Jacobi trace functions in the theory of vertex operator algebras

We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements in V, the finite-dimensional space spanned by the corresponding 1-point functions for the inequivalent irreducible modules is shown to be a vector-valued weak Jacobi form. A decomposition of 1-point functions for general elements is proved, and shows that such functions are typically quasi-Jacobi forms. Zhu-type recursion formulas are proved; they show how an n-point function can be written as a linear combination of (n-1)-point functions with coefficients that are quasi-Jacobi forms.Comment: 28 pages, additional references added, correction in the statement and proof of convergence in Theorem 1.

How to push a block along a wall

Some robot tasks require manipulation of objects that may be touching other fixed objects. The effects of friction and kinematic constraint must be anticipated, and may even be exploited to accomplish the task. An example task, a dynamic analysis, and appropriate effector motions are presented. The goal is to move a rectangular block along a wall, so that one side of the block maintains contact with the wall. Two solutions that push the block along the wall are discussed

Robust Execution of Contact-Rich Motion Plans by Hybrid Force-Velocity Control

In hybrid force-velocity control, the robot can use velocity control in some directions to follow a trajectory, while performing force control in other directions to maintain contacts with the environment regardless of positional errors. We call this way of executing a trajectory hybrid servoing. We propose an algorithm to compute hybrid force-velocity control actions for hybrid servoing. We quantify the robustness of a control action and make trade-offs between different requirements by formulating the control synthesis as optimization problems. Our method can efficiently compute the dimensions, directions and magnitudes of force and velocity controls. We demonstrated by experiments the effectiveness of our method in several contact-rich manipulation tasks. Link to the video: https://youtu.be/KtSNmvwOenM.Comment: Proceedings of IEEE International Conference on Robotics and Automation (ICRA2019

Productivity, Capital-Intensity and Labour Quality at Sector Level in New Zealand and the UK

Understanding productivity performance is important to informing policy advice on how to improve productivity and therefore New Zealand's overall economic performance. Given data limitations inherent in international productivity comparisons, this paper is not intended to inform policy in isolation but forms an important element of a wide and expanding body of evidence on the performance of the New Zealand economy. Previous international productivity comparisons involving New Zealand have been confined to the aggregate economy or to broadly-defined sectors such as manufacturing. This paper reports on a New Zealand-UK comparison which distinguishes 21 different ‘market sectors’ (ie, excluding public administration, education, health, property services and some personal, social and community services). It confirms the prevailing consensus that, in aggregate, New Zealand market sectors compare unfavourably with the UK on average labour productivity (ALP) - and by implication compare even more unfavourably with other countries such as the US. However, beneath this overall story there is considerable sectoral variation. While some NZ sectors out-perform the UK on ALP and/or multi-factor productivity (MFP), there is a large group of sectors which fall short of the UK on both productivity measures. Most of these low-productivity sectors are relatively low in physical capital-intensity compared to the UK. Overall, roughly a quarter of the New Zealand-UK gap in ALP for aggregate market sectors in 2002 was attributable to differences in employment structure such as the relatively high shares of New Zealand employment in comparatively low value added sectors such as agriculture. The remaining three quarters of the ALP gap were accounted for by within-sector productivity differences.productivity, capital-deepening, human capital

Contribution of Ethnicity to Subgingival Microbial Colonization

Introduction: Although it is known that the gingival sulcus contains a complex microbial ecosystem, the role of host-associated colonization factors, especially ethnicity, in determining the composition of this community is not known. Open-ended molecular approaches are comprehensive tools that allow us to compare profiles of microbial communities with several as-yet-uncultivated organisms. Objective: To compare the subgingival microbial profiles of periodontally healthy subjects belonging to four different ethnicities. Methods: 55 periodontally healthy subjects of Caucasian (n=17), African-American (n=14), Hispanic (n=17), and Chinese (n=17) ethnicities were recruited. All subjects were over age 18 without history of systemic disease, pregnancy, and recent or prophylactic antibiotic use. Ethnicity information and subgingival plaque samples were collected. 16S rRNA genes were amplified using polymerase chain reaction with fluorescently labeled broad-range primers and digested using MspI restriction enzyme. Terminal Restriction Fragment Length Polymorphism Analysis (t-RFLP) was used to examine microbial profiles. Non-parametric tests were used for between group comparisons. Results: A statistically significant difference was found in the total peaks measured between African-Americans and Chinese (p=0.0165), African-American and Latino (p=0.0001), Caucasian and Chinese (p=0.0468), and Caucasian and Latino (p=0.0005,Kruskal-Wallis analysis). Conclusions: There is an association between ethnic preference and the bacterial composition of the health- associated subgingival plaque. However, the effect of shared environment remains to be investigated.This research was supported by the Rudy Melfi undergraduate research fellowship to Matthew Mason through the OSU College of DentistryNo embarg