We spell out a formal equivalence between the naive Laplacian editing and semi-supervised learning by bi-Laplacian Regularized Least Squares. This allows us to write the solution to Laplacian mesh editing in a closed form, based on which we introduce the Generalized Linear Editing (GLE). GLE has both naive Laplacian editing and gradient based editing as special cases. GLE allows using diffusion...

Let η(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper, bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimize...

Calculation of watermarking capacities of private Laplacian watermarking systems with the magnitude-error distortion measure under fixed attacks is addressed. First, in the case of an additive Laplacian attack, a nice closed-form formula for the watermarking capacities is derived, which involves only the distortion level and the parameter of the Laplacian attack. Second, in the case of an arbit...

1 Laplacian Methods: An Overview 2 1.1 De…nition: The Laplacian operator of a Graph . . . . . . . . . . 2 1.2 Properties of the Laplacian and its Spectrum . . . . . . . . . . . 4 1.2.1 Spectrum of L and e L: Graph eigenvalues and eigenvectors: 4 1.2.2 Other interesting / useful properties of the normalized Laplacian (Chung): . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Laplacians of Weight...

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with establishe...

It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities. We identify the physical origin of these complex poles as the exponentially large degeneracy of the iterated eigenvalues of the Laplacian, and discuss applic...

According to recent advances in digital image processing techniques, interest in high-quality images has been increased. This paper presents a resolution enhancement (RE) algorithm based on the pyramid structure, in which Laplacian histogrammatching is utilized for high-frequency image prediction. The conventional RE algorithms yield blurring near-edge boundaries, degrading image details. In or...

Brain magnetic resonance image (MRI) segmentation is a complex problem in the field of medical imaging despite various presented method.MR image of human brain can be divided into several sub-regions especially soft tissues such as grey matter, white matter and cerebrospinal fluid the combinatorial algorithm provide a solution to overcome the associated challenges of segmented brain MRI. Asymme...

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction-diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for co...