In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0, 2], and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H+-eigenvalues of the Laplacian and all the smallest H+-eigenvalues of its sub-t...

In this paper, we introduce a new class of nonlocal p-Laplacian operators that interpolate between non-local Laplacian and infinity Laplacian. These operators are discrete analogous of the game p-laplacian operators on Euclidean spaces, and involve discrete morphological gradient on graphs. We study the Dirichlet problem associated with the new p-Laplacian equation and prove existence and uniqu...

Networks are increasingly recognized as important building blocks of various systems in nature and society. Water is known to possess an extended hydrogen bond network, in which the individual bonds are broken in the sub-picosecond range and still the network structure remains intact. We investigated and compared the topological properties of liquid water and methanol at various temperatures us...

The Laplacian and normalized Laplacian energy of G are given by expressions EL(G) = ∑n i=1 |μi − d|, EL(G) = ∑n i=1 |λi − 1|, respectively, where μi and λi are the eigenvalues of Laplacian matrix L and normalized Laplacian matrix L of G. An interesting problem in spectral graph theory is to find graphs {L,L}−noncospectral with the same E{L,L}(G). In this paper, we present graphs of order n, whi...

One of the biggest challenges in universal steganalysis is the identification of reliable features that can be used to detect stego images. In this paper, we present a steganalysis method using features calculated from a measure that is invariant for cover images and is altered for stego images. We derive this measure, which is the ratio of any two Fourier coefficients of the distribution of th...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. ...

In a previous work, the authors have introduced a Mixture of Laplacians model in order to cluster the observed data into the sound sources that exist in an underdetermined two-sensor setup. Since the assumed linear support of the ordinary Laplacian distribution is not valid to model angular quantities, such as the Direction of Arrival to the set of sensors, the authors investigate the performan...

Stephen R. Smoot and Lawrence A. Rowe Computer Science Division University of California at Berkeley Berkeley, CA 94720 [email protected],[email protected] ABSTRACT Many image and video compression schemes perform the discrete cosine transform to represent images in frequency space. An analysis of a suite of images conrms the previous nding of a Laplacian distribution to model th...

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domainD is killed; at the same time, a different particle splits into two particles. For large N , the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge...