A visual sense of number emerges from the dynamics of a recurrent on-center off-surround neural network

Sengupta, Rakesh; Surampudi, Bapi Raju; Melcher, David

doi:10.1016/j.brainres.2014.03.014

Cited by 29 publications

(82 citation statements)

References 29 publications

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“…According to recent proposals, subitizing might be due spatial interference among items. As mentioned above, Sengupta et al (2014) and Knops et al (2014) implemented a saliency map where neurons excite themselves and inhibit each other.…”

Section: The Role Of Interference In Other Cognitive Capacity Limitatmentioning

confidence: 99%

Interference and memory capacity limitations.

Endress

Szabó

2017

Psychological Review

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This is the accepted version of the paper.This version of the publication may differ from the final published version. However, the origins of these capacity limitations are debated, and generally attributed to active, attentional processes. Here, we show that the existence of interference among items in memory mathematically guarantees fixed and limited capacity limits under very general conditions, irrespective of any processing assumptions. Assuming that interference (i) increases with the number of interfering items and (ii) brings memory performance to chance levels for large numbers of interfering items, capacity limits are a simple function of the relative influence of memorization and interference. In contrast, we show that time-based memory limitations do not lead to fixed memory capacity limitations that are independent of the timing properties of an experiment. We show that interference can mimic both slot-like and continuous resource-like memory limitations, suggesting that these types of memory performance might not be as different as commonly believed. We speculate that slot-like WM limitations might arise from crowding-like phenomena in memory when participants have to retrieve items. Further, based on earlier research on parallel attention and enumeration, we suggest that crowding-like phenomena might be a common reason for the three major cognitive capacity limitations. As suggested by Miller (1956) and Cowan (2001), these capacity limitations might thus arise due to a common reason, even though they likely rely on distinct processes. Permanent repository link:

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Section: The Role Of Interference In Other Cognitive Capacity Limitatmentioning

confidence: 99%

Interference and memory capacity limitations.

Endress

Szabó

2017

Psychological Review

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“…Using this modified frequency and using Dawson's argument [23], phase mixing time is estimated, both in small and large ∆k/k limit. In section 3, we verify the analytically derived scalings of phase mixing time on amplitude "δ", using numerical simulations based on Dawson sheet model [31,32]. Finally in section 4, we present a summary of our work.…”

Section: Introductionmentioning

confidence: 74%

“…According to the Dawson sheet model description of a cold plasma [31,32], electrons are assumed to be infinite sheets of charges embedded in a cold immobile positive ion background. Evolution of any coherent mode can be studied in terms of oscillating motion of these sheets about their equilibrium positions.…”

Section: Equation Of Motion and Its Solutionmentioning

confidence: 99%

“…Phase mixing time is measured as the time taken by any two adjacent sheets to cross over. We terminate our code at this time because the expression for self-consistent electric field (E = 4πen 0 ξ) used in equation of motion becomes invalid beyond this point [19,20,31,32]. Figs.1 -3 respectively show the dependence of phase mixing time with amplitude δ for three different values of |∆k/k|; |∆k/k| = 0.1, 0.2 and 0.5.…”

Section: Numerical Verificationmentioning

confidence: 99%

“…In ref. [19] , the relativistic equation of motion of an electron is derived using Dawson sheet model [31,32] and solved in the weakly relativistic limit using Krylov and Bogoliubov method of averaging [33]. The relativistically correct frequency of oscillation is obtained upto second order in wave amplitude "δ".…”

Section: Introductionmentioning

confidence: 99%

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Phase mixing of relativistically intense longitudinal wave packets in a cold plasma

Mukherjee

Sengupta

2016

Physics of Plasmas

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Abstract. Phase mixing of relativistically intense longitudinal wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically using Dawson Sheet Model. A general expression for phase mixing time (ω p t mix ) as a function of amplitude of the wave packet(δ) and width of the spectrum(∆k/k) has been derived. It is found that phase mixing time crucially depends on the relative magnitude of amplitude "δ" and the spectral width "∆k/k". For ∆k/k ≤ 2ω 2 p δ 2 /c 2 k 2 , ω p t mix scales with δ as ∼ 1/δ 5 , whereas for ∆k/k > 2ω 2 p δ 2 /c 2 k 2 , ω p t mix scales with δ as ∼ 1/δ 3 , where ω p is the non-relativistic plasma frequency and c is the speed of light in vacuum. We have also verified the above theoretical scalings using numerical simulations based on Dawson Sheet Model.

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The Role of Lateral Inhibition on Visual Number Sense

Zhou

Chen

2021

Advances in Intelligent Automation and Soft Computing

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A visual sense of number emerges from the dynamics of a recurrent on-center off-surround neural network

Cited by 29 publications

References 29 publications

Interference and memory capacity limitations.

Interference and memory capacity limitations.

Phase mixing of relativistically intense longitudinal wave packets in a cold plasma

The Role of Lateral Inhibition on Visual Number Sense

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