Synchronization under matrix-weighted Laplacian
نویسندگان
چکیده
منابع مشابه
Polynomial Time Decidability of Weighted Synchronization under Partial Observability
We consider weighted automata with both positive and negative integer weights on edges and study the problem of synchronization using adaptive strategies that may only observe whether the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata. 1998 ACM Subject Classification F.1.1 Models of Co...
متن کاملComputing the additive degree-Kirchhoff index with the Laplacian matrix
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.
متن کاملWeighted Graph Laplacian and Image Inpainting
Abstract. Inspired by the graph Laplacian and the point integral method, we introduce a novel weighted graph Laplacian method to compute a smooth interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted graph Laplacian is a reliable and efficient interpolation method. In addition, it is easy ...
متن کاملLaplacian Matrix in Algebraic Graph Theory
In this paper we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are una...
متن کاملForest matrices around the Laplacian matrix
We study the matrices Qk of in-forests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Qk is the total weight of spanning converging forests (in-forests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Qk, can be calculated recursively and expressed by polynomials in the Laplacian matrix; they provide representation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Automatica
سال: 2016
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2016.06.012