockers are applied to the bath. It is not clear whether the irregular firing is due to stochastic processes or nonlinear deterministic processes. A previous study [Neuroscience 104 (2001) 829] used nonlinear forecasting methods applied to a continuous function derived from the interspike interval (ISI) data from irregularly firing dopamine neurons to show that the predictability scaled exponentially with forecast horizon and was consistent with nonlinear deterministic chaos. However, we show here that the observed exponential scaling is also consistent with a stochastic process, because it did not differ significantly from that of shuffled surrogate data. On the other hand, nonlinear forecasting directly from the ISI data using the package TISEAN provided some evidence for nonlinear deterministic structure in four of five records obtained in vitro and in two of nine records obtained in vivo. Although we cannot rule out a role for nonlinear chaotic dynamics in structuring the firing pattern, we suggest an alternate hypothesis that includes a mechanism by which the firing pattern can become more variable in the presence of a constant level of background noise.

Algorithms↗

PubMed1998

Does the covariance structure matter in longitudinal modelling for the prediction of future CD4 counts?

We investigate the importance of the assumed covariance structure for longitudinal modelling of CD4 counts. We examine how individual predictions of future CD4 counts are affected by the covariance structure. We consider four covariance structures: one based on an integrated Ornstein-Uhlenbeck stochastic process; one based on Brownian motion, and two derived from standard linear and quadratic random-effects models. Using data from the Multicenter AIDS Cohort Study and from a simulation study, we show that there is a noticeable deterioration in the coverage rate of confidence intervals if we assume the wrong covariance. There is also a loss in efficiency. The quadratic random-effects model is found to be the best in terms of correctly calibrated prediction intervals, but is substantially less efficient than the others. Incorrectly specifying the covariance structure as linear random effects gives too narrow prediction intervals with poor coverage rates. Fitting using the model based on the integrated Ornstein-Uhlenbeck stochastic process is the preferred one of the four considered because of its efficiency and robustness properties. We also use the difference between the future predicted and observed CD4 counts to assess an appropriate transformation of CD4 counts; a fourth root, cube root and square root all appear reasonable choices.

Acquired Immunodeficiency Syndrome↗