Paper Info
Title
Equation of motion and general solution for the one-dimensional complex cell response in the signal-tuned approach.
Abstract
A signal-tuned approach has been recently introduced for modeling stimulus-dependent cortical receptive fields. The approach is based on signal-tuned Gabor functions, which are Gaussian-modulated sinusoids whose parameters are obtained from a \"tuning\" signal. Given a stimulus to a cell, it is taken as the tuning signal for the Gabor function modeling the cell's receptive field, and the inner product of the stimulus and the stimulus-dependent field produces the cell's response. Here, we derive and solve the equation of motion for the signal-tuned complex cell response $$r(x,\\tau )$$r(x,¿), where x and $$\\tau $$¿ are receptive-field parameters: its center, and the delay with which it adapts to a change in input. The motion equation can be mapped onto the Schrödinger equation for a system with time-dependent imaginary mass and time-dependent complex potential, and yields a plane-wave solution and an Airy-packet solution. The plane-wave solution replicates responses previously obtained for temporally modulated and translating signals, and yields responses which seem compatible with apparent-motion effects, when the stimulus is a pair of alternating pulses. The Airy-packet solution can lead to long-range propagating responses.
Year
DOI
Venue
2015
10.1007/s00422-015-0653-7
Biological Cybernetics
Keywords
Field
DocType
Apparent motion,Complex cells,Schrödinger equation,Signal-tuned Gabor approach,Visual cortex
Receptive field,Complex cell,Visual cortex,Mathematical analysis,Control theory,Schrödinger equation,Equations of motion,Stimulus (physiology),Mathematics
Journal
Volume
Issue
ISSN
109
4-5
0340-1200
Citations 
PageRank 
References 
0
0.34
1
Authors
1
Name
Order
Citations
PageRank
José R. A. Torreão15910.18