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PubMed1997

Rapid fixation of deleterious alleles can be caused by Muller's ratchet.

Theoretical arguments are presented which suggest that each advance of Muller's ratchet in a haploid asexual population causes the fixation of a deleterious mutation at a single locus. A similar process operates in a diploid, fully asexual population under a wide range of parameter values, with respect to fixation within one of the two haploid genomes. Fixations of deleterious mutations in asexual species can thus be greatly accelerated in comparison with a freely recombining genome, if the ratchet is operating. In a diploid with segregation of a single chromosome, but no crossing over within the chromosome, the advance of the ratchet can be decoupled from fixation if mutations are sufficiently close to recessivity. A new analytical approximation for the rate of advance of the ratchet is proposed. Simulation results are presented that validate the assertions about fixation. The simulations show that none of the analytical approximations for the rate of advance of the ratchet are satisfactory when population size is large. The relevance of these results for evolutionary processes such as Y chromosome degeneration is discussed.

Alleles↗
PubMed2002

Assessing allelic dropout and genotype reliability using maximum likelihood.

A growing number of population genetic studies utilize nuclear DNA microsatellite data from museum specimens and noninvasive sources. Genotyping errors are elevated in these low quantity DNA sources, potentially compromising the power and accuracy of the data. The most conservative method for addressing this problem is effective, but requires extensive replication of individual genotypes. In search of a more efficient method, we developed a maximum-likelihood approach that minimizes errors by estimating genotype reliability and strategically directing replication at loci most likely to harbor errors. The model assumes that false and contaminant alleles can be removed from the dataset and that the allelic dropout rate is even across loci. Simulations demonstrate that the proposed method marks a vast improvement in efficiency while maintaining accuracy. When allelic dropout rates are low (0-30%), the reduction in the number of PCR replicates is typically 40-50%. The model is robust to moderate violations of the even dropout rate assumption. For datasets that contain false and contaminant alleles, a replication strategy is proposed. Our current model addresses only allelic dropout, the most prevalent source of genotyping error. However, the developed likelihood framework can incorporate additional error-generating processes as they become more clearly understood.

Alleles↗
PubMed1995

Synapse models for neural networks: from ion channel kinetics to multiplicative coefficient wij.

This paper relates different levels at which the modeling of synaptic transmission can be grounded in neural networks: the level of ion channel kinetics, the level of synaptic conductance dynamics, and the level of a scalar synaptic coefficient. The important assumptions to reduce a synapse model from one level to the next are explicitly exhibited. This coherent progression provides control on what is discarded and what is retained in the modeling process, and is useful to appreciate the significance and limitations of the resulting neural networks. This methodic simplification terminates with a scalar synaptic efficacy as it is very often used in neural networks, but here its conditions of validity are explicitly displayed. This scalar synapse also comes with an expression that directly relates it to basic quantities of synaptic functioning, and it can be endowed with meaningful physical units and realistic numerical values. In addition, it is shown that the scalar synapse does not receive the same expression in neural networks operating with spikes or with firing rates. These coherent modeling elements can help to improve, adjust, and refine the investigation of neural systems and their remarkable collective properties for information processing.

Action Potentials↗
PubMed1998

Molecular evolution modeled as a fractal renewal point process in agreement with the dispersion of substitutions in mammalian genes.

A fractal renewal point process (FRPP) is used to model molecular evolution in agreement with the relationship between the variance and the mean numbers of nonsynonymous and synonymous substitutions in mammals. Like other episodic models such as the doubly stochastic Poisson process, this model accounts for the large variances observed in amino acid substitution rates, but unlike certain other episodic models, it also accounts for the increase in the index of dispersion with the mean number of substitutions in Ohta's (1995) data. We find that this correlation is significant for nonsynonymous substitutions at the 1% level and for synonymous substitutions at the 10% level, even after removing lineage effects and when using Bulmer's (1989) unbiased estimator of the index of dispersion. This model is simpler than most other overdispersed models of evolution in the sense that it is fully specified by a single interevent probability distribution. Interpretations in terms of chaotic dynamics and in terms of chance and selection are discussed.

Animals↗
PubMed1984

Mathematical model of visual perception.

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.

Animals↗
PubMed2004

Stochastic equation for a jumping process with long-time correlations.

A jumping process, defined in terms of the jump size and waiting time distributions, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by a power-law autocorrelation function. Therefore, it can serve as a model of 1/f noise as well as of the stochastic force in the generalized Langevin equation. This equation is solved for noise correlations approximately 1/t ; the resulting velocity distribution has sharply falling tails. The system preserves memory about the initial condition for a very long time.

