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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Freese, Katherine; Gondolo, Paolo; Sellwood, J. A.; Spolyar, Douglas;

    The first stars in the universe form inside $\sim 10^6 M_\odot$ dark matter (DM) haloes whose initial density profiles are laid down by gravitational collapse in hierarchical structure formation scenarios. During the formation of the first stars in the universe, the baryonic infall compresses the dark matter further. The resultant dark matter density is presented here, using an algorithm originally developed by Young to calculate changes to the profile as the result of adiabatic infall in a spherical halo model; the Young prescription takes into account the non-circular motions of halo particles. The density profiles obtained in this way are found to be within a factor of two of those obtained using the simple adiabatic contraction prescription of Blumenthal et al. Our results hold regardless of the nature of the dark matter or its interactions and rely merely on gravity. If the dark matter consists of weakly interacting massive particles, which are their own antiparticles, their densities are high enough that their annihilation in the first protostars can indeed provide an important heat source and prevent the collapse all the way to fusion. In short, a ``Dark Star'' phase of stellar evolution, powered by DM annihilation, may indeed describe the first stars in the universe. Comment: 14 pages, 3 figures, and 1 table

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ The Astrophysical Jo...arrow_drop_down
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    arXiv.org e-Print Archive
    Other literature type . Preprint . 2008
    https://doi.org/10.48550/arxiv...
    Article . 2008
    License: arXiv Non-Exclusive Distribution
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    The Astrophysical Journal
    Article . 2009 . Peer-reviewed
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ The Astrophysical Jo...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      arXiv.org e-Print Archive
      Other literature type . Preprint . 2008
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      Article . 2008
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      The Astrophysical Journal
      Article . 2009 . Peer-reviewed
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/

    Abstract Hooks are prominent in representation theory (of symmetric groups) and they play a role in number theory (via cranks associated to Ramanujan's congruences). A partition of a positive integer n has a Young diagram representation. To each cell in the diagram there is an associated statistic called hook length, and if a number t is absent from the diagram then the partition is called a t-core. A partition is an ( s , t ) -core if it is both an s- and a t-core. Since the work of Anderson on ( s , t ) -cores, the topic has received growing attention. This paper expands the discussion to multiple-cores. More precisely, we explore ( s , s + 1 , … , s + k ) -core partitions much in the spirit of a recent paper by Stanley and Zanello. In fact, our results exploit connections between three combinatorial objects: multi-cores, posets and lattice paths (with a novel generalization of Dyck paths). Additional results and conjectures are scattered throughout the paper. For example, one of these statements implies a curious symmetry for twin-coprime ( s , s + 2 ) -core partitions.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    arXiv.org e-Print Archive
    Other literature type . Preprint . 2014
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    Advances in Applied Mathematics
    Article . 2015 . Peer-reviewed
    License: Elsevier Non-Commercial
    https://doi.org/10.48550/arxiv...
    Article . 2014
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      arXiv.org e-Print Archive
      Other literature type . Preprint . 2014
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      Advances in Applied Mathematics
      Article . 2015 . Peer-reviewed
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      https://doi.org/10.48550/arxiv...
      Article . 2014
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Storey, Brian D.; Edwards, Lee R.; Kilic, Mustafa Sabri; Bazant, Martin Z.;

    The current theory of alternating-current electro-osmosis (ACEO) is unable to explain the experimentally observed flow reversal of planar ACEO pumps at high frequency (above the peak, typically 10-100 kHz), low salt concentration (1-1000 $\mu$M), and moderate voltage (2-6 V), even if taking into account Faradaic surface reactions, nonlinear double-layer capacitance and bulk electrothermal flows. We attribute this failure to the breakdown of the classical Poisson-Boltzmann model of the diffuse double layer, which assumes a dilute solution of point-like ions. In spite of low bulk salt concentration, the large voltage induced across the double layer leads to crowding of the ions and a related decrease in surface capacitance. Using several mean-field models for finite-sized ions, we show that steric effects generally lead to high frequency flow reversal of ACEO pumps, similar to experiments. For quantitative agreement, however, an unrealistically large effective ion size (several nm) must be used, which we attribute to neglected correlation effects. Comment: 12 pages

