Information metric and Euclidean Janus correspondence

Metric and Euclidean TSP

Metric Transforms and Euclidean Embeddings

It is proved that if 0 < c < 0.72/« then for any «-point metric space (X, d), the metric space (X,dc) is isometrically embeddable into a Euclidean space. For 6-point metric space, c = j log2 | is the largest exponent that guarantees the existence of isometric embeddings into a Euclidean space. Such largest exponent is also determined for all «-point graphs with "truncated distance".

Euclidean vs Graph Metric

The theory of sparse graph limits concerns itself with versions of local convergence and global convergence, see e.g. [41]. Informally, in local convergence we look at a large neighborhood around a random uniformly chosen vertex in a graph and in global convergence we observe the whole graph from afar. In this note rather than surveying the general theory we will consider some concrete examples...

Correspondence Principle between Spherical and Euclidean Wavelets

Wavelets on the sphere are re-introduced and further developed independently of the original group theoretic formalism, in an alternative and completely equivalent approach, as inverse stereographic projection of wavelets on the plane. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB) anisotropies on the sky. In addition to off...

Metric Derivations on Euclidean and Non-euclidean Spaces

As introduced by Weaver, (metric) derivations extend the notion of differential operators on Euclidean spaces and provide a linear differentiation theory that is well-defined on all metric spaces with Borel measures. The main result of this paper is a rigidity theorem for measures on Euclidean spaces that support a maximal number of derivations. The proof relies substantially on ideas from geom...