JNTU B.Tech IV ARTIFICIAL NEURAL NETWORKS AND FUZZY SYSTEMS Previous Question Paper (July/August - 2022 - R16)

A single McCulloch-Pitts (M-P) neuron cannot implement the XOR function because XOR is not linearly separable. To implement XOR, we require a multi-layer M-P network. The XOR function can be expressed as: Y = (A AND NOT B) OR (NOT A AND B). We construct the network using three neurons: two neurons for the intermediate logic and one output neuron.

Let the inputs be A and B. The weights (w) and thresholds (θ) are chosen as follows:

1. Neuron 1 (A AND NOT B): Weights w1=1, w2=-1; Threshold θ=1.
2. Neuron 2 (NOT A AND B): Weights w1=-1, w2=1; Threshold θ=1.
3. Neuron 3 (Output OR): Weights w1=1, w2=1; Threshold θ=1.

The output of Neuron 1 is 1 only if A=1 and B=0. The output of Neuron 2 is 1 only if A=0 and B=1. Neuron 3 performs an OR operation on these outputs, resulting in 1 only when A and B are different, effectively realizing the XOR logic.

The Hodgkin-Huxley (H-H) model is a mathematical framework that describes how action potentials in neurons are initiated and propagated. It is based on the electrical properties of the neuronal membrane, treating the cell membrane as a capacitor and the ion channels as variable resistors.

Key aspects of the model include:

• Circuit Analogy: The membrane is modeled as an equivalent circuit where the lipid bilayer acts as a capacitor (Cm), and ion channels for Sodium (Na+), Potassium (K+), and leakage (L) act as voltage-dependent conductances (g).
• Current Equations: The total current I is the sum of capacitive current and ionic currents: I = Cm(dV/dt) + gNa(V - ENa) + gK(V - EK) + gL(V - EL), where E represents the equilibrium potentials.
• Gating Variables: The model introduces dimensionless variables (m, n, h) that represent the probability of ion channels being open, which change over time according to voltage-dependent differential equations.

This model is highly accurate in simulating the biophysical behavior of neurons, providing the foundation for computational neuroscience, though it is computationally intensive compared to simpler models like the integrate-and-fire model.