This material is a supplement to the paper “Distributed Consensus-based Weight Design for Cooperative Spectrum Sensing”. Section 1 offers related literature review on cooperative spectrum sensing and consensus algorithms. Section 2 presents related notations and models of the consensus-based graph theory. Section 3 offers further analysis of the proposed spectrum sensing scheme including detect...

In this paper, a variant of Backpropagation algorithm is proposed for feed-forward neural networks learning. The proposed algorithm improve the backpropagation training in terms of quick convergence of the solution depending on the slope of the error graph and increase the speed of convergence of the system. Simulations are conducted to compare and evaluate the convergence behavior and the spee...

We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define correctly the convergence of TVG sequences. Next, we provide a general framework that formally proves the convergence of the sequence of executions of any determin...

In this paper, sufficient conditions for the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents are proposed. More precisely, we consider the consensus algorithms in which the control input of each agent is a state-dependent combination of the relative positions of its neighbors in the information flow graph. It is shown that under some mild as...

This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the...

Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a bandlimited graph signal, the unknown data associated with unsampled vertices can be reconstructed from the sampled data by exploiting the spatial relationship of graph signal. In this paper, we propose a generalized analytical fra...

2 Preliminaries 2 2.1 Homomorphism numbers and densities . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Local convergence of a graph sequence . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Chromatic polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Subtree counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Weight...

We introduce the notion of a random walk in an undirected graph. What happens after we take T random steps in the walk? We show how to analyze walks and their convergence properties.

The asymptotic distributions of the number of vertices of given degree in random graph K n,p are given. By using the method of Poisson convergence, Poisson and normal distributions are obtained.

Abstract We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ( κ ) from photometric measurements of galaxies along given line sight (LOS). The method is particular interest in strong gravitational time-delay cosmography (TDC), where characterizing “external convergence” ext lens environment and LOS necessary for precise Hubble constant H 0 inference....