A maximum a-posteriori approach for overcomplete blind source separation based on Laplacian priors usually involves 1-normminimization. It requires different approaches for real and complex numbers as they appear for example in the frequency domain. In this paper we compare a combinatorial approach for real numbers with a second order cone programming approach for complex numbers. Although the ...

The spectral densities of the weighted Laplacian, random walk, and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent beta. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and beta.

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

We consider overdetermined boundary value problems for the ∞-Laplacian in a domain Ω of Rn and discuss what kind of implications on the geometry of Ω the existence of a solution may have. The classical ∞-Laplacian, the normalized or game-theoretic ∞-Laplacian and the limit of the p-Laplacian as p→∞ are considered and provide different answers. Mathematics Subject Classification (2000). 35R35, 4...

Suppose μ1, μ2, ... , μn are Laplacian eigenvalues of a graph G. The Laplacian energy of G is defined as LE(G) = ∑n i=1 |μi − 2m/n|. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of Kn are presented. AMS subject classifications: 05C50

We show in a unified manner that the factorization method describes completely the L2 -eigenspaces associated to the discrete part of the spectrum of the twisted Laplacian on constant curvature Riemann surfaces. Subclasses of two variable orthogonal polynomials are then derived and arise by successive derivations of elementary complex valued functions depending on the geometry of the surface. M...