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

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

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

In vitro inhibitory activities of selected Australian medicinal plant extracts against protein glycation, angiotensin converting enzyme (ACE) and digestive enzymes linked to type II diabetes

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Background There is a need to develop potential new therapies for the management of diabetes and hypertension. Australian medicinal plants collected from the Kuuku I’yu (Northern Kaanju) homelands, Cape York Peninsula, Queensland, Australia were investigated to determine their therapeutic potential. Extracts were tested for inhibition of protein glycation and key enzymes relevant to the management of hyperglycaemia and hypertension. The inhibitory activities were further correlated with the antioxidant activities. Methods Extracts of five selected plant species were investigated: Petalostigma pubescens, Petalostigma banksii, Memecylon pauciflorum, Millettia pinnata and Grewia mesomischa. Enzyme inhibitory activity of the plant extracts was assessed against α-amylase, α-glucosidase and angiotensin converting enzyme (ACE). Antiglycation activity was determined using glucose-induced protein glycation models and formation of protein-bound fluorescent advanced glycation endproducts (AGEs). Antioxidant activity was determined by measuring the scavenging effect of plant extracts against 1, 1-diphenyl-2-picryl hydrazyl (DPPH) and using the ferric reducing anti-oxidant potential assay (FRAP). Total phenolic and flavonoid contents were also determined. Results Extracts of the leaves of Petalostigma banksii and P. pubescens showed the strongest inhibition of α-amylase with IC50 values of 166.50 ± 5.50 μg/mL and 160.20 ± 27.92 μg/mL, respectively. The P. pubescens leaf extract was also the strongest inhibitor of α-glucosidase with an IC50 of 167.83 ± 23.82 μg/mL. Testing for the antiglycation potential of the extracts, measured as inhibition of formation of protein-bound fluorescent AGEs, showed that P. banksii root and fruit extracts had IC50 values of 34.49 ± 4.31 μg/mL and 47.72 ± 1.65 μg/mL, respectively, which were significantly lower (p < 0.05) than other extracts. The inhibitory effect on α-amylase, α-glucosidase and the antiglycation potential of the extracts did not correlate with the total phenolic, total flavonoid, FRAP or DPPH. For ACE inhibition, IC50 values ranged between 266.27 ± 6.91 to 695.17 ± 15.38 μg/mL. Conclusions The tested Australian medicinal plant extracts inhibit glucose-induced fluorescent AGEs, α-amylase, α-glucosidase and ACE with extracts of Petalostigma species showing the most promising activity. These medicinal plants could potentially be further developed as therapeutic agents in the treatment of hyperglycaemia and hypertension

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

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Sources of stakeholder salience in the responsible investment movement: why do investors sign the Principles for Responsible Investment?

Since its inception in 2006, the United Nations-backed Principles for Responsible Investment (PRI) have grown to over 1300 signatories representing over $45 trillion. This growth is not slowing down. In this paper, we argue that there is a set of attributes which make the PRI salient as a stakeholder and its claim to sign the six PRI important to institutional investors. We use Mitchell et al.’s (Acad Manag Rev 22:853–886, 1997) theoretical framework of stakeholder salience, as extended by Gifford (J Bus Eth 92:79–97, 2010). We use as evidence confidential data from the annual survey of signatories carried out by the PRI in a 5-year period between 2007 and 2011. The findings highlight pragmatic and organizational legitimacy, normative and utilitarian power, and management values as the attributes that contribute most to the salience of the PRI as a stakeholder

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

Discovery of a nearby 1700 km/s star ejected from the Milky Way by Sgr A*

Abstract We present the serendipitous discovery of the fastest Main Sequence hyper-velocity star (HVS) by the Southern Stellar Stream Spectroscopic Survey (S5). The star S5-HVS1 is a ∼2.35 M⊙ A-type star located at a distance of ∼9 kpc from the Sun and has a heliocentric radial velocity of 1017 ± 2.7  km s−1 without any signature of velocity variability. The current 3-D velocity of the star in the Galactic frame is 1755 ± 50  km s−1. When integrated backwards in time, the orbit of the star points unambiguously to the Galactic Centre, implying that S5-HVS1 was kicked away from Sgr A* with a velocity of ∼1800  km s−1 and travelled for 4.8 Myr to its current location. This is so far the only HVS confidently associated with the Galactic Centre. S5-HVS1 is also the first hyper-velocity star to provide constraints on the geometry and kinematics of the Galaxy, such as the Solar motion Vy, ⊙ = 246.1 ± 5.3  km s−1 or position R0 = 8.12 ± 0.23 kpc. The ejection trajectory and transit time of S5-HVS1 coincide with the orbital plane and age of the annular disk of young stars at the Galactic centre, and thus may be linked to its formation. With the S5-HVS1 ejection velocity being almost twice the velocity of other hyper-velocity stars previously associated with the Galactic Centre, we question whether they have been generated by the same mechanism or whether the ejection velocity distribution has been constant over time