# CS667

# The Biological Neuron and Simple Models

**Where Do We Think?**
- Where people thought they thought
- Thinking takes place in the brain

**The Classical Biological Neuron**
- Somma
- Dendrites
- Axon
- Synapses
- Synaptic Efficacy

**The Ping-Pong Ball Model**
- Ideal gas law explained in statistical physics using unrealistic model
- Model breaks down at extremes but extremely useful over large range
- Biologists haven't made headway studying single neurons
- Statistical physics is where a large number of simple units can be analyzed

**The McCulloch-Pitts Model**
- Neuron's state (firing or quiescent) represented by (0,1) or (-1,+1)
- Synaptic efficacies are represented by arbitrary real numbers
- PSP is the weighted sum of inputs
- Decision whether to fire or remain quiet is deterministic (step function)
- Can perform many logical, signal/image processing, computational tasks

**Comparison Of The Brain And A Computer**
- Can only directly compare two computers of identical architecture
- Can indirectly compare computers by cross emulation
- Computer and brain architectures are so radically different that you can't compare them
- Before trying to solve a problem choose correct architecture

## Assignment

- Find the connection between the (0,1) and (-1,+1) representations.
- Prove that the McCulloch-Pitts formulae for these neurons are equivalent.

Find formulae for the equivalence of weights and thresholds.
- Is this equivalence purely mathematical, or biological as well?

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