Periodic and synchronic firing in an ensemble of identical stochastic units: Structural stability

Ortiz, Francisco de Borja Rodríguez; López, Vicente

doi:10.1007/bfb0098193

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…Two different regimes are found depending on the degree of interaction among neurons. For strong interaction among network units, the system settles into a regime where units fire regularly in groups (Rodríguez & López, 1999). In this state, which closely resembles the one described in van Vreeswijk and Abbott (1993), the strength of incoming messages is enough to produce synchronization and even to override stochasticity.…”

Section: Introductionmentioning

confidence: 91%

“…As η approaches one, the feedback effect of the network becomes stronger, and correlations between the neurons are no longer negligible. In fact at η = 1, the oscillators fire periodically within synchronization clusters (van Vreeswijk & Abbott, 1993;Rodríguez & López, 1999). The theoretical analysis of such regime, where the simplifying assumptions we make in the formulation of this mean-field theory are no longer valid, is more involved and outside the scope of this article.…”

Section: Mean-field Theory Of the Oscillator Ensemblementioning

confidence: 96%

“…For small values of η, correlations are of crucial importance to understand the temporal firing patterns that appear in the system (van Vreeswijk & Abbott, 1993;Rodríguez & López, 1999). An analysis of the strong interaction regime is outside the scope of this work.…”

Section: The Limit Of Intermediate ηmentioning

confidence: 99%

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Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

2001

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The population dynamics of an ensemble of nonleaky integrate-and-fire stochastic neurons is studied. The model selected allows for a detailed analysis of situations where noise plays a dominant role. Simulations in a regime with weak to moderate interactions show that a mechanism of excitatory message interchange among the neurons leads to a decrease in the firing period dispersion of the individual units. The dispersion reduction observed is larger than what would be expected from the decrease in the period. This "period focusing" is explained using a mean-field model. It is a dynamical effect that arises from the progressive decrease of the effective firing threshold as a result of the messages received by each unit from the rest of the population. A back-of-the-envelope formula to calculate this nontrivial dispersion reduction and a simple geometrical description of the effect are also provided.

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Section: Introductionmentioning

confidence: 91%

Section: Mean-field Theory Of the Oscillator Ensemblementioning

confidence: 96%

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Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

2001

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Global dynamics of a network of stochastic neurons maximizes local mutual information

Rodrguez

Huerta

Lpez

2001

Network: Computation in Neural Systems

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We define a stochastic neuron as an element that increases its internal state with probability p until a threshold value is reached; after that its internal state is set back to the initial value. We study the local information of a stochastic neuron between the message arriving from the input neurons and the response of the neuron. We study the dependence of the local information on the firing probability alpha of the synaptic inputs in a network of such stochastic neurons. The values of alpha obtained in the simulations are the same as those obtained theoretically by maximization of local mutual information. We conclude that the global dynamics maximizes the local mutual information of single units, which means that the self-selected parameter value of the population dynamics is such that each neuron behaves as an optimal encoder.

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Global dynamics of a network of stochastic neurons maximizes local mutual information

Rodrguez

Huerta

Lpez

2001

Network: Computation in Neural Systems

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Periodic and synchronic firing in an ensemble of identical stochastic units: Structural stability

Cited by 4 publications

References 13 publications

Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

Global dynamics of a network of stochastic neurons maximizes local mutual information

Global dynamics of a network of stochastic neurons maximizes local mutual information

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