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

Cooperative Access in Cognitive Radio Networks: Stable Throughput and Delay Tradeoffs

In this paper, we study and analyze fundamental throughput-delay tradeoffs in cooperative multiple access for cognitive radio systems. We focus on the class of randomized cooperative policies, whereby the secondary user (SU) serves either the queue of its own data or the queue of the primary user (PU) relayed data with certain service probabilities. The proposed policy opens room for trading the PU delay for enhanced SU delay. Towards this objective, stability conditions for the queues involved in the system are derived. Furthermore, a moment generating function approach is employed to derive closed-form expressions for the average delay encountered by the packets of both users. Results reveal that cooperation expands the stable throughput region of the system and significantly reduces the delay at both users. Moreover, we quantify the gain obtained in terms of the SU delay under the proposed policy, over conventional relaying that gives strict priority to the relay queue.Comment: accepted for publication in IEEE 12th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 201

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

Transport and adsorption-desorption of heavy metals in different soils

Understanding the reactivity and mobility of heavy metals in soils is indispensable for assessing their potential risk to the environment. In this study, column transport and batch kinetic experiments were performed to assess the sorption-desorption and mobility of Cd, Cu, Pb, and Sn in alkaline and acidic soils. Furthermore, sequential extractions were accomplished to examine their behavior in soils. Also, the competitive reactivity of Sn and Pb in two acidic soils was quantified. Additionally, the effect of introducing Cd and Cu after a Pb pulse in calcareous soil was presented. Modeling of these heavy metals retention and transport was carried out using different models; multireaction and transport model, CXTFIT model, kinetic ion exchange formulation, and second-order two-site model. The results revealed that: 1) the studied heavy metals exhibited strong nonlinear and kinetic retention behavior; 2) Cd was nearly immobile in alkaline soil with 2.8% CaCO3, whereas 20 and 30% of the applied Cd was mobile in the acidic soil and the subsurface layer of the alkaline soil with 1.2% CaCO3, respectively; 3) for a short Cu pulse, the recoveries were \u3c1 and 11% for alkaline and acidic soils, respectively, whereas, for the long Cu pulse, the recoveries ranged from 27 to 85% for the studied soils; 4) tin was highly sorbed in acidic soils where more than 99% of applied Sn was retained in the acidic soils columns; 5) the presence of Sn in solution reduced Pb retention in soils since the Pb recovery in the effluent solution ranged from 37.4 to 96.4%; and 6) the multireaction approach was capable of describing heavy metals retention and transport in soil columns. Moreover, a field study of the spatial distributions and the accumulation of Pb, Cd, Cu, and Ni among soil depth as consequence of irrigation with domestic wastewater were studied. The results of this research showed that Pb, Cu, and Ni had high affinity for retention in the surface soil layer whereas Cd results showed homogeneous distribution within soil depth. The impact of time scale effect on accumulation and spatial distribution of heavy metals indicated the urgent need for remediation and rational management