September 11, two years later

Like other historical milestones, the second anniversary of the September 11, 2001 terrorist attack in the United States provides a good opportunity for critical evaluation. It invites an interim assessment of the successes and failures of the offensive launched by the US-led international coalition against terrorism and terrorist organizations, first and foremost al-Qaeda and its affiliates. Examining the unique..

Using the Incompressibility Method to obtain Local Lemma results for Ramsey-type Problems

We reveal a connection between the incompressibility method and the Lovasz local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated on the example of van der Waerden numbers. It applies to lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.Comment: 8 pages, 1 figur

Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect

The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities of non-interacting electrons are considered in detail. Results for the frequency scaling at the critical point and for the frequency dependent deviation of the Hall conductivity from the quantised plateau value are presented.Comment: 18 pages incl. 9 figures. "The Anderson Transition and its Ramifications -- Localisation, Quantum Interference, and Interactions", 'Lecture Notes in Physics' series, ed. T. Brandes and S. Kettemann, Springer Verlag, to be publishe

Towards an Isomorphism Dichotomy for Hereditary Graph Classes

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and algorithmic analysis of graphs. First, we develop a methodology to show isomorphism completeness of the isomorphism problem on graph classes by providing a general framework unifying various reduction techniques. Second, we generalize the concept of the modular decomposition to colored graphs, allowing for non-standard decompositions. We show that, given a suitable decomposition functor, the graph isomorphism problem reduces to checking isomorphism of colored prime graphs. Third, we extend the techniques of bounded color valence and hypergraph isomorphism on hypergraphs of bounded color size as follows. We say a colored graph has generalized color valence at most k if, after removing all vertices in color classes of size at most k, for each color class C every vertex has at most k neighbors in C or at most k non-neighbors in C. We show that isomorphism of graphs of bounded generalized color valence can be solved in polynomial time.Comment: 37 pages, 4 figure