A note on perfect partial elimination

In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard

Consistency of a system of equations: What does that mean?

The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of explicit density and stability results. We also illustrate, by typical examples, the limitations of the concept

Circulant Games

This paper presents a class of finite n x n bimatrix (2-player) games we coin Circulant Games. In Circulant Games, each player's payoff matrix is a circulant matrix, i.e.\ each row vector is rotated one element relative to the preceding row vector. We show that when the payoffs in the first row of each payoff matrix are strictly ordered, a single parameter describing the rotation symmetry between the players' matrices fully determines the exact number and the structure of all Nash Equilibria in these games. The class of Circulant Games contains well-known games such as matching pennies, rock-scissors-paper, circulant coordination and common interest games

On bounded block decomposition problems for under-specified systems of equations

When solving a system of equations, it can be beneficial not to solve it in its entirety at once, but rather to decompose it into smaller subsystems that can be solved in order. Based on a bisimplicial graph representation we analyze the parameterized complexity of two problems central to such a decomposition: The Free Square Block problem related to finding smallest subsystems that can be solved separately, and the Bounded Block Decomposition problem related to determining a decomposition where the largest subsystem is as small as possible. We show both problems to be W[1]-hard. Finally we relate these problems to crown structures and settle two open questions regarding them using our results

Das Internet zwischen Regulierung und Selbstregulierung

Das Internet hat nicht nur eine kaum vorhersehbare Revolution in der Kommunikation hervorgerufen, sondern stellt auch vielfältige Herausforderungen an das Recht. Die besondere Problematik ist dabei, dass die handelnden Personen dies praktisch anonym tun können und dass das Internet auf Grund seiner Struktur inhaltsneutral ist. Daraus wurde in der öffentlichen Diskussion abgeleitet, dass das Internet ein rechtsfreier Raum sei, was aber nicht sein dürfe. Darauf reagiert in einigen Fällen der Gesetzgeber, weitaus häufiger wird die Entwicklung aber von der Rechtsprechung vorangetrieben. Ziel der Arbeit ist es, die spezifisch auf das Internet bezogenen rechtlichen Entwicklungen des Rechts darzustellen und ihre spezifische Problematik aufzuzeigen. Im Kontrast dazu werden die Mechanismen der Rechtsetzung der Organisationen beschrieben, die für die Entwicklung des Internets verantwortlich sind und deren Verfahren auch Vorbild für staatliche Rechtsetzung sein könnten.The Internet has not only caused a non foreseeable revolution in human communication, it also defies legislation and jurisprudence in many ways. Acting over the internet causes unknown problems as communication on the internet is due to its structure non discriminating regarding the content. Discussion in the public has therefore concluded, that the internet were a anarchic space, a state which could not persist. In many cases this has caused reactions by legislation, although most of the development is carried by jurisprudence. The target of this publication is to show the internet-specific legal developments in Germany and to show their specific problems. In contrast to the state law the mechanisms of standardization by the institutions developing the internet and its standards are described

Naturnahe Umgestaltung von Fließgewässern : Teil 1: Leitfaden, Teil 2: Dokumentation ausgeführter Projekte

Teil I: Leitfaden Teil II: Dokumentation ausgeführter Projekt

Systemanalyse der Schaf- und Ziegenmilchproduktion in Deutschland

The production of sheep and goat milk in professional farming has become more important in the last decade. However, concrete underlying data are so far incomplete. Thus the aim of the system analysis was the accumulation of data and knowledge about sheep and goat milk production in Germany. Production processes and factors on farms are to be recorded as well as information about players in the processing and marketing sector. Through research, questionnaires and interviews with farmers, processors, commercial representatives and experts it was possible to generate a conclusive overview of this young sector. One outcome was a high proportion of organic farming (65% of dairy goat, 67% of dairy sheep farms). While there is much optimism with regards to further growth in production and demand, several hurdles from breeding to flock management and husbandry still have to be solve