Based on our previously developed signi cance-linked connected component analysis (SLCCA) data organization and representation strategy, two three-dimensional wavelet video coding techniques are proposed covering a wide range of applications areas. In three-dimensional SLCCA (3D-SLCCA), both the wavelet decomposition and SLCCA data organization and representation strategy are extended to 3-D ca...

We show that in long-time the heat semi-group on a path group associated to a Bilaplacian on the group tends to the Haar distribution on a path group.

We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N > M , distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ...

We review various notions of correspondences for locally compact groupoids with Haar systems, in particular a recent definition due to R.D. Holkar. We give the construction of the representations induced by such a correspondence. Finally, we extend the construction of induced representations to hypergroupoids.

Denote by S,, the set (x; 1 ~ji(x)~@> n), and put M, = m(S,). Then 2 M, converges. It is clear that the same holds if 1 $fk(x) 1 > n is replaced by I$ fx{x) I> c-n (replace fk(x) by c.fk(x)). It was conjectured that the conditions (1) and (2) are necessary for the convergence of 2 M, . Dr. Chung pointed it out to me that in this form the conjecture is ina”zurate; to see this it suffices to put ...

We develop further the topological theory of regular variation of [BOst13]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with realtime topological ‡ows on homogeneous spaces, we identify an index of...

We show that the empirical eigenvalue measure for sum of d independent Haar distributed n-dimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed n-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes t...

The MRTD adaptive gridding scheme that is based on the Haar expansion basis is discussed for arbitrary wavelet resolutions. Guidelines for the optimization of memory and execution time requirements are presented. A multi-time-stepping procedure enhances further the computational economies o ered by a combination of absolute and relative thresholding of the wavelet values.

An adaptive wavelet method for the chemical master equation is constructed. The method is based on the representation of the solution in a sparse Haar wavelet basis, the time integration by Rothe’s method, and an iterative procedure which in each time-step selects those degrees of freedom which are essential for propagating the solution. The accuracy and efficiency of the approach is discussed,...

The wavelet subspaces of the space of square integrable functions on the affine group with respect to the left invariant Haar measure dν are studied using the techniques from [9] with respect to wavelets whose Fourier transforms are related to Laguerre polynomials. The orthogonal projections onto each of these wavelet subspaces are described and explicit forms of reproducing kernels are establi...