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PubMed1985

The application of parametric multichannel spectral estimates in the study of electrical brain activity.

A parametric autoregressive model was applied to the multichannel EEG time series. Small statistical fluctuations of the spectral estimates obtained from the short data strings made possible to follow the time changes of the signals. The multiple and partial coherences were calculated for the four channel process and compared with the coherences computed between the pairs of channels. From the study it followed that the partial coherences are the proper measure of the synchronization of brain structures and their intrinsic relationships. The partial phase spectra give the information about the phase delays. The advantages of the parametric description of signals in the frequency domain in respect to the modelling of dynamic systems was pointed out.

Brain↗
PubMed1987

Selection, generalized transmission and the evolution of modifier genes. I. The reduction principle.

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.

Biological Evolution↗
PubMed2004

Probabilistic independent component analysis for functional magnetic resonance imaging.

We present an integrated approach to probabilistic independent component analysis (ICA) for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise. In order to avoid overfitting, we employ objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e., the number of activation and non-Gaussian noise sources. This enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data. It reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normalization of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternative-hypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and artificial FMRI data, and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses.

Algorithms↗
PubMed1985

Generalized stable population theory.

In generalizing stable population theory we give sufficient, then necessary conditions under which a population subject to time dependent vital rates reaches an asymptotic stable exponential equilibrium (as if mortality and fertility were constant). If chi 0 (t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of chi 0 (t) to chi 0 and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate chi 0-1. Convergence of chi 0 (t) to chi 0 and convergence of mortality rates are necessary. Therefore the two sets of conditions are very close. Various implications of these results are discussed and a conjecture is made in the continuous case.

Age Factors↗
PubMed2006

Building bridges between neural models and complex decision making behaviour.

Diffusion processes, and their discrete time counterparts, random walk models, have demonstrated an ability to account for a wide range of findings from behavioural decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. Recent studies that record neural activations in non-human primates during perceptual decision making tasks have revealed that neural firing rates closely mimic the accumulation of preference theorized by behaviourally-derived diffusion models of decision making. This article bridges the expanse between the neurophysiological and behavioural decision making literatures specifically, decision field theory [Busemeyer, J. R. & Townsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432-459], a dynamic and stochastic random walk theory of decision making, is presented as a model positioned between lower-level neural activation patterns and more complex notions of decision making found in psychology and economics. Potential neural correlates of this model are proposed, and relevant competing models are also addressed.

Action Potentials↗
PubMed2005

Managing molecular diversity.

The present work provides an overview of the different methods used in molecular diversity analysis. Issues like identifying voids in proprietary databases, reducing the number of redundancies present in databases, or designing focused libraries by grouping compounds similar to a template with the aim to fine tune its properties, are potent diversity analysis tools that may be used to optimize molecules based on their properties and specifically, to speed up the process of lead discovery and optimization. The present work describes first methods that are used to describe molecular systems. This is followed by a section devoted to describe different measures of similarity between molecules, to finish with a description of different methods used to select subsets molecules according to the constraints imposed. The final section deals with the validation of these methods, based on different studies available in the literature.

Cluster Analysis↗
PubMed1992

Self-organizing maps: stationary states, metastability and convergence rate.

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.

Algorithms↗
PubMed2003

A methodological note on nonlinear time series analysis: is the open- and closed-loop model of Collins and De Luca (1993) a statistical artifact?

The authors reexamined, theoretically and empirically, the method proposed by J. J. Collins and C. D. De Luca (1993) for the analysis of center-of-pressure trajectories. The main argument in this article is that Collins and De Luca's approach is not adapted to the analysis of bounded time series and leads to statistical artifacts such as underestimation of the diffusion process for long-term intervals. The open- and closed-loop model developed by Collins and De Luca is a direct consequence of those statistical problems. Applying more classical methods, such as rescaled range analysis or detrended fluctuation analysis, the authors show that center-of-pressure trajectories can be modeled as continuous, antipersistent fractional Brownian motion. More specifically, those trajectories behave like 1/f noise, a ubiquitous feature in adaptive biological systems.

Humans↗
PubMed2005

Phase transitions in multiplicative competitive processes.

We introduce a discrete multiplicative process as a generic model of competition. Players with different abilities successively join the game and compete for finite resources. Emergence of dominant players and evolutionary development occur as a phase transition. The competitive dynamics underlying this transition is understood from a formal analogy to statistical mechanics. The theory is applicable to bacterial competition, predicting novel population dynamics near criticality.

Animals↗
PubMed2005

The study of protein folding and dynamics by determination of intramolecular distance distributions and their fluctuations using ensemble and single-molecule FRET measurements.

The folding and dynamics of globular proteins is a multidimensional problem. The structures of the heterogeneous population of refolding protein molecules are characterized by multiple distances and time constants. Deciphering the mechanism of folding depends on studies of the processes rather than the folded structures alone. Spectroscopy is indispensable for these sorts of studies. Herein, it is shown that the determination of intramolecular distance distributions by ensemble and single-molecule FRET experiments enable the exploration of partially folded states of refolding protein molecules.

Adenylate Kinase↗
PubMed1994

A stem cell model for carcinogenesis.

A modification to the well-known two-stage model of carcinogenesis with clonal expansion is proposed. A true stem cell is applied to the production of intermediate cells by incorporating a birth-death process with a reflecting barrier into the model. The distribution of the number of detectable intermediate cell clones is derived, and systems of differential equations are formulated for the cumulative distribution function for the appearance of malignant tumors. The model is applied to data on papilloma formation in a mouse skin painting experiment. Tests for the importance of intermediate cells in tumor incidence can be derived.

