Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Large Deviations and Branching Processes

These lecture notes are devoted to present several uses of Large Deviation asymptotics in Branching Processes.

Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes

2000 Mathematics Subject Classification: 60J27.

Model Mining and Efficient Verification of Software Product Lines

Software product line modeling aims at capturing a set of software products in an economic yet meaningful way. We introduce a class of variability models that capture the sharing between the software artifacts forming the products of a software product line (SPL) in a hierarchical fashion, in terms of commonalities and orthogonalities. Such models are useful when analyzing and verifying all products of an SPL, since they provide a scheme for divide-and-conquer-style decomposition of the analysis or verification problem at hand. We define an abstract class of SPLs for which variability models can be constructed that are optimal w.r.t. the chosen representation of sharing. We show how the constructed models can be fed into a previously developed algorithmic technique for compositional verification of control-flow temporal safety properties, so that the properties to be verified are iteratively decomposed into simpler ones over orthogonal parts of the SPL, and are not re-verified over the shared parts. We provide tool support for our technique, and evaluate our tool on a small but realistic SPL of cash desks.

Feature Extraction for Classification in the Data Mining Process

Dimensionality reduction is a very important step in the data mining process. In this paper, we consider feature extraction for classification tasks as a technique to overcome problems occurring because of “the curse of dimensionality”. Three different eigenvector-based feature extraction approaches are discussed and three different kinds of applications with respect to classification tasks are considered. The summary of obtained results concerning the accuracy of classification schemes is presented with the conclusion about the search for the most appropriate feature extraction method. The problem how to discover knowledge needed to integrate the feature extraction and classification processes is stated. A decision support system to aid in the integration of the feature extraction and classification processes is proposed. The goals and requirements set for the decision support system and its basic structure are defined. The means of knowledge acquisition needed to build up the proposed system are considered.

A Statistical Approach for Multilingual Document Clustering and Topic Extraction from Clusters

2000 Mathematics Subject Classification: 62H30