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PubMedDate not supplied

Genetic models for plant pathosystems.

Deterministic, discrete time, genetics models for a resistant plant host and a virulent pathogen are developed and analyzed. The original model was developed by Leonard in 1977 for a single gene with haploid pathogens and diploid hosts [Ann. N.Y. Acad. Sci. 287 (1977) 207]. The original model is generalized to diploid hosts and pathogens with incomplete dominance of the heterozygote. In addition, the single gene model is extended to two genes and a stochastic model with random selection values is formulated and simulated. It is shown using local stability properties that stability of the polymorphic equilibrium is indeterminant; the equilibrium is non-hyperbolic. The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium.

Models, Genetic↗
PubMed2006

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

MOTIVATION: The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. RESULTS: In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. AVAILABILITY: Software and benchmark models used for this publication can be made available upon request from the authors.

Algorithms↗
PubMedDate not supplied

[Instrumental implementation of monitoring methods applicable to generation, tracing, reproduction and prognostication in deterministic and stochastic media].

The case study is based on the theory of functional systems described by Academician P.K. Anokhin and on an experimental model of space-time prognostication enabling the development and classification of test-procedures modality of an activity (generation, tracing, reproduction and prognostication) and by modality (dimension) of space (zero-, 1- and 2D etc.). Test procedures were suggested and investigated for evaluating the parameters of the central nervous system (CNS). A set of experimental test models can be presented as a combination of described space-time modes. The system of indices is based on an evaluation of the time structure of a behavioral model. The activity rate parameter and its variability (mean value and root-mean-square deviation of the trend) were made use of. The rate of erroneous responses in different pattern's points was used as an evaluation tool for the spacious structure of the behavior.

Central Nervous System↗
PubMed2005

A model for the effect of rhizodeposition on the fate of phenanthrene in aged contaminated soil.

Microcosm data were used to develop a deterministic model to describe how rhizodeposition affects the fate of phenanthrene in aged contaminated soil. Microbial mineralization and soil sequestration of 14C-phenanthrene were compared in microcosms amended weekly with phenolic-rich mulberry root extracts versus unamended controls. Mineralization was higher in the amended soils simulating the rhizosphere (57.7 +/- 0.9%) than in controls simulating bulk (unplanted) soils (53.2 +/- 0.7%) after 201 days (p < 0.05). Humin was the main soil sink for the residual 14C-label. Whereas the total 14C-label associated with humin remained constant in biologically active soils (at about 30%), it increased up to 80% after 201 days in sterile controls. The initial phenanthrene extraction with n-butanol (commonly used to assess bioavailability) slightly underestimated the fraction thatwas mineralized (assessed by 14CO2 recovery). Changes in the unextractable fraction (determined by combustion in a biological oxidizer) suggested the presence of two soil sequestration domains: (1) irreversibly bound residue, and (2) an intermediate transition phase that is unextractable by solvents at a given point in time but could become bioavailable due to physicochemical or biological transformations of the binding matrix. The fate of phenanthrene was accurately modeled by considering the transfer of the 14C label between different soil compartments as first-order kinetic processes. Model simulations suggested that the system was approaching a stable end-point after 201 days of simulated rhizoremediation, and corroborated that microorganisms have a significant impact on the fate of phenanthrene in soil.

Biodegradation, Environmental↗
PubMed2005

Connection between stochastic and deterministic modelling of microbial growth.

We present in this paper various links between individual and population cell growth. Deterministic models of the lag and subsequent growth of a bacterial population and their connection with stochastic models for the lag and subsequent generation times of individual cells are analysed. We derived the individual lag time distribution inherent in population growth models, which shows that the Baranyi model allows a wide range of shapes for individual lag time distribution. We demonstrate that individual cell lag time distributions cannot be retrieved from population growth data. We also present the results of our investigation on the effect of the mean and variance of the individual lag time and the initial cell number on the mean and variance of the population lag time. These relationships are analysed theoretically, and their consequence for predictive microbiology research is discussed.

Bacteria↗
PubMed2000

Synaptic efficacy and the transmission of complex firing patterns between neurons.

