a consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable hilbert space. it is proved, through a kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the hilbert space. as an application, this will naturally accomplish the work of kante...

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

In this paper, we investigate the efficacy of subdomain testing and random testing using the expected number of failures detected (the E-measure) as a measure of effectiveness. Simple as it is, the E-measure does provide a great deal of useful information about the fault-detecting capability of testing strategies. With the E-measure, we obtain new characterizations of subdomain testing, includi...

Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real Lévy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the hitting probabilities of points and descr...

Producing stable feature rankings is critical in many areas, such as in bioinformatics where the robustness of a list of ranked genes is crucial to interpretation by a domain expert. In this paper, we study Spearman’s rho as a measure of stability to training data perturbations not just as a heuristic, but here proving that it is the natural measure of stability when using mean rank aggregation...

The method of stable random projections [39, 41] is popular for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the lα distance between a pair of streams, for any 0 < α ≤ 2. [18] and [20] applied stable random pro...