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Results for “deterministic processes”

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PubMed2002

A CT image based deterministic approach to dosimetry and radiography simulations.

An integral transport equation based deterministic approach has been developed to compute individual specific absorbed dose distributions and photon flux distributions on a detector for image formation studies. An algorithm has been designed to take advantage of parallel processing platforms capable of processing large amounts of data imposed by the small pixel sizes of CT images. CT images have been used to form voxels that would represent both tissue variations and body geometry. Absorbed dose distributions calculated using the Visible Human dataset are provided.

Algorithms↗
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↗
PubMed2006

The Hill-Robertson effect and the evolution of recombination.

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.

Alleles↗
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↗
PubMed1979

Multiple transitions induced by light intensity fluctuations in illuminated chemical systems.

The influence of external noise on the steady-state properties of a chemical system with very simple kinetics was studied. We dealt with an isomerization reaction, in a closed system, coupled to a light absorption and radiationless deexcitation process involving only one of the isomers. The theoretical analysis established that external noise deeply modified the macroscopic properties of the system and even induced transition phenomena that are totally unexpected from the usual deterministic description.

Journal Article↗
PubMed1999

The kinetics of nerve-evoked quantal secretion.

Current views on quantal release of neurotransmitters hold that after the vesicle migrates towards release sites (active zones), multiple protein interactions mediate the docking of the vesicle to the presynaptic membrane and the formation of a multimolecular protein complex (the 'fusion machine') which ultimately makes the vesicle competent to release a quantum in response to the action potential. Classical biophysical studies of quantal release have modelled the process by a binomial system where n vesicles (sites) competent for exocytosis release a quantum, with probability p, in response to the action potential. This is likely to be an oversimplified model. Furthermore, statistical and kinetic studies have given results which are difficult to reconcile within this framework. Here, data are presented and discussed which suggest a revision of the biophysical model. Transient silencing of release is shown to occur following the pulse of synchronous transmitter release, which is evoked by the presynaptic action potential. This points to a schema where the vesicle fusion complex assembly is a reversible, stochastic process. Asynchronous exocytosis may occur at several intermediate stages in the process, along paths which may be differentially regulated by divalent cations or other factors. The fusion complex becomes competent for synchronous release (armed vesicles) only at appropriately organized sites. The action potential then triggers (deterministically rather than stochastically) the synchronous discharge of all armed vesicles. The existence of a specific conformation for the fusion complex to be competent for synchronous evoked fusion reconciles statistical and kinetic results during repetitive stimulation and helps explain the specific effects of toxins and genetic manipulation on the synchronization of release in response to an action potential.

Action Potentials↗
PubMed2005

Dizzy: stochastic simulation of large-scale genetic regulatory networks.

We describe Dizzy, a software tool for stochastically and deterministically modeling the spatially homogeneous kinetics of integrated large-scale genetic, metabolic, and signaling networks. Notable features include a modular simulation framework, reusable modeling elements, complex kinetic rate laws, multi-step reaction processes, steady-state noise estimation, and spatial compartmentalization.

Algorithms↗
PubMed1983

Theoretical framework for spectrum analysis in ultrasonic tissue characterization.

An analytic model is described for application in ultrasonic tissue characterization. The model is applicable to clinical broadband pulse echo systems. It treats spectra derived from received echo signals and relates them to physical tissue properties. The model can be applied to deterministic tissue structures (e.g., retinal detachments, larger blood vessels, and surface layers of the kidney) and to stochastic tissue structures (e.g., various tumors). The beam patterns included in the model are those generated by focused transducers typically used in high-resolution clinical ultrasound. Appropriate calibration procedures are also treated; these are needed for interpretation of absolute spectral parameters. The results obtained with the analytic model have been used to design a digital processing system and the associated techniques which are now being applied during examinations of the eye and abdominal organs. The results have proven useful in interpreting data from various types of tissues. To illustrate the application of these results, representative clinical data, obtained from the digital system, are presented for two types of tissue architectures. The first case is a detached retina representing a deterministic structure characterized by well-defined thickness and reflection coefficients. The second case is asteroid hyalosis and represents a stochastic entity in which the positions of small scattering particles are best described in statistical terms, and characterization is accompanied by means of normalized power spectra.

