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Fig. 3.18 Enabled AND
Enabled AND
Figure 3.18 illustrates the AND using assumed values for the purposes of
convenience (From the neural pulse given earlier, a realistic threshold is roughly
15 mV above the rest voltage 70 mV).
This is a three-input AND gate with “e” used as an optional enable that contributes
25 mV. The soma is triggered only if inputs “a” and “b” provide sufficient charge to
reach the threshold assumed to be at 70 mV in this illustration. The count of
pulses must be able to build up about 25 mV from a and about 25 mV from “b”.
Then z
¼
e(ab). Enabled logic does not depend as much on pulse coordination.
Enabled OR
The OR results in the above figure by requiring a contribution of at least 50 mV for
each input (a, b). Then z
¼
e(a + b)
Enabled NOT Gate
Without the availability of negative voltage as commonly used in artificial neurons,
one wonders if a NOT gate is indeed possible biologically. To investigate NOT
gates, consider the more complicated situation of enabled logic depicted in
Fig. 3.19 . A precharge in the soma could be 50 mV positive, for example, and it
might be defined to trigger at 70 mV. Thus another 50 mV from incoming pulses
would enable dendritic logic.
The code in this diagram is as in Table 3.1 .
Assume branch “b” is receiving dendritic solitons prior to the NOT operation
and that precharging to 50 mV has been completed via branch “e.” Assume branch
“a” in the left-most figure has impinging pulses. The propagation of solitons to the
soma is stopped at branch y, because, linked to neural input “a” are inhibitory
neurotransmitters for branch “y.” This linking is denoted by the primes in the
above figure, that is, “(+)' and (
)'.” The action potential applied as in input to
branch “b” is also stopped for similar reasons. Effectively there is an AND gate at y.
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