The effects of rotation on the lithium depletion of G- and K-dwarfs in Messier 35

ABSTRACT New fibre spectroscopy and radial velocities from the WIYN telescope are used to measure photospheric lithium in 242 high-probability, zero-age main-sequence F- to K-type members of the rich cluster M35. Combining these with published rotation periods, the connection between lithium depletion and rotation is studied in unprecedented detail. At Teff < 5500 K there is a strong relationship between faster rotation and less Li depletion, although with a dispersion larger than measurement uncertainties. Components of photometrically identified binary systems follow the same relationship. A correlation is also established between faster rotation rate (or smaller Rossby number), decreased Li depletion and larger stellar radius at a given Teff. These results support models where star-spots and interior magnetic fields lead to inflated radii and reduced Li depletion during the pre-main-sequence (PMS) phase for the fastest rotators. However, the data are also consistent with the idea that all stars suffered lower levels of Li depletion than predicted by standard PMS models, perhaps because of deficiencies in those models or because saturated levels of magnetic activity suppress Li depletion equally in PMS stars of similar Teff regardless of rotation rate, and that slower rotators subsequently experience more mixing and post-PMS Li depletion.

Open-World Probabilistic Databases: An Abridged Report

Large-scale probabilistic knowledge bases are becoming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics underlying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to default intervals. For this open-world setting, we lift the existing data complexity dichotomy of probabilistic databases, and propose an efficient evaluation algorithm for unions of conjunctive queries. We also show that query evaluation can become harder for non-monotone queries.

Early Disappointments: The Science Fiction Pulps

This chapter focuses on Ray Bradbury's early disappointments in getting his science fiction stories published. Publication of Bradbury's new short stories, written in collaboration with Henry Hasse, in science fiction pulps proved to be a far more difficult proposition than it had been with “Pendulum.” In October 1941, for example, Julius Schwartz was able to place “Gabriel's Horn” in Captain Future, but it reached print only in the spring 1943 issue. This chapter considers Bradbury's limited success with any of his science fiction stories after ending his collaboration with Hasse, including “Eat, Drink, and Be Wary,” which he sold to John Campbell for the “Probability Zero” contest in the July issue of Astounding; only “The Candle” appeared in print during the rest of the year—in the November 1942 issue of Weird Tales.

Coverage of the whole space

Consider an inhomogeneous germ-grain model with spherical grains whose radii depend on their positions through a rate function, possibly perturbed by a random noise. We find the critical rate function that separates the cases when the germ-grain model covers the whole space with a positive probability and when the total coverage occurs with probability zero.

Coverage of the whole space

Consider an inhomogeneous germ-grain model with spherical grains whose radii depend on their positions through a rate function, possibly perturbed by a random noise. We find the critical rate function that separates the cases when the germ-grain model covers the whole space with a positive probability and when the total coverage occurs with probability zero.

Stationary countable dense random sets

We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-stationarity (null-events stay null under the group action). In passing, it is noted that the property of being countable does not correspond to a measurable subset of the space of subsets of an uncountably infinite Polish space.

Stationary countable dense random sets

We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-stationarity (null-events stay null under the group action). In passing, it is noted that the property of being countable does not correspond to a measurable subset of the space of subsets of an uncountably infinite Polish space.

A Zero-One Result for the Least Squares Estimator

The least squares estimator for the linear regression model is shown to converge to the true parameter vector either with probability one or with probability zero. In the latter case, it either converges to a point not equal to the true parameter with probability one, or it diverges with probability one. These results are shown to hold under weak conditions on the dependent random variable and regressor variables. No additional conditions are placed on the errors. The dependent and regressor variables are assumed to be weakly dependent—in particular, to be strong mixing. The regressors may be fixed or random and must exhibit a certain degree of independent variability. No further assumptions are needed. The model considered allows the number of regressors to increase without bound as the sample size increases. The proof proceeds by extending Kolmogorov's 0-1 law for independent randomvariables to strong mixing random variables.