An algorithm to compute the polar decomposition of a 3 × 3 matrix

We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition

Carotid bruits as predictor for carotid stenoses detected by ultrasonography: an observational study

<p>Abstract</p> <p>Background</p> <p>Carotid surgery in asymptomatic subjects with carotid stenosis is effective to prevent ischemic stroke. There is, however, uncertainty how to find such persons at risk, because mass screening with carotid artery ultrasonography (US) is not cost-effective. Signs of carotid bruits corresponding to the carotid arteries may serve as a tool to select subjects for further investigation. This study is thus aimed at determining the usefulness of carotid bruits in the screening of carotid stenoses.</p> <p>Methods</p> <p>1555 consecutive carotid ultrasonography investigations from 1486 cases done between January 2004 and March 2006 at Norrlands University Hospital, Sweden, were examined. 356 subjects, medium age 69 (27–88) years, had a significant (≥ 50%) US-verified carotid stenosis uni- or bilaterally, 291 had been examined for signs of carotid bruits. The likelihood ratios for carotid bruits to predict US-verified carotid stenoses were calculated and expressed as likelihood percentages.</p> <p>Results</p> <p>Thirty-one out of 100 persons (31%) with carotid bruit as an indication to perform carotid US had a significant (≥ 50%) carotid stenosis. 281 of the 356 (79%) cases with significant carotid stenoses were found among patients with cerebrovascular disease (CVD). 145 of 226 (64%) CVD patients with a significant carotid stenosis had a carotid bruit. In patients with 50–99% carotid stenoses carotid bruits had an accuracy of 75% (436/582), a sensitivity of 71% (236/334), a specificity of 81% (200/248), a positive likelihood ratio at 3.65 and a negative likelihood at 0.36. Patients with 70–99% stenoses had the highest sensitivity at 77% (183/238). In patients with 100% carotid stenoses, carotid bruits had a sensitivity of 26% (15/57) and a specificity of 49% (256/525).</p> <p>Conclusion</p> <p>Although carotid bruits are not accurate to confirm or to exclude significant carotid stenoses, these signs are appropriate for directed screening for further investigation with carotid US if the patient lacks contraindications for surgery. Lack of carotid bruits in CVD patients does not exclude a carotid stenosis.</p

A rocky planet transiting a nearby low-mass star

M-dwarf stars -- hydrogen-burning stars that are smaller than 60 per cent of the size of the Sun -- are the most common class of star in our Galaxy and outnumber Sun-like stars by a ratio of 12:1. Recent results have shown that M dwarfs host Earth-sized planets in great numbers: the average number of M-dwarf planets that are between 0.5 to 1.5 times the size of Earth is at least 1.4 per star. The nearest such planets known to transit their star are 39 parsecs away, too distant for detailed follow-up observations to measure the planetary masses or to study their atmospheres. Here we report observations of GJ 1132b, a planet with a size of 1.2 Earth radii that is transiting a small star 12 parsecs away. Our Doppler mass measurement of GJ 1132b yields a density consistent with an Earth-like bulk composition, similar to the compositions of the six known exoplanets with masses less than six times that of the Earth and precisely measured densities. Receiving 19 times more stellar radiation than the Earth, the planet is too hot to be habitable but is cool enough to support a substantial atmosphere, one that has probably been considerably depleted of hydrogen. Because the host star is nearby and only 21 per cent the radius of the Sun, existing and upcoming telescopes will be able to observe the composition and dynamics of the planetary atmosphere.Comment: Published in Nature on 12 November 2015, available at http://dx.doi.org/10.1038/nature15762. This is the authors' version of the manuscrip

T cell lymphoproliferative disorders associated with anti-tumor necrosis factor alpha antibody therapy for ulcerative colitis: literature summary