In central neurons, the summation of inputs from presynaptic cells combined with the unreliability of synaptic transmission produces incessant variations of the membrane potential termed synaptic noise (SN). These fluctuations, which depend on both the unpredictable timing of afferent activities and quantal variations of postsynaptic potentials, have defied conventional analysis. We show here that, when applied to SN recorded from the Mauthner (M) cell of teleosts, a simple method of nonlinear analysis reveals previously undetected features of this signal including hidden periodic components. The phase relationship between these components is compatible with the notion that the temporal organization of events comprising this noise is deterministic rather than random and that it is generated by presynaptic interneurons behaving as coupled periodic oscillators. Furthermore a model of the presynaptic network shows how SN is shaped both by activities in incoming inputs and by the distribution of their synaptic weights expressed as mean quantal contents of the activated synapses. In confirmation we found experimentally that long-term tetanic potentiation (LTP), which selectively increases some of these synaptic weights, permits oscillating temporal patterns to be transmitted more effectively to the postsynaptic cell. Thus the probabilistic nature of transmitter release, which governs the strength of synapses, may be critical for the transfer of complex timing information within neuronal assemblies.

Animals↗
PubMed2000

Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency.

Deterministic differential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discrete-individual simulation studies arrive at similar conclusions, but from a very different modeling perspective. This paper presents a stochastic discrete-individual infection model that helps to unify these two approaches to infection modeling. The model allows for both partnership concurrency, as well as the infection, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are individuals and arcs represent partnerships. Connections between the differential equation and discrete-individual approaches are constructed with large-population limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form of the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Analytical and simulation results indicate that the basic reproduction number R(0) increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1-1/R(0), when partnerships are not point-time processes.

Computer Simulation↗
PubMed2000

Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs.

Numerical investigations have been made of responses of a Hodgkin-Huxley (HH) neuron to spike-train inputs whose interspike interval (ISI) is modulated by deterministic, semi-deterministic (chaotic), and stochastic signals. As deterministic one, we adopt inputs with the time-independent ISI and with time-dependent ISI modulated by sinusoidal signal. The Rössler and Lorentz models are adopted for chaotic modulations of ISI. Stochastic ISI inputs with the gamma distribution are employed. It is shown that distribution of output ISI data depends not only on the mean of ISIs of spike-train inputs but also on their fluctuations. The distinction of responses to the three kinds of inputs can be made by return maps of input and output ISIs, but not by their histograms. The relation between the variations of input and output ISIs is shown to be different from that of the integrate and fire (IF) model because of the refractory period in the HH neuron.

Animals↗
PubMed1996

Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors.

Mammalian cold thermoreceptors encode steady-state temperatures into characteristic temporal patterns of action potentials. We propose a mechanism for the encoding process. It is based on Plant's ionic model of slow wave bursting, to which stochastic forcing is added. The model reproduces firing patterns from cat lingual cold receptors as the parameters most likely to underlie the thermosensitivity of these receptors varied over a 25 degrees C range. The sequence of firing patterns goes from regular bursting, to simple periodic, to stochastically phase-locked firing or "skipping." The skipping at higher temperatures is shown to necessitate an interaction between noise and a subthreshold endogenous oscillation in the receptor. The basic period of all patterns is robust to noise. Further, noise extends the range of encodable stimuli. An increase in firing irregularity with temperature also results from the loss of stability accompanying the approach by the slow dynamics of a reverse Hopf bifurcation. The results are not dependent on the precise details of the Plant model, but are generic features of models where an autonomous slow wave arises through a Hopf bifurcation. The model also addresses the variability of the firing patterns across fibers. An alternate model of slow-wave bursting (Chay and Fan 1993) in which skipping can occur without noise is also analyzed here in the context of cold thermoreception. Our study quantifies the possible origins and relative contribution of deterministic and stochastic dynamics to the coding scheme. Implications of our findings for sensory coding are discussed.

Action Potentials↗
PubMed2001

Harmonization of future needs for dermal exposure assessment and modeling: a workshop report.

