Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Partitioning the triangles of the cross polytope into surfaces

We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope $\beta^k$ into closed surfaces of genus $g \leq 1$, each with a transitive automorphism group given by the vertex transitive $\mathbb{Z}_{2k}$-action on $\beta^k$. Furthermore we show that for each $k \equiv 1,5(6)$ the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\"obius strips.Comment: 13 pages, 1 figure. Minor update. Journal-ref: Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473-486, 201

Meiotic sex chromosome cohesion and autosomal synapsis are supported by Esco2.

In mitotic cells, establishment of sister chromatid cohesion requires acetylation of the cohesin subunit SMC3 (acSMC3) by ESCO1 and/or ESCO2. Meiotic cohesin plays additional but poorly understood roles in the formation of chromosome axial elements (AEs) and synaptonemal complexes. Here, we show that levels of ESCO2, acSMC3, and the pro-cohesion factor sororin increase on meiotic chromosomes as homologs synapse. These proteins are less abundant on the largely unsynapsed sex chromosomes, whose sister chromatid cohesion appears weaker throughout the meiotic prophase. Using three distinct conditional Esco2 knockout mouse strains, we demonstrate that ESCO2 is essential for male gametogenesis. Partial depletion of ESCO2 in prophase I spermatocytes delays chromosome synapsis and further weakens cohesion along sex chromosomes, which show extensive separation of AEs into single chromatids. Unsynapsed regions of autosomes are associated with the sex chromatin and also display split AEs. This study provides the first evidence for a specific role of ESCO2 in mammalian meiosis, identifies a particular ESCO2 dependence of sex chromosome cohesion and suggests support of autosomal synapsis by acSMC3-stabilized cohesion

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

Addition of cetuximab to first-line chemotherapy in patients with advanced non-small-cell lung cancer: a cost-utility analysis

Background: Adding cetuximab to standard chemotherapy results in a moderate increase of overall survival in patients with advanced non-small-cell lung cancer (NSCLC), but the cost-effectiveness is unknown. Materials and methods: A Markov model was constructed based on the results of the First-Line ErbituX in lung cancer randomized trial, adding cetuximab to cisplatin-vinorelbine first-line chemotherapy in patients with advanced NSCLC. The primary outcome was the incremental cost-effectiveness ratio (ICER) of adding cetuximab, expressed as cost per quality-adjusted life year (QALY) gained, and relative to a willingness-to-pay threshold of €60 000/QALY. The impact of cetuximab intermittent dosing schedules on the ICER was also evaluated. Results: Adding cetuximab to standard chemotherapy leads to a gain of 0.07 QALYs per patient at an additional cost of €26 088. The ICER for adding cetuximab to chemotherapy was €376 205 per QALY gained. Intermittent cetuximab dosing schedules resulted in ICERs per QALY gained between €31 300 and €83 100, under the assumption of equal efficacy. Conclusions: From a health economic perspective, the addition of cetuximab to standard first-line chemotherapy in patients with epidermal growth factor receptor-expressing advanced NSCLC cannot be recommended to date, due to a high ICER compared with other health care interventions. Treatment schedules resulting in more favorable cost-utility ratios should be evaluate

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra

Test of the REX-RFQ and status of the front part of the REX-ISOLDE linac

For REX-ISOLDE (Radioactive beam EXperiments at ISOLDE/CERN), a test beamline is built up at the Garching Accelerator Lab. to perform He$^{1+}$-experiments with the RFQ, the matching (rebunching) section between RFQ and IH-DT-linac, the IH-structure and several electrostatic lenses of the REX-ISOLDE-mass separator. In a first step, the beamline is conceived for tests with the RFQ. This paper presents the parameters and the status of the REX-RFQ, the experimental setup and the particle dynamics simulations with the COSY infinity code for beam injection and beam analysis. Furthermore it shows the design and status of the mass separator, the IH- structure and the buncher section. (5 refs)

Sequential and direct two-photon double ionization of D2 at FLASH

ABSTRACT: Sequential and direct two-photon double ionization (DI) of D2 molecule is studied experimentally and theoretically at a photon energy of 38.8 eV. Experimental and theoretical kinetic energy releases of D++D+ fragments, consisting of the contributions of sequential DI via the D2+(1ssg) state and direct DI via a virtual state, agree well with each other