4.5. This problem illustrates a theoretical model for detection of weak sensory signals received by noisy receptors. The system is illustrated in Figure P4.5. The sensory input stimulus causes a transient, analog depolarization, s(t), that is added to bandwidth-limited Gaussian noises, n1 and n2. n1 is statistically independent of n2; that is, uncorrelated noise sources are used to make n1(t) and n2(t). The rectified voltages, rVin1(t) = [n1(t) + s(t)]+ and rVin2(t) = [n2(t) + s(t)]+ are inputs to the two, IPFM spike generator models for the sensory neurons. The sensory neuron output spikes, y1 and y2, are passed through "a-function," two-equal-pole, low-pass filters to form epsp inputs to a T-neuron that acts as a coincidence detector. In Simnon notation, the noises are made by:

dn1 = -b*n1 + b*u1 " n1 is BW limited Gaussian noise.

du2 = -a*u2 + a*SD*NORM(t + To) " n1 and n2 are uncorrelated for large To. dn2 = -b*n2 + b*u2

One of the IPFM SGLs is:

y1 = IF x1 > 0 THEN x1 ELSE 0 " Unit output spikes.

The epsp1 is formed:

The RPFM T-neuron is simulated:

z3 = y3*phi3/tau " z3 is RPFM reset pulse.

w3 = IF v3 > phi 3 THEN 1 ELSE 0 s3 = DELAY (w3, tau) x3 = w3 - s3

y3 = IF x3 > 0 THEN x3 ELSE 0 " T-neuron output pulses

The input, s(t) is to be a 5 ms pulse of height So mV starting at t1 = 20 ms. Write the complete Simnon program for the coincidence detector. Use the following parameters: a = b = 4, c = 3, d = 2, phi = 0.5, phi3 = 0.55, tau = 0.001, SD = 2, So = 0.25, Do = 3, To = 100, t1 = 20, t2 = 25. Run the program using Euler integration with delT = 0.001. See how small one can make So and still see a y3 pulse (or pulses) correlated with s(t). Simulate over at least 100 ms. Note that this is a statistical detector; on some runs false positive y3 pulses, or false negatives (no y3 output for the input pulse) may be observed. Try adjusting the system parameters, phi, phi3, Do, and d to improve detection performance.

4.6. This problem involves modeling a simplified insect "ear"; that is, an air-backed, tympanal membrane, the center of which is connected to a stretchsensitive mechanoreceptor neuron. Assume that the membrane vibrates in response to sound pressure impinging on it. Upward (outward) deflec tion of the membrane causes stretch of the mechanoreceptor neuron neu-rite, and a consequent transient depolarization (positive generator potential). The neuron does not respond to downward (inward) deflection of the tympanum. The system is shown schematically in Figure P4.6. Because the membrane has mass, elasticity, and damping, it behaves like a linear second-order, low-pass system. That is,

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