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A Lyapunov approach is developed to establish the convergence rates of discrete-time linear consensus. The approach combines the use a quadratic time-varying comparison function and an adjoint dynamics of the linear consensus dynamics. New convergence rate results are obtained that are characterized with an explicit dependence on the graph structure including the longest shortest path.
On a binary erasure channel (BEC) with erasing probability e, the performance of a binary linear code is determined by the incorrigible sets of the code. The incorrigible set distribution (ISD) {Ii}ni=0 enumerates the number of incorrigible sets with size i of the code. The probability of unsuccessful decoding under optimal decoding for the code could be formulated by the ISD and ε. In this paper,...
Gossiping is a well-known approach to the distributed averaging problem whose purpose is to enable the members of a group of autonomous agents to iteratively determine the average of their initial scalar-valued gossip variables by allowing each agent to interchange information with at most one neighbor at each iterative step. In prior work we presented a deterministic request-based gossiping protocol...
We intend to understand how decentralized planning through local interactions can result in large-scale change from inactivity to global action cascades characteristic of social revolutions as well as innovation adoption. Building on the dynamic threshold model of threshold learning and collection action proposed in [1], this paper investigates the diffusion process in a number of canonical graph...
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