Discretization of a matrix in the problem of quadratic functional binary minimization

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that optimal procedure of replacement matrix elements by the integer quantities with the limited number of gradations exist, and the efficient of minimization does not reduce. Parameter depends on matrix properties, which allows estimate the capability of using described procedure for given type of matrix, is found. Computational complexities of algorithm and RAM requirements are reduced by 16 times, correct using of integer elements allows increase minimization algorithm speed by the orders.Comment: 11 pages, 4 figures, in Russian languag

Domain dynamics in hopfield model

We propose a domain model of a neural network, in which individual spin-neurons are joined into larger-scale aggregates, the so-called domains. The updating rule in the domain model is defined by analogy with the usual spin dynamics: if the state of a domain in an inhomogeneous local field is unstable, then it flips, in the opposite case its state undergoes no changes. The number of stable states of the domain network grows linearly with the domain\u27s size k, where k is the number of spins in the domain. We show that the proposed model is effective for optimization problems, since the use of domain dynamics lowers the number of calculations in k2 times and allows one to find deeper minima than the standard Hopfield model does. © 2006 IEEE