A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established in [1] in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution resulting in an ‘equivariant resolution structure’. Here, equivariant K-theory and t...

Note: The background and methods related to this project and a comparison of all Australian jurisdictions, along with a short summary for the Federal Government, are contained in the following journal article: Newman L, F Baum & E Harris (2006), ‘Federal, State and Territory government responses to health inequities and the social determinants of health in Australia’, Health Promotion Journal o...

This notion was first introduced and discussed by Hsu and Robbins in [3]. They proved that the sequence of arithmetic means of independent, identically distributed (i.i.d.) random variables converges completely to the expected value of summands, provided the variance is finite. The result proved by Hsu and Robbins [3] was further generalized and extended by many authors (see e.g. [1, 2, 4]). Ka...

We present the concept of a scaled random segmental model, which aims to overcome the modeling problem created by the fact that segment realizations of the same phonetic unit di er in length. In the scaled model the variance of the random mean trajectory is inversely proportional to the segment length. The scaled model enables a Baum-Welch type parameter reestimation, unlike the previously sugg...

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. We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, one implies the other, and, after inverting 2, the same is true for the injectivity or surjectivity part alone, ...

The computation of the equivariant K-theory K∗ G(V ) of the Thom space of a real vector bundle has been done successfully only under some spinoriality conditions [1], thanks to a clever use of the Atiyah–Singer index theorem (even if G is a finite group). One purpose of this paper is to fill this gap, at least for real vector spaces (considered as vector bundles over a point). For this purpose,...

In light of the complexity of individual neurons and the neurotransmission process, it should come as no surprise that the connections and structures formed by the neurons are complicated. Because each neuron can be connected to 80,000 other neurons, the total number of possible connections is astonishing. For instance, estimates of the number of neural connections within the brain fall in the ...

This paper explores the use of Hidden Markov Models (HMMs) for the recognition of head gestures. A gesture corresponds to a particular pattern of head movement. The facial plane is tracked using a parameterized model and the temporal sequence of three image rotation parameters are used to describe four gestures. A dynamic vector quantization scheme was implemented to transform the parameters in...