Some congruences involving central q-binomial coefficients

Motivated by recent works of Sun and Tauraso, we prove some variations on the Green-Krammer identity involving central q-binomial coefficients, such as $$\sum_{k=0}^{n-1}(-1)^kq^{-{k+1\choose 2}}{2k\brack k}_q \equiv (\frac{n}{5}) q^{-\lfloor n^4/5\rfloor} \pmod{\Phi_n(q)},$$ where $\big(\frac{n}{p}\big)$ is the Legendre symbol and $\Phi_n(q)$ is the $n$th cyclotomic polynomial. As consequences, we deduce that \sum_{k=0}^{3^a m-1} q^{k}{2k\brack k}_q &\equiv 0 \pmod{(1-q^{3^a})/(1-q)}, \sum_{k=0}^{5^a m-1}(-1)^kq^{-{k+1\choose 2}}{2k\brack k}_q &\equiv 0 \pmod{(1-q^{5^a})/(1-q)}, for $a,m\geq 1$, the first one being a partial q-analogue of the Strauss-Shallit-Zagier congruence modulo powers of 3. Several related conjectures are proposed.Comment: 16 pages, detailed proofs of Theorems 4.1 and 4.3 are added, to appear in Adv. Appl. Mat

Using foreign inclusion detection to improve parsing performance

Inclusions from other languages can be a significant source of errors for monolin-gual parsers. We show this for English in-clusions, which are sufficiently frequent to present a problem when parsing German. We describe an annotation-free approach for accurately detecting such inclusions, and de-velop two methods for interfacing this ap-proach with a state-of-the-art parser for Ger-man. An evaluation on the TIGER cor-pus shows that our inclusion entity model achieves a performance gain of 4.3 points in F-score over a baseline of no inclusion de-tection, and even outperforms a parser with access to gold standard part-of-speech tags.

Daniel Brack

https://digitalcommons.georgiasouthern.edu/willowhillheritage-obituaries/1452/thumbnail.jp

Scalar radius of the pion in the Kroll-Lee-Zumino renormalizable theory

The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next to leading (one loop) order in perturbation theory. Due to renormalizability, this determination involves no free parameters. The result is $_s = 0.40 {fm}^2$. This value gives for $\bar{\ell}_4$, the low energy constant of chiral perturbation theory, $\bar{\ell}_4 = 3.4$, and $F_\pi/F = 1.05$, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $\rho\pi\pi$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) NNLO contribution

Joseph Nathan Brack

https://digitalcommons.georgiasouthern.edu/willowhillheritage-obituaries/1385/thumbnail.jp

Book Review: Euroscepticism within the EU institutions: diverging views of europe

Since its origins, there have been competing views concerning the nature, scope and objectives of the process of integration and of the European Union. Attitudes towards Europe and European integration, both among political elites and citizens, have been much studied over the last 15 years. But there is no comprehensive analysis of these competing views of Europe at the supranational level. Stuart A. Brown reviews Nathalie Brack and Olivier Costa’s edited collection on the divergence in views about the European Union, which lends insight into its consequences for the functioning of the EU and its institutions

Green Beans

In this video the author describes the history of green beans in Appalachia, from their role as one of the Native American's "Three Sisters", and their adoption by European settlers, and also looks at how beans have been utilized in literature

Parsing coordinations

The present paper is concerned with statistical parsing of constituent structures in German. The paper presents four experiments that aim at improving parsing performance of coordinate structure: 1) reranking the n-best parses of a PCFG parser, 2) enriching the input to a PCFG parser by gold scopes for any conjunct, 3) reranking the parser output for all possible scopes for conjuncts that are permissible with regard to clause structure. Experiment 4 reranks a combination of parses from experiments 1 and 3. The experiments presented show that n- best parsing combined with reranking improves results by a large margin. Providing the parser with different scope possibilities and reranking the resulting parses results in an increase in F-score from 69.76 for the baseline to 74.69. While the F-score is similar to the one of the first experiment (n-best parsing and reranking), the first experiment results in higher recall (75.48% vs. 73.69%) and the third one in higher precision (75.43% vs. 73.26%). Combining the two methods results in the best result with an F-score of 76.69