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PubMed1998

Stability analysis of the FitzHugh-Nagumo differential equations driven by impulses: applied to the electrical firing of magnocellular neurons.

A stability analysis is carried out for a mathematical model which describes the electrical firing of a single vasopressin neuron. The model used in a FitzHugh-Nagumo-type system which is driven by impulses. The analysis is based on recent developments in the stability theory of impulsive differential equations. Conditions are derived under which the system of differential equations is stable at two of its equilibrium points. Biologically this bistability represents the cell alternating between periods of electrical activity and silence. The conditions for stability are specified in terms of the amplitude and frequency of the impulses perturbing the system. Both stochastic and deterministic impulses are considered.

Action Potentials↗
PubMed1985

Decision making under uncertainty: a comparison of simple scalability, fixed-sample, and sequential-sampling models.

The purpose of this article is to investigate the learning and memory processes involved in decision making under uncertainty. In two different experiments, subjects were given a choice between a certain alternative that produced a single known payoff and an uncertain alternative that produced a normal distribution of payoffs. Initially this distribution was unknown, and in the first experiment it was learned through feedback from past decisions, whereas in the second experiment it was learned by observing sample outcomes. In the first experiment, a response deadline was used to limit the amount of time available for making a decision. In the second experiment, an observation cost was used to limit the number of samples that could be purchased. The mean and variance of the uncertain alternative and the value of the certain alternative were factorially manipulated to study their joint effects on choice probability, choice response time (Experiment 1), and number of observations purchased (Experiment 2). Algebraic-deterministic theories developed for decision making with simple gambles fail to explain the present results. Two new models are developed and tested--fixed- and sequential-sampling models--that attempt to describe the learning and memory processes involved in decision making under uncertainty.

Adult↗
PubMed1977

A mechanistic model of the aerobic growth of Saccharomyces cerevisiae.

A two-stage deterministic model of the growth of Saccharomyces cerevisiae is presented. The cell cycle of this organism was used to suggest the basic model structure. The model represents the preparatory processes of substrate uptake and conversion separately from replication and division. The regulation of the fraction of the culture devoted to each of these broad areas of metabolism, and the overall growth rate, is related to the nature and availability of the energy substrate. The simulation of respiration and glycolysis is achieved by including two alternative energy producing pathways. The regulation of these pathways is described in terms of the postulated primary regulation of the proportion of the culture required for substrate uptake and conversion, and the overall kinetic constants for each pathway. This regulation is dictated primarily by the growth rate rather than the nature or concentration of the energy substrate. The model successfully describes both batch and continuous growth of S. cerevisiae under conditons of glucose limitation and oxygen excess. A preliminary assessment indicates that adjustment of the relevant parameters will allow the model to describe the growth of S. cerevisiae on other sugars and under oxygen limitation. Similarly the model could be expected to describe the growth characteristics of other yeast species.

Aerobiosis↗
PubMed2000

Can varying concepts of susceptibility in risk assessment affect particulate matter standards?

The Clean Air Act mandates that sensitive subpopulations be considered in setting standards to protect the public's health. The purposes of this paper are to point out different conceptualizations of susceptibility, examine how it is approached in risk-related processes, and recommend ways it may be more explicitly framed for risk assessment and management purposes. We studied the traditional risk assessment paradigm, the U.S. Environmental Protection Agency (EPA) guidelines and revised PM standard, discussions from recent interdisciplinary meetings, and peer-reviewed literature. Areas of controversy include what factors intrinsic and extrinsic to the host should be incorporated in susceptibility, what health endpoints are of concern, whether susceptibility is deterministic or stochastic, and whether it should be defined on an individual or population scale. Recent discussions about susceptibility applied to PM indicate that it needs to be more clearly defined and evaluated for scientific and policy purposes. We conclude that varying concepts of susceptibility can affect risk-related processes such as PM standard setting. We recommend that susceptibility be clearly defined in the problem statement of risk assessments and be addressed in a specific subsection of risk characterization, integrating all susceptibility findings from the prior three steps in the risk assessment paradigm.

Air Pollution↗
PubMed2001

Using a continuous time hidden Markov process, with covariates, to model bed occupancy of people aged over 65 years.

Previously, the application of a continuous time hidden Markov model with discrete states was used to model geriatric inpatient behaviour. This was itself built on research using a discrete deterministic model to represent the flow of geriatric patients around departments of geriatric medicine. This paper uses the continuous time hidden Markov models and includes the effect of covariates, age and sex, in the model. Fitting the models we can visually see that the two compartment models provides estimates that are much closer to those observed in the data. The addition of covariates provides us with evidence of a difference in length of stay between men and women. However, even significant alterations to the mean age of patients in the model does not effect the length of stay.

