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Results for “deterministic processes”

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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↗
PubMed2001

Bridge from diffusion-limited aggregation to the Saffman-Taylor problem.

We introduce a Monte Carlo mean-field scheme for the diffusion-limited aggregation (DLA) model, in order to simulate processes of viscous fingering. The patterns obtained demonstrate a striking resemblance to natural shapes in Hele-Shaw cells, reproducing the Saffman-Taylor analytical solutions in the stable regime. The corresponding deterministic equations of the mean-field DLA scheme are derived and studied.

Journal Article↗
PubMed2026

A step-wise, deterministic and fatal mouse model of myeloid neoplasm with spontaneous acquisition of patient-relevant RTK-RAS mutations.

Leukaemia arises through the stepwise transformation of healthy haematopoietic cells, yet the asymptomatic premalignant phase and its progression to overt disease remain poorly understood. To model this process, we engineered a patient-derived CEBPA mutation into Hoxb8-FL multipotent murine progenitors and transplanted them into syngeneic mice, capturing a clinically silent premalignant stage. All recipients developed overt disease after ~12 months with 100% penetrance and all acquired secondary RTK-RAS mutations, often with identical amino acid changes to those in patients. Single-cell transcriptomics and phenotypic profiling showed that premalignant mutant cells adopt a plasmacytoid dendritic progenitor-like state in vitro which generates both myeloid and B-lymphoid lineages during premalignancy in vivo, with individual tumours restricted to one lineage. The specificity for RTK-RAS mutations coupled with ongoing differentiation, reflects clinically relevant biological contexts thus providing a tractable model of myeloid neoplasm for mechanistic studies and drug discovery.

Journal Article↗
PubMed1995

Dynamical analysis of neuromuscular transmission jitter.

Utilizing prolonged axonal stimulation single fiber EMG, neuromuscular transmission becomes a time-series of interpotential intervals (IPIs). In this form, the underlying processes of neuromuscular transmission can be studied using standard numerical techniques to determine whether these processes can be described by a simple mathematical model. In particular, neuromuscular transmission jitter can be examined in this way. In this article, we attempt to determine whether healthy jitter is noise or deterministic chaos. The presence of deterministic chaos was assessed by analysis of the IPI time-series using visual inspection of both phase-space plots and their principal component dimensions, and using the Grassberger-Procaccia algorithm to determine the correlation dimension of the time-series dynamics. These graphical and mathematical techniques provided little evidence for the existence of deterministic chaos. Linear autoregression time-series prediction also failed to account for the variability of the data and IPI histograms exhibited simple gaussian distributions. These results suggest normal neuromuscular transmission jitter is the result of intrinsic noise.

Action Potentials↗
PubMed1991

A stochastic model for the development of an AIDS epidemic in a heterosexual population.

A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Quantal noise and decision rules in dynamic models of light adaptation.

To evaluate some of the consequences of including probabilistic processes (e.g. quantal noise) in a computable model of light-adaptation dynamics, we considered the behavior of a general class of models. These models contain four stages: (1) early noise; (2) a deterministic filtering and gain-changing stage; (3) late noise; (4) a decision rule that is either an ideal (signal-known-exactly) detector or a peak-trough detector. With the ideal detector and without late noise, the observer's sensitivity as a function of mean luminance and temporal frequency is not affected by the filtering and gain-changing stage. Consequently, if the early noise is entirely quantal fluctuations, sensitivity will always be a square-root function of mean luminance and a uniform (flat) function of temporal frequency. This latter prediction is contradicted by all known data; either the ideal-detector is the wrong decision rule or sensitivity is almost always limited by sources of noise other than quantal fluctuations. With the peak-trough detector, however, with or without late noise, the observer's sensitivity as a function of temporal frequency does reflect the sensitivity of the low-level filtering and gain-changing stage. Late noise is needed, however, if the observer's sensitivity as a function of mean luminance is to go through both a square-root and a Weber region. Comparing these conclusions to similar work on the spatial frequency dimension highlights differences between the spatial and temporal frequency domains. Finally, on the basis of these analyses and evidence from the literature, we question whether quantal fluctuations limit visual sensitivity under any condition.

