Eminence Grise Coalitions: On the Shaping of Public Opinion

We consider a network of evolving opinions. It includes multiple individuals with first-order opinion dynamics defined in continuous time and evolving based on a general exogenously defined time-varying underlying graph. In such a network, for an arbitrary fixed initial time, a subset of individuals forms an eminence grise coalition, abbreviated as EGC, if the individuals in that subset are capable of leading the entire network to agreeing on any desired opinion, through a cooperative choice of their own initial opinions. In this endeavor, the coalition members are assumed to have access to full profile of the underlying graph of the network as well as the initial opinions of all other individuals. While the complete coalition of individuals always qualifies as an EGC, we establish the existence of a minimum size EGC for an arbitrary time-varying network; also, we develop a non-trivial set of upper and lower bounds on that size. As a result, we show that, even when the underlying graph does not guarantee convergence to a global or multiple consensus, a generally restricted coalition of agents can steer public opinion towards a desired global consensus without affecting any of the predefined graph interactions, provided they can cooperatively adjust their own initial opinions. Geometric insights into the structure of EGC's are given. The results are also extended to the discrete time case where the relation with Decomposition-Separation Theorem is also made explicit.Comment: 35 page

Spectral Sequence Motif Discovery

Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big datasets produced by new high-throughput sequencing technologies. Most existing algorithms are computationally demanding and often cannot support the large size of new experimental data. We present a new motif discovery algorithm that is built on a recent machine learning technique, referred to as Method of Moments. Based on spectral decompositions, this method is robust under model misspecification and is not prone to locally optimal solutions. We obtain an algorithm that is extremely fast and designed for the analysis of big sequencing data. In a few minutes, we can process datasets of hundreds of thousand sequences and extract motif profiles that match those computed by various state-of-the-art algorithms.Comment: 20 pages, 3 figures, 1 tabl

Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs

The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field. We consider linear distributed estimators whose structure combines the information \emph{flow} among sensors (the \emph{consensus} term resulting from the local gossiping exchange among sensors when they are able to communicate) and the information \emph{gathering} measured by the sensors (the \emph{sensing} or \emph{innovations} term.) This leads to mixed time scale algorithms--one time scale associated with the consensus and the other with the innovations. The paper establishes a distributed observability condition (global observability plus mean connectedness) under which the distributed estimates are consistent and asymptotically normal. We introduce the distributed notion equivalent to the (centralized) Fisher information rate, which is a bound on the mean square error reduction rate of any distributed estimator; we show that under the appropriate modeling and structural network communication conditions (gossip protocol) the distributed gossip estimator attains this distributed Fisher information rate, asymptotically achieving the performance of the optimal centralized estimator. Finally, we study the behavior of the distributed gossip estimator when the measurements fade (noise variance grows) with time; in particular, we consider the maximum rate at which the noise variance can grow and still the distributed estimator being consistent, by showing that, as long as the centralized estimator is consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page