Info

Clearly, the use of feedback to raise the firing threshold following output pulses reduces the rate of FP pulses. If one uses the simple cost formula introduced in Section 2.1.4 above, feedback control of <p2 does indeed reduce C over the nonfeedback case. Calculations follow for the feedback case:

F 53 53

And without feedback,

N 54 54

Clearly, the use of feedback to raise <p2 gives a reduced cost, as simply defined. A topic for further study is to explore the effect of other system natural frequencies and gains on the degree of cost reduction.

FIGURE 2.1-5 Results of a Simnon simulation with the program, ADTHRESH.T. Ideally, y2 should fire every time y1 occurs. In the plot, the horizontal axis is time in milliseconds, the vertical axis is in arbitrary voltage units. Traces: (1) y1 (input) pulses; (2) y2 (output) pulses; (3) V2 (input to RPFM SG); (4) the variable threshold, See text for more details and tabulated results for the system with fixed q>2 vs. the variable q>2.

FIGURE 2.1-5 Results of a Simnon simulation with the program, ADTHRESH.T. Ideally, y2 should fire every time y1 occurs. In the plot, the horizontal axis is time in milliseconds, the vertical axis is in arbitrary voltage units. Traces: (1) y1 (input) pulses; (2) y2 (output) pulses; (3) V2 (input to RPFM SG); (4) the variable threshold, See text for more details and tabulated results for the system with fixed q>2 vs. the variable q>2.

The nonlinear and nonstationary nature of the speculative sensory neuron model above defies analysis; one must necessarily use simulation to study its signal-processing properties. Obviously, there are many system parameters that can be manipulated in seeking low operating cost. The results given above were obtained with just one combination of parameters that appeared to be "reasonable" to the author.

2.1.6 Discussion

This section examined some of the general properties of single sensory receptor neurons, including their dynamic response (to a step input of stimulus), their linearity (they are generally nonlinear, perhaps due to the transduction process and the spike generation dynamics), and factors affecting their sensitivity. A heuristic, dynamic, neural model for automatic adjustment of the firing threshold of a spiking sensory receptor having noise on its generator potential was shown to minimize detection cost.

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