Consensus with Linear Objective Maps

A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics

Distributed Evaluation and Convergence of Self-Appraisals in Social Networks

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable

Facile Synthesis Of Reduced Graphene Oxide-supported Pd/Cuo Nanoparticles As An Efficient Catalyst For Cross-coupling Reactions

The present communication reports a scientific investigation of a simple and versatile synthetic route for the synthesis of palladium nanoparticles decorated with copper oxide and supported on reduced graphene oxide (rGO). They are used as a highly active catalyst of Suzuki, Heck, and Sonogashira cross coupling reactions with a remarkable turnover number of 7000 and a turnover frequency of 85000 h-1. The Pd-CuO nanoparticles supported on reduced graphene oxide nanosheets (Pd-CuO/rGO) exhibit an outstanding performance through a high catalytic activity towards cross coupling reactions. A simple, reproducible, and reliable method is used to prepare this efficient catalyst using microwave irradiation synthetic conditions. The synthesis approach requires a simultaneous reduction of palladium and copper nitrates in presence of graphene oxide (GO) nanosheets using hydrazine hydrate as a strong reducing agent. The highly active and recyclable catalyst has many advantages including mild reaction conditions and short reaction durations in an environmentally benign solvent system. Moreover, the catalyst prepared can be recycled for up to five times with nearly identical high catalytic activity. Furthermore, the high catalytic activity and the recyclability of the catalyst prepared are due to the strong catalyst-support interaction. The defect sites of the reduced graphene oxide (rGO) act as nucleation centers that enable anchoring of both Pd and CuO nanoparticles and hence, minimize the possibility of agglomeration which leads to a severe decrease of the catalytic activity