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A mathematical description of the refractoriness period in neuronal diffusion modeling is given and its moments are explicitly obtained in a form that is suitable for quantitative evaluations. Then, for the Wiener, Ornstein-Uhlenbeck and Feller neuronal models, an analysis of the features exhibited by the mean and variance of the first passage time and of refractoriness period is performed.
We compute explicitly several abstract metrics for RNA secondary structures defined by Reidys and Stadler.
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the firing densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's firing probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes characterized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal firing densities are not available.
We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three possible evolutions of the system to distinct ecological balances. More precisely, the whole population may die out, the european beech may conquer the bracken, and coexistence of both species may occur.
We describe efficient methods for screening clone libraries, based on pooling schemes which we call ``random $k$-sets designs''. In these designs, the pools in which any clone occurs are equally likely to be any possible selection of $k$ from the $v$ pools. The values of $k$ and $v$ can be chosen to optimize desirable properties. Random $k$-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only one pass, thus facilitating automation. For design comparison, we assume a binomial distribution for the number of ``positive'' clones, with parameters $n$, the number of clones, and $c$, the coverage. We propose the expected number of {\em resolved positive} clones---clones which are definitely positive based upon the pool assays---as a criterion for the efficiency of a pooling design. We determine the value of $k$ which is optimal, with respect to this criterion, as a function of $v$, $n$ and $c$. We also describe superior $k$-sets designs called $k$-sets packing designs. As an illustration, we discuss a robotically implemented design for a 2.5-fold-coverage, human chromosome 16 YAC library of $n=1,298$ clones. We also estimate the probability each clone is positive, given the pool-assay data and a model for experimental errors.
We show that an important problem ($k$-ICG) in computational biology is equivalent to a colored version of a well-known graph layout problem ($k$-CVS).
Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele model, and then generalized, through the projective limit technique, to the infinite allele model. Explicit expressions are obtained for the rate functions.
The approach of N. Gay for estimating the coverage of a multivalent vaccine from antibody prevalence data in certain age cohorts is improved by using computer aided elimination theory of variables. Hereby, Gay's usage of numerical approximation can be replaced by exact formulas which are surprisingly nice, too.
This note presents a self-contained and streamlined exposition of chemical-network results due to Feinberg, Horn, and Jackson. As an application, it shows the global asymptotic stability to equilibria of McKeithan's kinetic proofreading model for T-cell receptor signal transduction.
A new evolutionary solution to Prisoner Dilemma situations is proposed in this paper. A specific genetic code may have different phenotypes, meaning different strategies for different individuals carrying that gene. This means that, under the right parameters, it is a good evolutionary solution to create two types of phenotypes with different strategies, here called as leaders and servants. In this solution, servants always cooperate with the leaders and leaders never do with the servants. Inside the same class, the usual strategies apply. Possible applications of this solution are discussed.
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary timescale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organised criticality.
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical experiments and it is difficult for the stochastic activity to reproduce them in the same simple framework. Our demonstration suggests functional usefulness of the chaotic activity in perceptual systems even at higher cognitive levels. The perceptual alternation may be an inherent feature built in the chaotic neuron assembly.
Complex systems with tightly coadapted parts frequently appear in living systems and are difficult to account for through Darwinian evolution, that is random variation and natural selection, if the constituent parts are independently coded in the genetic code. If the parts are independently coded, multiple simultaneous mutations appear necessary to create or modify these systems. It is generally believed that most proteins are independently coded. The textbook rule is one gene for one enzyme. Thus, biochemical systems with tightly coadapted parts such as the blood clotting cascade pose a difficulty for Darwinian evolution. This problem can be overcome if the current understanding of the genetic code is incomplete and a system-level genetic code in which seemingly independent proteins are encoded in an interdependent, highly correlated manner exists. The methods by which human beings design and fabricate complex systems of tightly coadapted parts are explored for insights into the requirements for a system-level genetic code. Detailed examples of system-level codes for networks of matching parts are presented. The implications of identifying and deciphering the system-level genetic code if it exists for the prevention, treatment, and cure of heart disease, cancer, immune disorders, and for rational drug design are discussed.
We set up a signal-driven scheme of the chaotic neural network with the coupling constants corresponding to certain information, and investigate the stochastic resonance-like effects under its deterministic dynamics, comparing with the conventional case of Hopfield network with stochastic noise. It is shown that the chaotic neural network can enhance weak subthreshold signals and have higher coherence abilities between stimulus and response than those attained by the conventional stochastic model.
A system-level genetic code is a hypothetical genetic code that exclusively or preferentially codes systems of interacting coadapted parts. System-level genetic codes differ from part-level genetic codes in which each discrete part is coded independently. In general, a system-level genetic code requires coding discrete interacting parts such as organs or proteins in an interdependent way. Changing a single symbol or "gene" in a system-level genetic code affects two or more parts in a coordinated way. System-level genetic codes provide a plausible mechanism for evolution by leaps also known as systemic macromutations or hopeful monsters without invoking an intelligent agent, vitalistic forces, or new laws of physics. A system-level genetic code may explain the rapid appearance of new forms of life in the fossil record such as the Cambrian Explosion in which most invertebrate phyla appeared. A system-level genetic code may explain the origin of complex integrative systems of tightly coadapted proteins such as the blood coagulation cascade in which the removal or structural modification of any single part breaks the system. It is demonstrated that a simple system-level genetic code can, in principle, be implemented using biochemical mechanisms similar or identical to the mechanisms used by transposable elements, regulation of gene expression, and the adaptive vertebrate immune system. It is further suggested that cancer in the body and both normal and tumor cell lines cultured in vitro are caused by mutations of the system-level genetic code. An explanation why multi-cellular organisms retain the ability to revert to uni-cellularity and thus a tendency to develop cancer is presented.
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement are considered. The model is built taking into account the range of motion of the elements of population. For small (large) values of this range, the behaviors described by partial (ordinary) differential equation models are reproduced. Emphasis is done in the study of those scenarios in which the above mentioned equations fail to describe. Some interesting results in these cases are reported.
Using a weak migration and weak mutation approximation, I study the average waiting time to and the average duration of parapatric speciation. The description of reproductive isolation used is based on the classical Dobzhansky model and its recently proposed multilocus generalizations. The dynamics of parapatric speciation is modeled as a biased random walk with absorption performed by the average genetic distance between the residents and immigrants. If a small number of genetic changes is sufficient for complete reproductive isolation, mutation and random genetic drift alone can cause speciation on the time scale of 10-1000 times the inverse of the mutation rate. Even relatively weak selection for local adaptation can dramatically decrease the waiting time to speciation. The duration of parapatric speciation is shorter by orders of magnitude than the waiting time to speciation. For a wide range of parameter values, the duration of speciation is order one over the mutation rate. In general, parapatric speciation is expected to be triggered by changes in the environment.
We present a method for the analysis of electroencephalograms (EEG). In particular, small signals due to stimulation, so called evoked potentials, have to be detected in the background EEG. This is achieved by using a denoising implementation based on the wavelet decomposition. One recording of visual evoked potentials, and recordings of auditory evoked potentials from 4 subjects corresponding to different age groups are analyzed. We find higher variability in older individuals. Moreover, since the evoked potentials are identified at the single stimulus level (without need of ensemble averaging), this will allow the calculation of better resolved averages. Since the method is parameter free (i.e. it does not need to be adapted to the particular characteristics of each recording), implementations in clinical settings are imaginable.