Noise-driven neuromorphic tuned amplifier.

@article{Fanelli2017NoisedrivenNT,
  title={Noise-driven neuromorphic tuned amplifier.},
  author={Duccio Fanelli and Francesco Ginelli and Roberto Livi and Niccol{\'o} Zagli and Cl{\'e}ment Zankoc},
  journal={Physical review. E},
  year={2017},
  volume={96 6-1},
  pages={
          062313
        }
}
We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a… 

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References

SHOWING 1-10 OF 73 REFERENCES
Stochastic Dynamics of a Finite-Size Spiking Neural Network
TLDR
The model is applicable to any network where the probability of firing of a neuron in the network depends on only the number of neurons that fired in a previous temporal epoch and the model completely accounts for the size of the network and correlations in the firing activity.
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics.
  • P. Bressloff
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
TLDR
A stochastic model of neuronal population dynamics with intrinsic noise is analyzed, reducing the dynamics to a neural Langevin equation, and showing how the intrinsic noise amplifies subthreshold oscillations (quasicycles).
Excitatory and inhibitory interactions in localized populations of model neurons.
TLDR
It is proved that the existence of limit cycle dynamics in response to one class of stimuli implies theexistence of multiple stable states and hysteresis in responseTo this work, coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons.
Intertangled stochastic motifs in networks of excitatory-inhibitory units.
TLDR
A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied, and patterns are lacking under the idealized deterministic scenario, and could provide hints on how living systems implement and handle a large gallery of delicate computational tasks.
Emergent Oscillations in Networks of Stochastic Spiking Neurons
TLDR
Two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate are described, shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency.
Stochastic resonance induced by exogenous noise in a model of a neuronal network
TLDR
Results show the onset of the Stochastic Resonance (SR) behavior, as long as the exogenous noise is properly tailored and filtered, indicating that both kinds of noise cooperate to the signal detection.
Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
TLDR
Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around -1.16 and it is shown that this power law is robust upon a variation of the refractory time over several orders of magnitude, however, the avalanche time distribution is biexponential.
Noise-Induced Precursors of State Transitions in the Stochastic Wilson–Cowan Model
TLDR
It is shown that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point.
Wilson–Cowan Equations for Neocortical Dynamics
TLDR
This work describes how the Markov models account for many recent measurements of the resting or spontaneous activity of the neocortex, and shows that the power spectrum of large-scale neocortical activity has a Brownian motion baseline, and that the statistical structure of the random bursts of spiking activity found near the resting state indicates that such a state can be represented as a percolation process on a random graph, called directed percolations.
A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States
TLDR
Using master equation formalism, a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks is derived, applicable to any neuron model as long as its transfer function can be characterized.
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5
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