Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 80

axon; and are arranged in functional constellation or assemblies according to the
synaptic contacts they make with one another. The dendrites, highly branched con-
struction, are receptive surfaces for input signals and conduct them to neuron cell.
Aggregation of these signals takes place in cell body (soma) in unique fashion whose
characteristic derive the computing capability of the neuron. Axon, that begins with
axon hillock, which generates the cell action potential and converts it into a train
of impulses through itself for transmission. In order to convey the action potential,
the dendrites of one neuron are connected with the axon of the other neurons via
synaptic connections or synapses. The synaptic transmission involves complicated
electrical and chemical processes in the system.
The spatial integration (aggregation) of the synapses on the dendritic tree is
reflected in the computations performed at local branches [ 1 - 3 ]. The linear inter-
action (summation) of synaptic inputs is popularly believed for long time to model
the computation abilities of neurons. Linearity is believed to be sufficient in captur-
ing the passive properties of dendritic membrane where synaptic inputs are currents.
However, many researches divulge the nonlinear interaction of synaptic inputs in
cell body for information processing. The multiplication of inputs is also found to
exist in real nervous systems by animals and in other biological evidences. The
synaptic inputs can interact nonlinearly when synapses are co-localized on patches
of dendritic membrane with specific properties. A Multiplication, the most basic of
all nonlinearity in neurons, often occurs in dendritic trees with voltage-dependent
membrane conductance [ 2 ]. But it is not very clear that how real neurons do the mul-
tiplication, where as it is clear that multiplication of the inputs of neuron can increase
the computational power and storage capacities of neural networks. Therefore, an
artificial neuron model should then be capable of including this inherent nonlinearity
in the mode of aggregation.
4.2 Artificial Neuron
An artificial neuron is a mathematical representation of the biological neuron which
tries to approximate its functional capabilities. A neuron model is characterized by its
formalism and its precise mathematical definition. Historically, McCulloch and Pitts
model [ 4 ] is supposed to be first formal mathematical model of an artificial neuron
based on the highly simplified consideration of biological neuron. This conventional
neuron possesses the weighted summation (as aggregation) of impinging signals and
neglects all possible nonlinear capabilities of the single neuron.
An important issue in artificial neuron model is the description of single neu-
ron computation and interaction among the input signals. A neuron model can be
described as a combination of aggregation and activation functions. The net potential
of a neuron is characterized by an aggregation function, which models the integra-
tion of impinging information. The activation function limits the amplitude of the
neuron output to some finite range. In order to qualitatively describe the functional