Animals↗
PubMed2000

Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: application to postural sway.

We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.

Algorithms↗
PubMed2004

Water quality modelling of Jadro spring.

Management of water quality in karst is a specific problem. Water generally moves very fast by infiltration processes but far more by concentrated flows through fissures and openings in karst. This enables the entire surface pollution to be transferred fast and without filtration into groundwater springs. A typical example is the Jadro spring. Changes in water quality at the spring are sudden, but short. Turbidity as a major water quality problem for the karst springs regularly exceeds allowable standards. Former practice in problem solving has been reduced to intensive water disinfection in periods of great turbidity without analyses of disinfection by-products risks for water users. The main prerequisite for water quality control and an optimization of water disinfection is the knowledge of raw water quality and nature of occurrence. The analysis of monitoring data and their functional relationship with hydrological parameters enables establishment of a stochastic model that will help obtain better information on turbidity in different periods of the year. Using the model a great number of average monthly and extreme daily values are generated. By statistical analyses of these data possibility of occurrence of high turbidity in certain months is obtained. This information can be used for designing expert system for water quality management of karst springs. Thus, the time series model becomes a valuable tool in management of drinking water quality of the Jadro spring.

Disinfection↗
PubMed1976

Estimation of age and rate of increase of rare variants.

The problem considered is that of estimating the age or rate of increase of a variant on the basis of the present number of replicates observed in a population. In place of previous diffusion equation analyses of age probability distributions, the likelihood for the age is studied on the basis of a discrete branching process model. It is shown that variations inherent in the process of gene evolution in natural populations make it impossible to provide a reliable point estimate of the age of a specified variant, although the likelihood analysis provides a confidence interval which may place useful bounds on the period in which a variant originated. The observed distribution of numbers of several variants may also provide useful information. The problems of estimation are discussed with reference to rare variants arising in American Indian populations.

Alleles↗
PubMed2006

Using reproductive value to estimate key parameters in density-independent age-structured populations.

The dynamics of reproductive value are used to provide a simple derivation of Tuljapurkar's approximation for the long-run growth rate and environmental variance of lnN, in a density-independent age-structured population in a random environment. With no environmental autocorrelation, the dynamics of total population size, N, generally shows time lags and autocorrelation caused by life history, which may strongly bias estimates of environmental variance obtained by ignoring age structure. In contrast, the total reproductive value, V, is Markovian and obeys a first-order autoregressive process. This suggests a simple method for estimating the environmental variance, and avoiding potentially large bias due to age-structure fluctuations, by converting a multivariate time series of age structure to a univariate time series of lnV. We illustrate the method by estimating the long-run growth rate and the environmental variance in an exponentially growing population of Bighorn Sheep.

Age Distribution↗
PubMed2004

A multi-algorithm, multi-timescale method for cell simulation.

MOTIVATION: Many important problems in cell biology require the dense nonlinear interactions between functional modules to be considered. The importance of computer simulation in understanding cellular processes is now widely accepted, and a variety of simulation algorithms useful for studying certain subsystems have been designed. Many of these are already widely used, and a large number of models constructed on these existing formalisms are available. A significant computational challenge is how we can integrate such sub-cellular models running on different types of algorithms to construct higher order models. RESULTS: A modular, object-oriented simulation meta-algorithm based on a discrete-event scheduler and Hermite polynomial interpolation has been developed and implemented. It is shown that this new method can efficiently handle many components driven by different algorithms and different timescales. The utility of this simulation framework is demonstrated further with a 'composite' heat-shock response model that combines the Gillespie-Gibson stochastic algorithm and deterministic differential equations. Dramatic improvements in performance were obtained without significant accuracy drawbacks. A multi-timescale demonstration of coupled harmonic oscillators is also shown.

Algorithms↗
PubMed1993

A parametric modeling of ionic channel current fluctuations using third-order statistics and its application to estimation of the kinetic parameters of single ionic channels.

A parametric modeling of stationary ionic-channel current fluctuations (SICF's) using third-order cumulants is presented and its application to estimation of the kinetic parameters of single ionic channels is discussed. We consider the case where third-order cumulants of SICF's are nonzero, and where SICF's are corrupted by an unobservable additive colored Gaussian noise that is independent of SICF's. First, we construct a virtual synthesizer that yields an output whose third-order cumulants are equivalent to those of SICF's on a specific slice. The synthesizer output is expressed by the sum of N5 - 1 first-order differential equation systems, where N8 denotes the number of states of single ionic channels. Next, discretizing the synthesizer output, we derive a discrete autoregressive (AR(N8 - 1)) process driven by the sum of N8 - 1 moving average (MA(N9 - 2)) processes. Then the AR coefficients are explicitly related to the kinetic parameters of single ionic channels, implying that the kinetic parameters can be estimated by identifying the ARMA coefficients using the third-order cumulants. In order to assess the validity of the proposed modeling and the accuracy of parameter estimates, Monte Carlo simulation is carried out in which the closed-open and closed-open-blocked schemes are treated as specific examples.

Ion Channels↗
PubMed2004

LARES: an artificial chemical process approach for optimization.

This article introduces a new global optimization procedure called LARES. LARES is based on the concept of an artificial chemical process (ACP), a new paradigm which is described in this article. The algorithm's performance was studied using a test bed with a wide spectrum of problems including random multi-modal random problem generators, random LSAT problem generators with various degrees of epistasis, and a test bed of real-valued functions with different degrees of multi-modality, discontinuity and flatness. In all cases studied, LARES performed very well in terms of robustness and efficiency.

Algorithms↗