Modern meta-GGAs based on the local kinetic energy density can predict properties of diverse systems with near experimental accuracy, but unexpectedly describe metallic solids poorly due to their underestimation screening in metals. In this work, authors replace dependence a sophisticated meta-GGA an approximation electronic gradient and Laplacian. This Laplacian-level is tested set solid-state...

In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on time-evolving simplicial complexes. The simplicial complexes model the connectivity of agents in the network, and the homology groups of the simplicial complexes provides information about th...

In this paper, some inequality relations between the Laplacian/signless Laplacian H-eigenvalues and the clique/coclique numbers of uniform hypergraphs are presented. For a connected uniform hypergraph, some tight lower bounds on the largest Laplacian H+-eigenvalue and signless Laplacian H-eigenvalue related to the clique/coclique numbers are given. And some upper and lower bounds on the clique/...

Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in th...

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

We establish the existence of multiple solutions for a nonvariational elliptic systems involving p(x)-Laplacian operator. The approach combines methods sub–supersolution and Leray–Schauder topological degree.

Abstract Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated at each node; maps often taken as unimodal, e.g. , logistic or tent maps. In this letter, we propose class higher-order coupled involving hypergraph Laplacian, w...

In directed network, algebraic connectivity is defined as the second smallest eigenvalue of graph Laplacian, and it captures the most conservative estimate of convergence rate and synchronicity of networked systems. In this paper, distributed estimation of algebraic connectivity of directed and connected graphs is studied using a decentralized power iteration scheme. Specifically, the proposed ...

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

A Laplacian matrix, L = (lij) ∈ R , has nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with − 1 n ≤ lij ≤ 0 at j 6= i. We study the spectra of Laplacian matrices and relations between Laplacian matrices and stochastic matrice...