Truth table invariant cylindrical algebraic decomposition

When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors presented an algorithm that can efficiently and directly construct a TTICAD for a list of formulae in which each has an equational constraint. This was achieved by generalising McCallum's theory of reduced projection operators. In this paper we present an extended version of our theory which can be applied to an arbitrary list of formulae, achieving savings if at least one has an equational constraint. We also explain how the theory of reduced projection operators can allow for further improvements to the lifting phase of CAD algorithms, even in the context of a single equational constraint. The algorithm is implemented fully in Maple and we present both promising results from experimentation and a complexity analysis showing the benefits of our contributions.Comment: 40 page

Program Veri¿cation in the presence of complex numbers, functions with branch cuts etc

Abstract-In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as "does the lowlevel arithmetic implement the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more dif¿cult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simpli¿cation rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities

The Time-Domain Spectroscopic Survey: Understanding the Optically Variable Sky with SEQUELS in SDSS-III

The Time-Domain Spectroscopic Survey (TDSS) is an SDSS-IV eBOSS subproject primarily aimed at obtaining identification spectra of ~220,000 optically-variable objects systematically selected from SDSS/Pan-STARRS1 multi-epoch imaging. We present a preview of the science enabled by TDSS, based on TDSS spectra taken over ~320 deg^2 of sky as part of the SEQUELS survey in SDSS-III, which is in part a pilot survey for eBOSS in SDSS-IV. Using the 15,746 TDSS-selected single-epoch spectra of photometrically variable objects in SEQUELS, we determine the demographics of our variability-selected sample, and investigate the unique spectral characteristics inherent in samples selected by variability. We show that variability-based selection of quasars complements color-based selection by selecting additional redder quasars, and mitigates redshift biases to produce a smooth quasar redshift distribution over a wide range of redshifts. The resulting quasar sample contains systematically higher fractions of blazars and broad absorption line quasars than from color-selected samples. Similarly, we show that M-dwarfs in the TDSS-selected stellar sample have systematically higher chromospheric active fractions than the underlying M-dwarf population, based on their H-alpha emission. TDSS also contains a large number of RR Lyrae and eclipsing binary stars with main-sequence colors, including a few composite-spectrum binaries. Finally, our visual inspection of TDSS spectra uncovers a significant number of peculiar spectra, and we highlight a few cases of these interesting objects. With a factor of ~15 more spectra, the main TDSS survey in SDSS-IV will leverage the lessons learned from these early results for a variety of time-domain science applications.Comment: 17 pages, 14 figures, submitted to Ap

Lymphoid aggregates that resemble tertiary lymphoid organs define a specific pathological subset in metal-on-metal hip replacements

Aseptic lymphocyte-dominated vasculitis-associated lesion (ALVAL) has been used to describe the histological lesion associated with metal-on-metal (M-M) bearings. We tested the hypothesis that the lymphoid aggregates, associated with ALVAL lesions resemble tertiary lymphoid organs (TLOs). Histopathological changes were examined in the periprosthetic tissue of 62 M-M hip replacements requiring revision surgery, with particular emphasis on the characteristics and pattern of the lymphocytic infiltrate. Immunofluorescence and immunohistochemistry were used to study the classical features of TLOs in cases where large organized lymphoid follicles were present. Synchrotron X-ray fluorescence (XRF) measurements were undertaken to detect localisation of implant derived ions/particles within the samples. Based on type of lymphocytic infiltrates, three different categories were recognised; diffuse aggregates (51%), T cell aggregates (20%), and organised lymphoid aggregates (29%). Further investigation of tissues with organised lymphoid aggregates showed that these tissues recapitulate many of the features of TLOs with T cells and B cells organised into discrete areas, the presence of follicular dendritic cells, acquisition of high endothelial venule like phenotype by blood vessels, expression of lymphoid chemokines and the presence of plasma cells. Co-localisation of implant-derived metals with lymphoid aggregates was observed. These findings suggest that in addition to the well described general foreign body reaction mediated by macrophages and a T cell mediated type IV hypersensitivity response, an under-recognized immunological reaction to metal wear debris involving B cells and the formation of tertiary lymphoid organs occurs in a distinct subset of patients with M-M implants

