The model of a neuron

A neuron is composed of:

• The input signals $x_m$
• The synaptic weighs $w_{km}$
• A summing junction that produces the induced local field: $v_k$
• The activation function $\varphi(\cdot)$
• The output $y_k$

The output of the neuron $k$ is:

$$y_k=\varphi(v_k) = \varphi(\sum_{j=0}^{j=m}w_{kj}x_{j}) = \varphi(\ve{w}_k^t \ve{x})$$