34 research outputs found
Isomorphisms and traversability of directed path graphs
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph \forw P_k(D) of a digraph is obtained by representing the directed paths on vertices of by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in form a directed path on vertices or form a directed cycle on vertices in . In this introductory paper several properties of \forw P_3(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs with \forw P_3(D)\cong D, we show that \forw P_3(D_1)\cong\forw P_3(D_2) ``almost always'' implies , and we characterize all digraphs with Eulerian or Hamiltonian \forw P_3-graphs
Isomorphisms and traversability of directed path graphs
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph Pk(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k+1 vertices or form a directed cycle on k vertices in D. In this introductory paper several properties of P3(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs D with P3(D) ≅ D, we show that P3(D1) ≅ P3(D2) "almost always'' implies D1 ≅ D2, and we characterize all digraphs with Eulerian or Hamiltonian P3-graphs
Directed path graphs
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k + 1 vertices or form a directed cycle on k vertices in D. Several properties of are studied, in particular with respect to isomorphism and traversability
Independence Number in Path Graphs
In the paper we present results, which allow us to compute the independence numbers of -path graphs and -path graphs of special graphs. As and are subgraphs of iterated line graphs and , respectively, we compare our results with the independence numbers of corresponding iterated line graphs
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Entwurf und Implementation einer auf Graph-Grammatiken beruhenden Sprache zur Funktions-Struktur-Modellierung von Pflanzen
Increasing biological knowledge requires more and more elaborate methods to translate the knowledge into executable model descriptions, and increasing computational power allows to actually execute these descriptions. Such a simulation helps to validate, extend and question the knowledge. For plant modelling, the well-established formal description language of Lindenmayer systems reaches its limits as a method to concisely represent current knowledge and to conveniently assist in current research. On one hand, it is well-suited to represent structural and geometric aspects of plant models - of which units is a plant composed, how are these connected, what is their location in 3D space -, but on the other hand, its usage to describe functional aspects - what internal processes take place in the plant structure, how does this interact with the structure - is not as convenient as desirable. This can be traced back to the underlying representation of structure as a linear chain of units, while the intrinsic nature of the structure is a tree or even a graph. Therefore, we propose to use graphs and graph grammars as a basis for plant modelling which combines structural and functional aspects. In the first part of this thesis, we develop the necessary theoretical framework. Starting with a presentation of the state of the art concerning Lindenmayer systems and graph grammars, we develop the formalism of relational growth grammars as a variant of graph grammars. We show that this formalism has a natural embedding of Lindenmayer systems which keeps all relevant properties, but represents branched structures directly as axial trees and not as linear chains with indirect encoding of branches. In the second part, we develop the main practical result, the XL programming language as an extension of the Java programming language by very general rule-based features. Short examples illustrate the application of the new language features. We describe the built-in pattern matching algorithm of the implemented run-time system for the XL programming language, and we sketch a possible implementation of an XL compiler. The third part is an application of relational growth grammars and the XL programming language. We show how the general XL interfaces can be customized for relational growth grammars. On top of this customization, several examples from a variety of disciplines demonstrate the usefulness of the developed formalism and language to describe plant growth, especially functional-structural plant models, but also artificial life, architecture or interactive games. Some examples operate on custom graphs like XML DOM trees or scene graphs of commercial 3D modellers, while the majority uses the 3D modelling platform GroIMP, a software developed in conjunction with this thesis. The appendix gives an overview of the GroIMP software. The practical usage of its plug-in for relational growth grammars is also illustrated.Das zunehmende Wissen über biologische Prozesse verlangt nach geeigneten Methoden, es in ausführbare Modelle zu übersetzen, und die zunehmende Rechenleistung der Computer ermöglicht es, diese Modelle auch tatsächlich auszuführen. Solche Simulationen dienen zur Validierung, Erweiterung und Hinterfragung des Wissens. Speziell für die Pflanzenmodellierung wurden Lindenmayer-Systeme mit Erfolg eingesetzt, jedoch stoßen diese bei aktuellen Modellierungsproblemen und Forschungsvorhaben an ihre Grenzen. Zwar sind sie gut geeignet, Pflanzenstruktur und Geometrie abzubilden - aus welchen Einheiten setzt sich eine Pflanze zusammen, wie sind diese verbunden, wie ist ihre räumliche Lage -, aber die lineare Datenstruktur erschwert die Integration von Funktionsmodellen, welche Prozesse innerhalb der verzweigten Struktur und des beanspruchten Raumes beschreiben. Daher wird in dieser Arbeit vorgeschlagen, anstelle der linearen Stuktur Graphen und Graph-Grammatiken als Grundlage für die kombinierte Funktions-Struktur-Modellierung von Pflanzen zu verwenden. Im ersten Teil der Dissertation wird der theoretische Unterbau entwickelt. Nach einer Vorstellung des aktuellen Wissensstandes auf dem Gebiet der Lindenmayer-Systeme und Graph-Grammatiken werden relationale Wachstumsgrammatiken eingeführt, die auf bekannten Mechanismen für parallele Graph-Grammatiken aufbauen und Lindenmayer-Systeme als Spezialfall enthalten, dabei jedoch verzweigte Strukturen direkt als axiale Bäume darstellen. Zur praktischen Anwendung wird im zweiten Teil die Programmiersprache XL entwickelt, die Java um allgemein gehaltene Sprachkonstrukte für Graph-Grammatiken erweitert. Kurze Beispiele zeigen die Anwendung der neuen Sprachmerkmale. Der Algorithmus zur Mustersuche wird erläutert, und die Implementation des XL-Compilers wird vorgestellt. Im dritten Teil werden mögliche Anwendungen relationaler Wachstumsgrammatiken aufgezeigt. Dazu werden zunächst die allgemeinen XL-Schnittstellen für relationale Wachstumsgrammatiken konkretisiert, um dieses System dann für Modelle aus verschiedenen Bereichen zu nutzen, darunter Funktions-Struktur-Modelle von Pflanzen, Künstliches Leben, Architektur und interaktive Spiele. Einige Beispiele nutzen spezifische Graphen wie XML-DOM-Bäume oder Szenengraphen kommerzieller 3D-Modellierprogramme, aber der überwiegende Teil baut auf der 3D-Plattform GroIMP auf, die zusammen mit dieser Dissertation entwickelt wurde. Im Anhang wird die Software GroIMP kurz vorgestellt und ihre praktische Anwendung für relationale Wachstumsgrammatiken erläutert
The 1995 Goddard Conference on Space Applications of Artificial Intelligence and Emerging Information Technologies
This publication comprises the papers presented at the 1995 Goddard Conference on Space Applications of Artificial Intelligence and Emerging Information Technologies held at the NASA/Goddard Space Flight Center, Greenbelt, Maryland, on May 9-11, 1995. The purpose of this annual conference is to provide a forum in which current research and development directed at space applications of artificial intelligence can be presented and discussed
1991-1993-UNM CATALOG
Course catalog for 1991-1993https://digitalrepository.unm.edu/course_catalogs/1095/thumbnail.jp