Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “deterministic processes”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

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

At least 1,099 records · Page 61Linked to original sources
PubMed2005

Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction.

The nonlinear prediction method based on the interspike interval (ISI) reconstruction is applied to the ISI sequence of noisy pulse trains and the detection of the deterministic structure is performed. It is found that this method cannot discriminate between the noisy periodic pulse train and the noisy chaotic one when noise-induced pulses exist. When the noise-induced pulses are eliminated by the grouping of ISI sequence with the genetic algorithm, the chaotic structure of the chaotic firings becomes clear, and the noisy chaotic pulse train could be discriminated from the periodic one.

Action Potentials↗
PubMed2006

Power spectra reveal the influence of stochasticity on nonlinear population dynamics.

Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.

Animals↗
PubMed2004

Augmented moment method for stochastic ensembles with delayed couplings. I. Langevin model.

By employing a semianalytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an N -unit ensemble described by Langevin equations with delays. In an AMM, original N -dimensional stochastic delay differential equations (SDDEs) are transformed to infinite-dimensional deterministic DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level m in the level-m AMM (AMMm), which yields (3+m)-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. In the nonlinear Langevin ensemble, the synchronization is shown to be enhanced near the transition point between the oscillating and nonoscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.

Action Potentials↗
PubMed1991

Epidemic curve characteristics for the Reed-Frost model.

Some useful approximations are developed in this paper that describe large-scale epidemic phenomena for the deterministic and stochastic Reed-Frost model. These characteristics provide an a priori quantitative description of the epidemic curve for the deterministic case, such as a threshold requirement, the total size of the epidemic, and the degree of skewness in the epidemic curve. A Poisson distribution asymptotically describes the distribution of the total size of an epidemic when the relative removal rate is well below threshold for the Reed-Frost chain binomial model. These properties are established by an extension of the large-scale epidemic phenomena of the Kermack-McKendrick model.

Binomial Distribution↗
PubMed2002

Approaches to interval mapping of QTL in a multigeneration pedigree: the example of porcine chromosome 4.

Quantitative trait loci (QTLs) have been mapped in many studies of F2 populations derived from crosses between diverse lines. One approach to confirming these effects and improving the mapping resolution is genetic chromosome dissection through a backcrossing programme. Analysis by interval mapping of the data generated is likely to provide additional power and resolution compared with treating data marker by marker. However, interval mapping approaches for such a programme are not well developed, especially where the founder lines were outbred. We explore alternative approaches to analysis using, as an example, data from chromosome 4 in an intercross between wild boar and Large White pigs where QTLs have been previously identified. A least squares interval mapping procedure was used to study growth rate and carcass traits in a subsequent second backcross generation (BC2). This procedure requires the probability of inheriting a wild boar allele for each BC2 animal for locations throughout the chromosome. Two methods for obtaining these probabilities were compared: stochastic or deterministic. The two methods gave similar probabilities for inheriting wild boar alleles and, hence, gave very similar results from the QTL analysis. The deterministic approach has the advantage of being much faster to run but requires specialized software. A QTL for fatness and for growth were confirmed and, in addition, a QTL for piglet growth from weaning at 5 weeks up to 7 weeks of age and another for carcass length were detected.

Alleles↗
PubMed2003

Analysis of penetrance and expressivity during ontogenesis supports a stochastic choice of zebrafish odorant receptors from predetermined groups of receptor genes.

Olfactory receptor neurons select a single odourant receptor gene for expression out of a large gene family. The mechanisms of this extreme selectivity are largely unknown. We have determined in detail the developmental expression dynamics of a representative subset of the zebrafish odourant receptor repertoire, using in situ hybridization analysis. We have thus generated a dataset, which allows us to test hypotheses of odourant receptor gene regulation. The receptors chosen belong to four different groups with respect to ontogenetic onset of expression (onset groups). Statistical analysis of the data supports a model in which the final choice of an individual odourant receptor gene occurs stochastically from within a group of genes sharing a deterministically defined onset of expression. Genomic mapping revealed a pronounced correlation of onset of expression with genomic neighbourhood. During a protracted juvenile developmental period individual regulatory influences seem to modify the expression of odourant receptor genes, a notable example being a transient decrease in expressivity of two odourant receptor genes.

Animals↗
PubMed2004

Phase synchronization in unidirectionally coupled chaotic ratchets.

We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states and perfect phase locking was observed as the coupling was gradually increased. We identified the region of phase synchronization for the ratchets and show that the transition to chaotic phase synchronization is via an interior crisis transition to strange attractor in the phase space.

Biological Clocks↗
PubMed2006

Stochastic models for regulatory networks of the genetic toggle switch.

Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Models, Genetic↗
PubMed2006

Integrating life history and cross-immunity into the evolutionary dynamics of pathogens.

