Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problems arising in evolutionary biology.

In this exciting and rapid development reflecting book twelve of the participants at the Symposium "From Simple Material Systems to Complex Ones" - "From Information to Structure" give a general view of todays knowledge with respect to multi-, inter- and transdisciplinary research in chemistry and science in general. How to analyse e. g. non-covalent interactions in the case of molecular recognitions or selfreplication, how to build up e. g. clusters and self-assembled molecules or how, in general, a knowledge of simple systems, acquired by the instruments of natural science research can be transferred to (more) complex systems and be utilized to improve our understanding, even of society was discussed by experts on chemical subjects like biochemistry, structure analysis, supramolecular chemistry and cluster formation up to biophysics, social sciences and philosophy.

This book constitutes the refereed proceedings of the First International Conference on Combinatorial Optimization and Applications, COCOA 2007, held in Xi'an, China in August 2007.

The 29 revised full papers presented together with 8 invited papers and 2 invited presentations were carefully reviewed and selected from 114 submissions. The papers feature original research in the areas of combinatorial optimization - both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.

The "raison d'etre" of hierarchical dustering theory stems from one basic phe nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first."

Erleben wir den Beginn eines visuellen Zeitalters? Technisch erzeugte Bilder pragen die alltaglichen Formen moderner Unterhaltung ebenso wie sie in Wissenschaft und Forschung zur Quelle neuer Erkenntnis werden. Angesiedelt im Spannungsfeld zwischen Kunst und Design auf der einen und Informatik und Mathematik auf der anderen Seite reichen die Anwendungsgebiete des neuen Arbeitsbereiches Visualisierung von der Architektur uber die Natur- und Ingenieurwissenschaften bis zur Medizin. Ein neues Berufsfeld entsteht: die Computervisualistik. Sein Ziel ist die Veranschaulichung komplexer Sachverhalte. Seine Bildleistungen beruhen auf der Kreativitat des Gestalters ebenso wie auf dem Wissen des Ingenieurs. Die dazu bereits existierenden Studiengange und Curricula sind ebenfalls Gegenstand dieser Publikation. In ihr setzen sich renommierte Wissenschaftler wie Herbert W. Franke, Wolfgang Dahmen, Achim Bachem, Heinz-Otto Peitgen oder Frieder Nake aus der jeweils unterschiedlichen Sicht ihres Fachgebietes mit dem Thema auseinander. Damit entsteht ein Kompendium der Visualisierung, das seine mathematischen Grundlagen ebenso anschaulich beschriebt, wie den aktuellen Stand seiner vielfaltigen Anwendungen.