A nonsingular configuration of m lines of ℝP3 is defined as an (unordered) collection of m nonoriented pairwise disjoint lines in ℝP3. An isotopy of such a collection in the process of which the lines remain pairwise disjoint lines is called a rigid isotopy. The main aim of the paper is to classify nonsingular configurations of 7 lines of ℝP3 up to rigid isotopy.
A Hopfield model with transverse fields that induce tunneling among neurons is presented. A set of equations for the order parameters describing retrieval and spin glass phases of Hopfield model in a transverse field are obtained without using the tedious replica method, and the memory storage capacity of networks is analysed as a function of the temperature and transverse field.
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