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2007
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    Article . 2007
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      arXiv.org e-Print Archive
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    Relational Hoare logics extend the applicability of modular, deductive verification to encompass important 2-run properties including dependency requirements such as confidentiality and program relations such as equivalence or similarity between program versions. A considerable number of recent works introduce different relational Hoare logics without yet converging on a core set of proof rules. This paper looks backwards to little known early work. This brings to light some principles that clarify and organize the rules as well as suggesting a new rule and a new notion of completeness. Comment: A version appears in proceedings of ISOLA 2020. Version2: fix typos, minor clarifications, add a citation. Version3: copy edits, add citations on completeness. Version 4: minor corrections. Version 5: restore missing precond in loop rule. Version 6: add two citations

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ http://arxiv.org/pdf...arrow_drop_down
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    http://arxiv.org/pdf/2007.0642...
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2020
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    https://doi.org/10.1007/978-3-...
    Part of book or chapter of book . 2020 . Peer-reviewed
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    Article . 2020
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      http://arxiv.org/pdf/2007.0642...
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      arXiv.org e-Print Archive
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      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      https://doi.org/10.1007/978-3-...
      Part of book or chapter of book . 2020 . Peer-reviewed
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      Article . 2020
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    Authors: Haines, Brian M.; Aranson, Igor S.; Berlyand, Leonid; Karpeev, Dmitry A.;

    Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions. Comment: 15 pages, 3 figures, submitted to Physical Biology

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    Physical Biology
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2008
    Physical Biology
    Article . 2008
    Physical Biology
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      arXiv.org e-Print Archive
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      Article . 2008
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    Authors: L. M. Taylor; G. J. Hakim;

    AbstractThere are two major challenges to improving interannual to decadal forecasts: (a) consistently initializing the coupled system so that variability is not dominated by initial imbalances, and (b) having a large sample of different initial conditions on which to test forecast skill. The second challenge requires consideration of time periods not only outside the recent period of intensive ocean observation, but also before the instrumental era, which increases the importance of the first challenge. Forecasts prior to the 1850s isolate internally generated sources of variability by removing the majority of anthropogenic forcing, and the sparse observational record during this time period motivates the use of paleoclimate proxy data. We address these issues by using a linear inverse model (LIM) approach and a recent proxy‐based reconstruction over the last millennium at annual resolution. The reconstruction is used to train, initialize, and validate LIM forecasts. The LIM trained on paleo‐data assimilated using a LIM trained on global climate model (GCM) simulation data outperforms a LIM trained on raw GCM data at forecast leads longer than 2 years for in‐sample experiments, and beyond 4‐year leads in most out‐of‐sample experiments validated on instrumental data. The most skillful normal mode of the paleo‐data LIM for the instrumental experiment represents a persistent pattern with a longer decay time than for the GCM‐LIM's modes, which accounts for the outperformance at longer leads. The paleo‐data LIM is consequently more sensitive to ocean initialization, which is reflected in forecasts during the instrumental era where ocean reanalyses exhibit large uncertainty.

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    Earth and Space Science
    Article . 2023
    Data sources: DOAJ
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    Earth and Space Science
    Article . 2023 . Peer-reviewed
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      Earth and Space Science
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      Earth and Space Science
      Article . 2023 . Peer-reviewed
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    For E/k an elliptic curve with CM by O, we determine a formula for (a generalization of) the arithmetic local constant of [4] at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to describe extensions F/Q over which the O-rank of E grows. Comment: 3 tables, updated acknowledgments

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    Rocky Mountain Journal of Mathematics
    Article . 2014 . Peer-reviewed
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      Rocky Mountain Journal of Mathematics
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    Authors: Jimmy A. Irwin; W. Peter Maksym; Gregory R. Sivakoff; Aaron J. Romanowsky; +7 Authors

    An X-ray flaring source was found near the galaxy NGC 4697. Two flares were seen, separated by four years. The flux increased by a factor of 90 on a timescale of about one minute. Both flares were very brief. There is no optical counterpart at the position of the flares, but if the source was at the distance of NGC 4697, the luminosities were 10^39 erg/s. Here we report the results of a search of archival X-ray data for 70 nearby galaxies looking for similar such flares. We found two flaring sources in globular clusters or ultra-compact dwarf companions of parent elliptical galaxies. One source flared once to a peak luminosity of 9 x 10^40 erg/s, while the other flared five times to 10^40 erg/s. All of the flare rise times were <1 minute, and they then decayed over about an hour. When not flaring, the sources appear to be normal accreting neutron star or black hole X-ray binaries, but they are located in old stellar populations, unlike the magnetars, anomalous X-ray pulsars or soft gamma repeaters that have repetitive flares of similar luminosities. Published in the Oct 20 2016 issue of Nature

