Language evolution is a primary problem in designing collaborative agents from a linguistic perspective. The problem of language evolution involves determining how the languages used by a collection of agents may change over time, and whether an initially homogeneous language will stay uniformly understandable or will diverge into mutually unintelligible dialects. In simple regimes, it has been...

Discussions about different graph Laplacians—mainly the normalized and unnormalized versions of graph Laplacian—have been ardent with respect to various methods of clustering and graph based semi-supervised learning. Previous research in the graph Laplacians, from a continuous perspective, investigated the convergence properties of the Laplacian operators on Riemannian Manifolds. In this paper,...

In this paper we improve the spectral convergence rates for graph-based approximations of weighted Laplace-Beltrami operators constructed from random data. We utilize regularity continuum eigenfunctions and strong pointwise consistency results to prove that are same as graph Laplacians. particular, an optimal choice connectivity ?, our show eigenvalues eigenvectors Laplacian converge those a op...

In the deterministic binary majority process we are given a simple graph where each node has one out of two initial opinions. In every round, each node adopts the majority opinion among its neighbors. It is known that this process always converges in O (|E|) rounds to a two-periodic state in which every node either keeps its opinion or changes it in every round. It has been shown by Frischknech...

We present the structure theorem for positive support of cube Grover transition matrix discrete-time quantum walk (the walk) on a general graph G under some condition. Thus, we introduce zeta function G, and its Euler product determinant expression. As corollary, give characteristic polynomial regular graph, so obtain spectra. Finally, poles radius convergence this function.

We consider the design of the topology of the communication graph G = (V, E) supporting distributed decision in sensor networks with N = |V | sensors. The number M of links connecting the sensors, i.e., the number of edges |E| = M in the graph G, is fixed. We assume a simple binary decision test where the data may be spatially correlated. The global detector performs a threshold test on a weigh...

Given a set of n randomly drawn sample points, spectral clustering in its simplest form uses the second eigenvector of the graph Laplacian matrix, constructed on the similarity graph between the sample points, to obtain a partition of the sample. We are interested in the question how spectral clustering behaves for growing sample size n. In case one uses the normalized graph Laplacian, we show ...

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schrödinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is sub...

The biclique graph of G, KB(G), is the intersection graph of the bicliques of G. Given a graph G, the iterated biclique graph of G, KBk(G), is the graph defined iteratively as follows: KBk+1(G) = KB(KBk(G)). Say that a graph G diverges (resp. converges) under the operator KB whenever limk→∞ |V (KBk(G))| = ∞ (resp. limk→∞KB(G) = KBm(G) for some m). Each of these behaviours were recently characte...