On various restricted sumsets

For finite subsets A_1,...,A_n of a field, their sumset is given by {a_1+...+a_n: a_1 in A_1,...,a_n in A_n}. In this paper we study various restricted sumsets of A_1,...,A_n with restrictions of the following forms: a_i-a_j not in S_{ij}, or alpha_ia_i not=alpha_ja_j, or a_i+b_i not=a_j+b_j (mod m_{ij}). Furthermore, we gain an insight into relations among recent results on this area obtained in quite different ways.Comment: 11 pages; final version for J. Number Theor

GRADUATE PIANO RECITAL

This thesis contains information pertaining to my Graduate Piano Recital. The recital consists of the following works: Piano Sonata Op. 26 by Ludwig Van Beethoven; French Suite No. 2 by Johann Sebastian Bach; Keyboard Concerto in D major, Hob. XVIII: 11 by Franz Joseph Haydn; Scherzo Op. 4 by Johannes Brahms. The thesis includes biographical information on each composer, introductions of each different genre and character; an analysis of each piece, and performance suggestions

Robustness of Bayesian Pool-based Active Learning Against Prior Misspecification

We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all $\alpha$-approximate algorithms are robust (i.e., near $\alpha$-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost setting, we can also obtain a robustness result for approximate AL algorithms. Our results imply that many commonly used AL algorithms are robust against perturbed priors. We then propose the use of a mixture prior to alleviate the problem of prior misspecification. We analyze the robustness of the uniform mixture prior and show experimentally that it performs reasonably well in practice.Comment: This paper is published at AAAI Conference on Artificial Intelligence (AAAI 2016

Charged basal stacking fault (BSF) scattering in nitride semiconductors

A theory of charge transport in semiconductors in the presence of basal stacking faults is developed. It is shown that the presence of basal stacking faults leads to anisotropy in carrier transport. The theory is applied to carrier transport in non-polar GaN films consisting of a large number BSFs, and the result is compared with experimental data.Comment: 4 pages, 3 figure

Study of the weak annihilation contributions in charmless Bs→VVB_s\to VV decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless $B_s\to VV$ (where $V$ stands for a light vector meson) decays, we perform the $\chi^2$-analyses for the end-point parameters within the QCD factorization framework, under the constraints from the measured $\bar B_{s}\to$$\rho^0\phi$, $\phi K^{*0}$, $\phi \phi$ and $K^{*0}\bar K^{*0}$ decays. The fitted results indicate that the end-point parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless $B\to PP$ and $PV$ (where $P$ stands for a light pseudo-scalar meson) decays observed in the previous work. Moreover, the abnormal polarization fractions $f_{L,\bot}(\bar B_{s}\to K^{*0}\bar K^{*0})=(20.1\pm7.0)\%\,,(58.4\pm8.5)\%$ measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of $\bar B_{s}\to\phi K^{*0}$ decay exhibits a tension between the data and theoretical result, which dominates the contributions to $\chi_{\rm min}^2$ in the fits. Using the fitted end-point parameters, we update the theoretical results for the charmless $B_s\to VV$ decays, which will be further tested by the LHCb and Belle-II experiments in the near future.Comment: 31 pages, 4 figures, 6 table

Confirmatory factor analysis of the Children's Eating Behaviour Questionnaire in a Chinese urban preschooler sample.

BackgroundUnderstanding young children's eating behaviours is vital to childhood obesity prevention. However, the widely used Children's Eating Behaviour Questionnaire (CEBQ) has not been validated in Chinese young children. Thus, the present study aimed to assess the validity of the CEBQ in a Chinese urban sample of preschool children.MethodsParticipants included 389 mothers with preschool children residing in Beijing, China. Confirmatory factor analysis was conducted, and measurement invariance between child genders was evaluated.ResultsThe modified 8-factor structure of the CEBQ exhibited acceptable model fit in our sample, and no measurement bias against any gender was observed. The associations between the CEBQ factors and child age showed that desire to drink, emotional overeating, and emotional undereating significantly decreased with age, but food responsiveness increased with age. The relation between child BMI and the CEBQ factors provided convergent validity for the CEBQ.ConclusionsOur study supported the validity of the CEBQ as a measurement tool for examining preschool children's eating behaviours in a Chinese urban sample