Form and Function: Linear and Nonlinear Analyses of Neural Networks in the Visual System

Form and function are closely related in the visual system. For example, if a retinal network responds acutely to certain fine detail in the spatial pattern of a visual stimulus, then there must be some comparable fine detail within the structure of the network. Otherwise, the pattern could not be resolved. Also, if a network responds selectively to some articular orientation of a stimulus, then there n1ust be some comparable orientation of the form of the network. Otherwise, the direction could not be sensed. Similarly, if a network responds faithfully to some regular temporal modulation of the stimulus, then there must be some omparable modulus in the temporal characteristics of the network. Otherwise, the variations in time could not be followed. In a very real sense, “like is known only by like.”

[1]  F. Ratliff.  The Logic of the Retina , 1973 .

[2]  E. Mach,et al.  Popular scientific lectures , 1897 .

[3]  K. H. Ruddock.  From theoretical physics to biology , 1974 .

[4]  D. Jameson,et al.  Mach bands : quantitative studies on neural networks in the retina , 1966 .

[5]  R. Shapley,et al.  Nonlinear analysis of cat retinal ganglion cells in the frequency domain. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[6]  L. Sirovich,et al.  Equivalence classes of visual stimuli , 1978, Vision Research.

[7]  F. Dodge,et al.  Voltage Noise in Limulus Visual Cells , 1968, Science.

[8]  F. Ratliff.  A Discourse on Edges , 1978 .

[9]  W. Elsasser.  The chief abstractions of biology , 1975 .

[10]  H K Hartline,et al.  Enhancement of Flicker by Lateral Inhibition , 1967, Science.

[11]  H. K. Hartline,et al.  INHIBITORY INTERACTION OF RECEPTOR UNITS IN THE EYE OF LIMULUS , 1957, The Journal of general physiology.

[12]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[13]  G. D. Lange,et al.  A Nonlinearity in the Inhibitory Interactions in the Lateral Eye of Limulus , 1974, The Journal of general physiology.

[14]  R. Shapley,et al.  Receptive field mechanisms of cat X and Y retinal ganglion cells , 1979, The Journal of general physiology.

[15]  C. H. Graham.  The relation of nerve response and retinal potential to number of sense cells illuminated in an eye lacking lateral connections , 1932 .

[16]  B W Knight,et al.  On tuning and amplification by lateral inhibition. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[17]  E. Adrian,et al.  The action of light on the eye , 1928, The Journal of physiology.

[18]  D. Fender,et al.  Nonlinearities of the human oculomotor system: gain. , 1969, Vision research.

[19]  F. Ratliff.  Contour and contrast. , 1972, Scientific American.

[20]  P. Heggelund,et al.  Edge-dependent lightness distributions at different adaptation levels , 1976, Vision Research.

[21]  W. Heisenberg,et al.  Nonlinear problems in physics , 1967 .

[22]  D. H. Kelly.  Adaptation effects on spatio-temporal sine-wave thresholds. , 1972, Vision research.

[23]  R. Shapley,et al.  Linear and nonlinear spatial subunits in Y cat retinal ganglion cells. , 1976, The Journal of physiology.

[24]  R. Shapley,et al.  Quantitative analysis of retinal ganglion cell classifications. , 1976, The Journal of physiology.

[25]  N Milkman,et al.  Superposition of excitatory and inhibitory influences in the retina of Limulus: effect of delayed inhibition. , 1970, Proceedings of the National Academy of Sciences of the United States of America.

[26]  C. H. Graham,et al.  Nerve impulses from single receptors in the eye , 1932 .

[27]  H. K. Hartline,et al.  Spatial and temporal aspects of retinal inhibitory interaction. , 1963, Journal of the Optical Society of America.

[28]  R. Shapley,et al.  The nonlinear pathway of Y ganglion cells in the cat retina , 1979, The Journal of general physiology.

[29]  B. Julesz.  Foundations of Cyclopean Perception , 1971 .

[30]  Henk Spekreijse,et al.  Linearizing: A method for analysing and synthesizing nonlinear systems , 1970, Kybernetik.

[31]  H K Hartline,et al.  Fourier analysis of dynamics of excitation and inhibition in the eye of Limulus: amplitude, phase and distance. , 1974, Vision research.

[32]  J. Victor.  Nonlinear systems analysis: comparison of white noise and sum of sinusoids in a biological system. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[33]  H. K. Hartline,et al.  Inhibitory Interaction in the Retina of Limulus , 1972 .

