Dynamic Pattern Formation Leads to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:mfrac></mml:math>Noise in Neural Populations

Usher, Marius; Stemmler, Martin B.; Olami, Zeev

doi:10.1103/physrevlett.74.326

Cited by 119 publications

(115 citation statements)

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“…We have also shown that in the case of onedimensional networks such patterns are consistent with those of a corresponding analog model. Numerical results by Usher et al [18] suggest that this result also holds for two-dimensional networks. A much more detailed analysis of two-dimensional networks will be presented elsewhere [21] where we shall also consider the more biologically realistic case of two populations of IF oscillators, one excitatory with short-range interactions and the other inhibitory with long-range interactions.…”

Section: (Received 9 April 1998)mentioning

confidence: 51%

“…However, the mean-rate description does not include any information concerning the dynamics on short time scales. It is likely that the latter plays a significant role in the metastability of patterns, as has been illustrated by Usher et al [18] in the case of noise-induced instabilities. Therefore, it is important to understand the basic mechanism of pattern formation in terms of the original spiking model without recourse to any mean-rate approximation.…”

Section: (Received 9 April 1998)mentioning

confidence: 75%

“…A number of studies of two-dimensional IF networks have shown that spontaneous excitations can occur leading to the formation of synchronized waves of activity across the network [14][15][16][17]. The analysis of pattern formation in such networks has so far been restricted to formulations in which the output of each oscillator is taken to be a mean firing rate [18]. This leads to an analog network model that is well known to undergo a Turing-like instability when there is competition between short-range excitation and long-range inhibition [19].…”

Section: (Received 9 April 1998)mentioning

confidence: 99%

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Spike Train Dynamics Underlying Pattern Formation in Integrate-and-Fire Oscillator Networks

Bressloff

Coombes

1998

Phys. Rev. Lett.

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Section: (Received 9 April 1998)mentioning

confidence: 51%

Section: (Received 9 April 1998)mentioning

confidence: 75%

Section: (Received 9 April 1998)mentioning

confidence: 99%

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Spike Train Dynamics Underlying Pattern Formation in Integrate-and-Fire Oscillator Networks

Bressloff

Coombes

1998

Phys. Rev. Lett.

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“…A number of recent numerical studies have shown that such waves can also occur in two-dimensional networks of integrate-and-fire neurons (Chu et al 1994;Horn and Opper 1997;Usher et al 1995;Kistler et al 1998). In this final section, we indicate how to extend our analysis of traveling waves in one dimension to the case of plane waves in two-dimensional networks, and relate our results to recent work by Kistler et al (1998) on the so-called spike response model (Gerstner 1995).…”

Section: Two-dimensional Networkmentioning

confidence: 62%

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

Bressloff¹

2000

Journal of Mathematical Biology

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“…In a homogeneous network (i.e., neurons and their connections are all identical), the locations of the clusters are unconstrained and have an equal likelihood of existing at any position. Therefore, clusters in a homogeneous network move in a random walk, constrained only by their interactions with nearby clusters [1].In contrast, networks with heterogeneous neurons tend to bias the locations where clusters reside. Clusters do not wander freely but are instead pinned to the locations that maximize their local recurrent feedback.…”

mentioning

confidence: 99%

Dynamic computation in a recurrent network of heterogeneous silicon neurons

Merolla¹,

Boahen²

2006 IEEE International Symposium on Circuits and Systems

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Abstract-We describe a neuromorphic chip with a twolayer excitatory-inhibitory recurrent network of spiking neurons that exhibits localized clusters of neural activity. Unlike other recurrent networks, the clusters in our network are pinned to certain locations due to transistor mismatch introduced in fabrication. As described in previous work, our pinned clusters respond selectively to oriented stimuli and the neurons' preferred orientations are distributed similar to the visual cortex. Here we show that orientation computation is rapid when activity alternates between layers (staccato-like), dislodging pinned clusters, which promotes fast cluster diffusion. I. PATTERN-FORMING RECURRENT NETWORKSA 2-D recurrent network of spiking neurons with Mexican hat connectivity (local excitation and distal inhibition) can exhibit clusters of activity when the feedback is sufficiently strong. These clusters are an emergent property of the network and are identified by contiguous regions of activity surrounded by dead zones (no activity). In a homogeneous network (i.e., neurons and their connections are all identical), the locations of the clusters are unconstrained and have an equal likelihood of existing at any position. Therefore, clusters in a homogeneous network move in a random walk, constrained only by their interactions with nearby clusters [1].In contrast, networks with heterogeneous neurons tend to bias the locations where clusters reside. Clusters do not wander freely but are instead pinned to the locations that maximize their local recurrent feedback. One intriguing possibility is that the interactions between spatio-temporal input patterns (e.g., visual scenes) and these pinned clusters can process information. For example, it has been shown that oriented stimuli are able to shift the clusters away from their preferred locations to produce orientation selective responses whose distribution resembles cortical maps of preferred orientation (PO) [2], [3]. The seemingly complicated task of assigning similar POs to nearby neurons is cleverly achieved by simply building an imprecise, recurrent network.Transforming fixed-pattern noise into a smoothly changing feature map is an impressive feat, but this transformation is poorly understood. In particular, it is not known how cluster dynamics, which can range from fluid (mobile clusters) to crystalline (immobile clusters), influence PO map creation. We address this issue by characterizing how clusters diffuse over a range of network states and by examining the speed at which orientation maps converge for two disparate diffusion rates.Exploring a detailed, large-scale recurrent network over a wide range of network parameters is a computationally daunting task that is poorly suited for software modeling. We refer to circuit parameters as typepar, where type specifies the section of the neural circuit, and par specifies the circuit parameter (e.g., the excitatory cell synapse parameter A is referenced as E A ).Previous attempts to model such networks in software have sacrifi...

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Dynamic Pattern Formation Leads to1fNoise in Neural Populations

Cited by 119 publications

References 20 publications

Spike Train Dynamics Underlying Pattern Formation in Integrate-and-Fire Oscillator Networks

Spike Train Dynamics Underlying Pattern Formation in Integrate-and-Fire Oscillator Networks

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

Dynamic computation in a recurrent network of heterogeneous silicon neurons

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