The enhanced risk of development of lymphoproliferative disorders in patients with inflammatory bowel disease has been attributed to immunosuppressive/immunomodulatory therapies. Infliximab is a chimeric monoclonal immunoglobulin G1 antibody directed against tumor necrosis factor alpha (TNF-α) that was approved by the Food and Drug Administration (FDA) in 1998 as an effective therapeutic agent against inflammatory bowel disease. Malignant lymphomas of both B and T cell lineage have been described in patients undergoing therapy involving TNF-α blockade. To date, eight cases of Epstein–Barr virus (EBV)-negative hepatosplenic T cell lymphoma associated with infliximab have been reported to the FDA’s Adverse Event Reporting System, as well as several other T cell lymphoproliferative disorders with aggressive clinical outcomes. We present the histologic, immunophenotypic, and molecular features of a T cell lymphoproliferative disorder involving the axillary lymph node of a 33-year-old male following infliximab treatment for ulcerative colitis. These EBV-negative lymphomas suggest that lymphoproliferative disorders following infliximab treatment for inflammatory bowel disease may involve EBV-independent immune dysregulation. The spectrum of lymphoproliferative disorders associated with infliximab and the potential mechanisms by which they occur are discussed

Multiple populations in globular clusters. Lessons learned from the Milky Way globular clusters

Recent progress in studies of globular clusters has shown that they are not simple stellar populations, being rather made of multiple generations. Evidence stems both from photometry and spectroscopy. A new paradigm is then arising for the formation of massive star clusters, which includes several episodes of star formation. While this provides an explanation for several features of globular clusters, including the second parameter problem, it also opens new perspectives about the relation between globular clusters and the halo of our Galaxy, and by extension of all populations with a high specific frequency of globular clusters, such as, e.g., giant elliptical galaxies. We review progress in this area, focusing on the most recent studies. Several points remain to be properly understood, in particular those concerning the nature of the polluters producing the abundance pattern in the clusters and the typical timescale, the range of cluster masses where this phenomenon is active, and the relation between globular clusters and other satellites of our Galaxy.Comment: In press (The Astronomy and Astrophysics Review

Toward a multiscale modeling framework for understanding serotonergic function

Despite its importance in regulating emotion and mental wellbeing, the complex structure and function of the serotonergic system present formidable challenges toward understanding its mechanisms. In this paper, we review studies investigating the interactions between serotonergic and related brain systems and their behavior at multiple scales, with a focus on biologically-based computational modeling. We first discuss serotonergic intracellular signaling and neuronal excitability, followed by neuronal circuit and systems levels. At each level of organization, we will discuss the experimental work accompanied by related computational modeling work. We then suggest that a multiscale modeling approach that integrates the various levels of neurobiological organization could potentially transform the way we understand the complex functions associated with serotonin

Refining the transit-timing and photometric analysis of TRAPPIST-1: Masses, Radii, densities, dynamics, and ephemerides

We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST and K2 transit time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets' densities may be described with a single rocky mass-radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition, but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3-5%, equivalent to a radial-velocity (RV) precision of 2.5 cm/sec, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small; the orbits are extremely coplanar; and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations, and speculate on possible implications of the planet densities for the formation, migration and evolution of the planet system

Measurements of daily energy intake and total energy expenditure in people with dementia in care homes: the use of wearable technology.

