Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Knowledge, attitudes and experience associated with testing for prostate cancer: a comparison between male doctors and men in the community

Background: Debate about testing for prostate cancer using prostate-specific antigen (PSA) and digital rectal examination (DRE) continues. The evidence of benefit from screening for prostate cancer using PSA tests is inconclusive, and it is unclear how PSA can be used most effectively in the detection of prostate cancer. Given the lack of consensus, it is important that consumers understand the issues in a way that will permit them to decide whether or not to have a test and, if symptomatic, how their condition is managed.Aims: To compare prostate cancer knowledge, attitudes and testing experiences reported by male doctors and men in the community, despite the lack of evidence of a benefit.Methods : The primary method for ascertaining the attitudes of male doctors (MD) was a telephone survey, with some doctors electing to complete a written survey. Each MD was selected, at random, from a register of male practitioners aged &ge; 49 years of age. A total of 266 MD participated in the survey. The community sample (CS) was accessed using a telephone survey. Five hundred male Victorian residents aged &ge; 49 years of age participated in the study.Results:Knowledge &minus; Overall, 55% of the CS indicated &shy;correctly that prostate disease is sometimes cancer, compared to 83% of MD.Attitudes &minus; Fifty-five per cent of MD believed men should be tested for prostate disease at least every 2 years, compared to 68% of men in the CS.Testing experience &minus; Forty-five per cent of MD had been tested for prostate cancer in the past, and 92% of those tests were reported as negative. In the CS, 56% had been tested for prostate cancer in the past, and 78% of the results were reported as negative. The &shy;significant independent predictors of having had a prostate test among MD were: (i) age (&ge; 60 years; odds ratio (OR): 1.59; 95% confidence intervals (CI): 1.30&minus;1.88) and (ii) positive attitudes towards regular testing for prostate cancer (OR: 2.27; 95% CI: 1.98&minus;2.56). The significant independent predictors for the CS were: (i) age (&ge; 60 years; OR: 1.65; 95% CI: 1.40&minus;1.89), (ii) being married (OR: 1.30; 95% CI: 1.00&minus;1.60), (iii) knowledge that prostate disease was sometimes cancer (OR: 1.46; 95% CI: 1.26&minus;1.66) and (iv) positive attitudes towards regular testing for prostate cancer (OR: 2.12; 95% CI: 1.90&minus;2.34).Conclusions: The results highlight that testing for prostate cancer is widespread in the community and in the medical profession. Further research should be undertaken to identify how to help men make fully informed decisions about prostate cancer testing.<br /

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

An ovary transcriptome for all maturational stages of the striped bass (Morone saxatilis), a highly advanced perciform fish

<p>Abstract</p> <p>Background</p> <p>The striped bass and its relatives (genus <it>Morone</it>) are important fisheries and aquaculture species native to estuaries and rivers of the Atlantic coast and Gulf of Mexico in North America. To open avenues of gene expression research on reproduction and breeding of striped bass, we generated a collection of expressed sequence tags (ESTs) from a complementary DNA (cDNA) library representative of their ovarian transcriptome.</p> <p>Results</p> <p>Sequences of a total of 230,151 ESTs (51,259,448 bp) were acquired by Roche 454 pyrosequencing of cDNA pooled from ovarian tissues obtained at all stages of oocyte growth, at ovulation (eggs), and during preovulatory atresia. Quality filtering of ESTs allowed assembly of 11,208 high-quality contigs ≥ 100 bp, including 2,984 contigs 500 bp or longer (average length 895 bp). Blastx comparisons revealed 5,482 gene orthologues (E-value < 10^-3), of which 4,120 (36.7% of total contigs) were annotated with Gene Ontology terms (E-value < 10^-6). There were 5,726 remaining unknown unique sequences (51.1% of total contigs). All of the high-quality EST sequences are available in the National Center for Biotechnology Information (NCBI) Short Read Archive (GenBank: <ext-link ext-link-id="SRX007394" ext-link-type="gen">SRX007394</ext-link>). Informative contigs were considered to be abundant if they were assembled from groups of ESTs comprising ≥ 0.15% of the total short read sequences (≥ 345 reads/contig). Approximately 52.5% of these abundant contigs were predicted to have predominant ovary expression through digital differential display <it>in silico </it>comparisons to zebrafish (<it>Danio rerio</it>) UniGene orthologues. Over 1,300 Gene Ontology terms from Biological Process classes of Reproduction, Reproductive process, and Developmental process were assigned to this collection of annotated contigs.</p> <p>Conclusions</p> <p>This first large reference sequence database available for the ecologically and economically important temperate basses (genus <it>Morone</it>) provides a foundation for gene expression studies in these species. The predicted predominance of ovary gene expression and assignment of directly relevant Gene Ontology classes suggests a powerful utility of this dataset for analysis of ovarian gene expression related to fundamental questions of oogenesis. Additionally, a high definition Agilent 60-mer oligo ovary 'UniClone' microarray with 8 × 15,000 probe format has been designed based on this striped bass transcriptome (eArray Group: Striper Group, Design ID: 029004).</p

