Motivation: The reconstruction of gene networks from gene expression microar-rays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance...

For a sequence of independent and identically distributed random vectors , we consider the conditional ordering of this random vectors with respect to the magnitudes of , where N is a p− variate continuous function defined on the support set of X and satisfying certain regularity conditions....

A previously proved theorem gives sufficient conditions for an estimator of the false discovery rate (FDR) to conservatively converge to the FDR with probability 1 as the number of hypothesis tests increases, even for small sample sizes. It does not follow that several thousand tests ensure that...

A Hilbert module over a planar algebra is essentially a Hilbert module over a eanonieally defined algebra spanned by the annular tangles in It follows that any planar algebra containing is a module over and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar...

A fundamental, educational exposition of a nonstandard number theory based upon perfect symmetry (in contrast to broken symmetry) modelled throughout arithmetic, algebra, analytic geometry, analytic trigonometry and calculus

Let () be a polynomial of degree 4 with four distinct real roots . Let be the critical points of , and define the ratios , = 1, 2, 3. For notational convenience, let = , = , and = . () is called the ratio vector of . We prove necessary and sufficient conditions for () to be a ratio vector...

Recently braid group cryptosystems have been invented these are the AAG and KLCHKP cryptosystems. We present an algebraic key establisment protocol based on the difficulty of solving equations over algebraic structures. In (our group theoretic illustration of) our protocol its security is based...