# Sigmoid Function in Neural Network

I am studying a doctoral thesis on control-theory and have trouble understanding the notions and the notation introduced there. I am doing this out of interest on the subject, so I haven't had a related class to rely on.

It says that static neural networks can be described as $$y=Z^T(x)\theta$$ where $y \in R^m ,x\in R^n ,\theta \in R^q,Z:R^n\rightarrow R^{q\times m}$ and Z is a continuous field that includes sigmoid functions.

I have actually taken Andrew Ng's ML course a few years ago. My problem is mainly the notation used here. Unfortunately the article I'm referring to is written in Greek, so you probably won't be able to understand it even if I post it.

For example, there is an unknown non-linearity $g(x)\in R^{m\times m }$ and it is stated that using neural networks we can approximate it as $$g(x)=g_a(x,\theta_g^*)+w_g(x)$$ where $w_g(x) \in R^{m \times m}$ is the modeling error and $$g_a(x,\theta_g^*)=\begin{bmatrix}Z_{g11}^T(x)\theta_g^* & \dots &Z_{g1m}^T(x)\theta_g^*\\\dots&\dots&\dots \\Z_{gm1}^T(x)\theta_g^* &\dots& Z_{mm}^T(x)\theta_g^*\end{bmatrix}$$ where $Z_{gij}:R^n\rightarrow R^{q_j}$ are continuous base functions (apparently sigmoid) but there is no other information on the form of $Z_{gij}$.Any idea what they might look like?