Age Factors↗
PubMed1996

Deterministic pressure dissociation and unfolding of triose phosphate isomerase: persistent heterogeneity of a protein dimer.

Subunit dissociation and unfolding of dimeric rabbit muscle triose phosphate isomerase (TIM) induced by hydrostatic pressure were investigated. Changes in fluorescence emission of TIM (both intrinsic and of covalently attached probes) indicated that pressure ranging from 1 bar to 3.5 kbar promoted subunit dissociation and unfolding. Instrinsic fluorescence changes upon unfolding by pressure included a 27 nm red-shift of the emission, a decrease in fluorescence anisotropy from 0.14 to about 0.01, and a 1.5-fold increase in fluorescence quantum yield, similar to that observed in the presence of guanidine hydrochloride. Kinetics of pressure-induced fluorescence changes were slow (t 1/2 approximately 15 min) and little dependent on pressure. In order to selectively monitor subunit dissociation, fluorescence resonance energy transfer (FRET) measurements were carried out with TIM that was separately labeled with 5-((((2-iodoacetyl)-amino)ethyl)amino)naphthalene-1-sulfonic acid (1,5-IAEDANS) or fluorescein-5-isothiocyanate (FITC). FRET measurements indicated that subunit dissociation and unfolding took place concomitantly, both under equilibrium conditions and in kinetic experiments in which dissociation/unfolding was triggered by a sudden increase in pressure. Release of pressure caused monomer refolding and dimerization. Contrary to what would be expected for a process involving subunit dissociation, pressure effects on TIM were not dependent on protein concentration. Experiments involving a series of pressure jumps demonstrated persistent heterogeneity in sensitivity toward pressure in the ensemble of TIM dimers. This kind of deterministic behavior is similar to that exhibited by higher order protein aggregates and indicates that not all individual dimers are energetically identical in solution. The heterogeneity of native TIM revealed by sensitivity to pressure could not be detected by traditional means of protein separation, such as polyacrylamide gel electrophoresis (under both native and denaturing conditions) and size exclusion gel chromatography. This suggests that energetic heterogeneity originates from conformational heterogeneity of the protein. The possible biological relevance of the deterministic character of stability of TIM is discussed.

Animals↗
PubMed1997

Time-frequency plane Wiener filtering of the high-resolution ECG: background and time-frequency representations.

This paper introduces the concept of a posteriori Wiener filtering (APWF), performed in the time-frequency plane. The objective is to improve the signal-to-noise ratio (SNR) of the ensemble-averaged high-resolution electrocardiogram (HRECG). APWF was developed to address the problem of a limited ensemble size for estimating ensemble-averaged evoked potentials. For the HRECG, we identify the major challenge as adapting the time-frequency structure of the filter to that of low-level cardiac signals. Technical limitations and the characteristics of HRECG signals make time-frequency analysis of the ensemble average problematic. Normal and abnormal signal components are difficult to distinguish due to low time-frequency energy concentration and limited spectrotemporal resolution. However, considering the entire ensemble of repetitive ECG records, signal and noise components are separable in the time-frequency plane. This forms the basis of the new time-frequency plane Wiener (TFPW) filter, applicable to any ensemble averaging problem involving repetitive deterministic signals mixed with uncorrelated noise.

Electrocardiography↗
PubMedDate not supplied

Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm.

Acquired Immunodeficiency Syndrome↗
PubMed2001

An introduction to microevolution: rate, pattern, process.

This special issue of Genetica brings together a diverse collection of contributions that examine evolution within and among populations (i.e., microevolution), and the role that microevolution plays in the formation of new species and morphological forms (i.e., macroevolution). Many of the papers present evidence of microevolution occurring over contemporary time frames, further validating the near ubiquity of ongoing evolution in the world around us. Several synthetic reviews of empirical work help to define the conditions under which microevolution is or is not likely to occur. Some of the studies speak directly to current controversies in evolutionary biology, such as the relative roles of determinism and contingency, and the nature of the relationship between microevolution and macroevolution. In general, microevolution seems driven largely by deterministic mechanisms, particularly natural selection, but contingency plays a role in (1) determining whether or not suitable conditions are present for evolution to proceed, and (2) guiding the precise manner by which evolution proceeds. Several theoretical treatments and empirical reviews confirm previous research in showing that microevolutionary processes are at least capable of generating macroevolutionary trends. Macroevolution may indeed reflect microevolution writ large but the pattern by which it arises is perhaps best characterized as microevolution writ in fits and starts.

