3 resultados para Linear behavior

em Boston University Digital Common


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A computational model of visual processing in the vertebrate retina provides a unified explanation of a range of data previously treated by disparate models. Three results are reported here: the model proposes a functional explanation for the primary feed-forward retinal circuit found in vertebrate retinae, it shows how this retinal circuit combines nonlinear adaptation with the desirable properties of linear processing, and it accounts for the origin of parallel transient (nonlinear) and sustained (linear) visual processing streams as simple variants of the same retinal circuit. The retina, owing to its accessibility and to its fundamental role in the initial transduction of light into neural signals, is among the most extensively studied neural structures in the nervous system. Since the pioneering anatomical work by Ramón y Cajal at the turn of the last century[1], technological advances have abetted detailed descriptions of the physiological, pharmacological, and functional properties of many types of retinal cells. However, the relationship between structure and function in the retina is still poorly understood. This article outlines a computational model developed to address fundamental constraints of biological visual systems. Neurons that process nonnegative input signals-such as retinal illuminance-are subject to an inescapable tradeoff between accurate processing in the spatial and temporal domains. Accurate processing in both domains can be achieved with a model that combines nonlinear mechanisms for temporal and spatial adaptation within three layers of feed-forward processing. The resulting architecture is structurally similar to the feed-forward retinal circuit connecting photoreceptors to retinal ganglion cells through bipolar cells. This similarity suggests that the three-layer structure observed in all vertebrate retinae[2] is a required minimal anatomy for accurate spatiotemporal visual processing. This hypothesis is supported through computer simulations showing that the model's output layer accounts for many properties of retinal ganglion cells[3],[4],[5],[6]. Moreover, the model shows how the retina can extend its dynamic range through nonlinear adaptation while exhibiting seemingly linear behavior in response to a variety of spatiotemporal input stimuli. This property is the basis for the prediction that the same retinal circuit can account for both sustained (X) and transient (Y) cat ganglion cells[7] by simple morphological changes. The ability to generate distinct functional behaviors by simple changes in cell morphology suggests that different functional pathways originating in the retina may have evolved from a unified anatomy designed to cope with the constraints of low-level biological vision.

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This article describes a nonlinear model of neural processing in the vertebrate retina, comprising model photoreceptors, model push-pull bipolar cells, and model ganglion cells. Previous analyses and simulations have shown that with a choice of parameters that mimics beta cells, the model exhibits X-like linear spatial summation (null response to contrast-reversed gratings) in spite of photoreceptor nonlinearities; on the other hand, a choice of parameters that mimics alpha cells leads to Y-like frequency doubling. This article extends the previous work by showing that the model can replicate qualitatively many of the original findings on X and Y cells with a fixed choice of parameters. The results generally support the hypothesis that X and Y cells can be seen as functional variants of a single neural circuit. The model also suggests that both depolarizing and hyperpolarizing bipolar cells converge onto both ON and OFF ganglion cell types. The push-pull connectivity enables ganglion cells to remain sensitive to deviations about the mean output level of nonlinear photoreceptors. These and other properties of the push-pull model are discussed in the general context of retinal processing of spatiotemporal luminance patterns.

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We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.