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

An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5

Quasars are the most luminous non-transient objects known and as a result they enable studies of the Universe at the earliest cosmic epochs. Despite extensive efforts, however, the quasar ULAS J1120+0641 at z=7.09 has remained the only one known at z>7 for more than half a decade. Here we report observations of the quasar ULAS J134208.10+092838.61 (hereafter J1342+0928) at redshift z=7.54. This quasar has a bolometric luminosity of 4e13 times the luminosity of the Sun and a black hole mass of 8e8 solar masses. The existence of this supermassive black hole when the Universe was only 690 million years old---just five percent of its current age---reinforces models of early black-hole growth that allow black holes with initial masses of more than about 1e4 solar masses or episodic hyper-Eddington accretion. We see strong evidence of absorption of the spectrum of the quasar redwards of the Lyman alpha emission line (the Gunn-Peterson damping wing), as would be expected if a significant amount (more than 10 per cent) of the hydrogen in the intergalactic medium surrounding J1342+0928 is neutral. We derive a significant fraction of neutral hydrogen, although the exact fraction depends on the modelling. However, even in our most conservative analysis we find a fraction of more than 0.33 (0.11) at 68 per cent (95 per cent) probability, indicating that we are probing well within the reionization epoch of the Universe.Comment: Updated to match the final journal versio

Unmasking Chaotic Attributes in Time Series of Living Cell Populations

. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth.Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations.Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled

The remnants of galaxy formation from a panoramic survey of the region around M31

In hierarchical cosmological models, galaxies grow in mass through the continual accretion of smaller ones. The tidal disruption of these systems is expected to result in loosely bound stars surrounding the galaxy, at distances that reach $10 - 100$ times the radius of the central disk. The number, luminosity and morphology of the relics of this process provide significant clues to galaxy formation history, but obtaining a comprehensive survey of these components is difficult because of their intrinsic faintness and vast extent. Here we report a panoramic survey of the Andromeda galaxy (M31). We detect stars and coherent structures that are almost certainly remnants of dwarf galaxies destroyed by the tidal field of M31. An improved census of their surviving counterparts implies that three-quarters of M31's satellites brighter than $M_V < -6$ await discovery. The brightest companion, Triangulum (M33), is surrounded by a stellar structure that provides persuasive evidence for a recent encounter with M31. This panorama of galaxy structure directly confirms the basic tenets of the hierarchical galaxy formation model and reveals the shared history of M31 and M33 in the unceasing build-up of galaxies.Comment: Published in Nature. Supplementary movie available at https://www.astrosci.ca/users/alan/PANDAS/Latest%20news%3A%20movie%20of%20orbit.htm

The ethics of digital well-being: a multidisciplinary perspective

This chapter serves as an introduction to the edited collection of the same name, which includes chapters that explore digital well-being from a range of disciplinary perspectives, including philosophy, psychology, economics, health care, and education. The purpose of this introductory chapter is to provide a short primer on the different disciplinary approaches to the study of well-being. To supplement this primer, we also invited key experts from several disciplines—philosophy, psychology, public policy, and health care—to share their thoughts on what they believe are the most important open questions and ethical issues for the multi-disciplinary study of digital well-being. We also introduce and discuss several themes that we believe will be fundamental to the ongoing study of digital well-being: digital gratitude, automated interventions, and sustainable co-well-being

The outer halo globular cluster system of M31 - III. Relationship to the stellar halo

We utilize the final catalogue from the Pan-Andromeda Archaeological Survey to investigate the links between the globular cluster system and field halo in M31 at projected radii R proj = 25-150 kpc. In this region the cluster radial density profile exhibits a power-law decline with index = −2.37 ± 0.17, matching that for the stellar halo component with [Fe/H] < −1.1. Spatial density maps reveal a striking correspondence between the most luminous substructures in the metal-poor field halo and the positions of many globular clusters. By comparing the density of metal-poor halo stars local to each cluster with the azimuthal distribution at commensurate radius, we reject the possibility of no correlation between clusters and field overdensities at 99.95 per cent significance. We use our stellar density measurements and previous kinematic data to demonstrate that ≈35-60 per cent of clusters exhibit properties consistent with having been accreted into the outskirts of M31 at late times with their parent dwarfs. Conversely, at least ∼40 per cent of remote clusters show no evidence for a link with halo substructure. The radial density profile for this subgroup is featureless and closely mirrors that observed for the apparently smooth component of the metal-poor stellar halo. We speculate that these clusters are associated with the smooth halo; if so, their properties appear consistent with a scenario where the smooth halo was built up at early times via the destruction of primitive satellites. In this picture the entire M31 globular cluster system outside R proj = 25 kpc comprises objects accumulated from external galaxies over a Hubble time of growth

