"A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, considered. This structure has a circulant matrix respect to some basis, i.e. circulant, and it acts as isometry metric. The product associated considered studied. Conditions for metric, which imply that belongs each of basic classes Staikova-Gribachev's classi cation, are obta...

We introduce the class of skew-circulant lattice rules. These are s-dimensional lattice rules that may be generated by the rows of an s×s skewcirculant matrix. (This is a minor variant of the familiar circulant matrix.) We present briefly some of the underlying theory of these matrices and rules. We are particularly interested in finding rules of specified trigonometric degree d. We describe so...

We describe the results of a computer-based search for 5 and 6dimensional lattice rules of specified trigonometric degree. In this search only lattice rules that can be generated by a circulant or skew-circulant generator matrix are considered, which makes this approach significantly faster than earlier approaches. The drawback is that we do not necessarily obtain optimal lattice rules. We also...

In this paper a new approach to the modelling of ATM-traffic is proposed. The traffic is measured and characterised by its first and second order statistic moments. A Markov Modulated Poisson Process (MMPP) is used to capture the information in these two stochastic moments. Instead of a general MMPP, a circulant MMPP is used to reduce the computational cost. A circulant MMPP (CMMPP) is an MMPP ...

The permanent of an n x n matrix A = (a;j) is the matrix function ( 1) per A = ∑ al1r(1)••• a .. ",( .. )".C~" where the summation is over all permutations in the symmetric group, S ... An n x n matrix A is a circulant if there are scalars ab ... ,a,. such that (2) A= ∑ a;pi-l where P is the n x n permutation matrix corresponding to the cycle (12• .. n) in s". In general the computation of the ...

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

We design heuristic algorithms to construct Hadamard matrices with two circulant cores. This hard combinatorial problem can be formulated in terms of objective functions of several binary variables, so that heuristic methodologies can be used. Our algorithms are based on local and tabu search and they use information on the geometry of the objective function landscapes. In addition, we use the ...

As part of a survey of state-of-the-art kernel approximation algorithms, we present a new sampling algorithm for circulant matrix construction to perform fast kernel matrix inversion in kernel ridge regression, comparing theoretical and experimental performance of that of multilevel circulant kernel approximation, incomplete Cholesky decomposition, and random features, all recent advances in th...