Page 952 - The Mechatronics Handbook

0066_Frame_C32.fm Page 2 Wednesday, January 9, 2002 7:54 PM

32.2 Neuron Cell

A biological neuron is a complicated structure, which receives trains of pulses on hundreds of excitatory
and inhibitory inputs. Those incoming pulses are summed with different weights (averaged) during the
time period of latent summation. If the summed value is higher than a threshold, then the neuron itself
is generating a pulse, which is sent to neighboring neurons. Because incoming pulses are summed with
time, the neuron generates a pulse train with a higher frequency for higher positive excitation. In other
words, if the value of the summed weighted inputs is higher, the neuron generates pulses more frequently.
At the same time, each neuron is characterized by the nonexcitability for a certain time after the firing
pulse. This so-called refractory period can be more accurately described as a phenomenon where after
excitation the threshold value increases to a very high value and then decreases gradually with a certain
time constant. The refractory period sets soft upper limits on the frequency of the output pulse train.
In the biological neuron, information is sent in the form of frequency modulated pulse trains.
This description of neuron action leads to a very complex neuron model, which is not practical.
McCulloch and Pitts (1943) show that even with a very simple neuron model, it is possible to build logic
and memory circuits. Furthermore, these simple neurons with thresholds are usually more powerful than
typical logic gates used in computers. The McCulloch–Pitts neuron model assumes that incoming and
outgoing signals may have only binary values 0 and 1. If incoming signals summed through positive or
negative weights have a value larger than threshold, then the neuron output is set to 1. Otherwise, it is
set to 0.

 1, if net ≥ T
T =  (32.1)
 0, if net < T

where T is the threshold and net value is the weighted sum of all incoming signals:

n
net = ∑ w i x i (32.2)
i=1

Examples of McCulloch–Pitts neurons realizing OR, AND, NOT, and MEMORY operations are shown
in Fig. 32.1. Note that the structure of OR and AND gates can be identical. With the same structure,
other logic functions can be realized, as Fig. 32.2 shows.
The perceptron model has a similar structure. Its input signals, the weights, and the thresholds could
have any positive or negative values. Usually, instead of using variable threshold, one additional constant
input with a negative or positive weight can added to each neuron, as Fig. 32.3 shows. In this case, the

MEMORY
A +1 OR A +1 AND NOT +1
+1 A + B + C +1 ABC −1 NOT A +1
B T = 0.5 B T = 2.5 A T = − 0.5 WRITE 1 T = 0.5
+1 +1 −2
(a) C (b) C (c) (d) WRITE 0
FIGURE 32.1 OR, AND, NOT, and MEMORY operations using networks with McCulloch–Pitts neuron model.

A +1 A +1
+1 AB + BC + CA +1 AB + C
B T = 1.5 B T = 1.5
+1 +2
(a) C (b) C
FIGURE 32.2 Other logic function realized with McCulloch–Pitts neuron model.

©2002 CRC Press LLC