A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

/pdf/a-simple-white-noise-analysis-of-neuronal-light-responses-a56aehnicm.pdf

A simple white noise analysis of neuronal light responses.

Adaptive nonlinear filters equipped with polynomial models of nonlinearity are explained. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in adaptive filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. Adaptive algorithms using system models involving recursive nonlinear difference equations are then treated. Such systems may be able to approximate many nonlinear systems with great parsimony in the use of coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is described. >

Adaptive polynomial filters

https://www.cns.nyu.edu/csh/csh06/PDFs/Baccus2002.pdf

Fast and Slow Contrast Adaptation in Retinal Circuitry

The neural code of the retina.

A flash of light evokes neural activity in the brain with a delay of 30-100 milliseconds, much of which is due to the slow process of visual transduction in photoreceptors. A moving object can cover a considerable distance in this time, and should therefore be seen noticeably behind its actual location. As this conflicts with everyday experience, it has been suggested that the visual cortex uses the delayed visual data from the eye to extrapolate the trajectory of a moving object, so that it is perceived at its actual location. Here we report that such anticipation of moving stimuli begins in the retina. A moving bar elicits a moving wave of spiking activity in the population of retinal ganglion cells. Rather than lagging behind the visual image, the population activity travels near the leading edge of the moving bar. This response is observed over a wide range of speeds and apparently compensates for the visual response latency. We show how this anticipation follows from known mechanisms of retinal processing.

Anticipation of moving stimuli by the retina

Systems that can be represented by a cascade of a dynamic linear subsystem preceded (Hammerstein cascade model) or followed (Wiener cascade model) by a static nonlinearity are considered Various identification schemes that have been proposed for the Hammerstein and Wiener systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems Examples of Wiener and Hammerstein systems are identified from limited duration input-output data using an iterative identification scheme

W I Hunter

Papers

The identification of nonlinear biological systems: Wiener and Hammerstein cascade models