In this paper a fast Kalman filter is derived for the nearly optimal recursive restoration of images degraded in a deterministic way by blur and in a stochastic way by additive white noise. Straightforwardly implemented optimal restoration schemes for two-dimensional images degraded by both blur and noise create dimensionality problems which, in turn, lead to large storage and computational req...

The existence of perfect state transfer in quantum spin networks based on integral circulant graphs has been considered recently by Saxena, Severini and Shparlinski. Motivated by the mentioned work, Bašić, Petković and Stevanović give the simple condition for the characterization of integral circulant graphs allowing the perfect state transfer in terms of its eigenvalues. They stated that integ...

We investigate a certain condition for isomorphism between circulant graphs (known as the Ad am property) in a stronger form by referring to isospectrality rather than to isomorphism of graphs. We describe a wide class of graphs for which the Ad am conjecture holds. We apply these results to establish an asymptotic formula for the number of non-isomorphic circulant graphs and connected circulan...

Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily exte...

Let G 1⁄4 ðV ;EÞ be a k-regular graph with connectivity j and edge connectivity k. G is maximum connected if j 1⁄4 k, and G is maximum edge connected if k 1⁄4 k. Moreover, G is super-connected if it is a complete graph, or it is maximum connected and every minimum vertex cut is fxjðv; xÞ 2 Eg for some vertex v 2 V ; and G is super-edge-connected if it is maximum edge connected and every minimum...

In this paper we present a method to search q circulant matrices; the concatenation of these circulant matrices with circulant identity matrix generates quasi-cyclic codes with high various code rate q/(q+1) (q an integer). This method searches circulant matrices in order to find the good quasi-cyclic code (QCC) having the largest minimum distance. A modified simulated annealing algorithm is us...

In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation. We tabulate these parameters. We also compare the discrete logarithm problem in the group of circulant matrices with the discrete logarithm problem in finite...

In this paper we rst review the basic computational properties of per-manents, and then address some problems concerning permanents of (0; 1) circulant matrices. In particular we analyze their role at the boundary between computational tractability and intractability, showing that (i) a generic circulant matrix contains large arbitrary submatrices, a fact which casts some doubt on the tractabil...