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 685 records · Page 38Linked to original sources
PubMed1974

A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malécot's paper).

Wright's model for the effects of random fluctuations in gene frequency in a population of fixed size is generalized to randomly fluctuating population size, and treated from the viewpoint of G. Malécot, using a martingale convergence theorem. The gene frequency approaches a limit, whose value depends on the actual realization, or history, of the process; that is, convergence is with probability one (or: almost surely) in statistical language. The limit does not necessarily represent a state of fixation of either allele; in particular, the limiting probability distribution is not necessarily trivial. For the special case of deterministically varying population size, a necessary and sufficient condition for such non-triviality is given.

Alleles↗
PubMed2005

Sustainability in single-species population models.

In this paper, we review the concept of sustainability with regard to a single-species, age-structured fish population with density dependence at some stage of its life history. We trace the development of the view of sustainability through four periods. The classical view of sustainability, prevalent in the 1970s and earlier, developed from deterministic production models, in which equilibrium abundance or biomass is derived as a function of fishing mortality. When there is no fishing mortality, the population equilibrates about its carrying capacity. We show that carrying capacity is the result of reproductive and mortality processes and is not a fixed constant unless these processes are constant. There is usually a fishing mortality, F(MSY), which results in MSY, and a higher value, F(ext), for which the population is eventually driven to extinction. For each F between 0 and F(ext), there is a corresponding sustainable population. From this viewpoint, the primary tool for achieving sustainability is the control of fishing mortality. The neoclassical view of sustainability, developed in the 1980s, involved population models with depensation and stochasticity. This view point is in accord with the perception that a population at a low level is susceptible to collapse or to a lack of rebuilding regardless of fishing. Sustainability occurs in a more restricted range from that in the classical view and includes an abundance threshold. A variety of studies has suggested that fishing mortality should not let a population drop below a threshold at 10-20% of carrying capacity. The modern view of sustainability in the 1990s moves further in the direction of precaution. The fishing mortality limit is the former target of F(MSY) (or some proxy), and the target fishing mortality is set lower. This viewpoint further reduces the range of permissible fishing mortalities and resultant desired population sizes. The objective has shifted from optimizing long-term catch to preserving spawning biomass and egg production for the future. The use of discount rates in objective functions involving catch is not a suitable alternative to protecting reproductive value. As we move into the post-modern time period, new definitions of sustainability will attempt to incorporate he economic and social aspects of fisheries and/or ecosystem and habitat requirements. These definitions now involve "warm and fuzzy" notions (healthy ecosystems and fishing communities, the needs of future generations, diverse fish communities) and value judgements of desired outcomes. Additional work is needed to make these definitions operational and to specify quantitative objectives to be achieved. In addition, multiple objectives may be incompatible, so trade-offs in what constitutes sustainability must be made. The advances made under the single-species approach should not be abandoned in the post-modern era, but rather enhanced and combined with new approaches in the multi-species and economic realms.

Animals↗
PubMed2005

Deterministic convergence of an online gradient method for BP neural networks.

Online gradient methods are widely used for training feedforward neural networks. We prove in this paper a convergence theorem for an online gradient method with variable step size for backward propagation (BP) neural networks with a hidden layer. Unlike most of the convergence results that are of probabilistic and nonmonotone nature, the convergence result that we establish here has a deterministic and monotone nature.

Algorithms↗
PubMed1978

Size variations and correlation of different cell cycle events in slow-growing Escherichia coli.

Cell lengths have been determined at which cycle events occur in the slow-growing Escherichia coli B/r substrains A, K, and F26. The radioautographic and electron microscope analyses allowed determination of the variations in length at birth, initiation and termination of DNA replication, and initiation of the constriction process and of cell separation. In all three substrains the standard deviation increased between cell birth and initiation of DNA replication. From there on, the standard deviation remained relatively constant until cell separation. These observations are consistent with the presence of a deterministic phase during the cell cycle in which the cell sizes at initation of DNA replication and at cell division are correlated.

Cell Cycle↗
PubMed2006

Ethyl alcohol production optimization by coupling genetic algorithm and multilayer perceptron neural network.

In this present article, genetic algorithms and multilayer perceptron neural network (MLPNN) have been integrated in order to reduce the complexity of an optimization problem. A data-driven identification method based on MLPNN and optimal design of experiments is described in detail. The nonlinear model of an extractive ethanol process, represented by a MLPNN, is optimized using real-coded and binary-coded genetic algorithms to determine the optimal operational conditions. In order to check the validity of the computational modeling, the results were compared with the optimization of a deterministic model, whose kinetic parameters were experimentally determined as functions of the temperature.

Algorithms↗
PubMedDate not supplied

[The theory of functional systems and purposeful behavior].

