Active influence in dynamical models of structural balance in social networks

We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social psychology called structural balance, the negative links play a key role in both the structure and dynamics of the network. Recent research has shown that in a nonlinear dynamical system modeling the time evolution of "friendliness levels" in the network, two opposing factions emerge from almost any initial condition. Here we study active external influence in this dynamical model and show that any agent in the network can achieve any desired structurally balanced state from any initial condition by perturbing its own local friendliness levels. Based on this result, we also introduce a new network centrality measure for signed networks. The results are illustrated in an international relations network using United Nations voting record data from 1946 to 2008 to estimate friendliness levels amongst various countries.Comment: 7 pages, 3 figures, to appear in Europhysics Letters (http://www.epletters.net

Accelerated Gradient Methods for Networked Optimization

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed-ups can be obtained over the standard gradient method. Furthermore, we quantify how the performance of the gradient method and its accelerated counterpart are affected by uncertainty in the problem data, and conclude that in most cases our proposed method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraints, distributed averaging, and Internet congestion control. In all cases, we demonstrate that our algorithm converges more rapidly than alternative algorithms reported in the literature

Promoting Truthful Behaviour in Participatory-Sensing Mechanisms

In this paper, the interplay between a class of nonlinear estimators and strategic sensors is studied in several participatory-sensing scenarios. It is shown that for the class of estimators, if the strategic sensors have access to noiseless measurements of the to-be-estimated-variable, truth-telling is an equilibrium of the game that models the interplay between the sensors and the estimator. Furthermore, performance of the proposed estimators is examined in the case that the strategic sensors form coalitions and in the presence of noise.Comment: IEEE Signal Processing Letters, In Pres

Corporate Risk-Taking and the Decline of Personal Blame

The ability to maintain state awareness in the face of unexpected and unmodeled errors and threats is a defining feature of a resilient control system. Therefore, in this paper, we study the problem of distributed fault detection and isolation (FDI) in large networked systems with uncertain system models. The linear networked system is composed of interconnected subsystems and may be represented as a graph. The subsystems are represented by nodes, while the edges correspond to the interconnections between subsystems. Considering faults that may occur on the interconnections and subsystems, as our first contribution, we propose a distributed scheme to jointly detect and isolate faults occurring in nodes and edges of the system. As our second contribution, we analyze the behavior of the proposed scheme under model uncertainties caused by the addition or removal of edges. Additionally, we propose a novel distributed FDI scheme based on local models and measurements that is resilient to changes outside of the local subsystem and achieves FDI. Our third contribution addresses the complexity reduction of the distributed FDI method, by characterizing the minimum amount of model information and measurements needed to achieve FDI and by reducing the number of monitoring nodes. The proposed methods can be fused to design a scalable and resilient distributed FDI architecture that achieves local FDI despite unknown changes outside the local subsystem. The proposed approach is illustrated by numerical experiments on the IEEE 118-bus power network benchmark.QC 20141114</p