Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Genetic, abiotic and social influences on sex differentiation in cichlid fishes and the evolution of sequential hermaphroditism

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73799/1/j.1467-2979.2005.00184.x.pd

Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter

Data collected by the Pierre Auger Observatory through 31 August 2007 showed evidence for anisotropy in the arrival directions of cosmic rays above the Greisen-Zatsepin-Kuz'min energy threshold, \nobreak{$6\times 10^{19}$eV}. The anisotropy was measured by the fraction of arrival directions that are less than $3.1^\circ$ from the position of an active galactic nucleus within 75 Mpc (using the V\'eron-Cetty and V\'eron $12^{\rm th}$ catalog). An updated measurement of this fraction is reported here using the arrival directions of cosmic rays recorded above the same energy threshold through 31 December 2009. The number of arrival directions has increased from 27 to 69, allowing a more precise measurement. The correlating fraction is $(38^{+7}_{-6})$, compared with $21$ expected for isotropic cosmic rays. This is down from the early estimate of $(69^{+11}_{-13})$. The enlarged set of arrival directions is examined also in relation to other populations of nearby extragalactic objects: galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in hard X-rays by the Swift Burst Alert Telescope. A celestial region around the position of the radiogalaxy Cen A has the largest excess of arrival directions relative to isotropic expectations. The 2-point autocorrelation function is shown for the enlarged set of arrival directions and compared to the isotropic expectation.Comment: Accepted for publication in Astroparticle Physics on 31 August 201

Atmospheric effects on extensive air showers observed with the Surface Detector of the Pierre Auger Observatory

Atmospheric parameters, such as pressure (P), temperature (T) and density, affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a ~10% seasonal modulation and ~2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of pressure and density. The former affects the longitudinal development of air showers while the latter influences the Moliere radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory.Comment: 24 pages, 9 figures, accepted for publication in Astroparticle Physic

Search for First Harmonic Modulation in the Right Ascension Distribution of Cosmic Rays Detected at the Pierre Auger Observatory

We present the results of searches for dipolar-type anisotropies in different energy ranges above $2.5\times 10^{17}$ eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% $C.L.$ for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations.Comment: 28 pages, 11 figure

Upper limit on the cosmic-ray photon fraction at EeV energies from the Pierre Auger Observatory

From direct observations of the longitudinal development of ultra-high energy air showers performed with the Pierre Auger Observatory, upper limits of 3.8%, 2.4%, 3.5% and 11.7% (at 95% c.l.) are obtained on the fraction of cosmic-ray photons above 2, 3, 5 and 10 EeV (1 EeV = 10^18 eV) respectively. These are the first experimental limits on ultra-high energy photons at energies below 10 EeV. The results complement previous constraints on top-down models from array data and they reduce systematic uncertainties in the interpretation of shower data in terms of primary flux, nuclear composition and proton-air cross-section.Comment: 20 pages, 7 figures, 2 tables. Minor changes. Accepted by Astroparticle Physic

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

A social basis for the development of primary males in a sex-changing fish

An example of alternative male strategies is seen in diandric protogynous (female first) hermaphrodites, where individuals either mature directly as male (primary males) or first reproduce as female and then change sex to male (secondary males). In some sex-changing fishes, the testes of primary males appear anatomically similar to those of non-sex-changing species, whereas the testes of secondary males have anatomical evidence of their former ovarian function. Here, we provide evidence that in the bluehead wrasse, Thalassoma bifasciatum, these strikingly different male phenotypes arise from differences in the ontogenetic timing of environmental sex determination, timing that can be experimentally altered through changes in the social circumstances. Juveniles differentiated almost exclusively as females when reared in isolation, regardless of whether they were collected from a reef with a high proportion of primary males or from a reef with a low proportion of primary males. In contrast, one individual usually differentiated as a primary male when reared in groups of three. Our results indicate that primary males of the bluehead wrasse are an environmentally sensitive developmental strategy that has probably evolved in response to variation in the reproductive success of primary males in populations of different sizes