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At least 433 records · Page 24Linked to original sources
arXiv2002

Using of Phenomenological Piecewise Continuous Map for Modeling of Neurons Behaviour

A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations generating by Rose-Hindmarsh model. The synchronization in small ensembles of the maps is investigated. It is considered the different number of elements in the ensemble and different connectivity topologies.

nlin.CD↗
arXiv2002

Selection of Catalysts through Cellular Reproduction

It has been pointed out that if an autocatalytic cycle produces primitive membrane chemicals, it can compose a self-maintaining proto cell. Moreover, it is known that a proto cell can divide itself spontaneously as it grows. An unsolved problem is how such a catalytic system can evolve in the pre-cellular environment. Here we examine, as the first step, the evolution of catalysts that have different activity in generating membrane chemicals using a Lattice-Gas-like model. We demonstrated that a self-replicating proto-cell emerges from random initial configuration. We also showed that cells with higher activity of membrane production evolve through cellular selection.

nlin.AO↗
arXiv2002

Survival in the replicator model: Dynamics and statistics

We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its average interaction with the rest of the system. The role of the interaction pattern of the ecosystem in defining survival and extinction probabilities is emphasized.

nlin.AO↗
arXiv2002

Emergence of a complex and stable network in a model ecosystem with extinction and mutation

We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the conventional replicator equation and the generalized Lotka-Volterra equation. We reach several significant conclusions as follows: (1) a complex ecosystem can emerge when mutants with respect to species-specific interaction are introduced; (2) such an ecosystem possesses strong resistance to invasion; (3) a typical fixation process of mutants is realized through the rapid growth of a group of mutualistic mutants with higher fitness than majority species; (4) a hierarchical taxonomic structure (like family-genus-species) emerges; and (5) the relative abundance of species exhibits a typical pattern widely observed in nature. Several implications of these results are discussed in connection with the relationship of the present model to the generalized Lotka-Volterra equation.

nlin.AO↗
arXiv2002

HebbNets: Dynamic network with Hebbian learning rule

It has been demonstrated that one of the most striking features of the nervous system, the so called 'plasticity' (i.e high adaptability at different structural levels) is primarily based on Hebbian learning which is a collection of slightly different mechanisms that modify the synaptic connections between neurons. The changes depend on neural activity and assign a special dynamic behavior to the neural networks. From a structural point of view, it is an open question what network structures may emerge in such dynamic structures under 'sustained' conditions when input to the system is only noise. In this paper we present and study the `HebbNets', networks with random noise input, in which structural changes are exclusively governed by neurobiologically inspired Hebbian learning rules. We show that Hebbian learning is able to develop a broad range of network structures, including scale-free small-world networks.

nlin.AO↗
arXiv2002

A model of cardiac tissue as a conductive system with interacting pacemakers and refractory time

A model of the heart tissue as a conductive system with two interacting pacemakers and a refractory time, is proposed. In the parametric space of the model the phase locking areas are investigated in detail. Obtained results allow us to predict the behaviour of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase. Comparison of the described phenomena with intrinsic pathologies of cardiac rhythms is presented.

nlin.CD↗
arXiv2002

The structure of evolutionary exploration: On crossover, buildings blocks and Estimation-Of-Distribution Algorithms

The notion of building blocks can be related to the structure of the offspring probability distribution: loci of which variability is strongly correlated constitute a building block. We call this correlated exploration. With this background we analyze the structure of the offspring probability distribution, or exploration distribution, for a GA with mutation only, a crossover GA, and an Estimation-Of-Distribution Algorithm (EDA). The results allow a precise characterization of the structure of the crossover exploration distribution. Essentially, the crossover operator destroys mutual information between loci by transforming it into entropy; it does the inverse of correlated exploration. In contrast, the objective of EDAs is to model the mutual information between loci in the fitness distribution and thereby they induce correlated exploration.

nlin.AO↗
arXiv2003

Learning a world model and planning with a self-organizing, dynamic neural system