The role of probability forecasting in the purposive behavior under conditions of subjective uncertainty is considered in terms of the theory of functional systems. Participation of the probability forecasting in the afferent synthesis, goal formation, formation of the acceptor of action result and action program, and, finally, in the action program actualization is substantiated. The model of behavior under conditions of subjective uncertainty is advanced. It includes all the classical elements of the model of behavioral act developed by P.K. Anokhin. In order to take into account the probability aspects of behavior, the role of probability forecasting is emphasized at every stage of the system functioning. In addition to the classical elements, two novel components are introduced. These are the "memory buffer" (results of searching reactions) and the apparatus of probability decisions about changes in the action program. By the memory buffer an apparatus is meant, which gathers and stores the information about the results of many behavioral acts performed during the actualization of the action program. This information is used in the process of making a probability decision as whether to alter or not the action program after each specific behavioral act. Such an approach integrates the probability forecasting and the theory of functional systems. The theory becomes universal, i.e., applicable not only to deterministic but also to probabilistic environments.

Animals↗
PubMedDate not supplied

[Optimal posology in the neoplastic treatment (author's transl)].

It is known that a single very large dose of cytotoxic agent administered at once does not result in the same biological consequences as those exerted in the cases where the same dose of the same treatment is distributed with uniformity along a wide interval of time. Moreover its is also clear that at least in some cases, at least with some forms of therapy, at least for some ephemeral time, a beneficial effect may be achieved actually, to some extent at least. In order to achieve reliable indications concerning the optimal time distribution of the antineoplastic treatment however a mathematical model is needed where a realistic balance is drawn for the benefits and harmful outcomes of any form of cancer management. For this purpose a formal representation is introduced in the present paper, that provides a summary description of all processes taking place within the "system" consisting of a population of neoplastic cells and of its natural host under any form of cytotoxic treatment applied with any time-dependent intensity phi (t). The behaviour of the system is depicted in a deterministic way by four linear ordinary differential equations containing ten scalar parameters of 1: demographic, 2: cytokinetic, 3: toxicologic, and 4: clinical meaning.

Antineoplastic Agents↗
PubMed2004

Quantum process tomography of the quantum Fourier transform.

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive-although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cumulative effect of small errors in the single qubit gates.

Journal Article↗
PubMedDate not supplied

A simple stochastic model of development and carcinogenesis.

Game theory can be a powerful tool for generating testable hypotheses concerning biological systems. We present a simple game that has many features analogous to a developing cellular system. The game mimics random turning on of genes in cells. Despite the randomness explicit in the mechanism, the game nonetheless results in deterministic outcomes that are extremely resistant to perturbation. Analysis of the types of mistakes or rule changes that are necessary in order to alter the outcome of the game suggests that there are a very limited number of mechanisms by which the differentiation process can result in tumor formation or carcinogenesis. The most significant causes of altered outcomes are alterations in gene order or number, and alteration of the rule by which the gene sequences are traversed. These alterations correspond to chromosomal defects or rearrangements, changes in chromosomal number, and changes in the "orders" delivered by regulatory genes. Notably, most common mistakes, which correspond to simple forms of mutations, have no effect on the outcome of the game, suggesting that mutation is relevant to tumorigenesis and carcinogenesis only to the extent that it results in altered "rules" for reading other gene sequences.

Cell Transformation, Neoplastic↗
PubMed2004

The dynamical consequences of developmental variability and demographic stochasticity for host-parasitoid interactions.

Few age-structured models of species dynamics incorporate variability and uncertainty in population processes. Motivated by laboratory data for an insect and its parasitoid, we investigate whether such assumptions are appropriate when considering the population dynamics of a single species and its interaction with a natural enemy. Specifically, we examine the effects of developmental variability and demographic stochasticity on different types of cyclic dynamics predicted by traditional models. We show that predictions based on the deterministic fixed-development approach are differentially sensitive to variability and noise in key life stages. In particular, we find that the demonstration of half-generation cycles in the single-species model and the multigeneration cycles in the host-parasitoid model are sensitive to the introduction of developmental variability and noise, whereas generation cycles are robust to the intrinsic variability and uncertainty that may be found in nature.

Animals↗
PubMed2005

Nutrients and toxin producing phytoplankton control algal blooms - a spatio-temporal study in a noisy environment.

A phytoplankton-zooplankton prey-predator model has been investigated for temporal, spatial and spatio-temporal dissipative pattern formation in a deterministic and noisy environment, respectively. The overall carrying capacity for the phytoplankton population depends on the nutrient level. The role of nutrient concentrations and toxin producing phytoplankton for controlling the algal blooms has been discussed. The local analysis yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the spatio-temporal behaviour, modelled by stochastic reaction-diffusion equations. The present study also reveals the fact that the rate of toxin production by toxin producing phytoplankton (TPP) plays an important role for controlling oscillations in the plankton system. We also observe that different mortality functions of zooplankton due to TPP have significant influence in controlling oscillations, coexistence, survival or extinction of the zoo-plankton population. External noise can enhance the survival and spread of zooplankton that would go extinct in the deterministic system due to a high rate of toxin production.

Animals↗
PubMed1991

Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics.

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

Chickenpox↗
PubMed2005

Stochastic discrete event simulation of germinal center reactions.

