QUAK: A Synthetic Quality Estimation Dataset for Korean-English Neural Machine Translation

With the recent advance in neural machine translation demonstrating its importance, research on quality estimation (QE) has been steadily progressing. QE aims to automatically predict the quality of machine translation (MT) output without reference sentences. Despite its high utility in the real world, there remain several limitations concerning manual QE data creation: inevitably incurred non-trivial costs due to the need for translation experts, and issues with data scaling and language expansion. To tackle these limitations, we present QUAK, a Korean-English synthetic QE dataset generated in a fully automatic manner. This consists of three sub-QUAK datasets QUAK-M, QUAK-P, and QUAK-H, produced through three strategies that are relatively free from language constraints. Since each strategy requires no human effort, which facilitates scalability, we scale our data up to 1.58M for QUAK-P, H and 6.58M for QUAK-M. As an experiment, we quantitatively analyze word-level QE results in various ways while performing statistical analysis. Moreover, we show that datasets scaled in an efficient way also contribute to performance improvements by observing meaningful performance gains in QUAK-M, P when adding data up to 1.58M

On the constant in the Turan-Kubilius inequality.

Since Kubilius in 1983 proved that the Turan-Kubilius inequality holds with the constant close to 1.5, it has been conjectured that the inequality holds with the constant 1.5. In this thesis the conjecture is settled positively in the case of strongly additive functions for all sufficiently large x. The key to the proof is a lower bound on a bilinear form. This is obtained by constructing very precise approximations for the lowest eigenvalue and eigenvector using the power method from numerical analysis. For the latter construction precise evaluations of the mean values of many complicated arithmetic functions on prime numbers. The mean values were sought using analytic methods and the method of hyperbola.Ph.D.MathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128372/2/9001667.pd

A NOTE ON THE ZEROS OF JENSEN POLYNOMIALS

Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.N