Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in $n + 1$ variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

Conical diffraction and the dispersion surface of hyperbolic metamaterials

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.Comment: 10 pages, 7 figure

Probing viscoelastic properties of a thin polymer film sheared between a beads layer and quartz crystal resonator

We report measurements of viscoelastic properties of thin polymer films of 10-100 nm at the MHz range. These thin films are confined between a quartz crystal resonator and a millimetric bead layer, producing an increase of both resonance frequency and dissipation of the quartz resonator. The shear modulus and dynamic viscosity of thin films extracted from these measurements are consistent with the bulk values of the polymer. This modified quartz resonator provides an easily realizable and effective tool for probing the rheological properties of thin films at ambient environment.Comment: submitted to ap

Deep-water macroalgae from the Canary Islands: new records and biogeographical relationships

Due to the geographical location and paleobiogeography of the Canary Islands, the seaweed flora contains macroalgae with different distributional patterns. In this contribution, the biogeographical relations of several new records of deep-water macroalgae recently collected around the Canarian archipelago are discussed. These are Bryopsidella neglecta (Berthotd) Rietema,Discosporangium mesarthrocarpum (Meneghini) Hauck, Hincksia onslowensis (Amsler et Kapraun)P.C. Silva, Syringoderma floridana Henry, Peyssonnelia harveyana J. Agardh, Cryptonemia seminervis(C. Agardh) J. Agardh, Botryodadia wynnei Ballantine, Gloiocladia blomquistii (Searles) R. E.Norris, PIahchrysis peltata (W. R. Taylor) P. Huv4 et H. Huv4, Leptofauchea brasiliensis Joly, and Sarcodiotheca divaricata W. R. Taylor. These new records, especially those in the Florideophyceae,support the strong affinity of the Canary Islands seaweed flora with the warm-temperate Mediterranean-Atlantic region. Some species are recorded for the first time from the east coast of the Atlantic Ocean, enhancing the biogeographic relations of the Canarian marine flora with that of the western Atlantic regions

Eco-engineered rock pools: a concrete solution to biodiversity loss and urban sprawl in the marine environment

journal_title: Environmental Research Letters article_type: lett article_title: Eco-engineered rock pools: a concrete solution to biodiversity loss and urban sprawl in the marine environment copyright_information: © 2016 IOP Publishing Ltd license_information: cc-by Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. date_received: 2016-05-12 date_accepted: 2016-08-10 date_epub: 2016-09-1

Social Pain and the Brain: Controversies, Questions, and Where to Go from Here

Emerging evidence has shown that social pain--the painful feelings that follow from social rejection, exclusion, or loss--relies on some of the same neural regions that process physical pain, highlighting a possible physical-social pain overlap. However, the hypothesis that physical pain and social pain rely on shared neural systems has been contested. This review begins by summarizing research supporting the physical-social pain overlap. Next, three criticisms of this overlap model are presented and addressed by synthesizing available research. These criticisms include the suggestions that (a) neural responses to social pain are indicative of conflict detection processes, rather than distress; (b) all negative affective processes, rather than social pain specifically, activate these pain-related neural regions; and (c) neural responses to social (and physical) pain reflect the processing of salience, rather than hurt. Implications of these findings for understanding social and physical pain are discussed, and key next steps are suggested

Redox properties of the iron-sulfur clusters in activated Fe-hydrogenase from Desulfovibrio vulgaris (Hildenborough)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65750/1/j.1432-1033.1992.tb17261.x.pd

Structural and Functional Loss in Restored Wetland Ecosystems

In restored wetland ecosystems with apparently natural hydrology and biological structure, biogeochemical function may remain degraded, even a century after restoration efforts

“Working the System”—British American Tobacco's Influence on the European Union Treaty and Its Implications for Policy: An Analysis of Internal Tobacco Industry Documents

Katherine Smith and colleagues investigate the ways in which British American Tobacco influenced the European Union Treaty so that new EU policies advance the interests of major corporations, including those that produce products damaging to health