We propose a general bottom-up approach using Laplacian eigenmaps to segment 3-D voxel data of human subjects into different body parts. The voxels are first transformed into a high dimensional space which is the eigenspace of the Laplacian of the neighbourhood graph. We exploit the properties of this transformation and fit 1-D splines to the voxels belonging to different body segments in eigen...

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the p...

Let G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial o...

We consider a twisted Laplacian $\Delta_{\nu,\mu}$ on the $n$-complex space associated with sub-Laplacian of Heisenberg group $\mathbb{C} \times_{\omega} \mathbb{C}^n$ realized as central extension real $H_{2n+1}$. The main results to which is aimed this paper concern spectral theory $\Delta_{\nu,\mu}^{\Gamma}$ when acting some $L^2$ $\Gamma$-automorphic functions biweight $(\nu,\mu)$ given coc...

The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian d...

Abs-Laplacian is a newer technique for detecting edges. While the Sobel and Prewitt seems to be used predominantly in image processing due to better edge detection. However they need higher amount of complexity twice than that of abs-Laplacin. Moreover, qualities of images are no better than the newer kernel. While the new technique seems to perform better in speed and quality, there seems a bi...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.