Objectives: To estimate daily total energy expenditure (TEE) using a physical activity monitor, combined with dietary assessment of energy intake to assess the relationship between daily energy expenditure and patterns of activity with energy intake in people with dementia living in care homes. Design and setting: A cross-sectional study in care homes in the UK. Participants: Twenty residents with confirmed dementia diagnosis were recruited from two care homes that specialised in dementia care. Measurements: A physical activity monitor (Sensewear TM Armband , Body Media, Pittsburgh, PA) was employed to objectively determine total energy expenditure, sleep duration and physical activity. The armband was placed around the left upper triceps for up to 7 days. Energy intake was determined by weighing all food and drink items over 4 days (3 weekdays and 1 weekend day) including measurements of food wastage. Results: The mean age was 78.7 (SD ± 11.8) years, Body Mass Index (BMI) 23.0 (SD ± 4.2) kg/m2 ; 50% were women. Energy intake (mean 7.4; SD ± 2.6) MJ/d) was correlated with TEE (mean 7.6; SD ± 1.8 MJ/d; r=0.49, p<0.05). Duration of sleeping ranged from 0.4-12.5 (mean 6.1) hrs/d and time spent lying down was 1.3-16.0 (8.3) hrs/d. On average residents spent 17.9 (6.3-23.4) hrs/d undertaking sedentary activity. TEE was correlated with BMI (r=0.52, p<0.05) and body weight (r=0.81, p<0.001) but inversely related to sleep duration (r=-0.59, p<0.01) and time lying down (r=-0.62, p<0.01). Multiple linear regression analysis revealed that after taking BMI, sleep duration and time spent lying down into account, TEE was no longer correlated with energy intake. Conclusions: The results show the extent to which body mass, variable activity and sleep patterns may be contributing to TEE and together with reduced energy intake, energy requirements were not satisfied. Thus wearable technology has the potential to offer real-time monitoring to provide appropriate nutrition management that is more person-centred to prevent weight loss in dementi

Disturbance and diversity at two spatial scales

The spatial scale of disturbance is a factor potentially influencing the relationship between disturbance and diversity. There has been discussion on whether disturbances that affect local communities and create a mosaic of patches in different successional stages have the same effect on diversity as regional disturbances that affect the whole landscape. In a microcosm experiment with metacommunities of aquatic protists, we compared the effect of local and regional disturbances on the disturbance–diversity relationship. Local disturbances destroyed entire local communities of the metacommunity and required reimmigration from neighboring communities, while regional disturbances affected the whole metacommunity but left part of each local community intact. Both disturbance types led to a negative relationship between disturbance intensity and Shannon diversity. With strong local disturbance, this decrease in diversity was due to species loss, while strong regional disturbance had no effect on species richness but reduced the evenness of the community. Growth rate appeared to be the most important trait for survival after strong local disturbance and dominance after strong regional disturbance. The pattern of the disturbance–diversity relationship was similar for both local and regional diversity. Although local disturbances at least temporally increased beta diversity by creating a mosaic of differently disturbed patches, this high dissimilarity did not result in regional diversity being increased relative to local diversity. The disturbance–diversity relationship was negative for both scales of diversity. The flat competitive hierarchy and absence of a trade-off between competition and colonization ability are a likely explanation for this pattern

Assessing Performance of Orthology Detection Strategies Applied to Eukaryotic Genomes

Orthology detection is critically important for accurate functional annotation, and has been widely used to facilitate studies on comparative and evolutionary genomics. Although various methods are now available, there has been no comprehensive analysis of performance, due to the lack of a genomic-scale ‘gold standard’ orthology dataset. Even in the absence of such datasets, the comparison of results from alternative methodologies contains useful information, as agreement enhances confidence and disagreement indicates possible errors. Latent Class Analysis (LCA) is a statistical technique that can exploit this information to reasonably infer sensitivities and specificities, and is applied here to evaluate the performance of various orthology detection methods on a eukaryotic dataset. Overall, we observe a trade-off between sensitivity and specificity in orthology detection, with BLAST-based methods characterized by high sensitivity, and tree-based methods by high specificity. Two algorithms exhibit the best overall balance, with both sensitivity and specificity>80%: INPARANOID identifies orthologs across two species while OrthoMCL clusters orthologs from multiple species. Among methods that permit clustering of ortholog groups spanning multiple genomes, the (automated) OrthoMCL algorithm exhibits better within-group consistency with respect to protein function and domain architecture than the (manually curated) KOG database, and the homolog clustering algorithm TribeMCL as well. By way of using LCA, we are also able to comprehensively assess similarities and statistical dependence between various strategies, and evaluate the effects of parameter settings on performance. In summary, we present a comprehensive evaluation of orthology detection on a divergent set of eukaryotic genomes, thus providing insights and guides for method selection, tuning and development for different applications. Many biological questions have been addressed by multiple tests yielding binary (yes/no) outcomes but no clear definition of truth, making LCA an attractive approach for computational biology