arXiv subjects

Boris Kryzhanovsky

Publications and source records attributed to Boris Kryzhanovsky.

22 records · Page 2Linked to original sources

arXiv2012

Optical Solver of Combinatorial Problems: Nano-Technological Approach

We report the first steps in creating an optical computing system. This system may solve NP-Hard problems by utilizing a setup of exponential sized masks. This is exponential space complexity but the production of those masks is done with a polynomial time preprocessing. These masks are later used to solve the problem in polynomial time. We propose to reduced the size of the masks to nano-scaled density. Simulations were done to choose a proper design, and actual implementations show the feasibility of such a system.

cs.ET↗

arXiv2011

Increasing the attraction area of the global minimum in the binary optimization problem

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10^3 in the case of the 10-by-10 Edwards-Anderson spin glass).

cond-mat.dis-nn↗

arXiv2010

Local Minima of a Quadratic Binary Functional with a Quasi-Hebbian Connection Matrix

The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight. For such matrices statistical physics methods allow one to derive an equation describing local minima of the functional. A model where only one weight differs from other ones is discussed in detail. In this case the equation can be solved analytically. The critical values of the weight, for which the energy landscape is reconstructed, are obtained. Obtained results are confirmed by computer simulations.

cond-mat.dis-nn↗

arXiv2010

Local Minima of a Quadratic Binary Functional with Quasi-Hebbian Connection Matrix

The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight. For such matrices statistical physics methods allow one to derive an equation describing local minima of the functional. A model where only one weight differs from other ones is discussed in details. In this case the above-mention equation can be solved analytically. Obtained results are confirmed by computer simulations.

cond-mat.dis-nn↗