Journal Article↗
PubMed1989

Effects of hemopoietic growth factors on stem cells in vitro.

The central feature of hemopoiesis is the lifelong, stable cell renewal. This process is supported by hemopoietic stem cells, which in the steady-state appear to be dormant in cell cycling. The entry into cell cycle of the dormant stem cells may be promoted by such factors as IL-1, IL-6, and G-CSF. Available evidence indicates that the effects of IL-1 on stem cells are indirectly mediated in part by IL-6 and G-CSF. Once the stem cells leave G0 and begin proliferation, the subsequent process is characterized by continued proliferation and differentiation. While several models of stem cell differentiation have been proposed, micromanipulation studies of individual progenitors suggest that the commitment of multipotential progenitors to single lineages is a stochastic (random) process. The proliferation of early hemopoietic progenitors appears to be supported by IL-3, IL-4, and/or GM-CSF. Once the progenitors are committed to individual lineages, the subsequent maturation process appears to be supported by late-acting, lineage-specific factors such as Ep (for erythropoiesis), G-CSF (for neutrophil production), and IL-5 (for eosinophilopoiesis). Thus, hemopoietic proliferation appears to be regulated by a cascade of factors directed at different developmental stages.

Animals↗
PubMed2002

A numerical method for estimating blood flow by dynamic functional imaging.

We present a numerical deconvolution scheme for estimating regional blood flow and tissue retention functions by dynamic functional imaging. The present approach implements the Tikhonov-Miller regularization in general form, which allows for prior knowledge or assumptions to be incorporated during the deconvolution process, so as to stabilize the solution against variations due to noise. Appropriate approximations and simplifications in the context of functional imaging, were also introduced to ease numerical computations. Monte Carlo simulation experiments were carried out to study the applicability of the present approach and to compare with other deconvolution techniques previously studied.

Algorithms↗
PubMed1996

The effects of nested primer binding sites on the reproducibility of PCR: mathematical modeling and computer simulation studies.

The polymerase chain reaction (PCR) has become an indispensable tool in modern biological research. Although the application of PCR is a standard routine, we widely lack a theoretical understanding of the dynamic processes involved, especially with respect to the amplification of nonreproducible and/or unexpected amplification products. For one potential source of uncertainty, the presence of nested primer binding sites within an amplifyable DNA locus, we consider a simple stochastic model for the dynamics of PCR amplification of competing products. For commonly used thermostable DNA polymerases lacking a 5'-3'-exonuclease activity, we predict the relative amplification frequencies of competing PCR products dependent on the primer binding probability, the number of PCR cycles, and the number of initial DNA template molecules. At low primer binding probabilities and low numbers of initial DNA template molecules and PCR cycles, we expect the amplification of two products. At high primer binding probabilities and/or high copy numbers of initial template molecules only one main amplification product is predicted at increasing cycle numbers. Furthermore, by means of computer simulation studies we quantify the stochastic variation for the amplification frequencies of competing products.

Bacteriophage lambda↗
PubMed2004

Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons.

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (nonPoissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have long-range dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

Action Potentials↗
PubMed1996

How dependencies between successive examples affect on-line learning.

We study the dynamics of on-line learning for a large class of neural networks and learning rules, including backpropagation for multilayer perceptrons. In this paper, we focus on the case where successive examples are dependent, and we analyze how these dependencies affect the learning process. We define the representation error and the prediction error. The representation error measures how well the environment is represented by the network after learning. The prediction error is the average error that a continually learning network makes on the next example. In the neighborhood of a local minimum of the error surface, we calculate these errors. We find that the more predictable the example presentation, the higher the representation error, i.e., the less accurate the asymptotic representation of the whole environment. Furthermore we study the learning process in the presence of a plateau. Plateaus are flat spots on the error surface, which can severely slow down the learning process. In particular, they are notorious in applications with multilayer perceptrons. Our results, which are confirmed by simulations of a multilayer perceptron learning a chaotic time series using backpropagation, explain how dependencies between examples can help the learning process to escape from a plateau.

Learning↗
PubMed2001

Centrifugal bias for second-order but not first-order motion.

Limited-lifetime Gabor stimuli were used to assess both first- and second-order motion in peripheral vision. Both first- and second-order motion mechanisms were present at a 20-deg eccentricity. Second-order motion, unlike first-order, exhibits a bias for centrifugal motion, suggesting a role for the second-order mechanism in optic flow processing.

Anisotropy↗
PubMed1997

On the simulation of biological diffusion processes.