Adaptation, Ocular↗
PubMed2001

Non-thermal melting in semiconductors measured at femtosecond resolution.

Ultrafast time-resolved optical spectroscopy has revealed new classes of physical, chemical and biological reactions, in which directed, deterministic motions of atoms have a key role. This contrasts with the random, diffusive motion of atoms across activation barriers that typically determines kinetic rates on slower timescales. An example of these new processes is the ultrafast melting of semiconductors, which is believed to arise from a strong modification of the inter-atomic forces owing to laser-induced promotion of a large fraction (10% or more) of the valence electrons to the conduction band. The atoms immediately begin to move and rapidly gain sufficient kinetic energy to induce melting--much faster than the several picoseconds required to convert the electronic energy into thermal motions. Here we present measurements of the characteristic melting time of InSb with a recently developed technique of ultrafast time-resolved X-ray diffraction that, in contrast to optical spectroscopy, provides a direct probe of the changing atomic structure. The data establish unambiguously a loss of long-range order up to 900 A inside the crystal, with time constants as short as 350 femtoseconds. This ability to obtain the quantitative structural characterization of non-thermal processes should find widespread application in the study of ultrafast dynamics in other physical, chemical and biological systems.

Journal Article↗
PubMed2001

New data and tools for integrating discrete and continuous population modeling strategies.

Realistic population models have interactions between individuals. Such interactions cause populations to behave as systems with nonlinear dynamics. Much population data analysis is done using linear models assuming no interactions between individuals. Such analyses miss strong influences on population behavior and can lead to serious errors--especially for infectious diseases. To promote more effective population system analyses, we present a flexible and intuitive modeling framework for infection transmission systems. This framework will help population scientists gain insight into population dynamics, develop theory about population processes, better analyze and interpret population data, design more powerful and informative studies, and better inform policy decisions. Our framework uses a hierarchy of infection transmission system models. Four levels are presented here: deterministic compartmental models using ordinary differential equations (DE); stochastic compartmental (SC) models that relax assumptions about population size and include stochastic effects; individual event history models (IEH) that relax the SC compartmental structure assumptions by allowing each individual to be unique. IEH models also track each individual's history, and thus, allow the simulation of field studies. Finally, dynamic network (DNW) models relax the assumption of the previous models that contacts between individuals are instantaneous events that do not affect subsequent contacts. Eventually it should be possible to transit between these model forms at the click of a mouse. An example is presented dealing with Cryptosporidium. It illustrates how transiting model forms helps assess water contamination effects, evaluate control options, and design studies of infection transmission systems using nucleotide sequences of infectious agents.

Data Interpretation, Statistical↗
PubMed1993

Statistical moments in pharmacokinetics: models and assumptions.

The modelling basis of statistical moments in pharmacokinetics is considered and the associated assumptions and restrictions highlighted. Both deterministic and statistical models are described and they are seen to give identical results on the basis of equivalent assumptions. It is shown that it is not necessary to assume that all kinetic processes are first order and that some of the pharmacokinetic parameters may be dependent on the dose of administered drug and on the route of administration.

Models, Statistical↗
PubMed1977

Mutation-selection balance with stochastic selection.

Diffusion theory has been used to analyze a model of mutation-selection balance in which the selection process is assumed to be stochastic in time. The limiting outcome of the mutation-stochastic selection process is determined qualitatively by the geometric mean fitnesses of the genotypes, and the conditions for fixation or polymorphism are similar to those that determine the outcome of the mutation-selection process when selection is constant. However, in the case of a completely recessive allele, detailed numerical study of the polymorphism associated with stochastic selection has shown that the average allele frequency maintained is greater than the equilibrium frequency expected when selection is constant, even when the geometric mean fitness of the recessive homozygotes is identical in the stochastic and deterministic models. Thus, allele frequencies in natural populations that are too high to be plausibly explained by a balance between mutation and constant selection can be accounted for if selection is stochastic.

Alleles↗
PubMed2000

Impossibility of deleting an unknown quantum state

A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store new information in an already computed state by deleting the old information. Here we show, however, that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.

Journal Article↗
PubMed1991

Radiobiological fundamentals in radioepidemiology and radiation protection.

