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PubMed2002

Continuously varying critical exponents in a sandpile model with internal disorder.

A sandpile model with an internal disorder is presented. The updating of critical sites is done according to a stochastic rule (with a probabilistic toppling q). Using a unified mean-field theory and numerical simulations, we have shown that the criticality is ensured for any value of q. The static critical exponents have been calculated and found to be the same as those obtained for the deterministic sandpile model, which is a particular case of the stochastic model. They have a universal q-independent behavior. In the limit of slow driving, we have developed a relation between our model and the branching process in order to compute the size exponent tau. It presents a continuous variation with the parameter of toppling q.

Journal Article↗
PubMed1995

Measuring "chaos" in the brain: a tutorial review of EEG dimension estimation.

The technique of dimension estimation is currently a leading application of nonlinear dynamics (popularly termed "chaos theory") to EEG analysis. A tutorial review of this technique is presented along with some elementary background concepts from nonlinear dynamics. Practical aspects of applying dimension estimation to EEG data are also reviewed, and the possible role of deterministic chaos in brain function is discussed.

Brain↗
PubMedDate not supplied

The importance of I.P. Pavlov for the development of neuroscience.

By his experimental and theoretical work on the physiology and pathophysiology of the higher nervous activity I.P. Pavlov significantly influenced the development of Neuroscience. During the 1950 Pavlovian Conference in Moscow, Stalin and the Communist Party tried to dogmatize his and his pupils' fundamental theories. But the Pavlovian ideas were developed by his pupils in open discussions with representatives of other schools in a very creative way, opening the doors for a systemic approach to understanding the integrative functional systems of brain and behavior. Pavlov emphasized the high plasticity of the central nervous system, investigated the complex functional systems within the brain and between the organism and its environment, and designed models for pathological deviations of the higher nervous activity. During his last years, he freed himself from the strong deterministic view and characterized the organism and its environment as a self-organizing system.

History, 19th Century↗
PubMed1992

Human exposure to large solar particle events in space.

Whenever energetic solar protons produced by solar particle events traverse bulk matter, they undergo various nuclear and atomic collision processes which significantly alter the physical characteristics and biologically important properties of their transported radiation fields. These physical interactions and their effect on the resulting radiation field within matter are described within the context of a recently developed deterministic, coupled neutron-proton space radiation transport computer code (BRYNTRN). Using this computer code, estimates of human exposure in interplanetary space, behind nominal (2 g/cm2) and storm shelter (20 g/cm2) thicknesses of aluminum shielding, are made for the large solar proton event of August 1972. Included in these calculations are estimates of cumulative exposures to the skin, ocular lens, and bone marrow as a function of time during the event. Risk assessment in terms of absorbed dose and dose equivalent is discussed for these organs. Also presented are estimates of organ exposures for hypothetical, worst-case flare scenarios. The rate of dose equivalent accumulation places this situation in an interesting region of dose rate between the very low values of usual concern in terrestrial radiation environments and the high dose rate values prevalent in radiation therapy.

Bone Marrow↗
PubMed1985

Possible forms for dwell-time histograms from single-channel current records.

Certain macromolecules embedded in the cell membranes of a variety of cells behave as gated ion-selective pores or channels. The length of time that a channel remains open or closed is not deterministic in nature and must be described in terms of relative probabilities. If channels act independently of each other and appropriate experimental conditions can be maintained, the behavior of a channel can be described by a homogeneous Markov process. Using this representation, the relative probability of observing openings (or closings) of various durations can be described by a sum of discrete components which are related to the underlying model of the kinetic behavior of the channel. Generally, these discrete components are taken to be simple decaying exponentials; however, exponentially decaying oscillatory components (as well as certain others which are discussed) are consistent with the Markov process representation. The presence of components other than simple decaying exponentials is shown to imply the violation of detailed balance in the steady-state (which requires energy), and thus, the presence of cyclic pathways in models which accurately represent the kinetic behavior of the channel. Oscillatory components, if present, will in general decay at a faster rate than the slowest decaying component, which, except under a very restricted set of conditions, will be a simple exponential.

Cell Membrane Permeability↗
PubMed2001

Kinetics of initiation, propagation, and termination for the [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)]-catalyzed polymerization of 1-hexene.