Many phenomena of interest in biology can be modeled using diffusion processes satisfying a stochastic differential equation. We consider first the stochastic differential equation dX = mu Xdt + sigma X, dW, where W is a standard Wiener process and representing a population growth process. This is simulated using both a strong Euler scheme involving normal pseudorandom numbers and a weak Euler scheme using Bernoulli pseudorandom numbers. Results are given for the mean of X(1) and its 95% confidence intervals for various numbers of simulations. It is found that there are no significant differences between the results obtained by these two schemes at a particular value of the time step, but the weak scheme takes less computer time than the strong scheme. We also consider the process satisfying dX = (-gamma 1X + gamma 2 (1-X))dt + square root of X(1-X)dW, representing a gene frequency under the influence of random mating and mutation. It is similarly found that the results of simulation by the two schemes are not significantly different. It is concluded that in simulations of many biological diffusion processes it is often advantageous to employ a scheme involving Bernoulli rather than Gaussian random variates not only because it involves fewer machine arithmetic operations but also because problems with large jumps that sometimes occur with extreme values of normal variates are less likely, thus enabling one to employ a larger time step with a concomitant saving in machine time.

Computer Simulation↗
PubMed1996

Long-run cooperation in the one-shot Prisoner's Dilemma: a hierarchic evolutionary approach.

This paper proposes a hierarchic evolutionary model leading to long-run cooperation in the Prisoner's Dilemma. The population is segmented into groups, and evolution and interaction take place 'in parallel' at two levels: (i) within groups at the lower level; (ii) among groups at the higher one. At each of these levels, what performs currently best tends to be imitated. On the other hand, occasionally, individuals also experiment with (or mutate to) some new strategy. If the number of groups is sufficiently large, the long-run (invariant) distribution of the process is shown to be concentrated on the cooperative outcome.

Animals↗
PubMed2005

Adaptive control of uncertain continuously stirred tank reactors with unknown actuator nonlinearities.

Adaptive nonlinear control is investigated for continuously stirred tank reactor (CSTR) systems using neural networks. The CSTR plant under study belongs to a class of nonaffine nonlinear systems, and contains an unknown parameter that enters the model nonlinearly. Using adaptive backstepping and neural network (NN) approximation techniques, an alternative adaptive NN controller is developed that achieves asymptotic output tracking control. A novel integral-type Lyapunov function, which includes both system states and control input as its arguments, is constructed to solve the difficulty associated with the nonaffine control problem. Numerical simulation is performed to show the feasibility of the proposed approach for chemical process control.

Bioreactors↗
PubMed1999

Kinetic parameter estimation from compartment models using a genetic algorithm.

Kinetic parameters were estimated from a three-compartment fluorodeoxyglucose model with three rate constants using a genetic algorithm. The performance of the genetic algorithm was investigated by simulation studies, in which brain time-activity data (TAD) were generated using cited mean values of rate constants and the plasma TAD obtained from positron emission tomographic studies. The accuracy of kinetic parameter estimation using the genetic algorithm was compared with that using the non-linear least-squares (NLSQ) method. The margin of error in the parameters estimated using the genetic algorithm tended to be smaller than that obtained by the NLSQ method. Although not statistically significant at a noise level of 5% in the brain TAD, the difference between the two methods became significant for all parameters at a noise level of 15% or higher. Our results suggest that the genetic algorithm is a promising means of estimating kinetic parameters from compartment models, because it is more robust against statistical noise than the NLSQ method and it can be rendered highly parallel for processing.

Algorithms↗
PubMed2001

Pitfalls in the clustering of neuroimage data and improvements by global optimization strategies.

In this paper, we examined three vector quantization (VQ) methods used for the unsupervised classification (clustering) of functional magnetic resonance imaging (fMRI) data. Classification means that each brain volume element (voxel), according to a given scanning raster, was assigned to one group of voxels based on similarity of the fMRI signal patterns. It was investigated how the VQ methods can isolate a cluster that describes the region involved in a particular brain function. As an example, word processing was stimulated by a word comparison task. VQ analysis methodology was verified using simulated fMRI response patterns. It was demonstrated in detail that VQ based on global rather than local optimization of the objective function yielded a higher performance. Performance was measured in statistically relevant series of VQ attempts using several indices for goodness, reliability and efficiency of VQ solutions. Furthermore, it was shown that a poor local optimization caused either an underestimation or an overestimation of the stimulus-induced brain activation. However, this was not observed if the cluster analysis was based upon a global optimization strategy.

Adult↗