Subword complexes, cluster complexes, and generalized multi-associahedra

In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k=1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes of types A and B coincide with known simplicial complexes, namely with the simplicial complexes of multi-triangulations and centrally symmetric multi-triangulations respectively. Furthermore, we show that the multi-cluster complex is universal in the sense that every spherical subword complex can be realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio

European Red List of Marine Fishes

The European Red List is a review of the conservation status of European species according to IUCN regional Red Listing guidelines. It identifies those species that are threatened with extinction at the regional level, so that appropriate conservation action can be taken to improve their status. This Red List publication summarises results for all described native European marine fishes.Postprin

An SMT Approach to Bounded Reachability Analysis of Model Programs

Abstract. Model programs represent transition systems that are used to specify expected behavior of systems at a high level of abstraction. The main application area is application-level network protocols or protocol-data types such as sets and maps, and comprehensions to express com-plex state updates. Such models are mainly used in model-based testing as inputs for test case generation and as oracles during conformance testing. Correctness assumptions about the model itself are usually ex-pressed through state invariants. An important problem is to validate the model prior to its use in the above-mentioned contexts. We intro-duce a technique of using Satisfiability Modulo Theories or SMT to per-form bounded reachability analysis of a fragment of model programs. We use the Z3 solver for our implementation and benchmarks, and we use AsmL as the modeling language. The translation from a model program into a verification condition of Z3 is incremental and involves selective quantifier instantiation of quantifiers that result from the comprehension expressions.

Top quark physics at hadron colliders

The top quark, discovered at the FERMILAB TEVATRON collider in 1995, is the heaviest known elementary particle. Today, ten years later, still relatively little is known about its properties. The strong and weak interactions of the top quark are not nearly as well studied as those of the other quarks and leptons. The strong interaction is most directly measured in top quark pair production. The weak interaction is measured in top quark decay and single top quark production, which remains thus far unobserved. The large top-quark mass of about 175 GeV/c2 suggests that it may play a special role in nature. It behaves differently from all other quarks due to its large mass and its correspondingly short lifetime. The top quark decays before it hadronises, passing its spin information on to its decay products. Therefore, it is possible to measure observables that depend on the top quark spin, providing a unique environment for tests of the Standard Model and for searches for physics beyond the Standard Model. This report summarises the latest measurements and studies of top quark properties and rare decays from the TEVATRON in Run II. With more than 1 fb-1 of luminosity delivered to each experiment, CDF and DO, top quark physics at the TEVATRON is at a turning point from first studies to precision measurements with sensitivity to new physics. An outlook onto top quark physics at the Large Hadron Collider (LHC) at CERN, planned to begin operation in the year 2007, is also given