Dynamics of Noisy Neural Nets with Chemical Markers and Gaussian-distributed Connectivities

Kotini, A; Anninos, P. A.

doi:10.1080/095400997116603

Cited by 9 publications

(7 citation statements)

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“…Following the suppositions of previous papers [1][2][3][4][5][6][7][8][9][10], the expectation value of the neural activity <α n+1 > at t=(n+1) τ, (i.e. the average value) of α n+1 generated by a collection of netlets with the same parameters (α n, μ + ,μ -,h, K + , K -,A, θ) at t=nτ with 2 markers m a and m b , is given by: where P l ,Q i ,P`l`,Q`i` are the possibilities that the neuron will receive l EPSPs, i IPSPs or l`-EPSPs, i`-IPSPs, at time t=(n+1)τ in the subsystems a or b.…”

Section: Poisson Distributionmentioning

confidence: 91%

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The Significance of Limit Cycles in a Neural Model with Poisson and Gauss Connectivity

Kotini

2016

JApl Theol

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Isolatedrandomly interconnected nets with chemical markers and noise are investigated, which follow Poisson or Gauss distribution. The obtained results reveal limit cycles. The Poisson limit cycles are primarily large and complex, while the Gauss ones are regularly small.The Poisson limit cycles have various types depending on the shape andtime ofthe transient part, whereas the Gauss ones have the same form, plain, with no particular types of the transient component and are small. The epilepticMEGs follow Poisson distributions with high magnetic amplitudes varying with time and repeatable at time intervals with similar characteristics like the limit cycles. Alternatively the MEGs from healthy subjects have Gauss distributions. The above mentioned differentiations are due to the fact that in Poisson distributed connectivity the activity of the system is organized and synchronized as in epileptic discharges while in Gauss one is random and disordered as in healthy subjects. Limit cycles have been used to form the behavior of many oscillatory systems.

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Section: Poisson Distributionmentioning

confidence: 91%

“…The basic hypotheses of this model have been described in detail previously [1][2][3][4].In short, a neural net with N neurotrasmitters (markers)is supposed to be constructed of A neurons. A portion h (0<h<1) of them are inhibitory while the rest are excitatory.…”

Section: The Neural Net Modelmentioning

confidence: 99%

The Significance of Limit Cycles in a Neural Model with Poisson and Gauss Connectivity

Kotini

2016

JApl Theol

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“…Consequently, as stated in our previous paper [8], the firing probabilities P(α n , δ n+1 , δ a ) and P'(α n , δ n+1 , δ b ) that a neuron in subpopulations a and b, respectively, will receive PSPs exceeding threshold at time t = (n+1)τ will be given by (29):…”

Section: Methodsmentioning

confidence: 99%

A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals

Kotini

Anninos

Anastasiadis

et al. 2005

Theor Biol Med Model

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“…The probabilistic neural nets initially were quite simple [5,6], but later got more involved [7][8][9][10][11][12], and incorporate today several advanced characteristics met in actual neural networks. Their theoretical basis is the binomial distribution, as one tries to attribute some specific properties to a fraction of units out of the total population.…”

Section: Introductionmentioning

confidence: 98%

Refractoriness in Poisson and Gaussian First-order Neural Nets with Chemical Markers

Fournou¹,

Argyrakis

Anninos

2005

Neural Process Lett

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In this work first order probabilistic Poisson and Gaussian neural nets with chemical markers are investigated, analytically and by computer simulations. The investigation of steady-state behavior of these systems is extended here to systems in which the refractory period is assigned to be 1 for all or some of the subpopulations of the net, whereas the remainder are characterized by zero refractory periods. The interest is focused on the effects of refractoriness on the neural activities. Results obtained show the existence of several critical points at high initial activities, which are a consequence of the nonzero refractory periods. For these points a larger initial activity, above a certain critical level, results in the reduction of activity to a lower stable steady-state, instead of the highest one. We also find that in the Gaussian nets each critical point is lower than the corresponding one as in the Poisson nets. Finally, a discussion of the results is made.

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Dynamics of Noisy Neural Nets with Chemical Markers and Gaussian-distributed Connectivities

Cited by 9 publications

References 0 publications

The Significance of Limit Cycles in a Neural Model with Poisson and Gauss Connectivity

The Significance of Limit Cycles in a Neural Model with Poisson and Gauss Connectivity

A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals

Refractoriness in Poisson and Gaussian First-order Neural Nets with Chemical Markers

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