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FIGURE 8.3-5 Block diagram illustrating the basic features of applying the white noise method to the retina. The input noise (visual object) can have both spatial and temporal properties that vary randomly.

Marmarelis and Marmarelis (1978) considered the canonical structure of a second-order, nonlinear dynamical system having two independent white noise inputs, and one output. A block diagram showing the system architecture is shown in Figure 8.3-10A. The Wiener system approximating the NSUS is shown in Figure 8.3-10B. The MSE between the actual system output, y(t), and the Wiener system output, y(t), theoretically decreases as high-order kernels (k S 3) are added to the system. However, the computational complexity and inability to understand and interpret kernels of order 3 and higher has limited their use in any practical application. The two-input, one-output approach was used by Marmarelis and Naka (1973b) to explore interactions between spot (center) and annulus (surround) stimulation of the RF of a catfish GC. Their results will not be described here; the interested reader should examine the original papers.

FIGURE 8.3-6 First-order kernel computed for a system consisting of noise-modulated light on the entire RF (input); the output was the transmembrane potential of an HC in the catfish retina that had that RF. Two different, mean input intensities were used. (From Marmarelis, P.Z. and K.I. Naka, J. Neurophysiol., 36(4): 619, 1973. American Physiological Society. With permission from The American Physiological Society.)

FIGURE 8.3-6 First-order kernel computed for a system consisting of noise-modulated light on the entire RF (input); the output was the transmembrane potential of an HC in the catfish retina that had that RF. Two different, mean input intensities were used. (From Marmarelis, P.Z. and K.I. Naka, J. Neurophysiol., 36(4): 619, 1973. American Physiological Society. With permission from The American Physiological Society.)

0 .032 .064 .096 .128 .16 0 .032 .064 .096 .128 .16

0 .032 .064 .096 .128 .16 0 .032 .064 .096 .128 .16

FIGURE 8.3-7 Two second-order kernel contour plots for the system described in Figure 8.3-6. (From Marmarelis, P.Z. and K.I. Naka, J. Neurophysiol., 36(4): 619, 1973. With permission.)

Time t, sec

FIGURE 8.3-8 (A) Linear [hj(T)] kernels for the system: Spot of noise-modulated light on the center of the RF (input); the output was the transmembrane potential of a horizontal cell in the catfish retina that had that RF. (B) Linear [hj(i)] kernels for the system: Annulus of noise-modulated light around the periphery of the RF (input); the output was the transmembrane potential of a horizontal cell in the catfish retina that had that RF. In both A and B, mean intensities are about I/2 for curve C, -0.8 log units in B, and -1.6 log units in A. Note that as the average light intensity increases, the h1 response becomes underdamped and develops an undershoot. (From Marmarelis, P.Z. and K.I. Naka, J. Neurophysiol., 36(4): 619, 1973. With permission.)

Time t, sec

FIGURE 8.3-8 (A) Linear [hj(T)] kernels for the system: Spot of noise-modulated light on the center of the RF (input); the output was the transmembrane potential of a horizontal cell in the catfish retina that had that RF. (B) Linear [hj(i)] kernels for the system: Annulus of noise-modulated light around the periphery of the RF (input); the output was the transmembrane potential of a horizontal cell in the catfish retina that had that RF. In both A and B, mean intensities are about I/2 for curve C, -0.8 log units in B, and -1.6 log units in A. Note that as the average light intensity increases, the h1 response becomes underdamped and develops an undershoot. (From Marmarelis, P.Z. and K.I. Naka, J. Neurophysiol., 36(4): 619, 1973. With permission.)

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