We consider lower bounding the maximum achievable rate of a differential unitary spacetime transmission subject to a prescribed performance. We characterize the performance using a suitably defined distance between two unitary matrices, which was previously obtained through pairwise error probability analysis. Considering the set of all unitary or orthogonal matrices as a compact manifold with ...

We present a family of adaptive pairwise tournaments which are provably robust against large error fractions when used to determine the largest element in a set. These tournaments use nk pairwise comparisons but have only O(k + log n) depth where n is the number of players and k is a robustness parameter (for reasonable values of n and k). We show how these tournaments can be used to prove mult...

We describe a new technique for conducting “partitioning arguments”. Partitioning arguments are a popular way to prove the security of a cryptographic scheme. For instance, to prove the security of a signature scheme, a partitioning argument could divide the set of messages into “signable” messages for which a signature can be simulated during the proof, and “unsignable” ones for which any sign...

Many exploratory microarray data analysis tools such as gene clustering and relevance networks rely on detecting pairwise gene co-expression. Traditional screening of pairwise co-expression either controls biological significance or statistical significance, but not both. The former approach does not provide stochastic error control, and the later approach screens many co-expressions with exces...

Item recommendation from implicit, positive only feedback is an emerging setup in collaborative filtering in which only one class examples are observed. In this paper, we propose a novel method, called User Graph regularized Pairwise Matrix Factorization (UGPMF), to seamlessly integrate user information into pairwise matrix factorization procedure. Due to the use of the available information on...

In the present paper, we will investigate weak laws of large numbers for weighted pairwise NQD random variables with infinite mean. The almost sure upper and lower bounds for a particular normalized weighted sum of pairwise NQD nonnegative random variables are established also.

We will say that a 3-manifold is almost compact if it can be obtained from a compact manifold N by removing a closed subset of dN. Then Theorem 1 is equivalent to the assertion that the universal covering of M is almost compact. A natural way to attempt to generalize Theorem 1 is to show that other coverings of M are almost compact. It was conjectured by Simon [Si] that if M is any compact P-ir...

A locally compact topological group G is called an (H) group if G has a maximal compact normal subgroup with Lie factor. In this note, we study the problem when a locally compact group is an (H) group. Let G be a locally compact Hausdorff topological group. Let G0 be the identity component of G. If G/G0 is compact, then we say that G is almost connected. The structure of almost connected locall...

In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...

Geneticists and twin researchers have long debated the relative merits of two alternative measures of twin concordance: the pairwise and probandwise concordance rates. The results of this debate are now quite clear, for almost every application the probandwise rate is preferred over the pairwise rate. In a recent review of schizophrenia twin studies, however, Torrey (1992) chose to analyze pair...