A theory of a saliency map in primary visual cortex (V1) tested by psychophysics of color-orientation interference in texture segmentation

It has been proposed that V1 creates a bottom-up saliency map, where saliency of any location increases with the firing rate of the most active V1 output cell responding to it, regardless the feature selectivity of the cell. Thus, a red vertical bar may have its saliency signalled by a cell tuned to red colour, or one tuned to vertical orientation, whichever cell is the most active. This theory predicts interference between colour and orientation features in texture segmentation tasks where bottom-up processes are significant. The theory not only explains existing data, but also provides a prediction. A subsequent psychophysical test confirmed the prediction by showing that segmentation of textures of oriented bars became more difficult as the colours of the bars were randomly drawn from more colour categories

Primary visual cortex as a saliency map: parameter-free prediction of behavior from V1 physiology

It has been hypothesized that neural activities in the primary visual cortex (V1) represent a saliency map of the visual field to exogenously guide attention. This hypothesis has so far provided only qualitative predictions and their confirmations. We report this hypothesis' first quantitative prediction, derived without free parameters, and its confirmation by human behavioral data. The hypothesis provides a direct link between V1 neural responses to a visual location and the saliency of that location to guide attention exogenously. In a visual input containing many bars, one of them saliently different from all the other bars which are identical to each other, saliency at the singleton's location can be measured by the shortness of the reaction time in a visual search task to find the singleton. The hypothesis predicts quantitatively the whole distribution of the reaction times to find a singleton unique in color, orientation, and motion direction from the reaction times to find other types of singletons. The predicted distribution matches the experimentally observed distribution in all six human observers. A requirement for this successful prediction is a data-motivated assumption that V1 lacks neurons tuned simultaneously to color, orientation, and motion direction of visual inputs. Since evidence suggests that extrastriate cortices do have such neurons, we discuss the possibility that the extrastriate cortices play no role in guiding exogenous attention so that they can be devoted to other functional roles like visual decoding or endogenous attention.Comment: 11 figures, 66 page

Mathematical analysis and simulations of the neural circuit for locomotion in lamprey

We analyze the dynamics of the neural circuit of the lamprey central pattern generator. This analysis provides insight into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behavior regimes (characterized by phase and amplitude relationships between oscillators) of forward or backward swimming, and turning, can be controlled using the neural connection strengths and external inputs

Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study the analytical property of the Melnikov function near the origin for near-Hamiltonian system having the origin as its elementary center or nilpotent center. Based on the method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Then, we consider the symmetric singular points and present the conditions for one of them to be elementary center or nilpotent center. Under the condition for the singular point to be a center, we obtain the normal form of the Hamiltonian systems near the center. Moreover, perturbing the symmetric cubic Hamiltonian systems by cubic polynomials, we consider limit cycles bifurcating from the center using the algorithm to compute the coefficients of Melnikov function. Finally, perturbing the symmetric hamiltonian system by symmetric cubic polynomials, we consider the number of limit cycles near one of the symmetric centers of the symmetric near-Hamiltonian system, which is same to that of another center