We present a connectionist architecture that can learn a model of the relations between perceptions and actions and use this model for behavior planning. State representations are learned with a growing self-organizing layer which is directly coupled to a perception and a motor layer. Knowledge about possible state transitions is encoded in the lateral connectivity. Motor signals modulate this lateral connectivity and a dynamic field on the layer organizes a planning process. All mechanisms are local and adaptation is based on Hebbian ideas. The model is continuous in the action, perception, and time domain.

nlin.AO↗
arXiv2003

Deterministic uncertainty

Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map with delay -- the deterministic part of the stochastic cerebral blood flow map (CBFM) recently introduced to elucidate the scaling properties of cerebral hemodynamics. We point out the existence of deterministic and nondeterministic subspaces in the reconstructed phase space of delay-difference equations and discuss the problem of detection of nonlinearities in time series generated by such dynamical systems.

nlin.CD↗
arXiv1995

Cancer Detection via Determination of Fractal Cell Dimension

We utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with normal blood lymphocytes.

patt-sol↗
arXiv1998

Two boundary model for freezing front propagation in biological tissue

The response of the living tissue to the effects of strong heating or cooling can cause the blood flow rate to vary by an order of magnitude. A mathematical model for the freezing of living tissue is formulated which takes into account the nonlocal temperature dependence of the blood flow rate when the temperature distribution in the tissue is substantially nonuniform, as in cryosurgery.

patt-sol↗
arXiv2000

Statistical mechanics of neocortical interactions: Reaction time correlates of the g factor

A statistical mechanics of neuronal interactions (SMNI) is explored as providing some substance to a physiological basis of the g factor. Some specific elements of SMNI, previously used to develop a theory of short-term memory (STM) and a model of electroencephalography (EEG) are key to providing this basis. Specifically, Hick's Law, an observed linear relationship between reaction time (RT) and the information storage of STM, in turn correlated to a RT-g relationship, is derived.

physics.bio-ph↗
arXiv2000

Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory

This paper focuses on how bottom-up neocortical models can be developed into eigenfunction expansions of probability distributions appropriate to describe short-term memory in the context of scalp EEG. The mathematics of eigenfunctions are similar to the top-down eigenfunctions developed by Nunez, albeit they have different physical manifestations. The bottom-up eigenfunctions are at the local mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. However, as described in several joint papers, our approaches have regions of substantial overlap, and future studies may expand top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model of scalp EEG that is ultimately expressed in terms of columnar states of neocortical processing of attention and short-term memory.

physics.bio-ph↗
arXiv2000

Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. Sets of EEG and evoked potential data were fit, collected to investigate genetic predispositions to alcoholism and to extract brain signatures of short-term memory. Adaptive Simulated Annealing (ASA), a global optimization algorithm, was used to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta indicators (CMI) are thereby derived for individual's EEG data. The CMI give better signal recognition than the raw data, and can be used to advantage as correlates of behavioral states. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons. This paper adds to these previous investigations two important aspects, a description of how the CMI may be used in source localization, and calculations using previously ASA-fitted parameters in out-of-sample data.

physics.bio-ph↗
arXiv2000

Formalizing the gene centered view of evolution

A historical dispute in the conceptual underpinnings of evolution is the validity of the gene centered view of evolution. \cite{dawkins,lewontin} We transcend this debate by formalizing the gene centered view as a dynamic version of the mean field approximation. This establishes the conditions under which it is applicable and when it is not. In particular, it breaks down for trait divergence which corresponds to symmetry breaking in evolving populations.

physics.bio-ph↗
arXiv2000

Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented which builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low variance Gaussian process. It is found that, in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale which is set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies, with little modification, to point process spectra, and is of utility in studying a point process driven by a continuous stimulus. While the material discussed is of general applicability to point processes attention will be confined to sequences of neuronal action potentials (spike trains) which were the motivation for this work.

physics.bio-ph↗
arXiv2000

On the genealogy of a population of biparental individuals

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.

physics.bio-ph↗