Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 46

Fig. 3.15 Simple junction
for the dendritic OR gate

But if both branches A and B have voltage pulse inputs, A and B work together, and
there is additional current (I) to charge the passive region to a greater voltage peak
(because of the basic formula

t/C). There can be enough voltage to trigger
the right most active region, assuming pulses from A and B impinge at the same time.
Define A, B, and Y to be Boolean variables which are false for no action
potentials and true if there are neural pulses. If A is true and B is false, Y is false,
as described above. Similarly, if B is true but A is false, Y is still false, because B
cannot by itself send enough charge through a passive segment to trigger segment Y.
But if both A and B are true, then Y is true, because by working together, sufficient
charge accumulates in the inhibited segment to continue the propagation of the
dendritic pulse. The result is an AND gate:

Δ V ¼ I Δ

Y ¼ AB : (3.4)

The length of the passive region has to fall within a certain range; if it is too
short, its capacitance will not stop pulses from a given branch; if too long, it will
stop even two combined pulses.
It is emphasized that in order for the above AND gate to work, the pulses must
arrive at about the same time.

Dendritic OR Gate

An OR gate assumes no inhibitors in either branch. In this case, the soma will be
activated for input to A or input to B, or if both inputs are active as in Fig. 3.15 .
This is an uncomplicated physical junction of dendritic branches. In this case, the
Boolean logic is

Y ¼ A þ B : (3.5)

The OR gate is not dependent upon pulse coordination since pulses arriving at
differing times are naturally passed through.

Exclusive OR and NOT Gates

Dendritic XOR Gate

Under certain fairly easy-to-achieve conditions, the OR will behave like an exclu-
sive OR, denoted as XOR, meaning that any one signal will be transmitted, but that
two applied together will not be transmitted. This has been shown by simulations [ 4 ].