Neural Networks - Algorithms, Applications,and ... - Csbdu.in

12 Introduction to ANS TechnologyThe neurotransmitters diffuse across the junction and join to the postsynapticmembrane at certain receptor sites. The chemical action at the receptor sitesresults in changes in the permeability of the postsynaptic membrane to certainionic species. An influx of positive species into the cell will tend to depolarizethe resting potential; this effect is excitatory. If negative ions enter, ahyperpolarization effect occurs; this effect is inhibitory. Both effects are localeffects that spread a short distance into the cell body and are summed at theaxon hillock. If the sum is greater than a certain threshold, an action potentialis generated.1.1.3 Neural Circuits and ComputationFigure 1.8 illustrates several basic neural circuits that are found in the centralnervous system. Figures 1.8(a) and (b) illustrate the principles of divergenceand convergence in neural circuitry. Each neuron sends impulses to many otherneurons (divergence), and receives impulses from many neurons (convergence).This simple idea appears to be the foundation for all activity in the centralnervous system, and forms the basis for most neural-network models that weshall discuss in later chapters.Notice the feedback paths in the circuits of Figure 1.8(b), (c), and (d). Sincesynaptic connections can be either excitatory or inhibitory, these circuits facilitatecontrol systems having either positive or negative feedback. Of course, thesesimple circuits do not adequately portray the vast complexity of neuroanatomy.Now that we have an idea of how individual neurons operate and of howthey are put together, we can pose a fundamental question: How do theserelatively simple concepts combine to give the brain its enormous abilities?The first significant attempt to answer this question was made in 1943, throughthe seminal work by McCulloch and Pitts [24]. This work is important for manyreasons, not the least of which is that the investigators were the first people totreat the brain as a computational organism.The McCulloch-Pitts theory is founded on five assumptions:1. The activity of a neuron is an all-or-none process.2. A certain fixed number of synapses (> 1) must be excited within a periodof latent addition for a neuron to be excited.3. The only significant delay within the nervous system is synaptic delay.4. The activity of any inhibitory synapse absolutely prevents excitation of theneuron at that time.5. The structure of the interconnection network does not change with time.Assumption 1 identifies the neurons as being binary: They are either onor off. We can therefore define a predicate, N t (t), which denotes the assertionthat the ith neuron fires at time t. The notation, -iATj(t), denotes the assertionthat the ith neuron did not fire at time t. Using this notation, we can describe