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PubMed1998

Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics.

Delayed effects for pharmacodynamic responses can be observed for many signal transduction processes. Three approaches are summarized in this report to describe such effects caused by cascading steps: stochastic process model, gamma distribution function, and transit compartment model. The gamma distribution function, a probability density function of the waiting time for the final step in a stochastic process model, is a function of time with two variables: number of compartments N, and the expected number of compartments occurring per unit time k. The parameter k is equal to 1/tau, where tau is the mean transit time in the stochastic process model. Effects of N and k on the gamma distribution function were examined. The transit compartment model can link the pharmacokinetic profile of the tested compound, receptor occupancy, and cascade steps for the signal transduction process. Time delays are described by numbers of steps, the mean transit time tau, and the amplification or suppression of the process as characterized by a power coefficient gamma. The effects of N, tau, and gamma on signal transduction profiles are shown. The gamma distribution function can be utilized to estimate N and k values when the final response profile is available, but it is less flexible than transit compartments when dose-response relationships, receptor dynamics, and efficiency of the transduction process are of concern. The transit compartment model is useful in pharmacokinetic/pharmacodynamic modeling to describe precursor/product relationships in signal transduction process.

Animals↗
PubMed2004

Point processes and stochastic displacement fields.

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. Particular attention is devoted to the kind of large-scale correlations that can be introduced by the displacement field and to the realizability of arbitrary "superhomogeneous" point processes.

Journal Article↗
PubMed1995

Trivial influences: a doubly stochastic Poisson process model permits the detection of arbitrarily small electromagnetic signals.

If a weak, exogenous, extremely low-frequency (ELF) electric or magnetic field is to produce biological sequelae, then there must exist averaging sufficient to lift some primary effect of that field above the endogenous stochastic variations of the biological system. One way in which a field could accomplish this is by changing the intensity of some stochastic operation that controls an important and not trivially reversible biological transformation. In this paper, this operation is modeled as a doubly stochastic Poisson process. It is then shown, first, that (in theory) even a minuscule exogenous influence might appreciably shift the incidence of a sufficiently rare transformation and, second, that this shift might be observable if a trial were allowed to run long enough over a sufficiently large population of exposed entities.

Algorithms↗
PubMed2002

Testing for non-linearity in EEG signal of healthy subjects.

Spontaneous EEG of 21 healthy human subjects obtained by standard procedure of recording is analysed using non-linear prediction methods to check whether the signals were generated by a non-linear dynamics process or by a linear stochastic process. The test for non-linearity is performed by surrogate data method with non-linear prediction error as the test statistic. The null hypothesis that EEG signal (in rest, with eyes closed) is generated by linear stochastic process can be rejected in 17 cases (5%) out of the 336 (21 subjects, 16 channels) studied epochs. However, most of these rejections concern 3 subjects. The 88% of rejections of the null hypothesis concern frontal channels. The null hypothesis is not rejected for epochs recorded with eyes open and during photostimulation.

Algorithms↗
PubMed2005

Effects of in-sewer processes: a stochastic model approach.

Transformations of organic matter, nitrogen and sulfur in sewers can be simulated taking into account the relevant transformation and transport processes. One objective of such simulation is the assessment and management of hydrogen sulfide formation and corrosion. Sulfide is formed in the biofilms and sediments of the water phase, but corrosion occurs on the moist surfaces of the sewer gas phase. Consequently, both phases and the transport of volatile substances between these phases must be included. Furthermore, wastewater composition and transformations in sewers are complex and subject to high, natural variability. This paper presents the latest developments of the WATS model concept, allowing integrated aerobic, anoxic and anaerobic simulation of the water phase and of gas phase processes. The resulting model is complex and with high parameter variability. An example applying stochastic modeling shows how this complexity and variability can be taken into account.

Aerobiosis↗
PubMed2005

Single-molecule observation and chromatography unified by Lévy process representation.

A renewed stochastic model of chromatography is proposed able to establish a conceptual link between the single-molecule dynamics observations in a given chromatographic system and chromatographic experiment results in the same media. The chromatographic peak is expressed through its Fourier transform as a function of the experimental sorption time distribution. The pertinent numerical procedure necessary for obtaining the chromatographic peak is described, and the numerical programming code is given. Two types of cases were considered, the first one where the sole discrete sorption time distribution is available, and the second one where the adsorption mechanism is made of a mixture of continuous and discrete sorption time distributions. The method is applied to experimental data found in the literature by determining typical chromatographic peak shapes on the basis of the experimental interface adsorption data. This renewed stochastic approach is based on the so-called Levy canonical description of stochastic processes and appears to be the most general basis for handling separation processes from a stochastic point of view.

Journal Article↗
PubMedDate not supplied

[Dynamic mobility of the histidine-containing domain of spin-labeled lysozyme].