Physical activity monitoring in obese people in the real life environment

<p>Abstract</p> <p>Background</p> <p>Obesity is a major problem especially in western countries and several studies underline the importance of physical activity to enhance diet. Currently there is increasing interest in instruments for monitoring daily physical activity. The purpose of this pilot study was to appraise the qualitative and quantitative differences in physical activities and gait analysis parameters in control and obese subjects by means of an innovative tool for the monitoring of physical activity.</p> <p>Methods</p> <p>Twenty-six obese patients, 16 women and 10 men, aged 22 to 69 years with Body Mass Index (BMI) between 30 and 51.4 kg/m², were compared with 15 control subjects, 4 men and 11 women, aged 24 to 69 with BMI between 18 and 25 kg/m²during daily physical activities. The IDEEA device (Minisun, Fresno, CA), based on a wearable system of biaxial accelerometers and able to continuously record the physical activities and energy expenditure of a subject in time was used. Time spent in different physical activities such as standing, sitting, walking, lying, reclining, stepping, energy expenditure and gait parameters (velocity, stance duration, etc) were measured during a 24-hours period.</p> <p>Results</p> <p>A trend toward a reduced number of steps was present, associated to reduced speed, reduced cadence and reduced rate of single and double limb support (SLS/DLS). Moreover, obese people spent significant less time stepping, less time lying and more time in a sitting or reclined position during the night. The energy expenditure during a 24-hours period was higher in the obese compared to controls.</p> <p>Conclusions</p> <p>The study provided objective parameters to differentiate the daily motor activity of obese subjects with respect to controls, even a larger population is required to confirm these findings. The device used can be of support in programming educational activities for life style modification in obese people as well as for monitoring the results of various kinds of intervention in these patients concerning weight and physical performance.</p

How Immunocontraception Can Contribute to Elephant Management in Small, Enclosed Reserves: Munyawana Population as a Case Study

Immunocontraception has been widely used as a management tool to reduce population growth in captive as well as wild populations of various fauna. We model the use of an individual-based rotational immunocontraception plan on a wild elephant, Loxodonta africana, population and quantify the social and reproductive advantages of this method of implementation using adaptive management. The use of immunocontraception on an individual, rotational basis stretches the inter-calving interval for each individual female elephant to a management-determined interval, preventing exposing females to unlimited long-term immunocontraception use (which may have as yet undocumented negative effects). Such rotational immunocontraception can effectively lower population growth rates, age the population, and alter the age structure. Furthermore, such structured intervention can simulate natural process such as predation or episodic catastrophic events (e.g., drought), which regulates calf recruitment within an abnormally structured population. A rotational immunocontraception plan is a feasible and useful elephant population management tool, especially in a small, enclosed conservation area. Such approaches should be considered for other long-lived, social species in enclosed areas where the long-term consequences of consistent contraception may be unknown

Observing the Stellar Halo of Andromeda in Cosmological Simulations: The AURIGA2PANDAS Pipeline

We present a direct comparison of the Pan-Andromeda Archaeological Survey (PAndAS) observations of the stellar halo of M31 with the stellar halos of six galaxies from the Auriga simulations. We process the simulated halos through the Auriga2PAndAS pipeline and create PAndAS-like mocks that fold in all observational limitations of the survey data (foreground contamination from the Milky Way stars, incompleteness of the stellar catalogs, photometric uncertainties, etc.). This allows us to study the survey data and the mocks in the same way and generate directly comparable density maps and radial density profiles. We show that the simulations are overall compatible with the observations. Nevertheless, some systematic differences exist, such as a preponderance for metal-rich stars in the mocks. While these differences could suggest that M31 had a different accretion history or has a different mass compared with the simulated systems, it is more likely a consequence of an underquenching of the star formation history of galaxies, related to the resolution of the Auriga simulations. The direct comparison enabled by our approach offers avenues to improve our understanding of galaxy formation as they can help pinpoint the observable differences between observations and simulations. Ideally, this approach will be further developed through an application to other stellar halo simulations. To facilitate this step, we release the pipeline to generate the mocks, along with the six mocks presented and used in this contribution

Protocol for a population-based Ankylosing Spondylitis (PAS) cohort in Wales

<p>Abstract</p> <p>Background</p> <p>To develop a population-based cohort of people with ankylosing spondylitis (AS) in Wales using (1) secondary care clinical datasets, (2) patient-derived questionnaire data and (3) routinely-collected information in order to examine disease history and the health economic cost of AS.</p> <p>Methods</p> <p>This data model will include and link (1) secondary care clinician datasets (i.e. electronic patient notes from the rheumatologist) (2) patient completed questionnaires (giving information on disease activity, medication, function, quality of life, work limitations and health service utilisation) and (3) a broad range of routinely collected data (including; GP records, in-patient hospital admission data, emergency department data, laboratory/pathology data and social services databases). The protocol involves the use of a unique and powerful data linkage system which allows datasets to be interlinked and to complement each other.</p> <p>Discussion</p> <p>This cohort can integrate patient supplied, primary and secondary care data into a unified data model. This can be used to study a range of issues such as; the true economic costs to the health care system and the patient, factors associated with the development of severe disease, long term adverse events of new and existing medication and to understand the disease history of this condition. It will benefit patients, clinicians and health care managers. This study forms a pilot project for the use of routine data/patient data linked cohorts for other chronic conditions.</p