We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.

In this paper, we first prove a general fixed point theorem for nonlinear mappings in a Banach space. Then we prove a nonlinear mean convergence theorem of Baillons type and a weak convergence theorem of Manns type for 2-generalized nonspreading mappings in a Banach space.

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For 4 k+ 2 dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaum and Witten in dimensions 2, 6 and 10 (\cite {AW}) as special cases. In dimension 4 k+ 2, we derive anomaly cancellation formulas for index gerbes. In dimension 4 k+ 2, we obtain certain results about eta invariants, which are interesting in spectral geometry.

This paper is concerned with the problem of top- K ranking from pairwise comparisons. Given a collection of K items and a few pairwise comparisons across them, one wishes to identify the set of K items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model---the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress towards characterizing the performance (eg the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top- K ranking remains unsettled.

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