A theory for the development of feature detecting cells in visual cortex

Nass, Menasche M.; Cooper, Leon N.

doi:10.1007/bf00319777

Cited by 122 publications

(31 citation statements)

References 23 publications

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“…We will, however, adopt the point of view that the measured tuning strength map does, in fact, reflect the distribution of orientation selectivity in cortex, and we will investigate the consequences of this assumption. We will show that the link between orientation preference and tuning strength permits description of the properties of both maps (preferred orientation and orientation strength) with a minimal set of parameters which probably also underlie most of the previously proposed models of cortical map formation and structure (von der Malsburg 1973;Nass and Cooper 1975;Perez et al 1975;Cooper et al 1979;von der Malsburg and Cowan 1982;Swindale 1982;Linsker 1986a, b;Soodak 1987;Durbin and Mitchison 1990;Miller 1990;Obermayer et al 1990Obermayer et al , 1991.…”

Section: Correspondence To: F W6rg6tter L Introductionmentioning

confidence: 80%

“…Note that this assumption only deals with the net excitatory or inhibitory effect as a function of distance; therefore, we cannot draw conclusions about subliminal excitation or inhibition occurring simultaneously with their much stronger, and thus dominating, antagonistic counterparts. The autocorrelation function appears to be a natural choice for the Mexican-hat functions that appear in Swindale's and other reports (von der Malsburg 1973;Nass and Cooper 1975;Legendy 1978;Swindale 1982;Linsker 1986a, b;Miller 1990) because the autocorrelation function inherently represents local correlation and medium distance anticorrelation.…”

Section: Related Modelsmentioning

confidence: 99%

“…Most developmental models assume synaptic links which reinforce the similarity between the orientation preferences of adjacent cells (positive correlation). The strength of this reinforcement mechanism decreases with distance, and most models introduce inhibitory coupling at larger distances, which results in a negative correlation of the activity of the cells which then develop (nearly) orthogonal orientation preferences (von der Malsburg 1973;Nass and Cooper 1975;Legendy 1978;Swindale 1982;Linsker 1986a, b;Miller 1990Miller , 1992.…”

Section: Relation Between Preferred Orientation and Orientation Tuninmentioning

confidence: 99%

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Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

Wörgötter

Niebur

1993

Biol. Cybern.

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Abstract. We demonstrate that the map of the preferred orientations and the corresponding map of the orientation tuning strengths as measured with optical imaging are not independent, but that band-pass filtering of the preferred orientation map at each location yields a good approximation of the orientation tuning strength. Bandpass filtering is performed by convolving the map of orientation preference with its own autocorrelation function. We suggest an interpretation of the autocorrelation function of the preferred orientations as synaptic coupling function, i.e., synaptic strength as a function of intracortical distance between cortical cells. In developmental models it has been shown previously that a "Mexican hat"-shaped synaptic coupling function (with a shape similar to that of the autocorrelation function) can produce a realistical-looking pattern of preferred orientations. Since optical imaging performs surface averaging, we discuss the possibility that the connection between the two maps is a measurement artifact of optical imaging. Whether this is the case can only be decided by combining electrode penetrations with optical imaging techniques for which we suggest experiments. We present a model for the generation of both maps from a single computational concept. The model is based on inverse Fourier transform of rather simple twodimensional annulus-shaped spectra which will produce a column structure very similar to real data. Thus, our approach shows that the complex appearance of cortical orientation columns has a rather simple description in the Fourier domain. Our theoretical analysis explains why singularities in the cortex do not have vorticities other than ± 1/2, a result which corresponds to recent experimental findings. This study combines the results from several modeling approaches with recently available optical imaging data to construct a model of both aspects (angle and strength) of the cortical orientation column system. This could alter ideas about cortical development if the link between the two maps can be established as a physiological result.

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Section: Correspondence To: F W6rg6tter L Introductionmentioning

confidence: 80%

Section: Related Modelsmentioning

confidence: 99%

Section: Relation Between Preferred Orientation and Orientation Tuninmentioning

confidence: 99%

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Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

Wörgötter

Niebur

1993

Biol. Cybern.

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“…Nevertheless, the integrate-and-fire biophysical model of neuronal responses shows that in the frequency domain a linear region of behaviour can exist (Nass andCooper 1975, Kohonen 1977, also see various papers in Anderson and Rosenfeld 1988). This linear region is the basis of the matrix models for associative memories.…”

Section: Matrix Memoriesmentioning

confidence: 99%

Neural memories and search engines

Mizraji

2008

International Journal of General Systems

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In this article we show the existence of a formal convergence between the matrix models of biological memories and the vector space models designed to extract information from large collections of documents. We first show that, formally, the term-by-document matrix (a mathematical representation of a set of codified documents) can be interpreted as an associative memory. In this framework, the dimensionality reduction of the term-bydocument matrices produced by the Latent Semantic Analysis (LSA) has a common factor with the matrix biological memories. This factor consists in the generation of a statistical 'conceptualization' of data using little dispersed weighted averages. Then, we present a class of matrix memory that built up thematic blocks using multiplicative contexts. The thematic memories define modular networks that can be acceded using contexts as passwords. This mathematical structure emphasizes the contacts between LSA and matrix memory models and invites to interpret LSA, and similar procedures, as a reverse engineering applied on context-deprived cognitive products, or on biological objects (e.g. genomes) selected during large evolutionary processes.

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“…Together, the synapse vector m and the value q(t) make up the newond state (req), an (N+l)-dimensional quantity. For simplicity, the components mi function as 'ideal synapses (Nass and Cooper, 1975) capable of changing sign. A treatment is given in the discussion (section 4.2.2) in which the signs of the synaptic weights does not change.…”

Section: The Traster Functimmentioning

confidence: 99%

A model for generalization and specification by single neurons

Munro

1984

Biol. Cybern.

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A theory for the development of feature detecting cells in visual cortex

Cited by 122 publications

References 23 publications

Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

Neural memories and search engines

A model for generalization and specification by single neurons

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