A Web Aggregation Approach for Distributed Randomized PageRank Algorithms

The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are treated as agents computing their own PageRank by communicating with linked pages. This paper builds upon this approach to reduce the computation and communication loads for the algorithms. In particular, we develop a method to systematically aggregate the web pages into groups by exploiting the sparsity inherent in the web. For each group, an aggregated PageRank value is computed, which can then be distributed among the group members. We provide a distributed update scheme for the aggregated PageRank along with an analysis on its convergence properties. The method is especially motivated by results on singular perturbation techniques for large-scale Markov chains and multi-agent consensus.Comment: To appear in the IEEE Transactions on Automatic Control, 201

Fermion localization on thick branes

We consider chiral fermion confinement in scalar thick branes, which are known to localize gravity, coupled through a Yukawa term. The conditions for the confinement and their behavior in the thin-wall limit are found for various different BPS branes, including double walls and branes interpolating between different AdS_5 spacetimes. We show that only one massless chiral mode is localized in all these walls, whenever the wall thickness is keep finite. We also show that, independently of wall's thickness, chiral fermionic modes cannot be localized in dS_4 walls embedded in a M_5 spacetime. Finally, massive fermions in double wall spacetimes are also investigated. We find that, besides the massless chiral mode localization, these double walls support quasi-localized massive modes of both chiralities.Comment: 8 pages, 3 figure