Eye Diseases↗
PubMed2005

Population dynamics in spatially heterogeneous systems with drift: The generalized contact process.

We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one and two dimensions. We consider in particular a situation in which space is divided into two regions: an oasis and a desert (low and high death rates). Carrying out computer simulations we find that the population in the (quasi) stationary state will be zero, localized, or delocalized, depending on the values of the drift and other parameters. The phase diagram is similar to that obtained by Nelson and coworkers from a deterministic, spatially continuous model of a bacterial population undergoing convection in a heterogeneous medium.

Algorithms↗
PubMed2004

Spike trains in a stochastic Hodgkin-Huxley system.

We consider a standard Hodgkin-Huxley model neuron with a Gaussian white noise input current with drift parameter mu and variance parameter sigma(2). Partial differential equations of second order are obtained for the first two moments of the time taken to spike from (any) initial state, as functions of the initial values. The analytical theory for a 2-component (V,m) approximation is also considered. Let mu(c) (approximately 4.15) be the critical value of mu for firing when noise is absent. Large sample simulation results are obtained for mu mu(c), for many values of sigma between 0 and 25. For the time to spike, the 2-component approximation is accurate for all sigma when mu=10, for sigma>7 when mu=5 and only when sigma>15 when mu=2. When mu >mu(c), most paths show similar behavior and the moments exhibit smoothly changing behavior as sigma increases. Thus there are a different number of regimes depending on the magnitude of mu relative to mu(c): one when mu is small and when mu is large; but three when mu is close to and above mu(c). Both for the Hodgkin-Huxley (HH) system and the 2-component approximation, and regardless of the value of mu, the CV tends to about 1.3 at the largest value (25) of sigma considered. We also discuss in detail the problem of determining the interspike interval and give an accurate method for estimating this random variable by decomposing the interval into stochastic and almost deterministic components.

Action Potentials↗
PubMed2006

A simple time delay model for eukaryotic cell cycle.

We propose a seven variable model with time delay in one of the variables for the cell cycle in higher eukaryotes. The model consists of four important phosphorylation-dephosphorylation (P-D) cycles that govern the cell cycle, namely Pre-MPF-MPF, Cdc25P-Cdc25, Wee1P-Wee1 and APCP-APC. Other variables are cyclin, free cyclin dependent kinase (Cdk) and mass. The mass acts as a G2/M checkpoint and the checkpoint is represented by a saddle node loop bifurcation. The key feature of the model is that a time lag has been introduced in the activation of anaphase promoting complex (APC) by maturation promoting factor (MPF). This is effected by treating MPF as a time-delayed variable in the activation step of APC. The time lag acts as a spindle checkpoint. Absence of time delay induces a bistability in our model. Time delay also brings about variability in G1 phase timings. The model also reproduces the mutant phenotype experiments on wee1 cells. Stochasticity has been introduced in the model to simulate the dependence of the cycle time on cell birth length. Mutant phenotypes in the stochastic model reproduce the experimental observations better than the deterministic model.

Animals↗
PubMed2004

Alternative life-history pathways and the elasticity of stochastic matrix models.

Loop analysis is a powerful tool for analyzing matrix population models. This note shows that the results of loop analysis, which have been proved for constant matrices only, apply to stochastic matrices as well if elasticity is defined as the effect of a proportional perturbation of both mean and variance. Using the ideas of loop analysis, it is shown that the structure of the stochastic matrix in terms of alternative life-history pathways has important consequences for the effect of stochasticity on elasticities. If the life cycle contains nonoverlapping, alternative life-history pathways, the ranking in terms of elasticity of the most critical vital rates may be reversed in stochastic and the corresponding average environments. This has obvious and important consequences for population management because focusing on a deterministic model would lead to an ineffective or counterproductive management strategy.

Brassica napus↗