These lectures are devoted to a description of anomalies in quantum field theory from the point of view of noncommutative geometry and topology. We will in particular introduce the basic methods of cyclic cohomology and explain the noncommutative counterparts of the Atiyah-Singer index theorem.

The main result of this paper is a version of the Atiyah-Singer index theorem for Dirac-type operators on (noncompact) complete Riemannian manifolds. The statement of the theorem involves a novel "cohomology" theory for such manifolds. This theory, called exotic cohomology, depends on the structure at infinity of a space; more precisely, it depends on the way that large bounded sets fit togethe...

Let M be a smooth closed spin manifold. The higher index theorem computes the pairing between the group cohomology of π1(M) and the Chern character of the “higher” index of a Dirac-type operator on M. Using superconnections, we give a heat equation proof of this theorem on the level of differential forms on a noncommutative base space. As a consequence, we obtain a new proof of the Novikov conj...

Near duplicate documents and their detection are studied to identify info items that convey the same (or very similar) content, possibly surrounded by diverse sets of side information like metadata, advertisements, timestamps, web presentations and navigation supports, and so on. Identification of near duplicate information allows the implementation of selection policies aiming to optimize an i...

Mapping by admixture linkage disequilibrium (MALD) is an economical and powerful approach for the identification of genomic regions harboring disease susceptibility genes in recently admixed populations. We develop an information-theory-based measure, called expected mutual information (EMI), which computes the impact of a set of markers on the ability to infer ancestry at each chromosomal loca...