The 2017 CLEF eHeath Task2 requires to rank the retrieval results given by medical database. The purpose is to reduce efforts that experts devote to finding indeed relevant documents. We utilize a customized Learning-to-Rank model to re-rank the retrieval result. Additionally, we adopt word2vec to represent queries and documents and compute the relevant score by cosine distance. We find that th...

Feature screening approaches are effective in selecting active features from data with ultrahigh dimensionality and increasing complexity; however, the majority of existing feature either restricted to a univariate response or rely on some distribution model assumptions. In this article, we propose novel sure independence approach based multivariate rank distance correlation (MrDc-SIS). The MrD...

Rank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowadays...

Let G and G be simple Lie groups of equal real rank and real rank at least 2. Let Γ < G and Λ < G be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of Γ into Λ is at bounded distance from a homomorphism. For example, any quasiisometric embedding of SL(n,Z) into SL(n,Z[i]) is at bounded distance from a homomorphism. We also include a discussion of ...

The present work proposes tests for reduced rank in multivariate regression coefficient matrices, under rather general conditions. A heuristic approach is to first estimate the regressions via standard methods, then compare the coefficient matrix rows (or columns) to assess their redundancy. A formal version of this approach utilizes the distance between an unrestricted coefficient matrix estim...

8. Introduction Critical points of distance functions Toponogov's theorem; first application:a Background on finiteness theorems Homotopy Finiteness Appendix. Some volume estimates Betti numbers and rank Appendix: The generalized Mayer-Vietoris estimate Rank, curvature and diameter Ricci curvature, volume and the Laplacian Appendix. The maximum principle Ricci curvature, diameter growth and fin...

R ank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowaday...

In this article, several theorems on perturbations of a complex matrix by a matrix of a given rank are presented. These theorems may be divided into two groups. The first group is about spectral properties of a matrix under such perturbations; the second is about almost-near relations with respect to the rank distance.