The support problem for abelian varieties

Let $A$ be an abelian variety over a number field $K$. If $P$ and $Q$ are $K$-rational points of $A$ such that the order of the reduction of $Q$ divides that of $P$ for all but finitely many primes of the ring of integers of $K$, then there exists a $K$-endomorphism $\phi$ of $A$ and a positive integer $k$ such that $kQ = \phi(P)$.Comment: 7 pages, plain TeX. The statements of the main theorem and main corollary are slightly weakened to coincide with what is actually proved in the paper. There are a few other minor changes. To appear in the Journal of Number Theor

How often is a permutation an n'th power?

We give a short argument that for any fixed n, the probability that a permutation on m letters is an n'th power is asymptotically C m^{phi(n)/n - 1}.Comment: 2 page

An Experiment with Hierarchical Bayesian Record Linkage

In record linkage (RL), or exact file matching, the goal is to identify the links between entities with information on two or more files. RL is an important activity in areas including counting the population, enhancing survey frames and data, and conducting epidemiological and follow-up studies. RL is challenging when files are very large, no accurate personal identification (ID) number is present on all files for all units, and some information is recorded with error. Without an unique ID number one must rely on comparisons of names, addresses, dates, and other information to find the links. Latent class models can be used to automatically score the value of information for determining match status. Data for fitting models come from comparisons made within groups of units that pass initial file blocking requirements. Data distributions can vary across blocks. This article examines the use of prior information and hierarchical latent class models in the context of RL.Comment: 14 pages, 0 figure

Discussion of "Calibrated Bayes, for Statistics in General, and Missing Data in Particular" by R. J. A. Little

Discussion of "Calibrated Bayes, for Statistics in General, and Missing Data in Particular" by R. Little [arXiv:1108.1917]Comment: Published in at http://dx.doi.org/10.1214/10-STS318B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Beauville surfaces and finite simple groups

A Beauville surface is a rigid complex surface of the form (C1 x C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates.Comment: 20 page