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Jack D Cowan

Publications and source records attributed to Jack D Cowan.

7 recordsLinked to original sources
PubMed2006

Simultaneous constraints on pre- and post-synaptic cells couple cortical feature maps in a 2D geometric model of orientation preference.

The most prominent feature of mammalian striate cortex (V1) is the spatial organization of response preferences for the position and orientation of elementary visual stimuli. Models for the formation of cortical maps of orientation and 'retinotopic' position typically rely on a combination of Hebbian or correlation-based synaptic plasticity, and constraints on the distribution of synaptic weights. We consider a simplified model of orientation and retinotopic specificity based on the geometry of the feed-forward synaptic weight distribution from an 'unoriented' layer of cells to a first weakly oriented layer. We model the feed-forward weight distribution as a system of planar Gaussian receptive fields each elongated in the direction matching the preferred orientation of the postsynaptic cell. Under the constraint of presynaptic weight normalization (each cell in the oriented layer receives the same net synaptic weight) and a uniform retinotopic map (displacement of centres of mass of receptive fields in the unoriented layer is strictly proportional to the displacement of the corresponding cells in the oriented layer), we find that imposing a pattern of orientation preference forces the system to violate postsynaptic weight normalization (each cell in the unoriented layer no longer sends forth the same net synaptic weight). We study this deviation from uniformity of the postsynaptic weight, and find that the deviation has a distinct form in the vicinity of the 'pinwheel' singularities of the orientation map. We show that uniform synaptic coverage of the unoriented layer can be restored by introducing a distortion in the retinotopic locations of the receptive fields. We calculate, to first order in the relative elongation of the receptive fields, the retinotopic distortion vector field. Both the pattern of postsynaptic weight non-uniformity and the corrective retinotopic distortion vector field fail to possess the reflection symmetry commonly assumed to relate orientation singularities with topological index +/- pi. Hence, we show that 'right-handed' and 'left-handed' orientation singularities are funda-mentally distinct anatomical structures when full 2D synaptic architecture is taken into account. Finally, we predict specific patterns of retinotopic distortion that should obtain in the vicinity of +/- pi-fold orientation singularities, if uniform pre- and post-synaptic weight constraints are strongly enforced.

Algorithms↗
PubMed2004

Symmetry induced coupling of cortical feature maps.

The mammalian visual cortex maps retinal position (retinotopy) and orientation preference (OP) across its surface. Simultaneous measurements in vivo suggest that positive correlation exists between the location of dislocations in these two maps, contradicting the predictions of classical dimension reduction models. Model symmetries exert a significant influence on pattern development. However, classical models for cortical map formation have inappropriate symmetry properties. By applying equivariant bifurcation theory we derive symmetry induced, model independent coupling of the OP and retinotopic maps and show that this coupling replicates observations.

Animals↗
PubMed2003

A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn.

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.

Brain Mapping↗
PubMed2002

What geometric visual hallucinations tell us about the visual cortex.

Many observers see geometric visual hallucinations after taking hallucinogens such as LSD, cannabis, mescaline or psilocybin; on viewing bright flickering lights; on waking up or falling asleep; in "near-death" experiences; and in many other syndromes. Klüver organized the images into four groups called form constants: (I) tunnels and funnels, (II) spirals, (III) lattices, including honeycombs and triangles, and (IV) cobwebs. In most cases, the images are seen in both eyes and move with them. We interpret this to mean that they are generated in the brain. Here, we summarize a theory of their origin in visual cortex (area V1), based on the assumption that the form of the retino-cortical map and the architecture of V1 determine their geometry. (A much longer and more detailed mathematical version has been published in Philosophical Transactions of the Royal Society B, 356 [2001].) We model V1 as the continuum limit of a lattice of interconnected hypercolumns, each comprising a number of interconnected iso-orientation columns. Based on anatomical evidence, we assume that the lateral connectivity between hypercolumns exhibits symmetries, rendering it invariant under the action of the Euclidean group E(2), composed of reflections and translations in the plane, and a (novel) shift-twist action. Using this symmetry, we show that the various patterns of activity that spontaneously emerge when V1's spatially uniform resting state becomes unstable correspond to the form constants when transformed to the visual field using the retino-cortical map. The results are sensitive to the detailed specification of the lateral connectivity and suggest that the cortical mechanisms that generate geometric visual hallucinations are closely related to those used to process edges, contours, surfaces, and textures.

Hallucinations↗
PubMed2002

An amplitude equation approach to contextual effects in visual cortex.

A mathematical theory of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the anisotropic nature of long-range lateral connections. Each hypercolumn is modeled as a ring of interacting excitatory and inhibitory neural populations with orientation preferences over the range 0 to 180 degrees. Analytical methods from bifurcation theory are used to derive nonlinear equations for the amplitude and phase of the population tuning curves in which the effective lateral interactions are linear in the amplitudes. These amplitude equations describe how mutual interactions between hypercolumns via lateral connections modify the response of each hypercolumn to modulated inputs from the lateral geniculate nucleus; such interactions form the basis of contextual effects. The coupled ring model is shown to reproduce a number of orientation-dependent and contrast-dependent features observed in center-surround experiments. A major prediction of the model is that the anisotropy in lateral connections results in a nonuniform modulatory effect of the surround that is correlated with the orientation of the center.

Animals↗
PubMedDate not supplied

The functional geometry of local and horizontal connections in a model of V1.

A mathematical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous activity patterns that can arise in cortex.

Animals↗