We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck process X(t) obeying dX = -β Xdt + σdW to reach a fixed threshold θ from a suprathreshold initial condition x0 > θ > 0 has a lower bound of the form ρ(t) > kexp[-pe6βt] for positive constants k and p for times t exceeding some positive value u. We obtain explicit expressions for k, p, and u in terms of β, σ, x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.

Psychophysical research has documented the existence of three processes in light adaptation: a fast subtractive process, a divisive process that is fast at light onset and slower at light offset, and a very slow subtractive process (Hayhoe et al., 1987). In the neural model developed here, the fast subtractive process is identified with horizontal cell feedback onto cones and the divisive process with amacrine cell feedback onto bipolar cells. The very slow subtractive process is identified with the modulatory feedback circuit from amacrines via interplexiform cells to horizontal cells. A nonlinear dynamical model is developed incorporating these aspects of retinal circuitry along with both ON- and OFF-center M and P pathways. This model is shown to account for many aspects of foveal light adaptation, including negative afterimage formation, and to explain a number of the physiological differences between M and P ganglion cells, including their differing contrast-response functions.

A recent model for two-dimensional motion processing in MT has demonstrated that perceived direction can be accurately predicted by combining Fourier and non-Fourier component motion signals using a vector sum computation. The vector sum direction is computed by a neural network that weights Fourier and non-Fourier components by the cosine of the component direction relative to that of each pattern unit, after which competitive inhibition extracts the signals of the most active units. It is shown here that a minor modification of the connectivity in this network suffices to predict transitions from motion coherence to transparency under a wide range of circumstances. It is only necessary that the cosine weighting function and competitive inhibition be limited to directions within ± 120 deg of each pattern unit's preferred direction. This network responds by signaling one pattern direction for coherent motion but two distinct directions for transparent motion. Based on this, neural networks with properties of MT and MST neurons can automatically signal motion coherence or transparency. In addition, the model accurately predicts motion repulsion under transparency conditions.

This paper presents results from psychophysical experiments on human binocular rivalry in central and peripheral vision. Results show that the incidence of periods of exclusive visibility of a given eye's rival target increased with decreasing target size, and for a given sized target exclusive visibility increased with retinal eccentricity. Control measures confirmed that these results were not attributable solely to reduced peripheral acuity, to Troxler's effect, or to spatial frequency. We computed the minimum-sized stimulus that would lead to a criterion level of exclusive visibility of one or the other eye; this we term the spatial zone of binocular rivalry. The change in estimated size of spatial zones of rivalry with eccentricity compares favorably with estimates of human cortical magnification. We propose a model that assumes concentrically organized zones of rivalry. These zones do not function independently, but instead exhibit a high degree of mutual excitatory cooperativity. The model has multiple solutions for the foveal zone size, but the best fits predict a diameter of 5.3 or 7.3 min of visual angle; these values dovetail nicely with our empirical estimates of the foveal zone size.