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

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

Pure-radiation gravitational fields with a simple twist and a Killing vector

Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.Comment: revtex, 9 page

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

Whole genome sequencing-based mapping and candidate identification of mutations from fixed zebrafish tissue

As forward genetic screens in zebrafish become more common, the number of mutants that cannot be identified by gross morphology or through transgenic approaches, such as many nervous system defects, has also increased. Screening for these difficult-to-visualize phenotypes demands techniques such as whole-mount in situ hybridization (WISH) or antibody staining, which require tissue fixation. To date, fixed tissue has not been amenable for generating libraries for whole genome sequencing (WGS). Here, we describe a method for using genomic DNA from fixed tissue and a bioinformatics suite for WGS-based mapping of zebrafish mutants. We tested our protocol using two known zebrafish mutant alleles, gpr126st49 and egr2bfh227, both of which cause myelin defects. As further proof of concept we mapped a novel mutation, stl64, identified in a zebrafish WISH screen for myelination defects. We linked stl64 to chromosome 1 and identified a candidate nonsense mutation in the F-box and WD repeat domain containing 7 (fbxw7) gene. Importantly, stl64 mutants phenocopy previously described fbxw7vu56 mutants, and knockdown of fbxw7 in wild-type animals produced similar defects, demonstrating that stl64 disrupts fbxw7. Together, these data show that our mapping protocol can map and identify causative lesions in mutant screens that require tissue fixation for phenotypic analysis

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