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    Nature
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    Authors: Randelle M. Bundy; Alessandro Tagliabue; Nicholas J. Hawco; Peter L. Morton; +7 Authors

    Cobalt (Co) is an important bioactive trace metal that is the metal cofactor in cobalamin (vitamin B12) which can limit or co-limit phytoplankton growth in many regions of the ocean. Total dissolved and labile Co measurements in the Canadian sector of the Arctic Ocean during the U.S. GEOTRACES Arctic expedition (GN01) and the Canadian International Polar Year GEOTRACES expedition (GIPY14) revealed a dynamic biogeochemical cycle for Co in this basin. The major sources of Co in the Arctic were from shelf regions and rivers, with only minimal contributions from other freshwater sources (sea ice, snow) and eolian deposition. The most striking feature was the extremely high concentrations of dissolved Co in the upper 100 m, with concentrations routinely exceeding 800 pmol L−1 over the shelf regions. This plume of high Co persisted throughout the Arctic basin and extended to the North Pole, where sources of Co shifted from primarily shelf-derived to riverine, as freshwater from Arctic rivers was entrained in the Transpolar Drift. Dissolved Co was also strongly organically complexed in the Arctic, ranging from 70 % to 100 % complexed in the surface and deep ocean, respectively. Deep-water concentrations of dissolved Co were remarkably consistent throughout the basin (∼55 pmol L−1), with concentrations reflecting those of deep Atlantic water and deep-ocean scavenging of dissolved Co. A biogeochemical model of Co cycling was used to support the hypothesis that the majority of the high surface Co in the Arctic was emanating from the shelf. The model showed that the high concentrations of Co observed were due to the large shelf area of the Arctic, as well as to dampened scavenging of Co by manganese-oxidizing (Mn-oxidizing) bacteria due to the lower temperatures. The majority of this scavenging appears to have occurred in the upper 200 m, with minimal additional scavenging below this depth. Evidence suggests that both dissolved Co (dCo) and labile Co (LCo) are increasing over time on the Arctic shelf, and these limited temporal results are consistent with other tracers in the Arctic. These elevated surface concentrations of Co likely lead to a net flux of Co out of the Arctic, with implications for downstream biological uptake of Co in the North Atlantic and elevated Co in North Atlantic Deep Water. Understanding the current distributions of Co in the Arctic will be important for constraining changes to Co inputs resulting from regional intensification of freshwater fluxes from ice and permafrost melt in response to ongoing climate change.

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    Biogeosciences
    Article . 2020 . Peer-reviewed
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    https://doi.org/10.5194/bg-202...
    Preprint . 2020
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    Biogeosciences (BG)
    Other literature type . 2020
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    Biogeosciences
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      Biogeosciences
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      https://doi.org/10.5194/bg-202...
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      DOAJ
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      Biogeosciences (BG)
      Other literature type . 2020
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      Biogeosciences
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    Authors: Opazo, Juan C.; Butts, G. Tyler; Nery, Mariana F.; Storz, Jay F.; +1 Authors

