The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism μ : K•(BG)→ K•(C ∗ redG) for our class of manifolds, and then classify μ in terms of the ideals in the ring of integers of a quadratic number field K. Next, ...

A doctor has a duty to give his patient what he believes to be the best treatment. An ethical prerequisite of recommending her to enter a randomised clinical trial (RCT), in which his patient will be randomly allotted to one of two or more treatments, is, as Michael Baum in his chapter stresses, that he is ignorant about their relative efficacy and, hence, justifiably indifferent as to which sh...

We present a learning algorithm for hidden Markov models with continuous state and observation spaces. All necessary probability density functions are approximated using samples, along with density trees generated from such samples. A Monte Carlo version of Baum-Welch (EM) is employed to learn models from data, just as in regular HMM learning. Regularization during learning is obtained using an...

There are several data compression Techniques available which are used for Efficient transmission and storage of the data With less memory space. In this paper, we have Proposed a two stage data compression Algorithm that is OLZWH which uses the Optimality of LempelZiv-Welch (OLZW) and Adaptive Huffman Coding. With this proposed Algorithm, the data Compression ratios are Compared with existing ...

In this paper we describe an unsupervised learning algorithm for automatically training a rule-based part of speech tagger without using a manually tagged corpus. We compare this algorithm to the Baum-Welch algorithm, used for unsupervised training of stochastic taggers. Next, we show a method for combining unsupervised and supervised rule-based training algorithms to create a highly accurate t...

This paper presents a new method of feature dimension reduction in hidden Markov modeling (HMM) for speech recognition. The key idea is to apply reduced rank maximum likelihood estimation in the M-step of the usual Baum-Welch algorithm for estimating HMM parameters such that the estimates of the Gaussian distribution parameters are restricted in a sub-space of reduced dimensionality. There are ...

The use of segment-based features and segmentation networks in a segment-based speech recognizer complicates the probabilistic modeling because it alters the sample space of all possible segmentation paths and the feature observation space. This paper describes a novel Baum-Welch training algorithm for segment-based speech recognition which addresses these issues by an innovative use of finite-...

MOTIVATION The Expectation Maximization (EM) algorithm, in the form of the Baum-Welch algorithm (for hidden Markov models) or the Inside-Outside algorithm (for stochastic context-free grammars), is a powerful way to estimate the parameters of stochastic grammars for biological sequence analysis. To use this algorithm for multiple-sequence evolutionary modelling, it would be useful to apply the ...