We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX-2-CSP and MIN-2-CSP), which gives the first exponential improvement over the trivial algorithm; more precisely, it is a constant factor improvement in the base of the runtime exponent. In the case where constraints have a...

We present a method to detect simple cycles of length 4 of a directed graph in O n1 ωe2 2 ω steps, where n denotes the number of nodes, e denotes the number of edges and ω is the exponent of matrix multiplication. This improves upon the currently fastest methods for α 2 4 ω ω 1 2 , where e nα.

In this paper, the effect of neuronal gain in discrete delayed neural network model is investigated. It is observed that such neural networks become highly chaotic due to the presence of high neuronal gain. On the basis of the largest Lyapunov exponent and largest eigenvalue of Jacobian matrix, chaos analysis has been done. Finally, some numerical simulations are presented to justify our results.

Ever since the dawn of the computer age, researchers have been trying to find an optimal way of multiplying matrices, a fundamental operation that is a bottleneck for many important algorithms. Faster matrix multiplication would give more efficient algorithms for many standard linear algebra problems, such as inverting matrices, solving systems of linear equations, and finding determinants. Eve...

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.

The new symmetric cipher S-box construction based on matrix power function is presented. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. The left and right side matrix powers are introduced. This operation is linked with two sound one-way func...

We investigate the onset of chaos in a periodically kicked Dicke model (KDM), using out-of-time-order correlator (OTOC) as diagnostic tool, both oscillator and spin subspaces. In large limit, classical Hamiltonian map is constructed, which allows us to corresponding phase space dynamics compute Lyapunov exponent. show that growth rate OTOC for canonically conjugate coordinates able capture expo...

Abstract: We study the level spacing distribution P (S) of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for P (S) is derived and its behaviour close to S = 0...

We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of '29 and '87 c...