Modeling and estimation problems in the visuomotor pathway

In this chapter we describe how a population of neurons model the dynamic activity of a suitable region of the visual cortex, responding to a class of visual inputs. Specifically, a large scale neuronal model has been described which generates a propagating wave of activity that has been independently recorded in experiments using multiple electrodes and voltage sensitive dyes. We show how the model cortex is able to discriminate location of target in the visual space. The discrimination is carried out using two separate algorithms. The first method utilizes statistical detection wherein the activity waves generated by the visual cortex are encoded using principal components analysis. The representation is carried out, first in the spatial domain and subsequently in the temporal domain over a sequence of sliding windows. Using the model cortex, we show that the representation of the activity waves, viewed as a ‘beta strand’, is sufficiently different from each other for alternative locations of point targets in the visual space. Discrimination is carried out assuming that the noise is additive and Gaussian. In the second method, the beta strands are discriminated using a nonlinear dynamical system with multiple regions of attraction. Each beta strand corresponds to a suitable initialization of the dynamical system and the states of attraction correspond to various target locations. The chapter concludes with a discussion of the motor control problem and how the cortical waves play a leading role in actuating movements that would track a moving target with some level of evasive maneuvers. Index Terms Cortex Model, Statistical Detection, Hypothesis Testing, Nonlinear Dynamics, Kuramoto Model. B. K. Ghosh and W. Wang are in the Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA. Z. V. Freudenburg is in the Department of Computer Science and Engineering, Washington University in St. Louis, MO, USA. This work is partially supported by NSF grant EIA-0218186 and NSF grant ECS-0323693. January 26, 2007 DRAFT BOOK CHAPTER, VOL. XX, NO. XX, DEC. 2006 1