Searching for the Slater Transition in the Pyrochlore Cd2_{2}Os2_{2}O7_{7} with Infrared Spectroscopy

Infrared reflectance measurements were made on the single crystal pyrochlore Cd$_{2}$Os$_{2}$O$_{7}$ in order to examine the transformations of the electronic structure and crystal lattice across the boundary of the metal insulator transition at $T_{MIT}=226K$. All predicted IR active phonons are observed in the conductivity over all temperatures and the oscillator strength is found to be temperature independent. These results indicate that charge ordering plays only a minor role in the MIT and that the transition is strictly electronic in nature. The conductivity shows the clear opening of a gap with $2\Delta=5.2k_{B}T_{MIT}$. The gap opens continuously, with a temperature dependence similar to that of BCS superconductors, and the gap edge having a distinct $\sigma(\omega)\thicksim\omega^{1/2}$ dependence. All of these observables support the suggestion of a Slater transition in Cd$_{2}$Os$_{2}$O$_{7}$.Comment: 4 pages, 4 figure

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

Many non-equivalent realizations of the associahedron

Hohlweg and Lange (2007) and Santos (2004, unpublished) have found two different ways of constructing exponential families of realizations of the n-dimensional associahedron with normal vectors in {0,1,-1}^n, generalizing the constructions of Loday (2004) and Chapoton-Fomin-Zelevinsky (2002). We classify the associahedra obtained by these constructions modulo linear equivalence of their normal fans and show, in particular, that the only realization that can be obtained with both methods is the Chapoton-Fomin-Zelevinsky (2002) associahedron. For the Hohlweg-Lange associahedra our classification is a priori coarser than the classification up to isometry of normal fans, by Bergeron-Hohlweg-Lange-Thomas (2009). However, both yield the same classes. As a consequence, we get that two Hohlweg-Lange associahedra have linearly equivalent normal fans if and only if they are isometric. The Santos construction, which produces an even larger family of associahedra, appears here in print for the first time. Apart of describing it in detail we relate it with the c-cluster complexes and the denominator fans in cluster algebras of type A. A third classical construction of the associahedron, as the secondary polytope of a convex n-gon (Gelfand-Kapranov-Zelevinsky, 1990), is shown to never produce a normal fan linearly equivalent to any of the other two constructions.Comment: 30 pages, 13 figure

Exploring young people's and youth workers' experiences of spaces for ‘youth development’: creating cultures of participation

The paper focuses on the emergence of ‘positive youth development’ and its impact on older, more established practices of working with young people, such as youth work. Drawing on ethnographic fieldwork in England between 2004 and 2006, in particular young people's and youth workers' accounts of participating in youth work, the analysis engages with the social spaces in which youth work takes place and asks key questions about why young people might participate in youth spaces, what they get out of participating and how such spaces can promote cultures of participation. The analysis shows that such spaces provide young people and their communities with biographical continuity and time becomes a key component for sustaining such spaces. The argument is made for a more nuanced understanding of what young people get out of their participation in youth spaces, and for an epistemological approach to youth praxis that embraces the messiness and inequalities of lived experience

Mangarara Formation: exhumed remnants of a middle Miocene, temperate carbonate, submarine channel-fan system on the eastern margin of Taranaki Basin, New Zealand

The middle Miocene Mangarara Formation is a thin (1–60 m), laterally discontinuous unit of moderately to highly calcareous (40–90%) facies of sandy to pure limestone, bioclastic sandstone, and conglomerate that crops out in a few valleys in North Taranaki across the transition from King Country Basin into offshore Taranaki Basin. The unit occurs within hemipelagic (slope) mudstone of Manganui Formation, is stratigraphically associated with redeposited sandstone of Moki Formation, and is overlain by redeposited volcaniclastic sandstone of Mohakatino Formation. The calcareous facies of the Mangarara Formation are interpreted to be mainly mass-emplaced deposits having channelised and sheet-like geometries, sedimentary structures supportive of redeposition, mixed environment fossil associations, and stratigraphic enclosure within bathyal mudrocks and flysch. The carbonate component of the deposits consists mainly of bivalves, larger benthic foraminifers (especially Amphistegina), coralline red algae including rhodoliths (Lithothamnion and Mesophyllum), and bryozoans, a warm-temperate, shallow marine skeletal association. While sediment derivation was partly from an eastern contemporary shelf, the bulk of the skeletal carbonate is inferred to have been sourced from shoal carbonate factories around and upon isolated basement highs (Patea-Tongaporutu High) to the south. The Mangarara sediments were redeposited within slope gullies and broad open submarine channels and lobes in the vicinity of the channel-lobe transition zone of a submarine fan system. Different phases of sediment transport and deposition (lateral-accretion and aggradation stages) are identified in the channel infilling. Dual fan systems likely co-existed, one dominating and predominantly siliciclastic in nature (Moki Formation), and the other infrequent and involving the temperate calcareous deposits of Mangarara Formation. The Mangarara Formation is an outcrop analogue for middle Miocene-age carbonate slope-fan deposits elsewhere in subsurface Taranaki Basin, New Zealand