We show that for pulse-coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of convergence and give explicit bounds on the convergence times. These results provide new and more robust methods for synchronization of sensor nets and also have biol...

The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R × R. We extend the earlier work of Arratia and of Tóth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing r...

Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas...

It is well known that orderings based on graph colorings can slow the convergence of many iterative methods. However, orderings based on graph colorings can be used to build scalable, parallel iterative methods. For example, SOR with consistent orderings, SSOR, and incomplete Cholesky can all be implemented in a scalable manner using graph colorings. It has been observed experimentally that if,...

Simulated Annealing is a family of randomized algorithms used to solve many combinatorial optimization problems. In practice they have been applied to solve some presumably hard (e.g., NP-complete) problems. The level of performance obtained has been promised [5, 2, 6, 14]. The success of its heuristic technique has motivated analysis of this algorithm from a theoretical point of view. In parti...

We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m ≫ n users that try to find an acceptable resource by moving along the edges of the graph. Users accept a resource if the load is below a threshold. Such thresholds have an intuitive meaning, e.g., as deadlines in a machin...

In this paper, we focus on the design of network topology to achieve fast information distribution. We present the information distribution performance of Borel Cayley graphs, a family of pseudo-random graphs, is far superior than that of other well-known graph families. To demonstrate the effectiveness of this pseudo-random approach, we compare the convergence speed of the average consensus pr...

The paper addresses the problem of exact average-consensus reaching in a prescribed time. The communication topology is assumed to be defined by a weighted undirected graph and the agents are represented by integrators. A nonlinear control protocol, which ensures a finite-time convergence, is proposed. With the designed protocol, any prescribed convergence time can be guaranteed regardless of t...

Isoperimetric inequalities form a very intuitive yet powerful characterization of the connectedness of a state space, that has proven successful in obtaining convergence bounds. Since the seventies they form an essential tool in differential geometry [1,2], graph theory [4,3] and Markov chain analysis [8,5,6]. In this paper we use isoperimetric inequalities to construct a bound on the convergen...

In this article, we study multi-agent consensus algorithms with information reuse by intentionally introducing the outdated state information into the traditional consensus algorithms. In the continuous-time case, we first show that the outdated state information combined with the current state information does not necessarily jeopardise the stability of a single system, but may improve the con...