The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

Copyright q 2010 Fengjuan Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By topological degree theory and some analysis skills, we consider a class of generalized Liénard type p-Laplacian equations. Upon some suitable ...

Absrruct-This paper discussed the spatial 'or angular spreading properties of wireless propagation in the urban microcell environment, which is of great interests of future mobile technology, especially in case of using smart antennas. Based on the elliptical scattering model, the power azimuth spectrum in microcell environments is derived and it is found that the result approximately followed ...

Standard JPEG decompression reconstructs quantized DCT coefficients to the center of the quantization bin. This fails to exploit the nonuniform distribution of the AC coefficients. Assuming a Laplacian distribution, we derive a maximum likelihood estimate of the Laplacian parameter, based on the quantized coefficients available at the decoder, and use this estimate to optimally bias the reconst...

We present an algorithm for approximating the LaplaceBeltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the ddimensional space. We show that this PCD Laplace (PointCloud Data Laplace) operator converges to the LaplaceBeltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that the ...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

This paper presents the group sparse hidden Markov models (GS-HMMs) where a sequence of acoustic features is driven by Markov chain and each feature vector is represented by two groups of basis vectors. The group of common bases represents the features across states within a HMM. The group of individual bases compensates the intra-state residual information. Importantly, the sparse prior for se...

We study the low energy asymptotics of periodic and random Laplace operators on Cayley graphs of amenable, finitely generated groups. For the periodic operator the asymptotics is characterised by the van Hove exponent or zeroth Novikov-Shubin invariant. The random model we consider is given in terms of an adjacency Laplacian on site or edge percolation subgraphs of the Cayley graph. The asympto...

This paper proposes a quantization parameter estimation algorithm for HEVC CTU rate control. Several methods were proposed, mostly based on Lagrangian optimization combined with Laplacian distribution for transformed coefficients. These methods are accurate but increase the encoder complexity. This paper provides an innovative reduced complexity algorithm based on a ρ-domain rate model. Indeed,...

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...