Infinite dimensional Lie algebras in 4D conformal quantum field theory

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.Comment: 16 pages, with minor improvements as to appear in J. Phys.

Physical properties, starspot activity, orbital obliquity, and transmission spectrum of the Qatar-2 planetary system from multi-colour photometry

We present seventeen high-precision light curves of five transits of the planet Qatar-2b, obtained from four defocussed 2m-class telescopes. Three of the transits were observed simultaneously in the SDSS griz passbands using the seven-beam GROND imager on the MPG/ESO 2.2-m telescope. A fourth was observed simultaneously in Gunn grz using the CAHA 2.2-m telescope with BUSCA, and in r using the Cassini 1.52-m telescope. Every light curve shows small anomalies due to the passage of the planetary shadow over a cool spot on the surface of the host star. We fit the light curves with the prism+gemc model to obtain the photometric parameters of the system and the position, size and contrast of each spot. We use these photometric parameters and published spectroscopic measurements to obtain the physical properties of the system to high precision, finding a larger radius and lower density for both star and planet than previously thought. By tracking the change in position of one starspot between two transit observations we measure the orbital obliquity of Qatar-2 b to be 4.3 \pm 4.5 degree, strongly indicating an alignment of the stellar spin with the orbit of the planet. We calculate the rotation period and velocity of the cool host star to be 11.4 \pm 0.5 d and 3.28 \pm 0.13 km/s at a colatitude of 74 degree. We assemble the planet's transmission spectrum over the 386-976 nm wavelength range and search for variations of the measured radius of Qatar-2 b as a function of wavelength. Our analysis highlights a possible H2/He Rayleigh scattering in the blue.Comment: 20 pages, 14 figures, to appear in Monthly Notices of the Royal Astronomical Societ

Simultaneous follow-up of planetary transits: revised physical properties for the planetary systems HAT-P-16 and WASP-21

Context. By now more than 300 planets transiting their host star have been found, and much effort is being put into measuring the properties of each system. Light curves of planetary transits often contain deviations from a simple transit shape, and it is generally difficult to differentiate between anomalies of astrophysical nature (e.g. starspots) and correlated noise due to instrumental or atmospheric effects. Our solution is to observe transit events simultaneously with two telescopes located at different observatories. Aims. Using this observational strategy, we look for anomalies in the light curves of two transiting planetary systems and accurately estimate their physical parameters. Methods. We present the first photometric follow-up of the transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b, obtained simultaneously with two medium-class telescopes located in different countries, using the telescope defocussing technique. We modeled these and other published data in order to estimate the physical parameters of the two planetary systems. Results. The simultaneous observations did not highlight particular features in the light curves, which is consistent with the low activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm 0.037 RJup) than the initial estimates, suggesting the presence of a massive core. Our physical parameters for this system point towards a younger age than previously thought. The results obtained for WASP-21 reveal lower values for the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma respectively) with respect to those found in the discovery paper, in agreement with a subsequent study. We found no evidence of any transit timing variations in either system.Comment: 8 pages, 6 figures, accepted for publication in A&

Opportunistic screening for hypertension in the general population in Bulgaria: international society of hypertension may measurement month campaign

Cardiovascular diseases are not only the leading causes of mortality in Bulgaria but also the mortality rate is twice as high as the European Union average, so screening programmes identifying subjects with elevated blood pressure (BP) are of utmost importance. May Measurement Month (MMM) is an annual global initiative of the International Society of hypertension that began in 2017 aimed at raising awareness of high BP. Bulgaria joined the 3rd campaign of MMM in 2019 and an overview of the results of Bulgarian participation are presented in this paper. Hypertension was defined as systolic BP ≥ 140 mm Hg and diastolic BP ≥ 90 mm Hg or treatment for hypertension, statistical analysis followed the standard MMM protocol. In Bulgaria, 150 screening points were set up in primary and secondary care facilities, in pharmacies, and outdoor spaces across 21 administrative districts. Out of 3678 individuals screened, 2587 participants (70.3%) had hypertension. Of 2896 participants with hypertension, 35.6% had controlled BP. Out of 1760 participants not on antihypertensive medication, 669 (38%) had elevated BP. In the case of treated individuals (n = 1918), 997 (52%) had uncontrolled hypertension. In the untreated cohort, every 4th subject had elevated BP, whilst among patients on antihypertensive medication, every second had uncontrolled BP, the worst results in terms of diagnosis and treatment are observed in men. By identifying almost two-third of the whole screened cohort with the possibility of newly diagnosed or uncontrolled hypertension, our results confirm the importance of BP screening campaigns

The 2D/3D Best-Fit Problem

In computer systems, the best-fit problem can be described as a search for the best transformation matrix to transform input mea- sured points from their coordinate system into a CAD model coordinate system using a criteria function for optimization. For example, if the criterion is Mini- mum Sum of Deviations, we search for a transformation matrix M that minimizes the sum of all distances from an matrix-transformed measure points to a CAD model