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

Global Minimum Depth In Edwards-Anderson Model

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit $N\to\infty$. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.Comment: 10 pages, 4 figures, 2 tables, submitted to conference on Engineering Applications of Neural Networks (EANN 2019