We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. In this paper we concentrate on the issues specific to the case when G is trivial, so the action reduces to the action of a Lie group G. For G simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result b...

In this paper, the problem of the automatic identification of a singer is investigated using methods known from speaker identification. Ways for using world models are presented and the usage of Cepstral Mean Subtraction (CMS) is evaluated. In order to minimize the difference due to musical style we use a novel data set, consisting of samples from greek Rembetiko music, being very similar in st...

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...

This is an introduction to the problems connecting frame theory and the Kadison-Singer Problem. 1. Overview For an extensive introduction to the aspects of frame theory needed for an understanding of the Kadison-Singer Problem we refer to the survey paper [3], which is posted in this section of the web page “The Kadison-Singer Problem”. In the following section we will just give the basic defin...

Let H be `2 (over C) and let B(H) denote the C*-algebra of all bounded operators on H. Fix an orthonormal basis (en) for H. The atomic masa corresponding to this basis is `∞; equivalently, the algebra of all operators that are diagonalized by the basis (en). The projections in `∞ are exactly the projections onto subspaces spanned by a subset of {en}. That is, P(`∞) ∼= P(N) (here P(A) denotes th...

A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...

This paper concerns a rather concrete phenomenon in abstract operator algebras. The main examples of the algebras we study are algebras of singular integral operators (pseudo-differential operators of order zero). As everyone knows, the Fredhohn index of a pseudo-differential operator depends only on its symbol and the Atiyah-Singer Index Theorem gives an explicit formula for computing the depe...

This paper presents a novel statistical singing voice conversion (SVC) technique with direct waveform modification based on the spectrum differential that can convert voice timbre of a source singer into that of a target singer without using a vocoder to generate converted singing voice waveforms. SVC makes it possible to convert singing voice characteristics of an arbitrary source singer into ...

— In this paper we consider smooth extensions of cohomology theories. In particular we construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion p : W → B and define the associated push-forward p̂! : K̂(W ) → K̂(B). We show that the push-forward has the expected properties as functoriality, compatibility with pul...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...