We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on local geometry of system. Placing such 2D lattice, composed an arbitrary connected graph and 1D line, we find that fusion rules quasiparticle are described by Laplacian number superselection sectors is ...

This paper deals with the dynamics of stochastic delay lattice systems fractional discrete Laplacian driven by nonlinear noise. The existence a invariant measure for nonlocal is established under certain conditions. idea uniform estimates on tails solutions, technique diadic division and Arzela-Ascoli theorem are employed to show tightness family probability distributions solutions.

Scales in RNA, based on geometrical considerations, can be exploited for the analysis and prediction of RNA structures. By using spectral decomposition, geometric information that relates to a given RNA fold can be reduced to a single positive scalar number, the second eigenvalue of the Laplacian matrix corresponding to the tree-graph representation of the RNA secondary structure. Along with th...

Docking-i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)-represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor-ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in to...

Invariance is an attractive principle for specifying image processing algorithms. In this presentation, we promote affine invariance—more precisely, invariance with respect to translation, scaling and rotation. As starting point, we identify the corresponding class of invariant 2D operators: these are combinations of the (fractional) Laplacian and the complex gradient (or Wirtinger operator). W...

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

The study of extremal properties of the spectrum often involves restricting the metrics under consideration. Motivated by the work of Abreu and Freitas in the case of the sphere S endowed with S-invariant metrics, we consider the subsequence λ k of the spectrum of a Riemannian manifold M which corresponds to metrics and functions invariant under the action of a compact Lie group G. If G has dim...

For a simple digraph G of order n with vertex set {v1, v2, . . . , vn}, let d+i and d − i denote the out-degree and in-degree of a vertex vi in G, respectively. Let D (G) = diag(d+1 , d + 2 , . . . , d + n ) and D−(G) = diag(d1 , d − 2 , . . . , d − n ). In this paper we introduce S̃L(G) = D̃(G)−S(G) to be a new kind of skew Laplacian matrix of G, where D̃(G) = D+(G)−D−(G) and S(G) is the skew-adj...

By embedding images as surfaces in a high dimensional coordinate space defined by each pixel’s Cartesian coordinates and color values, we directly define and employ cotangent-based, discrete differentialgeometry operators. These operators define discrete energies useful for image segmentation and colorization.