Metallocene-catalyzed polymerization of 1-alkenes offers fine control of critical polymer attributes such as molecular weight, polydispersity, tacticity, and comonomer incorporation. Enormous effort has been expended on the synthesis and discovery of new catalysts and activators, but elementary aspects of the catalytic processes remain unclear. For example, it is unclear how the catalyst is distributed among active and dormant sites and how this distribution influences the order in monomer for the propagation rates, for which widely varying values are reported. Similarly, although empirical relationships between average molecular weights and monomer have been established for many systems, the underlying mechanisms of chain termination are unclear. Another area of intense interest concerns the role of ion-pairing in controlling the activity and termination mechanisms of metallocene-catalyzed polymerizations. Herein we report the application of quenched-flow kinetics, active site counting, polymer microstructure analysis, and molecular weight distribution analysis to the determination of fundamental rate laws for initiation, propagation, and termination for the polymerization of 1-hexene in toluene solution as catalyzed by the contact ion-pair, [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)] (1) over the temperature range of -10 to 50 degrees C. Highly isotactic (>99% mmmm) poly-1-hexene is produced with no apparent enchained regioerrors. Initiation and propagation processes are first order in the concentrations of 1-hexene and 1 but independent of excess borane or the addition of the contact ion-pair [PhNMe(3)][MeB(C(6)F(5))(3)]. Active site counting and the reaction kinetics provide no evidence of catalyst accumulation in dormant or inactive sites. Initiation is slower than propagation by a factor of 70. The principal termination process is the formation of unsaturates of two types: vinylidene end groups that arise from termination after a 1,2 insertion and vinylene end groups that follow 2,1 insertions. The rate law for the former termination process is independent of the 1-hexene concentration, whereas the latter is first order. Analysis of (13)C-labeled polymer provides support for a mechanism of vinylene end group formation that is not chain transfer to monomer. Deterministic modeling of the molecular weight distributions using the fundamental rate laws and kinetic constants demonstrates the robustness of the kinetic analysis. Comparisons of insertion frequencies with estimated limits on the rates of ion-pair symmetrization obtained by NMR suggest that ion-pair separation prior to insertion is not required, but the analysis requires assumptions that cannot be validated.

Alkenes↗
PubMed1996

Computing marginal expectations for large compartmentalized models with application to AIDS evolution in a prison system.

The customary models for the AIDS epidemic are compartmentalized according to criteria such as risk factors, sexual habits, gender, race, age, and HIV status and stage. Hitherto, with very few exceptions, investigators have resorted to deterministic approximations or to simulation for the computational investigation of such models, which do not yield to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compartmentalized Markov population processes. Analytic error bounds and computational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, with ten interrelated prisons, twenty compartments, and thousands of individuals. This model is of increasing interest in itself because the HIV/AIDS epidemic is particularly virulent among prison populations, where the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computational techniques are shown to be effective for the analysis of such a prison system, even though the resulting Markov process is an order of magnitude more complicated than other stochastic epidemic models currently being investigated. The modelling approach and numerical device appear to be applicable to a wide variety of population processes involving migration between population patches.

Acquired Immunodeficiency Syndrome↗
PubMed1965

SOME KINETIC PROPERTIES OF A DETERMINISTIC EPIDEMIC CONFIRMED BY COMPUTER SIMULATION.

Representative epidemic transients were generated by computer by a known, plausible mechanism. Accurate retrieval of the individual rate constants and confirmation of their predictive value resulted from a manual test of the mechanism by which the computer outputs were generated. The method is applicable in principle to any regenerative process opposed by exponential decay.

Computer Simulation↗
PubMed2000

On the comparative static properties of the expected population density in the presence of stochastic fluctuations.

We consider the impact of increased stochastic fluctuations on the expected density of an unstructured population evolving according to a regular diffusion process subject to a concave expected growth rate. By relying on the flow nature of the solutions of stochastic differential equations and Girsanov's theorem, we demonstrate that typically increased volatility decreases the expected future population density. As a consequence, we are able to characterize the sensitivity of the expected population density with respect to changes in the diffusion coefficient measuring the size of the stochastic fluctuations. We provide both qualitative and quantitative information about the consequences of a mis-specified volatility structure and, especially, of a deterministic approximation to stochastic population growth. We also consider the effect of uncertainty in the initial density and demonstrate that the sign of the relationship between the expected population density and initial uncertainty is unambiguosly negative.

Animals↗
PubMed2002

Pathological tremors as diffusional processes.

Two types of pathological tremors, essential and Parkinsonian, are studied using dynamical systems theory. It is shown that pathological tremors can be characterized as diffusional processes. The time-scale range for the diffusional scaling law to be valid starts from about one to several tens of the mean oscillation period. This time-scale range contrasts sharply with the predictable time scale for deterministic chaos, which is usually only a small fraction of the mean oscillation period. The diffusions in pathological tremors are usually anomalous. A number of quantities are designed to characterize the diffusions in the tremor. Their relevance to potential clinical applications is discussed. It is argued that in order to discriminate between Parkinsonian and essential tremors, quantities not of purely dynamical origin may be more useful, since purely dynamical quantities emphasize more the dynamical similarities between the two types of tremors.

