The central result of this paper is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby gener...

An extension of the Connes–Lott model is proposed. It is also within the framework of the A.Connes construction based on a generalized Dirac–Yukawa operator and the K–cycle (H,D), with H a fermionic Hilbert space. The basic algebra A which may be considered as representing the non–commutative extension, plays a less important role in our approach. This allows a new class of natural extensions. ...

We show that Connes’ embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is nonnegative whenever self-adjoint contraction matrices of the same size are substituted for the variables. These algebraic certificates involve sums of hermitia...

In this paper we discuss the design of sequential detection networks for nonparametric sequential analysis. We present a general probabilistic model for sequential detection problems where the sample size as well as the statistics of the sample can be varied. A general sequential detection network handles three decisions. First, the network decides whether to continue sampling or stop and make ...

Classical differential geometry can be encoded in spectral data, such as Connes’ spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes’ non-commutative spin geometry encompassing noncommutative Riemannian, symplectic, complex-Hermitian and (Hyper-) Kähler geometry...

This is a survey of the relationship between C *-algebraic deformation quan-tization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We first explain how C *-algebraic versions of deformation quantization are related to the bivariant E-theory of Connes and Higson. With this background, we review how Weyl–Moyal quantization may be described using the ta...

We are interested in making sense of an integral over a singular space, for example the quotient of the torus T 2 by the lines of irrational slope α / ∈ Q. More generally, we would like to study the quotient space of the global unstable manifolds for a hyperbolic dynamical system. In this chapter we present an “easy” version of Connes’ noncommutative integration theory. We start by studying int...

We give a natural and complete description of Ecalle’s mould–comould formalism within a Hopf–algebraic framework. The arborification transform thus appears as a factorization of characters, involving the shuffle or quasishuffle Hopf algebras, thanks to a universal property satisfied by Connes–Kreimer Hopf algebra. We give a straightforward characterization of the fundamental process of homogene...

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C∗ -algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the re...

Activity in Sequential Logic Circuits Jos e Monteiro, Srinivas Devadas Department of EECS, MIT, Cambridge Bill Lin IMEC, Leuven Abstract We describe a computationally e cient scheme to approximate average switching activity in sequential circuits which requires the solution of a non-linear system of equations of size N , where the variables correspond to state line probabilities. We show that t...