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At least 379 records · Page 21Linked to original sources
PubMed1990

Toward modeling a dynamic biological neural network.

Mammalian macular endorgans are linear bioaccelerometers located in the vestibular membranous labyrinth of the inner ear. In this paper, the organization of the endorgan is interpreted on physical and engineering principles. This is a necessary prerequisite to mathematical and symbolic modeling of information processing by the macular neural network. Mathematical notations that describe the functioning system were used to produce a novel, symbolic model. The model is six-tiered and is constructed to mimic the neural system. Initial simulations show that the network functions best when some of the detecting elements (type I hair cells) are excitatory and others (type II hair cells) are weakly inhibitory. The simulations also illustrate the importance of disinhibition of receptors located in the third tier in shaping nerve discharge patterns at the sixth tier in the model system.

Acceleration↗
PubMed1994

Non-linear dynamics in neural networks.

A general framework for the analysis of neurons as stochastic, three-dimensionally complex and non-linear units with a range of temporal properties is outlined, and a class of problems delineated. Some general mathematical properties of the resulting network are deduced, together with information-theoretic questions to be pursued. In particular examples of the relevance of the nonlinear, temporal and stochastic properties of neurons in effective information processing are briefly outlined.

Animals↗
PubMed2001

Dynamics of neural networks: a proposed mechanism to account for changes in clinical symptomatology through time in patients with psychotic diseases.

The classical Kraepelinean dichotomy between manic depressive insanity and the schizophrenias has been recently challenged from clinical and neurobiological quarters. It is not so infrequent to see patients shift from a manic to a schizophrenic symptomatology and vice versa. This paper proposes neurobiological mechanisms as to how these changes may occur, based on recent data on the functioning of neural networks at different modes.

Humans↗
PubMed1992

Evolution of host-parasitoid network through homeochaotic dynamics.

Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.

Journal Article↗
PubMed2000

More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure.

BACKGROUND: Mathematical models of sexually transmitted disease transmission have proven powerful tools for interpreting observed epidemiologic pattern. However, the most commonly used formulation of such models largely fail to capture the effect of partnership concurrency and contact network structure on transmission. GOAL: The development of a compartmental model of partnership formation and dissolution that includes approximations for the influence of the sexual-partner network. STUDY DESIGN: Theoretical analysis of ordinary differential equation models for sexually transmitted disease transmission within sex-partner networks. RESULTS: The approach developed advances earlier pair models, allows for the influence of concurrent sexual partnerships, and illustrates the importance of concurrency to the persistence of diseases with relatively short durations of infectiousness. The authors also illustrate that heterogeneity in risk is possible even in model populations in which all individuals follow the same behavioral rules. CONCLUSION: Deterministic extended pair models offer a powerful approach to modelling sexually transmitted disease transmission that usefully complement computationally intensive microsimulation models.

Female↗
PubMed2002

Information space dynamics for neural networks.

We propose a coupled map lattice defined on a hypercube in M dimensions, the information space, to model memory retrieval by a neural network. We consider that both neuronal activity and the spiking phase may carry information. In this model the state of the network at a given time t is completely determined by a function y(sigma-->,t) of the bit strings sigma-->=(sigma1,sigma2,...,sigmaM), where sigma(i)=+/-1 with i=1,2, ...,M, that gives the intensity with which the information sigma--> is being expressed by the network. As an example, we consider logistic maps, coupled in the information space, to describe the evolution of the intensity function y(sigma-->,t). We propose an interpretation of the maps in terms of the physiological state of the neurons and the coupling between them, obtain Hebb-like learning rules, show that the model works as an associative memory, numerically investigate the capacity of the network and the size of the basins of attraction, and estimate finite size effects. We finally show that the model, when exposed to sequences of uncorrelated stimuli, shows recency and latency effects that depend on the noise level, delay time of measurement, and stimulus intensity.

Journal Article↗
PubMed2004

Extreme fluctuations in small-world networks with relaxational dynamics.

We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes finite (synchronized state) and the extreme height diverges only logarithmically in the large system-size limit. This latter property ensures synchronization in a practical sense in small-world coupled multi-component autonomous systems. The statistics of the extreme heights is governed by the Fisher-Tippett-Gumbel distribution.

Journal Article↗
PubMed1987

Frequency modulation dynamics in neural networks.

The VCON model described here shares certain qualitative features of stimulus-response characteristics with the data in FIGURE 1 and TABLE 1. At the same time, it provides an uncomplicated methodology for modelling neural networks that emphasizes their frequency aspects. In particular, models based on VCONs are amenable to the rotation vector method, which can be used to uncover stable synchronization of firing within a network. This is described in the appendix, where it is shown that the stable firing patterns within the network correspond to minima of an associated (local) energy function. We have seen here how a model of a simple CPG for breathing can be constructed and analyzed. Similar models for rhythm splitting of small mammal activity cycles, sound location networks, and motility in the gastrointestinal tract have been constructed, and large networks of VCONs have been shown to have stable spatial patterns of synchronization.

Action Potentials↗
PubMed2000

Intrinsic dynamics in neuronal networks. II. experiment.

Neurons in many regions of the mammalian CNS remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How these firing patterns are maintained in the presence of powerful recurrent excitation, and how networks switch between them, is not well understood. In the previous paper, we addressed these issues theoretically; in this paper we address them experimentally. We found in both studies that a key parameter in controlling firing patterns is the fraction of endogenously active cells. The theoretical analysis indicated that steady firing rates are possible only when the fraction of endogenously active cells is above some threshold, that there is a transition to bursting when it falls below that threshold, and that networks becomes silent when the fraction drops to zero. Experimentally, we found that all steadily firing cultures contain endogenously active cells, and that reducing the fraction of such cells in steadily firing cultures causes a transition to bursting. The latter finding implies indirectly that the elimination of endogenously active cells would cause a permanent drop to zero firing rate. The experiments described here thus corroborate the theoretical analysis.

Action Potentials↗