symmetric second rank tensor

symmetric second rank tensor fields in the plane.

In the original PageRank algorithm for improving the ranking of search-query results, a single PageRank vector is computed, using the link structure of the Web, to capture the relative "importance" of Web pages, independent of any particular search query. To yield more accurate search

We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data

We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building meta-search engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations

. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads

The applications of eigentheory to many branches of mathematical physics (e.g., rotational dynamics, continuum mechanics) is an unquestionable fact. This work expands the conventional methodology by introducing equations to compute the covariance matrices of eigenvalues and eigenvectors of second-rank

in the tandem mass spectrum. In general, a difference greater than 0.1 between the normalized cross-correlation functions of the first- and second-ranked search results indicates a successfol match between sequence and spectrum. Searches of species-specific protein databases with tandem mass spectra acquired

search strategies, each of which is a query expansion for a given domain. For this task, we compare the performance of RankBoost to the individual search strategies. The second experiment is a collaborative-filtering task for making movie recommendations. Here, we present results comparing Rank

remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal