This paper proves the Baum–Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties slowly varying functions and de Bruijn conjugates, uses techniques developed by Rio (1995) to avoid using maximal type inequalities.

Lorenz Fries: Chronik der Bischöfe von Würzburg 742-1495, hg. Ulrich Wagner und Walter Ziegler. Bd. V: Wappen Register, bearb. Hans-Peter Baum, Rainer Leng, Renate Schindler Florian Sepp mit einem Beitrag Karl Borchardt (Fontes Herbipolenses. Editionen Studien aus dem Stadtarchiv Würzburg), (Schöningh) 2004, 396 S., zahlr. farbige Abb.

In this paper we introduce an improved binary correlation matrix memory (CMM) with better storage capacity when storing sparse fixed weight codes generated with the algorithm of Baum et al. [3]. We outline associative memory, and describe the binary correlation matrix memory— a specific example of a distributed associative memory. The importance of the representation used in a CMM for input and...

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse Baum-Connes assembly map is injective; the coarse Baum-Connes assembly map is not surjective; the maximal coarse BaumConnes assembly map is an isomorphism. These res...

This paper reports the results of a system that performs network anomaly detection through the use of Hidden Markov Models (HMMs). The HMMs used to detect anomalies are designed and trained using Genetic Algorithms (GAs). The use of GAs helps automating the use of HMMs, by liberating users from the need of statistical knowledge, assumed by software that trains HMMs from data. The number of stat...

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an “addition formula” for the Dirac operator on the circle and for the Dolbeault operator on closed surfaces. Two proofs are provided, one using topology and the other one, surprisingly involved, sti...

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...

Senones were introduced to share Hidden Markov model (HMM) parameters at a sub-phonetic level in [3] and decision trees were incorporated to predict unseen phonetic contexts in [4]. In this paper, we will describe two applications of the senonic decision tree in (1) dynamically downsizing a speech recognition system for small platforms and in (2) sharing the Gaussian covariances of continuous d...