Heritable components of the human fecal microbiome are associated with visceral fat

Background: Variation in the human fecal microbiota has previously been associated with body mass index (BMI). Although obesity is a global health burden, the accumulation of abdominal visceral fat is the specific cardio-metabolic disease risk factor. Here, we explore links between the fecal microbiota and abdominal adiposity using body composition as measured by dual-energy X-ray absorptiometry in a large sample of twins from the TwinsUK cohort, comparing fecal 16S rRNA diversity profiles with six adiposity measures.Results: We profile six adiposity measures in 3666 twins and estimate their heritability, finding novel evidence for strong genetic effects underlying visceral fat and android/gynoid ratio. We confirm the association of lower diversity of the fecal microbiome with obesity and adiposity measures, and then compare the association between fecal microbial composition and the adiposity phenotypes in a discovery subsample of twins. We identify associations between the relative abundances of fecal microbial operational taxonomic units (OTUs) and abdominal adiposity measures. Most of these results involve visceral fat associations, with the strongest associations between visceral fat and Oscillospira members. Using BMI as a surrogate phenotype, we pursue replication in independent samples from three population-based cohorts including American Gut, Flemish Gut Flora Project and the extended TwinsUK cohort. Meta-analyses across the replication samples indicate that 8 OTUs replicate at a stringent threshold across all cohorts, while 49 OTUs achieve nominal significance in at least one replication sample. Heritability analysis of the adiposity-associated microbial OTUs prompted us to assess host genetic-microbe interactions at obesity-associated human candidate loci. We observe significant associations of adiposity-OTU abundances with host genetic variants in the FHIT, TDRG1 and ELAVL4 genes, suggesting a potential role for host genes to mediate the link between the fecal microbiome and obesity.Conclusions: Our results provide novel insights into the role of the fecal microbiota in cardio-metabolic disease with clear potential for prevention and novel therapies

The Multi-Object, Fiber-Fed Spectrographs for SDSS and the Baryon Oscillation Spectroscopic Survey

We present the design and performance of the multi-object fiber spectrographs for the Sloan Digital Sky Survey (SDSS) and their upgrade for the Baryon Oscillation Spectroscopic Survey (BOSS). Originally commissioned in Fall 1999 on the 2.5-m aperture Sloan Telescope at Apache Point Observatory, the spectrographs produced more than 1.5 million spectra for the SDSS and SDSS-II surveys, enabling a wide variety of Galactic and extra-galactic science including the first observation of baryon acoustic oscillations in 2005. The spectrographs were upgraded in 2009 and are currently in use for BOSS, the flagship survey of the third-generation SDSS-III project. BOSS will measure redshifts of 1.35 million massive galaxies to redshift 0.7 and Lyman-alpha absorption of 160,000 high redshift quasars over 10,000 square degrees of sky, making percent level measurements of the absolute cosmic distance scale of the Universe and placing tight constraints on the equation of state of dark energy. The twin multi-object fiber spectrographs utilize a simple optical layout with reflective collimators, gratings, all-refractive cameras, and state-of-the-art CCD detectors to produce hundreds of spectra simultaneously in two channels over a bandpass covering the near ultraviolet to the near infrared, with a resolving power R = \lambda/FWHM ~ 2000. Building on proven heritage, the spectrographs were upgraded for BOSS with volume-phase holographic gratings and modern CCD detectors, improving the peak throughput by nearly a factor of two, extending the bandpass to cover 360 < \lambda < 1000 nm, and increasing the number of fibers from 640 to 1000 per exposure. In this paper we describe the original SDSS spectrograph design and the upgrades implemented for BOSS, and document the predicted and measured performances.Comment: 43 pages, 42 figures, revised according to referee report and accepted by AJ. Provides background for the instrument responsible for SDSS and BOSS spectra. 4th in a series of survey technical papers released in Summer 2012, including arXiv:1207.7137 (DR9), arXiv:1207.7326 (Spectral Classification), and arXiv:1208.0022 (BOSS Overview

Early fibrinogen concentrate therapy for major haemorrhage in trauma (E-FIT 1): results from a UK multi-centre, randomised, double blind, placebo-controlled pilot trial.

