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.

Fliesslochformen und Gewindefurchen in dünne Bleche und Rohre aus Kupfer und Kupferlegierungen

This thesis in Thermal Flow Drilling and Flowtap in thin metal sheet and pipes of copper and copper alloys had as objectives to know the comportment of copper and copper alloys sheet metal during the Thermal Flow Drill processes with normal tools, to know the best Speed and Feed machine data for the best bushing quality, to known the best Speed for Form Tapping processes and to know the best bush long in pure copper pipes for water solar interchange equipment. Thermal Flow Drilling (TFD) and Form Tapping (FT) is one of the research lines of the Institute of Production and Logistics (IPL) at University of Kassel. At December 1995, a work meeting of IPL, Santa Catarina University, Brazil, Buenos Aires University, Argentine, Tarapacá University (UTA), Chile members and the CEO of Flowdrill B.V. was held in Brazil. The group decided that the Manufacturing Laboratory (ML) of UTA would work with pure copper and brass alloys sheet metal and pure copper pipes in order to develop a water interchange solar heater. The Flowdrill BV Company sent tools to Tarapacá University in 1996. In 1999 IPL and the ML carried out an ALECHILE research project promoted by the DAAD and CONICyT in copper sheet metal and copper pipes and sheet metal a-brass alloys. The normal tools are lobed, conical tungsten carbide tool. When rotated at high speed and pressed with high axial force into sheet metal or thin walled tube generated heat softens the metal and allows the drill to feed forward produce a hole and simultaneously form a bushing from the displacement material. In the market exist many features but in this thesis is used short and longs normal tools of TFD. For reach the objectives it was takes as references four qualities of the frayed end bushing, where the best one is the quality class I. It was used pure copper and a-brass alloys sheet metals, with different thickness. It was used different TFD drills diameter for four thread type, from M-5 to M10. Similar to the Aluminium sheet metals studies it was used the predrilling processes with HSS drills around 30% of the TFD diameter (1,5 – 3,0 mm D). In the next step is used only 2,0 mm thick metal sheet, and 9,2 mm TFD diameter for M-10 thread. For the case of pure commercial copper pipes is used for ¾” inch diameter and 12, 8 mm (3/8”) TFD drill for holes for 3/8” pipes and different normal HSS drills for predrilling processes. The chemical sheet metal characteristics were takes as reference for the material behaviour. The Chilean pure copper have 99,35% of Cu and 0,163% of Zinc and the Chilean a-brass alloys have 75,6% of Cu and 24,0% of Zinc. It is used two German a-brass alloys; Nº1 have 61,6% of Cu, 36,03 % of Zinc and 2,2% of Pb and the German a-brass alloys Nº2 have 63,1% of Cu, 36,7% of Zinc and 0% of Pb. The equipments used were a HAAS CNC milling machine centre, a Kistler dynamometer, PC Pentium II, Acquisition card, TESTPOINT and XAct software, 3D measurement machine, micro hardness, universal test machine, and metallographic microscope. During the test is obtained the feed force and momentum curves that shows the material behaviour with TFD processes. In general it is take three phases. It was possible obtain the best machining data for the different sheet of copper and a-brass alloys thick of Chilean materials and bush quality class I. In the case of a-brass alloys, the chemical components and the TFD processes temperature have big influence. The temperature reach to 400º Celsius during the TFD processes and the a-brass alloys have some percents of Zinc the bush quality is class I. But when the a-brass alloys have some percents of Lead who have 200º C melting point is not possible to obtain a bush, because the Lead gasify and the metallographic net broke. During the TFD processes the recrystallization structures occur around the Copper and a-brass alloy bush, who gives more hardness in these zones. When the threads were produce with Form Tapping processes with Flowtap tools, this hardness amount gives a high limit load of the thread when hey are tested in a special support that was developed for it. For eliminated the predrilling processes with normal HSS drills it was developed a compound tool. With this new tool it was possible obtain the best machining data for quality class I bush. For the copper pipes it is made bush without predrilling and the quality class IV was obtained. When it is was used predrilling processes, quality classes I bush were obtained. Then with different HSS drill diameter were obtained different long bush, where were soldering with four types soldering materials between pipes with 3/8” in a big one as ¾”. Those soldering unions were tested by traction test and all the 3/8” pipes broken, and the soldering zone doesn’t have any problem. Finally were developed different solar water interchange heaters and tested. As conclusions, the present Thesis shows that the Thermal Flow Drilling in thinner metal sheets of cooper and cooper alloys needs a predrilling process for frayed end quality class I bushings, similar to thinner sheets of aluminium bushes. The compound tool developed could obtain quality class I bushings and excludes predrilling processes. The bush recrystalization, product of the friction between the tool and the material, the hardness grows and it is advantageous for the Form Tapping. The methodology developed for commercial copper pipes permits to built water solar interchange heaters.

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.

A survey of brassica vegetable smallholder farmers in the Gauteng and Limpopo provinces of South Africa

A study was taken to investigate the types of brassica vegetables mostly grown by smallholder farmers in two provinces of South Africa. Thirty-one smallholder vegetable farmers in the Gauteng province and Waterberg district in the Limpopo province were surveyed. In addition, the study also sought to establish the common diseases, the management strategies used and problems encountered by the farmers. Farmers were interviewed using a questionnaire with closed and open–ended questions. The results indicated that the smallholder farmers mostly grew cabbage (93.6%) as their main brassica crop followed by rape (41.2%). Thirty percent of farmers could not identify or name the predominant disease/s encountered in their fields. Major diseases encountered by farmers surveyed were an unknown disease/s (33.3%), black rot (26.7%), Alternaria leaf spot (6.7%) and white rust (6.7%). Smallholder farmers have inadequate technical information available especially relating to crop diseases, their identification and control. Farmers encountered challenges with black rot disease especially on cabbage, rape and kale and the disease was a problem during winter and summer. Generally, the smallholder farmers used crop rotation (74.2%) as a major practice to manage the diseases experienced. They rotated their brassica vegetables with other crops/vegetables like tomatoes, onions, beetroots and maize. Most of the farmers interviewed (61.3%) did not use chemicals to control diseases, whereas 38.7% of them used chemicals. This was mostly because they lacked information and knowledge, high costs associated with use of chemical fungicides and some were shifting towards organic farming. From the study it was noted that there was a need for technical support to improve farmers’ knowledge on disease identification and control within the surveyed areas.