Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder, A. Deza, and A. Ivic Weiss (eds), Springe

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space

A transdisciplinary and community-driven database to unravel subduction zone initiation

Subduction zones are pivotal for the recycling of Earth’s outer layer into its interior. However, the conditions under which new subduction zones initiate are enigmatic. Here, we constructed a transdisciplinary database featuring detailed analysis of more than a dozen documented subduction zone initiation events from the last hundred million years. Our initial findings reveal that horizontally forced subduction zone initiation is dominant over the last 100 Ma, and that most initiation events are proximal to pre-existing subduction zones. The SZI Database is expandable to facilitate access to the most current understanding of subduction zone initiation as research progresses, providing a community platform that establishes a common language to sharpen discussion across the Earth Science community

In adult onset myositis, the presence of interstitial lung disease and myositis specific/associated antibodies are governed by HLA class II haplotype, rather than by myositis subtype

The aim of this study was to investigate HLA class II associations in polymyositis (PM) and dermatomyositis (DM), and to determine how these associations influence clinical and serological differences. DNA samples were obtained from 225 UK Caucasian idiopathic inflammatory myopathy patients (PM = 117, DM = 108) and compared with 537 randomly selected UK Caucasian controls. All cases had also been assessed for the presence of related malignancy and interstitial lung disease (ILD), and a number of myositis-specific/myositis-associated antibodies (MSAs/MAAs). Subjects were genotyped for HLA-DRB1, DQA1 and DQB1. HLA-DRB1*03, DQA1*05 and DQB1*02 were associated with an increased risk for both PM and DM. The HLA-DRB1*03-DQA1*05-DQB1*02 haplotype demonstrated strong association with ILD, irrespective of myositis subtype or presence of anti-aminoacyl-transfer RNA synthetase antibodies. The HLA-DRB1*07-DQA1*02-DQB1*02 haplotype was associated with risk for anti-Mi-2 antibodies, and discriminated PM from DM (odds ratio 0.3, 95% confidence interval 0.1–0.6), even in anti-Mi-2 negative patients. Other MSA/MAAs showed specific associations with other HLA class II haplotypes, irrespective of myositis subtype. There were no genotype, haplotype or serological associations with malignancy. The HLA-DRB1*03-DQA1*05-DQB1*02 haplotype associations appear to not only govern disease susceptibility in Caucasian PM/DM patients, but also phenotypic features common to PM/DM. Though strongly associated with anti-Mi-2 antibodies, the HLA-DRB1*07-DQA1*02-DQB1*02 haplotype shows differential associations with PM/DM disease susceptibility. In conclusion, these findings support the notion that myositis patients with differing myositis serology have different immunogenetic profiles, and that these profiles may define specific myositis subtypes

Calabi-Yau Duals of Torus Orientifolds

We study a duality that relates the T^6/Z_2 orientifold with N=2 flux to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T^4) fibrations over P^1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H_1(X,Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description. The analysis is facilitated by the existence of an explicit Calabi-Yau metric on an open subset of the geometry that becomes an arbitrarily good approximation to the actual metric (at most points) in the limit that the fiber is much smaller than the base.Comment: 39 pages; uses harvmac.tex, amssym.tex; v4: minor correction