It is well known that there is a one-to-one correspondence between the entropy vector of a collection of n random variables and a certain group-characterizable vector obtained from a finite group and n of its subgroups [1]. However, if one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al [2] that lin...

In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear spaces are also obtained.

We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.

Discrete versions of Ostrowski’s inequality for vectors in normed linear spaces are given.

We provide a deterministic construction of the sparse JohnsonLindenstrauss transform of Kane & Nelson (J.ACM 2014) which runs, under a mild restriction, in the time necessary to apply the sparse embedding matrix to the input vectors. Specifically, given a set of n vectors in R and target error ε, we give a deterministic algorithm to compute a {−1, 0, 1} embedding matrix of rank O((lnn)/ε) with ...

A FAMILY of inequalities concerning inner products of vectors and functions began with Cauchy. The extensions and generalizations later led to the inequalities of Schwarz, Minkowski and Holder. The well known Holder inequality involves the inner product of vectors measured by Minkowski norms. In this paper, another step of extension is taken so that a Holder type inequality may apply to general...

(8) we have that the ghost attractor G(c) is given by G(c) i = X p x x c i : (19) The region R(c) corresponding to c consists of all aaerent input vectors a such that g(a i ? X j z j) = c i ; (20) where g the Heavyside step function. Substituting (19) into (20) we see that for G(c) to lie in the region R(c) we must have X p x x c i ? X k z k > 0 (21) if c i = 1 and the opposite inequality if c ...