[34]  J. Cowan,et al.  Some mathematical questions in biology , 1974 .

[35]  H. Barlow,et al.  The mechanism of directionally selective units in rabbit's retina. , 1965, The Journal of physiology.

[36]  G. Fry.  Mechanisms subserving simultaneous brightness contrast. , 1948, American journal of optometry and archives of American Academy of Optometry.

[37]  R. Barlow,et al.  Mach bands in the lateral eye of Limulus , 1975, The Journal of general physiology.

[38]  R. M. Shapley,et al.  Edge detectors in human vision , 1973, The Journal of physiology.

[39]  R. Purple,et al.  Interaction of excitation and inhibition in the eccentric cell in the eye of Limulus. , 1965, Cold Spring Harbor symposia on quantitative biology.

[40]  D. Hood,et al.  Brightness of ramp stimuli as a function of plateau and gradient widths. , 1968, Journal of the Optical Society of America.

[41]  Floyd Ratliff,et al.  Studies on Excitation and Inhibition in the Retina , 1975 .

[42]  G. Békésy,et al.  Experiments in Hearing , 1963 .

[43]  Vivian O'Brien,et al.  Contour Perception, Illusion and Reality* , 1958 .

[44]  R. L. de Valois,et al.  Psychophysical studies of monkey vision. 3. Spatial luminance contrast sensitivity tests of macaque and human observers. , 1974, Vision research.

[45]  M. Corballis,et al.  The Psychology of Left and Right , 2020 .

[46]  J. C. R. Licklider,et al.  Place Mechanisms of Auditory Frequency Analysis , 1951 .

[47]  Campbell Fw,et al.  The appearance of gratings with and without the fundamental Fourier component. , 1971 .

[48]  S. W. Kuffler.  Discharge patterns and functional organization of mammalian retina. , 1953, Journal of neurophysiology.

[49]  Robert Shapley,et al.  An electronic visual stimulator , 1976 .

[50]  D. Tolhurst.  On the possible existence of edge detector neurones in the human visual system , 1972 .

[51]  H. F. Crovitz,et al.  A two-stage model of brightness. , 1972, Vision research.

[52]  F. Ratliff,et al.  The spatiotemporal transfer function of the Limulus lateral eye , 1978, The Journal of general physiology.

[53]  R. Barlow.  Inhibitory Fields in the Limulus Lateral Eye , 1969, The Journal of general physiology.

[54]  H. Barlow.  Summation and inhibition in the frog's retina , 1953, The Journal of physiology.

[55]  Patrick Colas-Baudelaire.  Digital Picture Processing and Psychophysics: A Study of Brightness Perception, , 1973 .

[56]  Kennehi J. W. Craik,et al.  THE NATURE OF PSYCHOLOGY: A SELECTION OF PAPERS, ESSAYS AND OTHER WRITINGS , 1966 .

[57]  P. Suppes,et al.  Contemporary Developments in Mathematical Psychology , 1976 .

[58]  Effect of boundaries on the response of a neural network. , 1979, Biophysical journal.

[59]  H. K. Hartline,et al.  SPATIAL SUMMATION OF INHIBITORY INFLUENCES IN THE EYE OF LIMULUS, AND THE MUTUAL INTERACTION OF RECEPTOR UNITS , 1958, The Journal of general physiology.

[60]  F. Ratliff,et al.  The response of the Limulus retina to moving stimuli: a prediction by Fourier synthesis , 1978, The Journal of general physiology.

[61]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[62]  M. Sanders.  Handbook of Sensory Physiology , 1975 .

[63]  G L WALLS,et al.  The filling-in process. , 1954, American journal of optometry and archives of American Academy of Optometry.

[64]  A. S. Patel.  Spatial resolution by the human visual system. The effect of mean retinal illuminance. , 1966, Journal of the Optical Society of America.

[65]  Werner Reichardt,et al.  Processing of optical data by organisms and by machines , 1969 .

[66]  B. Knight,et al.  Nonlinear analysis with an arbitrary stimulus ensemble , 1979 .

[67]  R. Shapley,et al.  Linear systems analysis of the Limulus retina. , 1970, Behavioral science.

[68]  R. W. Rodieck,et al.  Response of cat retinal ganglion cells to moving visual patterns. , 1965, Journal of neurophysiology.

[69]  Bruce W. Knight,et al.  A Quantitative Description of the Dynamics of Excitation and Inhibition in the Eye of Limulus , 1970, The Journal of general physiology.