MOTIVATION The analysis of differentially expressed gene sets became a routine in the analyses of gene expression data. There is a multitude of tests available, ranging from aggregation tests that summarize gene-level statistics for a gene set to true multivariate tests, accounting for intergene correlations. Most of them detect complex departures from the null hypothesis but when the null hypo...

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.

This is a preliminary sketch of several new ideas and questions concerning Aronszajn-null sets. 1. Motivation Aronszajn null sets were introduced by Aronszajn in the context of studying a.e. differentiability of Lipschitz mappings between Banach spaces. Christensen, Phelps and Mankiewicz studied the same problem independently and used Haar null, Gaussian null and cube null sets, respectively. S...

The repeated testing of a null univariate hypothesis in each of many sites (either regions of interest or voxels) is a common approach to the statistical analysis of brain functional images. Procedures, such as the Bonferroni, are available to maintain the Type I error of the set of tests at a specified level. An initial assumption of these methods is a "global null hypothesis," i.e., the stati...

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...

We show that if $M$ is a sub-Riemannian manifold and $N$ Carnot group such the nilpotentization of at almost every point isomorphic to $N$, then there are subsets positive measure embed into by bilipschitz maps. Furthermore, countably $N$--rectifiable, i.e., all except for null set can be covered many

A vertex v of a graph G is domination null in G if g(v) = 0 for every minimum fractional dominating function g on G. Packing nullity is defined analogously, with reference to fractional closed neighborhood packings. We give classes of examples and examine graph operations that produce or preserve such vertices; several open problems are posed.

While we agree that the base-generated phonologically null nominal known as PRO has Case, we dispute the recent contention of Chomsky & Lasnik (1995) and Martin(2001) that there is a special Null Case, assigned in English by certain instances of infinitival to. We show that, contrary to Martin’s claims, there is no consistent distinction between instances of to that license PRO, and instances o...

The main result of this paper is the following. Given countably many multivariate polynomials with rational coefficients and maximum degree d, we construct a compact set E ⊂ Rn of Hausdorff dimension n/d which does not contain finite point configurations corresponding to the zero sets of the given polynomials. Given a set E ⊂ Rn, we study the angles determined by three points of E. The main res...