Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex

Abstract

Complex cells in the cat's visual cortex show nonlinearities in processing of image luminance and movement. To study mechanisms, initially we have represented the chain of neurons from retina to cortex as a black-box model. Independent information about the visual system has helped us cast this "Wiener-kernel" model into a dynamic-linear/static-nonlinear/dynamic-linear (LNL) cascade. We then use system identification techniques to define the nature of these transformations directly from responses of the neuron to a single presentation of a stimulus composed of a sequence of white-noise-modulated luminance values. The two dynamic linear filters are mainly low-pass, and the static nonlinearity is mainly of even polynomial degree. This approximate squaring function may be effected in the animal by soft-thresholding each of the linear ON- and OFF-channel signals and then summing them, which account for "ON-OFF" responses and for the squaring operation needed for computation of "motion energy", both observed in these neurons.

Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network

“…Correspondence to: J. Wray, The Neurosciences Institute, 3377 North Torrey Pines Court, La Jolla, CA 92037, USA (Marmarelis and Naka 1972), in the determination of the non-linear properties of cells in the visual cortex (Emerson et al 1992) and in the investigation of the dynamics of cockroach ocellar neurones (Mizunami et al 1986). The Volterra series can be shown to be a general solution of non-linear differential equations using differential algebraic approaches (Fliess et al 1983).…”

Adaptive Regulator for Hammerstein and Wiener Systems With Noisy Observations

“…By stability of C(z), there is 2 > 0 such that kYjk 2j =(1+) ; and hence jyjj 2j =(1+) 8j > 2: Finally, the second limit in (24) follows from the fact that 1 i=1 a i " i < 1 a.s. [9]. …”

“…. ; 0] p (8) and for the Wiener system V k+1 = CV k + Du k+1 v k = HV k y k = f(v k ): (9) It is clear that By A1), C is a stable matrix, and hence there are r > 0, > 0 such that kC k k re 0k 8k 0: …”

Pathwise Convergence of Recursive Identification Algorithms for Hammerstein Systems

“…The estimate defined by (8)(9) is used to estimate , while defined by (10)(11) is for estimating It is worth pointing out that we cannot expect a fast rate of convergence from all algorithms (6)-(7), (8)- (9), and (10)-(11), since the asymptotic rate of stochastic approximation algorithms is not faster than .…”

“…and are related by the linear system as follows: (2) Because of its importance in engineering applications (see, e.g., [9], [10], and [21] among others), the Hammerstein system, in particular, its identification issue has been an active research topic for many years. When identifying the system presented in Fig.…”