Neuron
The control structure underpinning the human brain.
In roughly 1 \( {mm}^{3} \) each neuron typically [see page 4, connects] to 10,000 other neurons and there're 10,000 Post-synaptic neurons in 3km of wires.
Structure
The neuron is [see page 5, divided] into:
| Part | Description |
|---|---|
| Synapses | Controls the strength of the interaction between neurons |
| Dendrites | Collects (accumulates) inputs into the Soma |
| Soma | Performs a non-linear transformation of the inputs (processes them) |
| Axon | Connects the output of the Soma to other neurons through (Axon terminals) |
Excitation
We [see page 9, define] the excitation of a neuron as:
\begin{align} v_i^{\text{post}} = f( \sum_{j}{w_{ij} v_j^{\text{pre}}} ) \end{align}
You can visualise this as the weighted sum of the output of each neuron \( j \) connected to the current neuron \( i \), passed through some activation function \( f \). Or equivalently: \[ \text{output} = \text{transform}(\sum_{j}{\text{Connection weight $j \rightarrow i$} \times \text{Input from neuron $j$}}) \]
Once the sum of the EPSPs at a given point exceeds some threshold \( \Theta \) the current neuron also excites.
We often represent this spike in potential as binary. An instantaneous jump from
0 output to full output. However in reality this transition is generally over a
short period of time. We represent this gradual increase in potential by using a
non-linear transformation. It's a non linear response to the input.