The hen egg-white lysozyme was modified by the spin label (2,2,6,6-tetramethylpiperidine-N1-oxyl-4-iodacetamide) at the single histidine residue His-15. The rotational correlation time of the molecular carrier was found to be defined by the mobility of the histidine-bearing domain and not influenced by the protein monomer shape at pH 4.7 and dimer shape at pH 7.1. The dependence of viscosity at 1 degree C on the distance between outer wide peaks in the immobilized EPR spectra enabled us to evaluate rotational correlation time of the domain. The molecular mass of the latter was close to the data obtained by X-ray analysis. The spin label was highly mobile at room temperature, as the EPR spectrum displayed the triple shape; at 1 degree C it was immobilized. The new general approach to the EPR spectra simulation was applied to all experimental EPR spectra. This approach is based on a substitution of an undefined stochastic process of the spin label reorientation relative to the lysozyme domain by the defined modelled stochastic processes: axial rotation of the nitroxide relative to the preferable axis and angular oscillations of the nitroxide relative to axes of the molecular coordinate system. Each of the modelled stochastic processes leads to a relative partial averaging of the magnetic tensor components. A set of discrete partially averaged states is introduced with the relative cluster of the spin-labelled molecules. The resulting EPR spectrum is assumed to be the sum of EPR spectra from all the clusters. A good fitting of all simulated EPR spectra is obtained.

Animals↗
PubMed1993

Analyzing and modeling fractal intensity point processes.

Fractal intensity point processes--doubly stochastic point processes with a fractal waveform intensity process--are required to describe the discharge patterns recorded from the auditory and visual systems. The Fano factor--the ratio of the variance of the number of events in an interval to the mean of this number--captures the self-similar characteristics of the intensity via two quantities: fractal dimension and fractal time. The fractal dimension is the exponent of the asymptotic power law behavior of the Fano factor with interval duration. The fractal time delineates long-term fractal behavior from short-term characteristics of the data. The average rate and self-similarity parameter of the intensity process, absolute and relative refractory effects, and serial dependence all modify the fractal time. To generate fractal intensity point processes, stochastic fractal processes are derived by applying memoryless, nonlinear transformations to fractional Gaussian noise. The intensity's amplitude distribution in combination with the Fano factor form criteria to choose the transformation that best describes data.

Auditory Perception↗
PubMed2005

Effect of mobile phase composition on the SMB processes efficiency. Stochastic optimization of isocratic and gradient operation.

The solvent composition was adjusted in a theoretical study in order to maximize the efficiency of a simulated moving bed (SMB) process. The isocratic realization of the process as well as the solvent gradient mode were considered. The solvent composition and the flow rates were used as decision variables in a random search optimization algorithm known to be a reliable tool for nonlinear programming problems. The results of the optimization indicate that the optimal composition of the mobile phase depends strongly on the feed concentration. The asymmetry of the internal concentration profiles, which has a negative effect on the separation efficiency, can be partly damped by an increase of the solvent strength. In the cases studied the optimal solvent strength determined for concentrated feed streams is higher than that for diluted ones. Moreover, the optimum is strongly influenced by the value of the selectivity factor and its dependency on the mobile phase composition. Different results were obtained for cases, in which the separation factor increases with increasing the modifier concentration, than for cases, in which the separation factor decreases with increasing the modifier concentration. A similar analysis was performed for a solvent gradient SMB process, in which different solvents are used at the two inlet ports: a weak solvent in the feed stream and a strong solvent in the desorbent stream. Again the optimal mobile phase composition was strongly affected by the type of the isotherms and their non-linearity. The potential of a gradient SMB process in terms of increasing the productivity and reducing the eluent consumption is exemplified.

Chromatography, Liquid↗
PubMed2001

Stochastic exclusion processes with extended hopping.

We study the effects of extended hopping in the stochastic asymmetric simple exclusion process (ASEP) of one dimension. A modified ASEP with four parameters is proposed. The current and bulk density are calculated. Two different phases with a curved boundary are observed. The phase of maximum current is absent. We also present the unusual density fluctuations near both boundaries. The characteristic of the stochastic dynamics with extended hopping is pointed out.

Journal Article↗
PubMed2003

Fingerprints of determinism in an apparently stochastic corrosion process.

We detect hints of determinism in an apparently stochastic corrosion problem. This experimental system has industrial relevance as it mimics the corrosion processes of pipelines transporting water, hydrocarbons, or other fuels to remote destinations. We subject this autonomous system to external periodic perturbations. Keeping the amplitude of the superimposed perturbations constant and varying the frequency, the system's response is analyzed. It reveals the presence of an optimal forcing frequency for which maximal response is achieved. These results are consistent with those for a deterministic system and indicate a classical resonance between the forcing signal and the autonomous dynamics. Numerical studies using a generic corrosion model are carried out to complement the experimental findings.