    Subsequent to the two rounds of whole-genome duplication that occurred in the common ancestor of vertebrates, a third genome duplication occurred in the stem lineage of teleost fishes. This teleost-specific genome duplication (TGD) is thought to have provided genetic raw materials for the physiological, morphological, and behavioral diversification of this highly speciose group. The extreme physiological versatility of teleost fish is manifest in their diversity of blood-gas transport traits, which reflects the myriad solutions that have evolved to maintain tissue O(2) delivery in the face of changing metabolic demands and environmental O(2) availability during different ontogenetic stages. During the course of development, regulatory changes in blood-O(2) transport are mediated by the expression of multiple, functionally distinct hemoglobin (Hb) isoforms that meet the particular O(2)-transport challenges encountered by the developing embryo or fetus (in viviparous or oviparous species) and in free-swimming larvae and adults. The main objective of the present study was to assess the relative contributions of whole-genome duplication, large-scale segmental duplication, and small-scale gene duplication in producing the extraordinary functional diversity of teleost Hbs. To accomplish this, we integrated phylogenetic reconstructions with analyses of conserved synteny to characterize the genomic organization and evolutionary history of the globin gene clusters of teleosts. These results were then integrated with available experimental data on functional properties and developmental patterns of stage-specific gene expression. Our results indicate that multiple α- and β-globin genes were present in the common ancestor of gars (order Lepisoteiformes) and teleosts. The comparative genomic analysis revealed that teleosts possess a dual set of TGD-derived globin gene clusters, each of which has undergone lineage-specific changes in gene content via repeated duplication and deletion events. Phylogenetic reconstructions revealed that paralogous genes convergently evolved similar functional properties in different teleost lineages. Consistent with other recent studies of globin gene family evolution in vertebrates, our results revealed evidence for repeated evolutionary transitions in the developmental regulation of Hb synthesis.

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    Molecular Biology and Evolution
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      Molecular Biology and Evolution
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    Authors: Freese, Katherine; Gondolo, Paolo; Sellwood, J. A.; Spolyar, Douglas;

    The first stars in the universe form inside $\sim 10^6 M_\odot$ dark matter (DM) haloes whose initial density profiles are laid down by gravitational collapse in hierarchical structure formation scenarios. During the formation of the first stars in the universe, the baryonic infall compresses the dark matter further. The resultant dark matter density is presented here, using an algorithm originally developed by Young to calculate changes to the profile as the result of adiabatic infall in a spherical halo model; the Young prescription takes into account the non-circular motions of halo particles. The density profiles obtained in this way are found to be within a factor of two of those obtained using the simple adiabatic contraction prescription of Blumenthal et al. Our results hold regardless of the nature of the dark matter or its interactions and rely merely on gravity. If the dark matter consists of weakly interacting massive particles, which are their own antiparticles, their densities are high enough that their annihilation in the first protostars can indeed provide an important heat source and prevent the collapse all the way to fusion. In short, a ``Dark Star'' phase of stellar evolution, powered by DM annihilation, may indeed describe the first stars in the universe. Comment: 14 pages, 3 figures, and 1 table

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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2008
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    The Astrophysical Journal
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    Abstract Hooks are prominent in representation theory (of symmetric groups) and they play a role in number theory (via cranks associated to Ramanujan's congruences). A partition of a positive integer n has a Young diagram representation. To each cell in the diagram there is an associated statistic called hook length, and if a number t is absent from the diagram then the partition is called a t-core. A partition is an ( s , t ) -core if it is both an s- and a t-core. Since the work of Anderson on ( s , t ) -cores, the topic has received growing attention. This paper expands the discussion to multiple-cores. More precisely, we explore ( s , s + 1 , … , s + k ) -core partitions much in the spirit of a recent paper by Stanley and Zanello. In fact, our results exploit connections between three combinatorial objects: multi-cores, posets and lattice paths (with a novel generalization of Dyck paths). Additional results and conjectures are scattered throughout the paper. For example, one of these statements implies a curious symmetry for twin-coprime ( s , s + 2 ) -core partitions.

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    Advances in Applied Mathematics
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      Advances in Applied Mathematics
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    Authors: Storey, Brian D.; Edwards, Lee R.; Kilic, Mustafa Sabri; Bazant, Martin Z.;

    The current theory of alternating-current electro-osmosis (ACEO) is unable to explain the experimentally observed flow reversal of planar ACEO pumps at high frequency (above the peak, typically 10-100 kHz), low salt concentration (1-1000 $\mu$M), and moderate voltage (2-6 V), even if taking into account Faradaic surface reactions, nonlinear double-layer capacitance and bulk electrothermal flows. We attribute this failure to the breakdown of the classical Poisson-Boltzmann model of the diffuse double layer, which assumes a dilute solution of point-like ions. In spite of low bulk salt concentration, the large voltage induced across the double layer leads to crowding of the ions and a related decrease in surface capacitance. Using several mean-field models for finite-sized ions, we show that steric effects generally lead to high frequency flow reversal of ACEO pumps, similar to experiments. For quantitative agreement, however, an unrealistically large effective ion size (several nm) must be used, which we attribute to neglected correlation effects. Comment: 12 pages

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