Models for the diversity and evolution of pathogens have branched into two main directions: the adaptive dynamics of quantitative life-history traits (notably virulence) and the maintenance and invasion of multiple, antigenically diverse strains that interact with the host's immune memory. In a first attempt to reconcile these two approaches, we developed a simple modelling framework where two strains of pathogens, defined by a pair of life-history traits (infectious period and infectivity), interfere through a given level of cross-immunity. We used whooping cough as a potential example, but the framework proposed here could be applied to other acute infectious diseases. Specifically, we analysed the effects of these parameters on the invasion dynamics of one strain into a population, where the second strain is endemic. Whereas the deterministic version of the model converges towards stable coexistence of the two strains in most cases, stochastic simulations showed that transient epidemic dynamics can cause the extinction of either strain. Thus ecological dynamics, modulated by the immune parameters, eventually determine the adaptive value of different pathogen genotypes. We advocate an integrative view of pathogen dynamics at the crossroads of immunology, epidemiology and evolution, as a way towards efficient control of infectious diseases.

Antigenic Variation↗
PubMed2006

Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control.

A linear stochastic delay differential equation of second order is studied that can be regarded as a Kramers model with time delay. An analytical expression for the stationary probability density is derived in terms of a Gaussian distribution. In particular, the variance as a function of the time delay is computed analytically for several parameter regimes. Strikingly, in the parameter regime close to the parameter regime in which the deterministic system exhibits Hopf bifurcations, we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks. These peaks are interpreted as delay-induced destabilization resonances arising from oscillatory ghost instabilities. On the basis of the obtained theoretical findings, reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided.

Computer Simulation↗
PubMedDate not supplied

A real-time, interactive steering environment for integrated ground water modeling.

We present in this note an innovative software environment, called Interactive Ground Water (IGW), for unified deterministic and stochastic ground water modeling. Based on efficient computational algorithms, IGW allows simulating three-dimensional (3D) unsteady flow and transport in saturated media subject to systematic and "random" stresses and geological and chemical heterogeneity. Adopting a new computing paradigm, IGW eliminates the fragmentation in the traditional modeling schemes and allows fully utilizing today's dramatically increased computing power. For many problems, IGW enables real-time modeling, visualization, mapping, and analysis. The software environment functions as a "numerical laboratory" in which an investigator may freely explore the following: creating visually an aquifer system of desired configurations, interactively applying stresses and boundary conditions, and then investigating and visualizing on the fly the geology and flow and transport dynamics. At any time, a researcher can pause to interact dynamically with virtually any aspects of the modeling process and then resume the integrated visual exploration; he or she can initiate, pause, or resume particle tracking, plume modeling, subscale modeling, stochastic modeling, monitoring, and budget analyses. IGW continually provides results that are dynamically processed, overlaid, and displayed. It dynamically merges modeling inputs and outputs into composite two-dimensional/3D images-integrating related data to provide a more complete view of the complex interplay among the geology, hydrology, flow system, and transport. These unique capabilities of real-time modeling, steering, analysis, and mapping expand the utility of models as tools for research, education, and professional investigations.

Computer Simulation↗
PubMed2000

The galvanotaxis response mechanism of keratinocytes can be modeled as a proportional controller.

Human keratinocytes actively crawl in vitro when plated onto a collagen-coated glass substrate, and their direction of migration is totally random. In response to an imposed DC electric field, they migrate asymmetrically, moving mostly toward the negative pole of the field. The authors have analyzed experimental data reported by others to determine the basic characteristics of the cellular response machinery in these keratinocytes. This movement can be completely described mathematically using two independent variables: the speed, V, and the angle of migration, phi. The authors propose a model in which a steerer (controller without feedback) is responsible for determining the speed, and an automatic controller (controller with feedback) is responsible for determining the angle of migration. The torque to rotate is induced by a deterministic cellular signal and a stochastic cellular signal. The cellular machine characteristics are determined as follows: The angular dependence of the detection unit is sin phi; the detection unit detects the guiding field in a linear fashion; the cellular reaction unit can be described by a constant; the chemical amplifier, as well as the cellular motor work, is linear; the cellular characteristic time, which quantifies the cellular stochastic signal, is 50 min.

Cell Movement↗
PubMedDate not supplied

Discriminating deterministic versus stochastic dynamics in neuronal activity.

An approach to discriminating deterministic versus stochastic dynamics from neuronal data is presented. Direct tests for determinism are emphasized, as well as using time series with clear physical correlates measured from small ensembles of neurons. Surrogate data are used to provide null hypotheses that the dynamics in our data could be accounted for by linear stochastic systems. Algorithms are given in full, and the analysis of an experimental example is given.

