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 is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

Editor Associate Editors H. Joseph Newton Christopher F. Baum, Boston College Department of Statistics Nicholas J. Cox, University of Durham Texas A & M University Joanne M. Garrett, University of North Carolina College Station, Texas 77843 Marcello Pagano, Harvard School of Public Health 979-845-3142 J. Patrick Royston, UK Medical Research Council 979-845-3142 Jeroen Weesie, Utrecht University...

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute alg...

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to com...

In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes conjecture for a totally disconnected group is isomorphic to cosheaf homology. Moreover, it is shown that our transfo...

Abstract. Let X1, X2, . . . be a sequence of independent and identically distributed random variables, and put Sn = X1 + · · ·+ Xn. Under some conditions on the positive sequence τn and the positive increasing sequence an, we give necessary and sufficient conditions for the convergence of ∑ ∞ n=1 τnP (|Sn| ≥ εan) for all ε > 0, generalizing Baum and Katz’s (1965) generalization of the Hsu-Robbi...

For a large class of word hyperbolic groups Γ the cross product C∗-algebras C(∂Γ)⋊Γ, where ∂Γ denotes the Gromov boundary of Γ satisfy Poincaré duality in K-theory. This class strictly contains fundamental groups of compact, negatively curved manifolds. We discuss the general notion of Poincaré duality for C∗-algebras, construct the fundamental classes for the aforementioned algebras, and prove...

In this lecture, we will address problems 3 and 4. First, continuing from the previous lecture, we will view BaumWelch Re-estimation as an instance of the Expectation-Maximization (EM) algorithm and prove why the EM algorithm maximizes data likelihood. Then, we will proceed to discuss discriminative training under the maximum mutual information estimation (MMIE) framework. Specifically, we will...

The standard method for training Hidden Markov Models optimizes a point estimate of the model parameters. This estimate, which can be viewed as the maximum of a posterior probability density over the model parameters, may be susceptible to over-tting, and contains no indication of parameter uncertainty. Also, this maximummay be unrepresentative of the posterior probability distribution. In this...

Hidden Markov model (HMM) as a sequential classifier has important applications in speech and language processing [Rab89] [JM08] and biological sequence analysis [Kro98]. In this project, we analysis the parallelism in the three algorithms for HMM training and classification, i.e. forward algorithm, Viterbi algorithm, and Baum-Welch algorithm, for graphical processing units (GPU). Based on the ...