Essential Tremor↗
PubMed1995

The D-1 dopamine receptor: past, present and future an idiosyncratic review.

1. Key events in the experimental investigation of the D-1 dopamine receptor are reviewed. 2. The efficacy of D-1 receptor agonists in the treatment of experimental parkinsonism in MPTP-treated primates is demonstrated. The diminished dyskinetic liability of D-1 agonists is discussed. 3. The significance of the dopa-induced dyskinesias is discussed from the perspective of deterministic chaos. The unpredictibility and irreproducibility of dyskinetic movements is highlighted and compared with features of the logistic equation. 4. The authors propose that the dopa-induced dyskinesias should be considered to be a manifestation of a chaotic process within the basal ganglia. The loss of the dopaminergic innervation and the subsequent repeated exposure to dopamine (derived from the exogenous dopa administered to the subjects) alters the response properties of the basal ganglia circuitry so that stimulation of dopamine receptors now elicits the dyskinetic movements.

Animals↗
PubMed2002

On the slow dynamics of density fluctuations near the colloidal glass transition.

Slow dynamics of density fluctuations near the colloidal glass transition is discussed from a new viewpoint by numerically solving a nonlinear stochastic diffusion equation for the density fluctuations recently proposed by one of the present authors (MT). The effects of spatial heterogeneities on the dynamics of density fluctuations are then investigated in an equilibrium system. The spatial heterogeneities are generated by the nonlinear density fluctuations, while in a nonequilibrium system they are described by a nonlinear deterministic equation for the average number density. The dynamics of equilibrium density fluctuations is thus shown to be quite different from that of nonequilibrium ones, leading to a logarithmic decay followed by less distinct alpha- and beta-relaxation processes.

Journal Article↗
PubMed2002

Advances in space radiation shielding codes.

Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary concept to the final design. For the last few decades, we have pursued deterministic solutions of the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard Finite Element Method (FEM) geometry common to engineering design methods. A single ray trace in such geometry requires 14 milliseconds and limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given.

Cosmic Radiation↗
PubMed1993

Time series analysis of complex dynamics in physiology and medicine.

A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.

Animals↗
PubMed1997

Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent.

Ecology has long been troubled by the controversy over how populations are regulated. Some ecologists focus on the role of environmental effects, whereas others argue that density-dependent feedback mechanisms are central. The relative importance of both processes is still hotly debated, but clear examples of both processes acting in the same population are rare. Key-factor analysis (regression of population changes on possible causal factors) and time-series analysis are often used to investigate the presence of density dependence, but such approaches may be biased and provide no information on actual demographic rates. Here we report on both density-dependent and density-independent effects in a murid rodent pest species, the multimammate rat Mastomys natalensis (Smith, 1834), using statistical capture-recapture models. Both effects occur simultaneously, but we also demonstrate that they do not affect all demographic rates in the same way. We have incorporated the obtained estimates of demographic rates in a population dynamics model and show that the observed dynamics are affected by stabilizing nonlinear density-dependent components coupled with strong deterministic and stochastic seasonal components.

Africa↗
PubMed2004

Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks.

The biochemical reaction networks include elementary reactions differing by many orders of magnitude in the numbers of molecules involved. The kinetics of reactions involving small numbers of molecules can be studied by exact stochastic simulation. This approach is not practical for the simulation of metabolic processes because of the computational cost of accounting for individual molecular collisions. We present the "maximal time step method," a novel approach combining the Gibson and Bruck algorithm with the Gillespie tau-leap method. This algorithm allows stochastic simulation of systems composed of both intensive metabolic reactions and regulatory processes involving small numbers of molecules. The method is applied to the simulation of glucose, lactose, and glycerol metabolism in Escherichia coli. The gene expression, signal transduction, transport, and enzymatic activities are modeled simultaneously. We show that random fluctuations in gene expression can propagate to the level of metabolic processes. In the cells switching from glucose to a mixture of lactose and glycerol, random delays in transcription initiation determine whether lactose or glycerol operon is induced. In a small fraction of cells severe decrease in metabolic activity may also occur. Both effects are epigenetically inherited by the progeny of the cell in which the random delay in transcription initiation occurred.

Biochemistry↗
PubMed1993

Recurrence plots of neuronal spike trains.

The recently developed qualitative method of diagnosis of dynamical systems-recurrence plots-has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.

Action Potentials↗