A geometrical heuristic for drawing concept lattices

Concept lattices are used in formal concept analysis to represent data conceptually so that the original data are still recognizable. Their line diagrams should reflect the semantical relationships within the data. Up to now, no satisfactory automatic drawing programs for this task exist. The geometrical heuristic is the most successful tool for drawing concept lattices manually. It ueses a geometric representation as intermediate step between the list of upper covers and the line diagram of the lattice.

Conceptual knowledge discovery with frequent concept lattices

Knowledge discovery support environments include beside classical data analysis tools also data mining tools. For supporting both kinds of tools, a unified knowledge representation is needed. We show that concept lattices which are used as knowledge representation in Conceptual Information Systems can also be used for structuring the results of mining association rules. Vice versa, we use ideas of association rules for reducing the complexity of the visualization of Conceptual Information Systems.

Fast computation of concept lattices using data mining techniques

We present a new algorithm called TITANIC for computing concept lattices. It is based on data mining techniques for computing frequent itemsets. The algorithm is experimentally evaluated and compared with B. Ganter's Next-Closure algorithm.

Iceberg query lattices for datalog

In this paper we study two orthogonal extensions of the classical data mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed representations of frequent datalog queries. We demonstrate that iceberg query lattices provide a natural way to visualize relational association rules in a non-redundant way.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Concept exploration - a tool for creating and exploring conceptual hierarchies

Concept exploration is a knowledge acquisition tool for interactively exploring the hierarchical structure of finitely generated lattices. Applications comprise the support of knowledge engineers by constructing a type lattice for conceptual graphs, and the exploration of large formal contexts in formal concept analysis.

A contextual-logic extension of TOSCANA

The aim of this paper is to indicate how TOSCANA may be extended to allow graphical representations not only of concept lattices but also of concept graphs in the sense of Contextual Logic. The contextual-logic extension of TOSCANA requires the logical scaling of conceptual and relatioal scales for which we propose the Peircean Algebraic Logic as reconstructed by R. W. Burch. As graphical representations we recommend, besides labelled line diagrams of concept lattices and Sowa's diagrams of conceptual graphs, particular information maps for utilizing background knowledge as much as possible. Our considerations are illustrated by a small information system about the domestic flights in Austria.

Efficient data mining based on formal concept analysis

Formal Concept Analysis is an unsupervised learning technique for conceptual clustering. We introduce the notion of iceberg concept lattices and show their use in Knowledge Discovery in Databases (KDD). Iceberg lattices are designed for analyzing very large databases. In particular they serve as a condensed representation of frequent patterns as known from association rule mining. In order to show the interplay between Formal Concept Analysis and association rule mining, we discuss the algorithm TITANIC. We show that iceberg concept lattices are a starting point for computing condensed sets of association rules without loss of information, and are a visualization method for the resulting rules.

A finite state model for on-line analytical processing in triadic contexts

About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the basic ideas of OLAP, and show how they may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.

Transformationale Führung als Erfolgsfaktor des Interim Management

In der vorliegenden Arbeit wurde untersucht, wie Führung zur Bewältigung von Unternehmenskrisen und Umsetzung von Veränderungen im Kontext des Interim Management beitragen kann. Dazu wurde die Theorie transformationaler Führung um aufgabenbezogene und indirekte Führung und den Einsatz von Positionsmacht ergänzt. Damit wurden diese erfolgskritischen Führungsdimensionen erstmals in einem gemeinsamen theoretischen Rahmen verbunden und die Auswirkungen einer kombinierten Anwendung untersucht. Dieser neue Ansatz wurde als „Total Range of Leadership“ bezeichnet. In der vorliegenden Untersuchung konnten neue Erkenntnisse zum Kontext und den Erfolgsfaktoren des Interim Management sowie zu den Auswirkungen und Wirkungsmechanismen transformationaler Führung und des Total Range of Leadership gewonnen werden. Die Untersuchungsergebnisse deuten darauf hin, dass Interim Management ein hoch effektives Veränderungsinstrument ist. Als erfolgsrelevante Rahmenbedingungen wurden die Ausstattung der Interim Manager mit umfassenden Vollmachten sowie die Unterstützung durch die Auftraggeber, als wichtigster Erfolgsfaktor des Interim Management aber eindeutig die Anwendung transformationaler Führung und des Total Range of Leadership identifiziert. Die Anwendung transformationaler Führung im Rahmen des Total Range of Leadership wirkt sich positiv auf Persönlichkeit, Einstellungen, Kompetenz und Verhalten der Mitarbeiter sowie Organisationsstruktur, Unternehmenskultur, organisationale Lernfähigkeit und finanziellen und marktbezogenen Erfolg von Unternehmens aus. Dabei erzielt transformationale Führung die bei Weitem größte Wirkung aller Führungsdimensionen. Es konnte aufgezeigt werden, dass transformationale Führung diese Wirkung nur in Verbindung mit der kompetenten Anwendung von transaktionaler, aufgabenbezogener und indirekter Führung entfalten kann. Die Untersuchungsergebnisse deuten außerdem darauf hin, dass eine transformationale Führungsbeziehung nur dann entstehen kann, wenn die Mitarbeiter Vertrauen in die professionelle Kompetenz und die Integrität ihrer Führungskraft fassen. Als normative Grundlagen transformationaler Führung wurden die Gewährleistung der Wohlfahrt und des Nutzens der Geführten sowie der Bezug auf und die Berücksichtigung von geteilten und allgemein akzeptierte Werten, insbesondere der distributiven und prozeduralen Gerechtigkeit, identifiziert. Insgesamt deuten die Erkenntnisse der Untersuchung darauf hin, dass mit dem Total Range of Leadership ein ganzheitlicher Führungsansatz entwickelt wurde, der alle aktiven und positiven Führungsverhaltensweisen umfasst, die zur Bewältigung von Krisen und Durchführung von Veränderungen in Unternehmen sowie für effektive Führung überhaupt erforderlich sind.

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.