Algorithms↗
PubMed2003

On the performances of noise filters in the restoration of oscillatory behavior in continuous yeast cultures.

Continuous flow microbial fermentations under industrial conditions are subject to the influx of noise, mainly through the feed stream. Noise upsets the normal deterministic behavior. For continuous cultures of Saccharomyces cerevisiae exhibiting oscillatory responses, four kinds of commonly used noise filters, three algorithmic and one neural, have been compared for their ability to restore noise-free oscillations. An auto-associative neural filter was the best, similar to earlier observations for other organisms under non-oscillatory conditions. This enhances the general applicability of neural filters for industrial scale fermentations.

Algorithms↗
PubMed1994

In search of power and significance: issues in the design and analysis of stochastic cost-effectiveness studies in health care.

Application of techniques such as cost-effectiveness analysis (CEA) is growing rapidly in health care. There are two general approaches to analysis: deterministic models based upon assumptions and secondary analysis of retrospective data, and prospective stochastic analyses in which the design of a clinical experiment such as randomised controlled trial is adapted to collect patient-specific data on costs and effects. An important methodological difference between these two approaches is in the quantification and analysis of uncertainty. Whereas the traditional CEA model utilizes sensitivity analysis, the mean-variance data on costs and effects from a prospective trial presents the opportunity to analyze cost-effectiveness using conventional inferential statistical methods. In this study we explored some of the implications of moving economic appraisal away from deterministic models and toward the experimental paradigm. Our specific focus was on the feasibility and desirability of constructing statistical tests of economic hypotheses and estimation of cost-effectiveness ratios with associated 95% confidence intervals. We show how relevant variances can be estimated for this task and discuss the implications for the design and analysis of prospective economic studies.

Confidence Intervals↗
PubMed2004

Figures of merit for detectors in digital radiography. II. Finite number of secondaries and structured backgrounds.

The current paradigm for evaluating detectors in digital radiography relies on Fourier methods. Fourier methods rely on a shift-invariant and statistically stationary description of the imaging system. The theoretical justification for the use of Fourier methods is based on a uniform background fluence and an infinite detector. In practice, the background fluence is not uniform and detector size is finite. We study the effect of stochastic blurring and structured backgrounds on the correlation between Fourier-based figures of merit and Hotelling detectability. A stochastic model of the blurring leads to behavior similar to what is observed by adding electronic noise to the deterministic blurring model. Background structure does away with the shift invariance. Anatomical variation makes the covariance matrix of the data less amenable to Fourier methods by introducing long-range correlations. It is desirable to have figures of merit that can account for all the sources of variation, some of which are not stationary. For such cases, we show that the commonly used figures of merit based on the discrete Fourier transform can provide an inaccurate estimate of Hotelling detectability.

Algorithms↗
PubMed1990

Comparison of stochastic and deterministic methods for modeling spur kinetics.

Stochastic and deterministic kinetic methods have been used to model the temporal evolution of spatially nonhomogeneous clusters of reactants resulting from the dissociation of one to six water molecules into either H3O+, OH, and e-aq, or H atoms and OH radicals. When the ionic fragmentation initially producing H3O+, OH, and e-aq is considered, the stochastic and deterministic methods predict similar time dependences for the decay of the reactive species; however, the two methods suggest very different product yields. For a two-dissociation spur, the deterministic treatment overestimates both the H2 and the H2O2 yields by about 70%. The error decreases to less than 15% for a spur with six water dissociations. For a distribution of spurs representing a high-energy electron track, the differences in the predicted yields of reactants are less than 6% at 0.1 microseconds, but the stochastic and deterministic predictions for the yields of H2 and H2O2 differ by about 50%. The kinetics of spurs produced by the fragmentation of water to H atom and OH radical shows discrepancies in both the reactant and the product yields. The size of the discrepancy decreases as the number of H/OH pairs increases, and the predictions of the two techniques are almost the same for clusters of six water dissociations.

Computer Simulation↗
PubMed1999

Analysis of growth kinetics by division tracking.

Cell division tracking using fluorescent dyes, such as carboxyfluorescein diacetate succinimidyl ester, provides a unique opportunity for analysis of cell growth kinetics. The present review article presents new methods for enhancing resolution of division tracking data as well as derivation of quantities that characterize growth from time-series data. These include the average time between successive divisions, the proportion of cells that survive and the proliferation per division. The physical significance of these measured quantities is interpreted by formulation of a two-compartment model of cell cycle transit characterized by stochastic and deterministic cell residence times, respectively. The model confirmed that survival is directly related to the proportion of cells that enter the next cell generation. The proportion of time that cells reside in the stochastic compartment is directly related to the proliferation per generation. This form of analysis provides a starting point for more sophisticated physical and biochemical models of cell cycle regulation.

Cell Count↗