Dermal exposure assessment and modeling is still in early phases of development. This article presents the results of a workshop organized to harmonize the future needs in this field. Methods for dermal exposure assessment either assess the mass of contaminant that is transferred to the skin, or the transfer of contaminant through the skin. Models for dermal exposure are either knowledge-based or deterministic. Any method or model should be transparent, validated, and open to further development. Some (partly) validated and standardized methods are available for measuring or modeling permeation of the skin or of personal protective equipment (PPE). Further validation and standardization is necessary. More research is needed on permeation of dusts and aerosols and more realistic tests should be developed and used for PPE. Several methods have been developed to measure contamination of surfaces or skin, but they are not validated or standardized. A number of non-validated models exist to assess dermal exposure. A clear need exists for more studies of dermal exposure, regarding measurement methods, models and actual exposure levels. A running four-year European study will greatly expand the knowledge in this field. Simple tools to assess and control the risks of dermal exposure in small and medium sized enterprises are also needed. Increasing the general knowledge of practitioners (e.g., safety professionals, occupational hygienists and physicians) in the field of dermal exposure is a first requirement. Available data, for example, on the permeation of PPE, should be made more readily available, using modern information technology. When information on dermal exposure is gathered and stored, the core information needs are partly the same as those for inhalation exposure. Some elements of process and activity, substance and product or worker, specific for dermal exposure, have been suggested by the workshop.

Europe↗
PubMedDate not supplied

Variable effort harvesting models in random environments: generalization to density-dependent noise intensities.

In a previous paper [Math. Biosci. 156 (1999) 1], we have studied quite general stochastic differential equation models for the growth of populations subjected to harvesting in a random environment. We have obtained conditions for non-extinction and for the existence of stationary distributions (as well as expressions for such distributions) similar to conditions for non-extinction and for the existence of a stable equilibrium in the corresponding deterministic model. The models were quite general, considering density-dependent natural growth functions and harvesting policies of very general form, so that our results would be model independent and provide minimal requirements for the choice of a wise density-dependent harvesting policy. Those models, however, although quite general on all other respects, have a serious limitation. In fact, the ways environmental fluctuations affect the population per capita growth rate are poorly known and those models only considered two possible ways, namely the noise intensity could be constant or proportional to that rate. To overcome this limitation, in this paper we generalize the previous results to density-dependent positive noise intensities of very general form so that they also become independent from the way environmental fluctuations affect population growth rates.

Animals↗
PubMed2006

Dose conversion coefficients for interventional procedures.

Effective dose (E) is a convenient quantity to estimate the stochastic risk of radiation applied to patients in interventional procedures and can be used for optimisation. Relatively long exposure times may cause deterministic effects. Hence it is necessary to know the (maximum local) doses in organs owing to the interventional procedure. In practice, organ doses cannot be measured directly. They are derived by applying a conversion coefficient to a measurable quantity, e.g. dose-area product (DAP) or entrance skin dose. For a number of interventional procedures, dose conversion coefficients (DCCs) can be found in the literature. Various DCCs are stated for nominally equal procedures, e.g. for percutaneous transluminal coronary angioplasty both 0.18 and 0.27 mSv Gy(-1) cm(-2) were reported to convert DAP to effective dose. Dependence of DCC on protocol and equipment parameters, as demonstrated through Monte Carlo simulation in this paper, makes it hazardous to simply adopt a literature value.

Arteries↗
PubMed1996

Characterization of complex heart rate dynamics and their pharmacological disorders by non-linear prediction and special data transformations.

OBJECTIVE: The aim of the presented method was the characterization of different complex heart rate dynamics in conscious rabbits as well as during general anaesthesia and vagal blockade. This was done by non-linear prediction of original measured and special surrogate data in the phase space. METHOD: The development of the prediction error in dependence on the prediction time interval was investigated in the phase space. Two kinds of surrogate data were produced and tested with regard to non-linearities and orientation in the phase space. Typical characteristics of prediction error development were shown for simulated uncorrelated stochastic, correlated stochastic, regular deterministic, and deterministic chaotic signals. These characteristics were used to evaluate the measured heart rate data in connection with tests of surrogate data. RESULTS: It could be shown that heart rate fluctuation cannot be described by one of these ideal models alone. Common consideration of all investigated prediction characteristics indicated chaos in the heart rate of conscious rabbits as well as during anaesthesia and vagal blockade, where non-linear correlated stochastic properties could not be excluded. The different amount of non-linearities and orientation was described quantitatively. CONCLUSIONS: Detailed analysis of prediction error development in the phase space, connected with tests for non-linearities and orientation, enabled a specific quantitative characterization of complex heart rate dynamics and their pharmacological disorders.

