Network, parameters used often defining

The structure of a perfect network may be defined by two variables, the cycle rank and the average junction functionality (f>. Cycle rank is defined as the number of chains that must be cut to reduce the network to a tree. The three other parameters used often in defining a network are (i) the number of network chains (chains between junctions) v, (ii) the number of junctions p, and (iii) the molecular weight Mc of chains between two junctions. They may be obtained from and using the relations... 

The constants a, b, and c define the sigmoid curve, which has the asymptotic values zero for x —> —X and a for x 4-Y (a and c are expected to have positive values). The position and steepness of the curve between the two asymptotic values depend on the parameters b and c. A logistic function is the result of a logistic regression analysis, where b + cx is replaced by a linear combination of all x-variables. With values 1, 0, and 1 for a, b, and c, respectively, the logistic function is often used as a transfer function for back-propagation networks, a type of artificial neural network. See Neural Networks in Chemistry. 

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