Spectral geometries on a compact metric space

Tchebycheff Approximation in a Compact Metric Space

On the Conformal Gauge of a Compact Metric Space

In this article we study the Ahlfors regular conformal gauge of a compact metric space (X, d), and its conformal dimension dimAR(X, d). Using a sequence of finite coverings of (X, d), we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gaug...

Dynamical distance as a semi-metric on nuclear conguration space

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.

Quantum isometry group of a compact metric space

We give a definition of isometric action of a compact quantum group on a compact metric space, generalizing the definition given by Banica for finite metric spaces, and prove the existence of the universal object in the category of compact quantum groups acting isometrically on a given compact metric space.

A compact space decomposition for effective metric indexing

The metric space model abstracts many proximity search problems, from nearest-neighbor classifiers to textual and multimedia information retrieval. In this context, an index is a data structure that speeds up proximity queries. However, indexes lose their efficiency as the intrinsic data dimensionality increases. In this paper we present a simple index called list of clusters (LC), which is bas...