Uniform infinite planar triangulation and related time-reversed critical branching process

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe

Towards a Continuous Record of the Sky

It is currently feasible to start a continuous digital record of the entire sky sensitive to any visual magnitude brighter than 15 each night. Such a record could be created with a modest array of small telescopes, which collectively generate no more than a few Gigabytes of data daily. Alternatively, a few small telescopes could continually re-point to scan and reco rd the entire sky down to any visual magnitude brighter than 15 with a recurrence epoch of at most a few weeks, again always generating less than one Gigabyte of data each night. These estimates derive from CCD ability and budgets typical of university research projects. As a prototype, we have developed and are utilizing an inexpensive single-telescope system that obtains optical data from about 1500 square degrees. We discuss the general case of creating and storing data from a both an epochal survey, where a small number of telescopes continually scan the sky, and a continuous survey, composed of a constellation of telescopes dedicated each continually inspect a designated section of the sky. We compute specific limitations of canonical surveys in visible light, and estimate that all-sky continuous visual light surveys could be sensitive to magnitude 20 in a single night by about 2010. Possible scientific returns of continuous and epochal sky surveys include continued monitoring of most known variable stars, establishing case histories for variables of future interest, uncovering new forms of stellar variability, discovering the brightest cases of microlensing, discovering new novae and supernovae, discovering new counterparts to gamma-ray bursts, monitoring known Solar System objects, discovering new Solar System objects, and discovering objects that might strike the Earth.Comment: 38 pages, 9 postscript figures, 2 gif images. Revised and new section added. Accepted to PASP. Source code submitted to ASCL.ne

Improving together : collaboration needs to start with regulators

The regulatory landscape in the UK is changing again. From 1 April 2019 NHS England and NHS Improvement became what is effectively a single organisation with far reaching responsibility for the oversight of the system. The structural features of this change, which will eventually require legislative reform, have been widely debated, not least by those affected by plans for a collaborative approach to improvement in the NHS.12 But there has been less discussion about the style and approach to regulation that might be best suited to drive improvement in the NHS as set out in the long term plan.3 We contend that a major change is required in the way the system interacts with service providers if we are to be successful in developing a new service model for the 21st century

The Discovery of Cepheids and a New Distance to NGC 2841 Using the Hubble Space Telescope

We report on the discovery of Cepheids in the spiral galaxy NGC 2841, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. NGC 2841 was observed over 12 epochs using the F555W filter, and over 5 epochs using the F814W filter. Photometry was performed using the DAOPHOT/ALLFRAME package. We discovered a total of 29 variables, including 18 high-quality Cepheids with periods ranging from 15 to 40 days. Period-luminosity relations in the V and I bands, based on the high-quality Cepheids, yield an extinction-corrected distance modulus of 30.74 +/- 0.23 mag, which corresponds to a distance of 14.1 +/- 1.5 Mpc. Our distance is based on an assumed LMC distance modulus of 18.50 +/- 0.10 mag (D = 50+/- 2.5 kpc) and a metallicity dependence of the Cepheid P-L relation of gamma (VI) = -0.2 +/- 0.2 mag/dex.Comment: 31 preprint pages including 10 figures. Accepted for publication in ApJ. High-resolution version available from http://cfa-www.harvard.edu/~lmacri/n2841.p

Recent origin of low trabecular bone density in modern humans

Humans are unique, compared with our closest living relatives (chimpanzees) and early fossil hominins, in having an enlarged body size and lower limb joint surfaces in combination with a relatively gracile skeleton (i.e., lower bone mass for our body size). Some analyses have observed that in at least a few anatomical regions modern humans today appear to have relatively low trabecular density, but little is known about how that density varies throughout the human skeleton and across species or how and when the present trabecular patterns emerged over the course of human evolution. Here, we test the hypotheses that (i) recent modern humans have low trabecular density throughout the upper and lower limbs compared with other primate taxa and (ii) the reduction in trabecular density first occurred in early Homo erectus, consistent with the shift toward a modern human locomotor anatomy, or more recently in concert with diaphyseal gracilization in Holocene humans. We used peripheral quantitative CT and microtomography to measure trabecular bone of limb epiphyses (long bone articular ends) in modern humans and chimpanzees and in fossil hominins attributed to Australopithecus africanus, Paranthropus robustus/early Homo from Swartkrans, Homo neanderthalensis, and early Homo sapiens. Results show that only recent modern humans have low trabecular density throughout the limb joints. Extinct hominins, including pre-Holocene Homo sapiens, retain the high levels seen in nonhuman primates. Thus, the low trabecular density of the recent modern human skeleton evolved late in our evolutionary history, potentially resulting from increased sedentism and reliance on technological and cultural innovations