The doubling constant of a metric space (X, d) is the smallest value/spl lambda/such that
every ball in X can be covered by/spl lambda/balls of half the radius. The doubling …

We prove that every n-point metric space of negative type (in particular, every n-point subset
of L1) embeds into a Euclidean space with distortion O (√ log n log log n), a result which is …

We survey recent advances in analysis and geometry, where first order differential analysis
has been extended beyond its classical smooth settings. Such studies have applications to …

Metric Embedding plays an important role in a vast range of application areas such as
computer vision, computational biology, machine learning, networking, statistics, and …

We devise a new embedding technique, which we call measured descent, based on
decomposing a metric space locally, at varying speeds, according to the density of some …

In this article we introduce the notion of nearest-neighbor-preserving embeddings. These
are randomized embeddings between two metric spaces which preserve the (approximate) …

We present geometric conditions on a metric space (Y, dY) ensuring that, almost surely, any
isometric action on Y by Gromov's expander-based random group has a common fixed …

Given k∊ ℕ, the k'th discrete Heisenberg group, denoted ℍ ℤ 2 k+ 1, is the group generated
by the elements a 1, b 1,…, ak, bk, c, subject to the commutator relations a 1, b 1=···= ak, bk …

A metric space X has Markov-type 2 if for any reversible finite-state Markov chain {Zt}(with Z0
chosen according to the stationary distribution) and any map f from the state space to X, the …

This survey article considers methods and algorithms for fast estimation of data
distance/similarity measures from formed real-valued vectors of small dimension. The …