Radiation is a convenient tool to study fundamental processes of life. Biological effects of irradiation may result from indirect actions which are mediated by free radicals (e.g. OH-radicals) or from direct actions which involve ionizations in the DNA and other biomolecules. Damage to the DNA is the principal, but not exclusive target for cell death, loss of reproductive integrity, mutation, cancer, developmental anomalies and other radiobiological effects. Repair of damaged DNA and cellular recovery processes play an essential role in affecting the survival of cells. Dose, dose rate, radiation quality, biological and chemical modifiers also have a pronounced effect upon the extent of radiation responses. The biological effects of ionizing radiation are somatic or hereditary and can further be classified into stochastic and deterministic effects. For radiation epidemiology and protection the stochastic action is more relevant because the probability of an effect is a function of dose, without a threshold. Induction of cancer, hereditary diseases and probably also mental retardation are regarded as stochastic effects.

Cell Survival↗
PubMed2002

Who killed Laius?: On Sophocles' enigmatic message.

Using Laplanche's basic conceptualisation of the role of the other in unconscious processes, the author proposes a reading of Sophocles' tragedy, Oedipus the King, according to basic principles of dream interpretation. This reading corroborates contemporary literary perspectives suggesting that Sophocles' tragedy may not only convey the myth but also provide a critical analysis of how myths work. Important textual inconsistencies and incoherence, which have been noted through the centuries, suggest the existence of another, repressed story. Moreover, the action of the play points to enigmatic parental messages of infanticide and the silencing of Oedipus's story, as well as their translation into primordial guilt, as the origins of the tragic denouement. Oedipus's self-condemnation of parricide follows these enigmatic codes and is unrelated to, and may even contradict, the evidence offered in the tragedy as to the identity of Laius's murderers. Moreover, Sophocles' text provides a complex intertwining of hermeneutic and deterministic perspectives. Through the use of the mythical deterministic content, the formal characteristics of Sophocles' text, mainly its complex time perspective and extensive use of double meaning, dramatise in the act of reading an acute awareness of interpretation. This reading underscores the fundamental role of the other in the constitution of unconscious processes.

Adult↗
PubMed2002

WHO KILLED LAIUS?: ON SOPHOCLES' ENIGMATIC MESSAGE.

Using Laplanche's basic conceptualisation of the role of the other in unconscious processes, the author proposes a reading of Sophocles' tragedy, Oedipus the King, according to basic principles of dream interpretation. This reading corroborates contemporary literary perspectives suggesting that Sophocles' tragedy may not only convey the myth but also provide a critical analysis of how myths work. Important textual inconsistencies and incoherence, which have been noted through the centuries, suggest the existence of another, repressed story. Moreover, the action of the play points to enigmatic parental messages of infanticide and the silencing of Oedipus's story, as well as their translation into primordial guilt, as the origins of the tragic denouement. Oedipus's self-condemnation of parricide follows these enigmatic codes and is unrelated to, and may even contradict, the evidence offered in the tragedy as to the identity of Laius's murderers. Moreover, Sophocles' text provides a complex intertwining of hermeneutic and deterministic perspectives. Through the use of the mythical deterministic content, the formal characteristics of Sophocles' text, mainly its complex time perspective and extensive use of double meaning, dramatise in the act of reading an acute awareness of interpretation. This reading underscores the fundamental role of the other in the constitution of unconscious processes.

Journal Article↗
PubMed1999

Population dynamics under parasitic sex ratio distortion.

We analyse the population dynamic effects of sex ratio distortion by vertically transmitted, feminizing parasites. We show that, for diploid hosts, sex ratio distortion may lead to extinction as males become too rare to maintain the host population through reproduction. Feminizers can magnify Allee effects, broadening the range of conditions leading to extinction of small populations. Depending on male mating constraints and strength of density dependence, feminizers may either increase or decrease the equilibrium host density. Under conditions leading to deterministic host extinction, stochastic elimination of the parasite may allow the host population to recover. Hence, infection by parasitic sex ratio distorters may be transient in finite populations. We consider the implications of this process for parasite prevalence, host population regulation, and sex ratio evolution.

Animals↗