Many years ago, longer than I may care to admit, I had to take my Board Exam in Pulmonary Medicine. I decided to prepare for the exam by reading a reference textbook cover-to-cover. Because Dr Gerald Baum had been one of my favorite teachers while I was a medical student in Cleveland, I naturally felt inclined towards an earlier edition of Baum’s Textbook of Pulmonary Medicine. It was a most fo...

(Joint work with Alexandru Chirvasitu.) The Borsuk-Ulam theorem in algebraic topology indicates restrictions for equivariant maps between spheres; in particular, there is no odd map from a sphere to another sphere of lower dimension. This idea may be generalized greatly in both the topological and operator algebraic settings for actions of compact (quantum) groups, leading to the the noncommuta...

We report evidence from a dataset of federal district judges from 2001 to 2002 that district judges adjust their opinion-writing practices to minimize their workload while maximizing their reputation and chance for elevation to a higher court. District judges in circuits with politically uniform circuit judges are better able to predict what opinions will get affirmed by the circuit court, lead...

For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra we construct a canonical K-homology class, which induces a Poincaré duality map K∗(C(∂Γ)⋊Γ) → K (C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case of Γ = F2 the free group on two generators. We point out a direct connection between our constructions and the ...

These extended notes are based on a series of six lectures presented at the summer school “Cohomology of groups and algebraic K-theory” which took place in Hangzhou, China from July 1 until July 12 in 2007. They give an introduction to the Farrell-Jones and the Baum-Connes Conjecture.

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture and Atiyah’s L-index theorem implies that the range consists of the integers. If the group is not torsion free, Baum and Connes conjecture ...

Discriminative learning techniques for sequential data have proven to be more effective than generative models for named entity recognition, information extraction, and other tasks of discrimination. However, semi-supervised learning mechanisms that utilize inexpensive unlabeled sequences in addition to few labeled sequences – such as the Baum-Welch algorithm – are available only for generative...

In this work we compare two parameter optimization techniques for discriminative training using the MMI criterion: the extended Baum-Welch (EBW) algorithm and the generalized probabilistic descent (GPD) method. Using Gaussian emission densities we found special expressions for the step sizes in GPD, leading to reestimation formula very similar to those derived for the EBW algorithm. Results wer...

Spectral methods propose new and elegant solutions in probabilistic grammatical inference. We propose two ways to improve them. We show how a linear representation, or equivalently a weighted automata, output by the spectral learning algorithm can be taken as an initial point for the Baum Welch algorithm, in order to increase the likelihood of the observation data. Secondly, we show how the inf...

Partially observable Markov decision processes (POMDPs) are a convenient representation for reasoning and planning in mobile robot applications. We investigate two algorithms for learning POMDPs from series of observation/action pairs by comparing their performance in fourteen synthetic worlds in conjunction with four planning algorithms. Experimental results suggest that the traditional Baum-W...