Cutting edges at random in large recursive trees

We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or disconnect certain distinguished vertices when the size of the tree tends to infinity. New probabilistic explanations are given in terms of the so-called cut-tree and the tree of component sizes, which both encode different aspects of the destruction process. Finally, we establish the connection to Bernoulli bond percolation on large RRT's and present recent results on the cluster sizes in the supercritical regime.Comment: 29 pages, 3 figure

Global affordability of fluoride toothpaste

<p>Abstract</p> <p>Objective</p> <p>Dental caries remains the most common disease worldwide and the use of fluoride toothpaste is a most effective preventive public health measure to prevent it. Changes in diets following globalization contribute to the development of dental caries in emerging economies. The aim of this paper is to compare the cost and relative affordability of fluoride toothpaste in high-, middle- and low-income countries. The hypothesis is that fluoride toothpaste is not equally affordable in high-, middle- and low-income countries.</p> <p>Methods</p> <p>Data on consumer prices of fluoride toothpastes were obtained from a self-completion questionnaire from 48 countries. The cost of fluoride toothpaste in high-, middle- and low-income countries was compared and related to annual household expenditure as well as to days of work needed to purchase the average annual usage of toothpaste per head.</p> <p>Results</p> <p>The general trend seems to be that the proportion of household expenditure required to purchase the annual dosage of toothpaste increases as the country's per capita household expenditure decreases. While in the UK for the poorest 30% of the population only 0.037 days of household expenditure is needed to purchase the annual average dosage (182.5 g) of the lowest cost toothpaste, 10.75 days are needed in Kenya. The proportion of annual household expenditure ranged from 0.02% in the UK to 4% in Zambia to buy the annual average amount of lowest cost toothpaste per head.</p> <p>Conclusion</p> <p>Significant inequalities in the affordability of this essential preventive care product indicate the necessity for action to make it more affordable. Various measures to improve affordability based on experiences from essential pharmaceuticals are proposed.</p

Discovery of an Unbound Hyper-Velocity Star in the Milky Way Halo

We have discovered a star, SDSS J090745.0+024507, leaving the Galaxy with a heliocentric radial velocity of +853+-12 km/s, the largest velocity ever observed in the Milky Way halo. The star is either a hot blue horizontal branch star or a B9 main sequence star with a heliocentric distance ~55 kpc. Corrected for the solar reflex motion and to the local standard of rest, the Galactic rest-frame velocity is +709 km/s. Because its radial velocity vector points 173.8 deg from the Galactic center, we suggest that this star is the first example of a hyper-velocity star ejected from the Galactic center as predicted by Hills and later discussed by Yu & Tremaine. The star has [Fe/H]~0, consistent with a Galactic center origin, and a travel time of <80 Myr from the Galactic center, consistent with its stellar lifetime. If the star is indeed traveling from the Galactic center, it should have a proper motion of 0.3 mas/yr observable with GAIA. Identifying additional hyper-velocity stars throughout the halo will constrain the production rate history of hyper-velocity stars at the Galactic center.Comment: 4 pages, submitted to ApJ Letter

Defects and boundary layers in non-Euclidean plates

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers -- deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet

Development of a Cartilage Oligomeric Matrix Protein Neo-Epitope Assay for the Detection of Intra-Thecal Tendon Disease

The diagnosis of tendon injury relies on clinical signs and diagnostic imaging but imaging is subjective and does not always correlate with clinical signs. A molecular marker would potentially offer a sensitive and specific diagnostic tool that could also provide objective assessment of healing for the comparison of different treatments. Cartilage Oligomeric Matrix Protein (COMP) has been used as a molecular marker for osteoarthritis in humans and horses but assays for the protein in tendon sheath synovial fluids have shown overlap between horses affected by tendinopathy and controls. We hypothesized that quantifying a COMP neoepitope would be more discriminatory of injury. COMP fragments were purified from synovial fluids of horses with intra-thecal tendon injuries and media from equine tendon explants, and mass spectrometry of a consistent and abundant fragment revealed a ~100 kDa COMP fragment with a new N-terminus at the 78th amino-acid (NH2-TPRVSVRP) located just outside the junctional region of the protein. A competitive inhibition ELISA based on a polyclonal antibody raised to this sequence yielded more than a 10-fold rise in the mean neoepitope levels for tendinopathy cases compared to controls (5.3 ± 1.3 µg/mL (n = 7) versus 58.8 ± 64.3 µg/mL (n = 13); p = 0.002). However, there was some cross-reactivity of the neoepitope polyclonal antiserum with intact COMP, which could be blocked by a peptide spanning the neoepitope. The modified assay demonstrated a lower concentration but a significant > 500-fold average rise with tendon injury (2.5 ± 2.2 ng/mL (n = 6) versus 1029.8 ± 2188.8 ng/ml (n = 14); p = 0.013). This neo-epitope assay therefore offers a potentially useful marker for clinical use

Revised physical elements of the astrophysically important O9.5+O9.5V eclipsing binary system Y Cyg

Thanks to its long and rich observational history and rapid apsidal motion, the massive eclipsing binary Y Cyg represents one of the cornestones to critical tests of stellar evolution theory for massive stars. Yet, the determination of the basic physical properties is less accurate than it could be given the existing number of spectral and photometric observations. Our goal is to analyze all these data simultaneously with the new dedicated series of our own spectral and photometric observations from observatories widely separated in longitude. We obtained new series of UBV observations at three observatories separated in local time to obtain complete light curves of Y Cyg for its orbital period close to 3 days. This new photometry was reduced and carefully transformed to the standard UBV system using the HEC22 program. We also obtained new series of red spectra secured at two observatories and re-analyzed earlier obtained blue electronic spectra. Our analyses provide the most accurate so far published value of the apsidal period of 47.805 +/- 0.030 yrs and the following physical elements: M1=17.72+/-0.35$ Msun, M2=17.73+/-0.30 Msun, R1=5.785+/-0.091 Rsun, and R2=5.816+/-0.063 Rsun. The disentangling thus resulted in the masses, which are somewhat higher than all previous determinations and virtually the same for both stars, while the light curve implies a slighly higher radius and luminosity for star 2. The above empirical values imply the logarithm of the internal structure constant log k2 = -1.937. A comparison with Claret's stellar interior models implies an age close to 2 millions yrs for both stars. The claimed accuracy of modern element determination of 1-2 per cent seems still a bit too optimistic and obtaining new high-dispersion and high-resolution spectra is desirable.Comment: 13 pages; accepted for publication in Astronomy and Astrophysic

The ATLAS tile calorimeter digitizer

The ATLAS Tile Calorimeter digitizer system samples photomultiplier signals from the scintillating tiles of the hadronic calorimeter. For each channel a pair of 10-bit ADCs digitize high and low gain signals at 40.08 MHz to provide the necessary 16-bit dynamic range. The sampled data is temporarily stored in digital pipelines for up to 6.375 \mu­s, awaiting a level-1 accept. For each accept received, the corresponding sampled pulse is transferred to a derandomizer buffer for subsequent readout to the data acquisition system (DAQ). The main functionality of the digitizer is implemented in radiation tolerant ASICs, using a fault tolerant architecture to minimize the consequences of radiation induced faults