BACKGROUND: There is increasing interest in the timely administration of concentrated sources of fibrinogen to patients with major traumatic bleeding. Following evaluation of early cryoprecipitate in the CRYOSTAT 1 trial, we explored the use of fibrinogen concentrate, which may have advantages of more rapid administration in acute haemorrhage. The aims of this pragmatic study were to assess the feasibility of fibrinogen concentrate administration within 45 minutes of hospital admission and to quantify efficacy in maintaining fibrinogen levels ≥ 2 g/L during active haemorrhage. METHODS: We conducted a blinded, randomised, placebo-controlled trial at five UK major trauma centres with adult trauma patients with active bleeding who required activation of the major haemorrhage protocol. Participants were randomised to standard major haemorrhage therapy plus 6 g of fibrinogen concentrate or placebo. RESULTS: Twenty-seven of 39 participants (69%; 95% CI, 52-83%) across both arms received the study intervention within 45 minutes of admission. There was some evidence of a difference in the proportion of participants with fibrinogen levels ≥ 2 g/L between arms (p = 0.10). Fibrinogen levels in the fibrinogen concentrate (FgC) arm rose by a mean of 0.9 g/L (SD, 0.5) compared with a reduction of 0.2 g/L (SD, 0.5) in the placebo arm and were significantly higher in the FgC arm (p < 0.0001) at 2 hours. Fibrinogen levels were not different at day 7. Transfusion use and thromboembolic events were similar between arms. All-cause mortality at 28 days was 35.5% (95% CI, 23.8-50.8%) overall, with no difference between arms. CONCLUSIONS: In this trial, early delivery of fibrinogen concentrate within 45 minutes of admission was not feasible. Although evidence points to a key role for fibrinogen in the treatment of major bleeding, researchers need to recognise the challenges of timely delivery in the emergency setting. Future studies must explore barriers to rapid fibrinogen therapy, focusing on methods to reduce time to randomisation, using 'off-the-shelf' fibrinogen therapies (such as extended shelf-life cryoprecipitate held in the emergency department or fibrinogen concentrates with very rapid reconstitution times) and limiting the need for coagulation test-based transfusion triggers. TRIAL REGISTRATION: ISRCTN67540073 . Registered on 5 August 2015

The Ninth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Baryon Oscillation Spectroscopic Survey

The Sloan Digital Sky Survey III (SDSS-III) presents the first spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS). This ninth data release (DR9) of the SDSS project includes 535,995 new galaxy spectra (median z=0.52), 102,100 new quasar spectra (median z=2.32), and 90,897 new stellar spectra, along with the data presented in previous data releases. These spectra were obtained with the new BOSS spectrograph and were taken between 2009 December and 2011 July. In addition, the stellar parameters pipeline, which determines radial velocities, surface temperatures, surface gravities, and metallicities of stars, has been updated and refined with improvements in temperature estimates for stars with T_eff<5000 K and in metallicity estimates for stars with [Fe/H]>-0.5. DR9 includes new stellar parameters for all stars presented in DR8, including stars from SDSS-I and II, as well as those observed as part of the SDSS-III Sloan Extension for Galactic Understanding and Exploration-2 (SEGUE-2). The astrometry error introduced in the DR8 imaging catalogs has been corrected in the DR9 data products. The next data release for SDSS-III will be in Summer 2013, which will present the first data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) along with another year of data from BOSS, followed by the final SDSS-III data release in December 2014.Comment: 9 figures; 2 tables. Submitted to ApJS. DR9 is available at http://www.sdss3.org/dr