Anesthesia, General↗
PubMedDate not supplied

Confidence intervals for cost-effectiveness ratios: an application of Fieller's theorem.

Application of cost-effectiveness analysis (CEA) is growing rapidly in health care. Two general approaches to analysis are differentiated by the type of data available: (i) deterministic models based upon secondary analysis of retrospective data from one or more trials and other sources; and (ii) stochastic analyses in which the design of a randomized controlled trial is adapted to collect prospectively patient-specific data on costs and effectiveness. An important methodological difference between these two approaches is in how uncertainty is handled. Deterministic CEA models typically rely upon sensitivity analysis to determine the robustness of findings to alternative assumptions, whereas stochastic (CEA) analysis, as part of prospective studies, permits the use of conventional statistical methods on the cost and effectiveness data for both inference (hypothesis testing) and estimation. This paper presents a procedure for the statistical analysis of cost-effectiveness data, with specific application to those studies for which effectiveness is measured as a binary outcome. Specifically, Fieller's Theorem was used to calculate confidence intervals for ratios of the two random variables of between-treatment differences in observed costs and effectiveness, i.e. the incremental cost-effectiveness ratio.

Computer Simulation↗
PubMed2006

The emergence of goals in a self-organizing network: a non-mentalist model of intentional actions.

A model of intentional actions is presented through the operation of two connected neural networks. A deterministic causal recurrent network relates a random initial state to an ordered final state. A perceptron-like, feed-forward network provides a memory mechanism that links the final states to the original initial states. A non-supervised learning mechanism that selects which final states are defined as goals to be retrieved together with initial states leading to them. Causal sequences of states are transformed into procedures directed towards the achievements of goals. We propose a mechanism through which goals and their achievement in goal-directed actions can be emerging properties of self-organizing networks, not initially endowed with intentionality. This allows for a monist, non-mentalist description which does not need to resort to intentional mental states as causes of intentional actions. Cognitive, neurophysiological and philosophical implications are discussed.

Animals↗
PubMed1992

Single evoked potential reconstruction by means of wavelet transform.

We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach--the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Başar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two conditions: high signal to noise ratio and clear separation of the EEG and EP spectra.(ABSTRACT TRUNCATED AT 250 WORDS)

Algorithms↗
PubMed2001

The effect that genotyping errors have on the robustness of common linkage-disequilibrium measures.

The rapid development of a dense single-nucleotide-polymorphism marker map has stimulated numerous studies attempting to characterize the magnitude and distribution of background linkage disequilibrium (LD) within and between human populations. Although genotyping errors are an inherent problem in all LD studies, there have been few systematic investigations documenting their consequences on estimates of background LD. Therefore, we derived simple deterministic formulas to investigate the effect that genotyping errors have on four commonly used LD measures-D', r, Q, and d-in studies of background LD. We have found that genotyping error rates as small as 3% can have serious affects on these LD measures, depending on the allele frequencies and the assumed error model. Furthermore, we compared the robustness of D', r, Q, and d, in the presence of genotyping errors. In general, Q and d are more robust than D' and r, although exceptions do exist. Finally, through stochastic simulations, we illustrate how genotyping errors can lead to erroneous inferences when measures of LD between two samples are compared.

Chromosome Mapping↗
PubMed2003

Event-driven simulation of spiking neurons with stochastic dynamics.

We present a new technique, based on a proposed event-based strategy (Mattia & Del Giudice, 2000), for efficiently simulating large networks of simple model neurons. The strategy was based on the fact that interactions among neurons occur by means of events that are well localized in time (the action potentials) and relatively rare. In the interval between two of these events, the state variables associated with a model neuron or a synapse evolved deterministically and in a predictable way. Here, we extend the event-driven simulation strategy to the case in which the dynamics of the state variables in the inter-event intervals are stochastic. This extension captures both the situation in which the simulated neurons are inherently noisy and the case in which they are embedded in a very large network and receive a huge number of random synaptic inputs. We show how to effectively include the impact of large background populations into neuronal dynamics by means of the numerical evaluation of the statistical properties of single-model neurons under random current injection. The new simulation strategy allows the study of networks of interacting neurons with an arbitrary number of external afferents and inherent stochastic dynamics.

Action Potentials↗