We introduce a generic reaction-diffusion model for germinal center reactions and perform numerical simulations within a stochastic discrete event approach. In contrast to the frequently used deterministic continuum approach, each single reaction event is monitored in space and time in order to simulate the correct time evolution of this complex biological system. Germinal centers play an important role in the immune system by performing a reaction that aims at improving the affinity between antibodies and antigens. Our model captures experimentally observed features of this reaction, such as the development of the remarkable germinal center morphology and the maturation of antibody-antigen affinity in the course of time. We model affinity maturation within a simple affinity class picture and study it as a function of the distance between the initial antibody-antigen affinity and the highest possible affinity. The model reveals that this mutation distance may be responsible for the experimentally observed all-or-none behavior of germinal centers; i.e., they generate either mainly output cells of high affinity or no high-affinity output cells at all. Furthermore, the exact simulation of the system dynamics allows us to study the hypothesis of cell recycling in germinal centers as a mechanism for affinity optimization. A comparison of three possible recycling pathways indicates that affinity maturation is optimized by a recycling pathway that has previously not been taken into account in deterministic continuum models.

Animals↗
PubMed2002

Controller performance analysis with LQG benchmark obtained under closed loop conditions.

This paper proposes a new method for obtaining a linear quadratic Gaussian (LQG) benchmark in terms of the variances of process input and output from closed-loop data, for assessing the controller performance. LQG benchmark has been proposed in the literature to assess controller performance since the LQG tradeoff curve represents the limit of performance in terms of input and output variances. However, an explicit parametric model is required to calculate the LQG benchmark. In this work, we propose a data driven subspace approach to calculate the LQG benchmark under closed-loop conditions with certain external excitations. The optimal LQG-benchmark variances are obtained directly from the subspace matrices corresponding to the deterministic inputs and the stochastic inputs, which are identified using closed-loop data with setpoint excitation. These variances are used for assessing the controller performance. The method proposed in this paper is applicable to both univariate and multivariate systems. Profit analysis for the implementation of feedforward control to the existing feedback-only control system is also analyzed under the optimal LQG performance framework. The proposed method is illustrated through a simulation example and an application on a pilot scale process.

Benchmarking↗
PubMed2004

Bell states of atoms with ultralong lifetimes and their tomographic state analysis.

Arbitrary atomic Bell states with two trapped ions are generated in a deterministic and preprogrammed way. The resulting entanglement is quantitatively analyzed using various measures of entanglement. For this, we reconstruct the density matrix using single qubit rotations and subsequent measurements with near-unity detection efficiency. This procedure represents the basic building block for future process tomography of quantum computations. As a first application, the temporal decay of entanglement is investigated in detail. We observe ultralong lifetimes for the Bell states Psi(+/-), close to the fundamental limit set by the spontaneous emission from the metastable upper qubit level and longer than all reported values by 3 orders of magnitude.

Journal Article↗
PubMed2005

A 3D Monte Carlo analysis of the role of dyadic space geometry in spark generation.

In multiple biological systems, vital intracellular signaling processes occur locally in minute periplasmic subspaces often referred to as signaling microdomains. The number of signaling molecules in these microdomains is small enough to render the notion of continuous concentration changes invalid, such that signaling events are better described using stochastic rather than deterministic methods. Of particular interest is the dyadic cleft in the cardiac myocyte, where short-lived, local increases in intracellular Ca2+ known as Ca2+ sparks regulate excitation-contraction coupling. The geometry of dyadic spaces can alter in disease and development and display significant interspecies variability. We created and studied a 3D Monte Carlo model of the dyadic cleft, specifying the spatial localization of L-type Ca2+ channels and ryanodine receptors. Our analysis revealed how reaction specificity and efficiency are regulated by microdomain geometry as well as the physical separation of signaling molecules into functional complexes. The spark amplitude and rise time were found to be highly dependent on the concentration of activated channels per dyadic cleft and on the intermembrane separation, but not very sensitive to other cleft dimensions. The role of L-type Ca2+ channel and ryanodine receptor phosphorylation was also examined. We anticipate that this modeling approach may be applied to other systems (e.g., neuronal growth cones and chemotactic cells) to create a general description of stochastic events in Ca2+ signaling.

Animals↗
PubMed2004

Stochastic models in population biology and their deterministic analogs.

We introduce a class of stochastic population models based on "patch dynamics." The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean-field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and nonspatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean-field equations (and their first-order corrections in the nonspatial case), and simulation results. These mean-field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean-field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by interpatch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean-field theory even in a spatial setting.

Adaptation, Physiological↗
PubMed1993

Cortico-cortical connections, non-linear multicolumnar parallel distributed networks and memory processes in humans. A review.

This review outlines the knowledge gained in the last 50 years concerning the neuroanatomy and neuro-psychophysiology of memory processes in humans. The first part traces the history of the most important findings from ablations of specific cerebral structures and/or stimulations performed on numerous patients using different surgical and neurophysiological methodologies. The interpretation of these findings is discussed. The most recent hypotheses on the neuronal substrates likely to be involved in memory and recall processes are then presented. In particular the concept of parallel distributed non-linear multicolumnar cortical networks is described as well as the recent hypothesis concerning the chaotic oscillatory properties of these complex non-linear neuronal systems which are said to behave as chaotic deterministic attractors.

Cerebral Cortex↗