We give a superconnection proof of Connes’ index theorem for proper cocompact actions of étale groupoids. This includes Connes’ general foliation index theorem for foliations with Hausdor¤ holonomy groupoid.

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequenti...

Hypersonic vehicle has gained increasing attention due to its high cruise speed and long voyage. In this paper, an enhanced Sequential Approximate Optimization method is proposed for aerodynamic optimization of a hypersonic vehicle. method, constrained design experiment adopted generate the initial sampling set with adequate number feasible points. A field metamodel surrogate parameters distrib...

If there is a mathematician eagerly waiting for the Large Hadron Collider near Geneva to start up next year, it is Alain Connes of the Collège de France in Paris. Like many physicists, Connes hopes that the Higgs particle will show up in detectors. The Higgs is the still missing crowning piece of the so-called Standard Model--the theoretical framework that describes subatomic particles and thei...

We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic higher Chow groups and the Connes higher Chow groups of a variety are defined in the process and various properties of them are deduced from the known properti...