Generalised Umbral Moonshine

Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the more general moonshine phenomenon which connects finite groups and distinguished modular objects. In this paper we introduce the notion of generalised umbral moonshine, which includes the generalised Mathieu moonshine [Gaberdiel M.R., Persson D., Ronellenfitsch H., Volpato R., Commun. Number Theory Phys. 7 (2013), 145-223] as a special case, and provide supporting data for it. A central role is played by the deformed Drinfel'd (or quantum) double of each umbral finite group $G$, specified by a cohomology class in $H^3(G,U(1))$. We conjecture that in each of the 23 cases there exists a rule to assign an infinite-dimensional module for the deformed Drinfel'd double of the umbral finite group underlying the mock modular forms of umbral moonshine and generalised umbral moonshine. We also discuss the possible origin of the generalised umbral moonshine

Assessing and presenting summaries of evidence in Cochrane Reviews

Cochrane Reviews are intended to help providers, practitioners and patients make informed decisions about health care. The goal of the Cochrane Applicability and Recommendation Methods Group (ARMG) is to develop approaches, strategies and guidance that facilitate the uptake of information from Cochrane Reviews and their use by a wide audience with specific focus on developers of recommendations and on healthcare decision makers. This paper is part of a series highlighting developments in systematic review methodology in the 20 years since the establishment of The Cochrane Collaboration, and its aim is to present current work and highlight future developments in assessing and presenting summaries of evidence, with special focus on Summary of Findings (SoF) tables and Plain Language Summaries. A SoF table provides a concise and transparent summary of the key findings of a review in a tabular format. Several studies have shown that SoF tables improve accessibility and understanding of Cochrane Reviews. The ARMG and GRADE Working Group are working on further development of the SoF tables, for example by evaluating the degree of acceptable flexibility beyond standard presentation of SoF tables, developing SoF tables for diagnostic test accuracy reviews and interactive SoF tables (iSoF). The plain language summary (PLS) is the other main building block for dissemination of review results to end-users. The PLS aims to summarize the results of a review in such a way that health care consumers can readily understand them. Current efforts include the development of a standardized language to describe statistical results, based on effect size and quality of supporting evidence. Producing high quality PLS and SoF tables and making them compatible and linked would make it easier to produce dissemination products targeting different audiences (for example, providers, health policy makers, guideline developers). Current issues of debate include optimal presentation formats of SoF tables, the training required to produce SoF tables, and the extent to which the authors of Cochrane Reviews should provide explicit guidance to target audiences of patients, clinicians and policy-makers

Out-of-plane behaviour of concrete block walls with unbonded reinforcement

The use of grout in conventional reinforced masonry construction increases the cost and time of construction but, when used in combination with reinforcing steel, allows walls subject to out-of-plane loads an enhanced ability to span between lateral support levels. Reinforced concrete block walls constructed in this manner can typically span at least two stories in constrast to the limited single storey capacity of unreinforced walls. However, the use of grout as needed for the construction of these walls increases their self-weight, and requires an additional trade on-site. A novel, potentially cost-efficient, approach to achieve reasonable load-carrying capacity in masonry walls was therefore investigated that involves the use of minimally stressed reinforcement anchored at the top and bottom of the wall. This allows for a grout-free structural system that relies upon arching to resist the flexural effects resulting from out-of-plane loads and so make more effective use of the compressive capacity of the masonry assembly. An experimental program was therefore conducted at the University of Saskatchewan to investigate the performance of concrete masonry block walls reinforced with non-prestressed, unbonded reinforcement. This study included a total of 21 walls that were built to identify potential alternatives to unreinforced and conventionally grouted and reinforced walls. The strength and serviceability of these walls was evaluated. All walls in this program were two and a half blocks wide and 14 courses tall and were built in running bond using standard 200 mm concrete blocks. Six replicates of both unreinforced and partially grouted, conventionally reinforced walls served as control specimens. An analysis of the data obtained during testing revealed that the walls with unbonded reinforcement were inherently stable with maximum loads approaching those of partially grouted, conventionally reinforced walls. Furthermore, an analytical approach is presented herein that is based on the assumption that the walls with unbonded reinforcement could be modeled using a three hinged mechanism. The analytical model was found to match with the experimentally obtained load versus mid-height deflection data reasonably well throughout the post-cracking range

Fukunaga-Koontz transform for small sample size problems

In this paper, we propose the Fukunaga-Koontz Transform (FKT) as applied to small-sample size (SSS) problems and formulate a feature scatter matrix based equivalent of the FKT. We establish the classical linear discriminant analysis (LDA) analogy of the FKT and apply it to a SSS situation. We demonstrate the significant computational savings and robustness associated with our approach using a multi-class face detection proble

Metallurgical Evaluation of the Hoidas Lake Rare Earth Deposit

Hoidas Lake lies in the Northern Rae Geological Province, in the general vicinity of many of Saskatchewan's large uranium mines. The mineralogy of the Hoidas Lake rare-earth deposit differs from most other such deposits in that it is hosted in equal abundance in veins containing apatite and allanite mineral groups. Hoidas Lake also differs from other deposits in that it contains a significant amount of heavy rare-earth elements, such as dysprosium. This abundance of heavy Rare Earth Elements (REE’s) is significant, as there is a growing demand for the heavier rare earths in high-tech manufacturing (such as the use of dysprosium in the manufacturing of hybrid car components). Recently, metallurgical testing was performed on a Hoidas Lake REE deposit composite. These investigations included characterization, flotation testing, heavy media separation, magnetic separation testing, whole ore leaching studies, bond work index grindability testing, and relative abrasion index testing. This paper summarizes this research effort

Examining the causes of rarity for the Odonata of Illinois

Odonata (dragonflies and damselflies) play an important role in habitat management and conservation, but our understanding of the causes of commonness versus rarity in this group is limited. In this study we examined the causes of rarity for the Odonata of Illinois. Using S-ratings for conservation status and published habitat classifications for Illinois odonates, we investigated whether habitat type (lotic versus lentic) or habitat specificity (whether they were limited to a specific type of aquatic habitat) was related to commonness. We found that lotic species and habitat specialists were more likely to be rare than lentic and generalist species. More information, however, is needed on the distributions and natural histories of Illinois odonates if we are to more fully understand the causes of rarity in this important group

Multispectral fingerprinting for improved in vivo cell dynamics analysis

Background: Tracing cell dynamics in the embryo becomes tremendously difficult when cell trajectories cross in space and time and tissue density obscure individual cell borders. Here, we used the chick neural crest (NC) as a model to test multicolor cell labeling and multispectral confocal imaging strategies to overcome these roadblocks. Results: We found that multicolor nuclear cell labeling and multispectral imaging led to improved resolution of in vivo NC cell identification by providing a unique spectral identity for each cell. NC cell spectral identity allowed for more accurate cell tracking and was consistent during short term time-lapse imaging sessions. Computer model simulations predicted significantly better object counting for increasing cell densities in 3-color compared to 1-color nuclear cell labeling. To better resolve cell contacts, we show that a combination of 2-color membrane and 1-color nuclear cell labeling dramatically improved the semi-automated analysis of NC cell interactions, yet preserved the ability to track cell movements. We also found channel versus lambda scanning of multicolor labeled embryos significantly reduced the time and effort of image acquisition and analysis of large 3D volume data sets. Conclusions: Our results reveal that multicolor cell labeling and multispectral imaging provide a cellular fingerprint that may uniquely determine a cell's position within the embryo. Together, these methods offer a spectral toolbox to resolve in vivo cell dynamics in unprecedented detail