Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

TB-Structure : Collective Intelligence for Exploratory Keyword Search

In this paper we address an exploratory search challenge by presenting a new (structure-driven) collaborative filtering technique. The aim is to increase search effectiveness by predicting implicit seeker’s intents at an early stage of the search process. This is achieved by uncovering behavioral patterns within large datasets of preserved collective search experience. We apply a specific tree-based data structure called a TB (There-and-Back) structure for compact storage of search history in the form of merged query trails – sequences of queries approaching iteratively a seeker’s goal. The organization of TB-structures allows inferring new implicit trails for the prediction of a seeker’s intents. We used experiments to demonstrate both: the storage compactness and inference potential of the proposed structure.peerReviewe