Journal Article↗
PubMed1991

Stochastic interactive processes and the effect of context on perception.

The effects of context on perceptual identification responses given without time pressure are well-described by classical models in which contextual and stimulus information exert independent effects. A recent article by Massaro (1989) raises the possibility that interactive models, such as the TRACE model of speech perception, are inherently incompatible with these classical context effects. The present article shows that this incompatibility hypothesis can be rejected. Mathematical analysis and computer simulation methods are used to show that interactive models can exhibit the classical effects of context, if there is variability in the input to the network or if there is intrinsic variability in the network itself. A variety of interactive models which incorporate variability can all produce the classical context effects, at least under some conditions; the conditions are rather general in the case of one of the variants. The findings suggest that interactive models should not be viewed as alternatives to classical accounts, but as hypotheses about the dynamics of information processing that lead to the global asymptotic behavior that the classical models describe.

Attention↗
PubMed2006

Partially observed branching processes for stochastic epidemics.

At the offset of a (stochastic) epidemic, it is of importance to have a mathematical model that will assist in the making of an informed judgement on whether the epidemic will explode, or will be minor and die out. In this paper, we consider probabilistic inferences related to the event of extinction of a discrete time branching process when this cannot be directly observed. Instead, we are able to observe only a random "trace" of the process, which not only trails the latter, but also directly affects it (in terms of interventions). A simple model is proposed that provides tractability, preserves a marginal branching property, and gives reasonable closed form expressions.

Disease Outbreaks↗
PubMed1994

On some formulas in a partnership model from the perspective of a semi-Markov process.

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways for extensions to the age-dependent case.

Female↗
PubMed2003

Application of pseudo amino acid composition for predicting protein subcellular location: stochastic signal processing approach.

The function of a protein is closely correlated with its subcellular location. With the success of human genome project and the rapid increase in the number of newly found protein sequences entering into data banks, it is highly desirable to develop an automated method for predicting the subcellular location of proteins. The establishment of such a predictor will no doubt expedite the functionality determination of newly found proteins and the process of prioritizing genes and proteins identified by genomics efforts as potential molecular targets for drug design. Based on the concept of pseudo amino acid composition originally proposed by K. C. Chou (Proteins: Struct. Funct. Genet. 43: 246-255, 2001), the digital signal processing approach has been introduced to partially incorporate the sequence order effect. One of the remarkable merits by doing so is that many existing tools in mathematics and engineering can be straightforwardly used in predicting protein subcellular location. The results thus obtained are quite encouraging. It is anticipated that the digital signal processing may serve as a useful vehicle for many other protein science areas as well.

Algorithms↗
PubMed1989

Pharmacokinetics from a dynamical systems point of view.

The pharmacological action of many drugs depends on several variables at the same time and therefore will be dominated by an attractor of a dimension greater than zero. The pharmacokinetic behavior is likely to be dominated by a zero dimensional point attractor so that it is highly predictable. Pharmacokinetics is discussed from a dynamical systems point of view, whereby the transport of drugs in the tissues and organs is considered a stochastic process characterized by density functions of transit times and blood flows. In the body, the tissues and organs are arranged in parallel, in series, and in a feedback-loop fashion. Consequently, the single-pass transport of drugs through the body is again a stochastic process characterized by the density function of total body transit times, the cardiac output, and the total body extraction. The drug molecules, however, may pass through the body several times before ultimately leaving the system by metabolism or excretion. As a result, the body may be regarded as a positive feedback system with the pulmonary circulation (and its tissues) as the forward transfer function and the systemic circulation (with all its tissues) as the feedback transfer function. Consequently, the total body transport function (closed loop) is again a stochastic process characterized by a density function of total body residence times. The relationship between the body transit time distribution and the body residence distribution is determined by the feedback-loop arrangement, the cardiac output, and the extraction ratio which can easily be written in the Laplace domain. The pharmacokinetic parameters logically follow from the systems approach. They are the cardiac output, the mean transit time, the extraction ratio, the clearance, the volume of distribution in steady state, the mean residence time, and the average number of recirculations. The dynamic systems approach in pharmacokinetics has been illustrated with some examples notably with caffeine.

Absorption↗
PubMed1992

On inherited fertility in biological systems: a model of correlated fluctuations in the stochastic branching process.

A new evolutionary model with hereditary modes considered as correlated fluctuations of fertility has been proposed. It has been demonstrated that the model allows the global statistical properties of the system to be evaluated, e.g. the ensemble average and the probability of extinction. The results obtained show the increase of instability of a population with the enhancement of inheritance efficiency. The existence of at least an exponential stratification in the population has also been shown. Possible applications of the present model are discussed.

Animals↗