An artificial neural network (ANN) with a distinguished external input may be considered as a tuple 〈U, W, A, O, NET, ex〉 having the following properties (this is the definition stated by Nauck et al. [113], pp.19–24, where also a general overview of ANNs is to be found): 1. U is a finite and non-empty set of units 2. W : U × U → ℝ is the pattern of (weight-) connectivity, which assigns a weight to each edge between units 3. A is a function which maps each unit u ∈ U to an activation mapping A u : ℝ3 → ℝ, s.t. the activation state a u (t + 1) of u at time t + 1 is dependent on the previous activation state a u (t) of u, the current net input net u (t + 1) of u, and the (constant) external input ex(u) fed into u, i.e. $$ {a_u}\left( {t + 1} \right) = {A_u}\left( {{a_u}\left( t \right),ne{t_u}\left( {t + 1} \right),ex\left( u \right)} \right) $$ 4. O is a function which maps each unit u ∈ U to an output mapping O u : ℝ → ℝ, s.t. the output state o u (t + 1) of u at time t + 1 is solely dependent on the activation state a u (t + 1) of u, i.e. o u (t + 1) = O u (a u (t + 1))