171,419 research outputs found

    The Lecture Hall Parallelepiped

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    The s-lecture hall polytopes P_s are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-M\'elou. We define a half-open parallelopiped Par_s associated with P_s and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the \delta-vector (or h^*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.Comment: 14 pages. To appear in Annals of Combinatoric

    To germinate or not to germinate : a question of dormancy relief not germination stimulation

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    A common understanding of the control of germination through dormancy is essential for effective communication between seed scientists whether they are ecologists, physiologists or molecular biologists. Vleeshouwers et al. (1995) realized that barriers between disciplines limited progress and through insightful conclusions in their paper ‘Redefining seed dormancy: an attempt to integrate physiology and ecology’, they did much to overcome these barriers at that time. However, times move on, understanding develops, and now there is a case for ‘Redefining seed dormancy as an integration of physiology, ecology and molecular biology’. Finch-Savage and Leubner-Metzger (2006) had this in mind when they extended and re-interpreted the definition of dormancy proposed by Vleeshouwers et al. (1995), by considering dormancy as a having a number of layers that must be removed, with the final layer of dormancy being synonymous with the stimulation/induction of germination

    How to Do Things Without Words: Infants, utterance-activity and distributed cognition

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    Clark and Chalmers (1998) defend the hypothesis of an ‘Extended Mind’, maintaining that beliefs and other paradigmatic mental states can be implemented outside the central nervous system or body. Aspects of the problem of ‘language acquisition’ are considered in the light of the extended mind hypothesis. Rather than ‘language’ as typically understood, the object of study is something called ‘utterance-activity’, a term of art intended to refer to the full range of kinetic and prosodic features of the on-line behaviour of interacting humans. It is argued that utterance activity is plausibly regarded as jointly controlled by the embodied activity of interacting people, and that it contributes to the control of their behaviour. By means of specific examples it is suggested that this complex joint control facilitates easier learning of at least some features of language. This in turn suggests a striking form of the extended mind, in which infants’ cognitive powers are augmented by those of the people with whom they interact

    How to do things without words

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    Clark and Chalmers (1998) defend the hypothesis of an ‘Extended Mind’, maintaining that beliefs and other paradigmatic mental states can be implemented outside the central nervous system or body. Aspects of the problem of ‘language acquisition’ are considered in the light of the extended mind hypothesis. Rather than ‘language’ as typically understood, the object of study is something called ‘utterance-activity’, a term of art intended to refer to the full range of kinetic and prosodic features of the on-line behaviour of interacting humans. It is argued that utterance activity is plausibly regarded as jointly controlled by the embodied activity of interacting people, and that it contributes to the control of their behaviour. By means of specific examples it is suggested that this complex joint control facilitates easier learning of at least some features of language. This in turn suggests a striking form of the extended mind, in which infants’ cognitive powers are augmented by those of the people with whom they interact

    Unimodality Problems in Ehrhart Theory

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    Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart h∗h^*-vector. Ehrhart h∗h^*-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart h∗h^*-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

    On the Relative Strength of Pebbling and Resolution

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    The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula and then argue that proofs of this formula must inherit (various aspects of) the pebbling properties of the underlying graph. Unfortunately, the reductions used here are not tight. To simulate resolution proofs by pebblings, the full strength of nondeterministic black-white pebbling is needed, whereas resolution is only known to be able to simulate deterministic black pebbling. To obtain strong results, one therefore needs to find specific graph families which either have essentially the same properties for black and black-white pebbling (not at all true in general) or which admit simulations of black-white pebblings in resolution. This paper contributes to both these approaches. First, we design a restricted form of black-white pebbling that can be simulated in resolution and show that there are graph families for which such restricted pebblings can be asymptotically better than black pebblings. This proves that, perhaps somewhat unexpectedly, resolution can strictly beat black-only pebbling, and in particular that the space lower bounds on pebbling formulas in [Ben-Sasson and Nordstrom 2008] are tight. Second, we present a versatile parametrized graph family with essentially the same properties for black and black-white pebbling, which gives sharp simultaneous trade-offs for black and black-white pebbling for various parameter settings. Both of our contributions have been instrumental in obtaining the time-space trade-off results for resolution-based proof systems in [Ben-Sasson and Nordstrom 2009].Comment: Full-length version of paper to appear in Proceedings of the 25th Annual IEEE Conference on Computational Complexity (CCC '10), June 201

    Bayesian methods of astronomical source extraction

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    We present two new source extraction methods, based on Bayesian model selection and using the Bayesian Information Criterion (BIC). The first is a source detection filter, able to simultaneously detect point sources and estimate the image background. The second is an advanced photometry technique, which measures the flux, position (to sub-pixel accuracy), local background and point spread function. We apply the source detection filter to simulated Herschel-SPIRE data and show the filter's ability to both detect point sources and also simultaneously estimate the image background. We use the photometry method to analyse a simple simulated image containing a source of unknown flux, position and point spread function; we not only accurately measure these parameters, but also determine their uncertainties (using Markov-Chain Monte Carlo sampling). The method also characterises the nature of the source (distinguishing between a point source and extended source). We demonstrate the effect of including additional prior knowledge. Prior knowledge of the point spread function increase the precision of the flux measurement, while prior knowledge of the background has onlya small impact. In the presence of higher noise levels, we show that prior positional knowledge (such as might arise from a strong detection in another waveband) allows us to accurately measure the source flux even when the source is too faint to be detected directly. These methods are incorporated in SUSSEXtractor, the source extraction pipeline for the forthcoming Akari FIS far-infrared all-sky survey. They are also implemented in a stand-alone, beta-version public tool that can be obtained at http://astronomy.sussex.ac.uk/∼\simrss23/sourceMiner\_v0.1.2.0.tar.gzComment: Accepted for publication by ApJ (this version compiled used emulateapj.cls

    QSO Absorption Systems Detected in Ne VIII: High-Metallicity Clouds with a Large Effective Cross Section

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    Using high resolution, high signal-to-noise ultraviolet spectra of the z = 0.9754 quasar PG1148+549 obtained with the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope, we study the physical conditions and abundances of NeVIII+OVI absorption line systems at z(abs) =0.68381, 0.70152, 0.72478. In addition to NeVIII and OVI, absorption lines from multiple ionization stages of oxygen (OII, OIII, OIV) are detected and are well-aligned with the more highly ionized species. We show that these absorbers are multiphase systems including hot gas (T ~ 10^{5.7} K) that produces NeVIII and OVI, and the gas metallicity of the cool phase ranges from Z = 0.3 Z_{solar} to supersolar. The cool (~10^{4} K) phases have densities n_{H} ~ 10^{-4} cm^{-3} and small sizes (< 4kpc); these cool clouds are likely to expand and dissipate, and the NeVIII may be within a transition layer between the cool gas and a surrounding, much hotter medium. The NeVIII redshift density, dN/dz = 7^{+7}_{-3}, requires a large number of these clouds for every L > 0.1L* galaxy and a large effective absorption cross section (>~ 100 kpc), and indeed, we find a star forming ~L* galaxy at the redshift of the z(abs)=0.72478 system, at an impact parameter of 217 kpc. Multiphase absorbers like these NeVIII systems are likely to be an important reservoir of baryons and metals in the circumgalactic media of galaxies.Comment: Final published version (Astrophysical Journal
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