Adaptation, Biological↗
PubMed2000

Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model.

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules [K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992)] and with maximum velocity v(max)>1, which is an extension of the asymmetric exclusion process (ASEP). It turns out that the behavior of the system is dominated by two features: (a) the competition between the left and the right boundary, (b) the development of so-called "buffers" due to the hindrance that an injected car feels from the front car at the beginning of the system. As a consequence, there is a first-order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers, and the phase diagram essentially differs from that for v(max)=1 (ASEP).

Journal Article↗
PubMed2001

Diffusion of particles bouncing on a one-dimensional periodically corrugated floor.

We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.

Journal Article↗
PubMed1990

[The EEG and thinking].

The on-going EEG contains information on thinking strategies during cognitive and creative tasks and during listening to music. This was demonstrated by a method taking use of the fact that both the amount of local current production and the degree of electric coupling of brain regions is characteristically changed by mental tasks. In groups of volunteers the significant changes of absolute power and coherence caused by different mental tasks are computed and entered into schematic brain maps (EEG probability maps). The results indicate the existence of general brain strategies even in mental activities as specific as those referred to above. Moreover, several relationships between EEG, psychological test scores, degree of special education and intelligence were found. Studies with extreme value validation according to intelligence and creativity test scores yielded significant differences between the groups of the best and the poorest performers during a creative task in the EEG. The EEG thus can be conceived of as deterministic chaos with different degrees of organization according to its information content. In this context, the question arises as to a possible function of the EEG for the optimization of thinking processes.

Cognition↗
PubMed1991

Dynamic population epidemic models.

Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move among the populations and can infect only within their current population. Both the stochastic and deterministic versions of such models are considered. Their threshold behavior is analyzed in some depth, as are their final outcomes. Velocities of spread of infection are considered when the populations have a spatial structure. A criterion for finding the equivalent contact distribution epidemic for any given dynamic population epidemic is provided, enabling comparisons to be made for the velocities and final outcomes displayed by the two classes of models. The relationship between deterministic and stochastic epidemic models is also discussed briefly.

Disease Outbreaks↗
PubMed2002

On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment.

In this paper we extend the deterministic model for the epidemics induced by virulent phages on bacteria in marine environment introduced by Beretta and Kuang [Math. Biosci. 149 (1998) 57], allowing random fluctuations around the positive equilibrium. The stochastic stability properties of the model are investigated both analytically and numerically suggesting that the deterministic model is robust with respect to stochastic perturbations.

Bacteriophages↗
PubMed1999

Insufficient evidence: the problems of evidence-based nursing.

Evidence-based medicine was first proposed in the early 1990s as a means of integrating clinical expertise with the best evidence from research. It has recently gained a foothold in nursing, where despite calls for a broad and nursing-oriented definition of what should count as evidence, it appears to be propounding the randomized controlled trial (RCT) as the gold standard. This paper challenges the wisdom of basing nursing practice on the findings of large-scale statistical research studies, and offers a number of logical objections to the underpinning philosophy of evidence-based nursing and the randomized controlled trial. It concludes by arguing for a rethinking of what should count as evidence, and suggests a quasi-legal model based on reflection rather than research, in which evidence is employed to understand and justify practice after the event rather than being used deterministically to plan practice in advance.

Clinical Competence↗
PubMed1990

Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities. We compare the predictions of the probabilistic model with those of a deterministic model, and show how a deterministic approach can yield some inaccurate results; e.g., it cannot account for temporally continuous cell attach mentor detachment, it can underestimate the time needed for cell attachment, it can overestimate the time required for cell detachment for a given level of force, and it can overestimate the force necessary for cell detachment.

Biophysical Phenomena↗
PubMed2000

Hitchhiking under positive Darwinian selection.

Positive selection can be inferred from its effect on linked neutral variation. In the restrictive case when there is no recombination, all linked variation is removed. If recombination is present but rare, both deterministic and stochastic models of positive selection show that linked variation hitchhikes to either low or high frequencies. While the frequency distribution of variation can be influenced by a number of evolutionary processes, an excess of derived variants at high frequency is a unique pattern produced by hitchhiking (derived refers to the nonancestral state as determined from an outgroup). We adopt a statistic, H, to measure an excess of high compared to intermediate frequency variants. Only a few high-frequency variants are needed to detect hitchhiking since not many are expected under neutrality. This is of particular utility in regions of low recombination where there is not much variation and in regions of normal or high recombination, where the hitchhiking effect can be limited to a small (<1 kb) region. Application of the H test to published surveys of Drosophila variation reveals an excess of high frequency variants that are likely to have been influenced by positive selection.

Animals↗