On Dissecting Polygons into Rectangles

What is the smallest number of pieces that you can cut an n-sided regular polygon into so that the pieces can be rearranged to form a rectangle? Call it r(n). The rectangle may have any proportions you wish, as long as it is a rectangle. The rules are the same as for the classical problem where the rearranged pieces must form a square. Let s(n) denote the minimum number of pieces for that problem. For both problems the pieces may be turned over and the cuts must be simple curves. The conjectured values of s(n), 3 <= n <= 12, are 4, 1, 6, 5, 7, 5, 9, 7, 10, 6. However, only s(4)=1 is known for certain. The problem of finding r(n) has received less attention. In this paper we give constructions showing that r(n) for 3 <= n <= 12 is at most 2, 1, 4, 3, 5, 4, 7, 4, 9, 5, improving on the bounds for s(n) in every case except n=4. For the 10-gon our construction uses three fewer pieces than the bound for s(10). Only r(3) and r(4) are known for certain. We also briefly discuss q(n), the minimum number of pieces needed to dissect a regular n-gon into a monotile.Comment: 26 pages, one table, 41 figures, 14 reference

Accuracy of medical billing data against the electronic health record in the measurement of colorectal cancer screening rates.

ObjectiveMedical billing data are an attractive source of secondary analysis because of their ease of use and potential to answer population-health questions with statistical power. Although these datasets have known susceptibilities to biases, the degree to which they can distort the assessment of quality measures such as colorectal cancer screening rates are not widely appreciated, nor are their causes and possible solutions.MethodsUsing a billing code database derived from our institution's electronic health records, we estimated the colorectal cancer screening rate of average-risk patients aged 50-74 years seen in primary care or gastroenterology clinic in 2016-2017. 200 records (150 unscreened, 50 screened) were sampled to quantify the accuracy against manual review.ResultsOut of 4611 patients, an analysis of billing data suggested a 61% screening rate, an estimate that matches the estimate by the Centers for Disease Control. Manual review revealed a positive predictive value of 96% (86%-100%), negative predictive value of 21% (15%-29%) and a corrected screening rate of 85% (81%-90%). Most false negatives occurred due to examinations performed outside the scope of the database-both within and outside of our institution-but 21% of false negatives fell within the database's scope. False positives occurred due to incomplete examinations and inadequate bowel preparation. Reasons for screening failure include ordered but incomplete examinations (48%), lack of or incorrect documentation by primary care (29%) including incorrect screening intervals (13%) and patients declining screening (13%).ConclusionsBilling databases are prone to substantial bias that may go undetected even in the presence of confirmatory external estimates. Caution is recommended when performing population-level inference from these data. We propose several solutions to improve the use of these data for the assessment of healthcare quality

Trio-One: Layering Uncertainty and Lineage on a Conventional DBMS

Trio is a new kind of database system that supports data, uncertainty, and lineage in a fully integrated manner. The first Trio prototype, dubbed Trio-One, is built on top of a conventional DBMS using data and query translation techniques together with a small number of stored procedures. This paper describes Trio-One's translation scheme and system architecture, showing how it efficiently and easily supports the Trio data model and query language

Field-Weighted XML Retrieval Based on BM25.

This is the first year for the Centre for Interactive Systems Research participation of INEX. Based on a newly developed XML indexing and retrieval system on Okapi, we extend Robertson’s field-weighted BM25F for document retrieval to element level retrieval function BM25E. In this paper, we introduce this new function and our experimental method in detail, and then show how we tuned weights for our selected fields by using INEX 2004 topics and assessments. Based on the tuned models we submitted our runs for CO.Thorough, CO.FetchBrowse, the methods we propose show real promise. Existing problems and future work are also discussed

Body Size, Rather Than Male Eye Allometry, Explains Chrysomya megacephala (Diptera: Calliphoridae) Activity in Low Light

Male Chrysomya megacephala (F.) blow fly compound eyes contain an unusual area of enlarged dorsal facets believed to allow for increased light capture. This region is absent in females and has been hypothesized to aid in mate tracking in low light conditions or at greater distances. Many traits used in the attraction and capture of mates are allometric, growing at different rates relative to body size. Previous reports concerning C. megacephala eye properties did not include measurements of body size, making the relationship between the specialized eye region and body size unclear. We examined different morphological features of the eye among individuals of varying sizes. We found total eye size scaled proportionately to body size, but the number of enlarged dorsal facets increased as body size increased. This demonstrated that larger males have an eye that is morphologically different than smaller males. On the basis of external morphology, we hypothesized that since larger males have larger and a greater number of dorsally enlarged facets, and these facets are believed to allow for increased light capture, larger males would be active in lower light levels than smaller males and females of equal size. In a laboratory setting, larger males were observed to become active earlier in the morning than smaller males, although they did not remain active later in the evening. However, females followed the same pattern at similar light levels suggesting that overall body size rather than specialized male eye morphology is responsible for increased activity under low light conditions

Metabolic Profiling of Heathland Plants in the Diet of Sheep

Little is known about how plant biochemistry influences the grazing behaviour of animals grazing heterogeneous vegetation communities. Furthermore, most biochemical profiles of grassland species are restricted to major nutritional characteristics. Recent developments in analytical techniques have made possible the detailed analysis of minor components, which can potentially affect animal feeding preferences, performance and health. Gas chromatography/time of flight mass spectroscopy (GC/TOF-MS) coupled with automated library annotation is ideally suited to the acquisition of detailed metabolite profiles of plant extracts (Wagner et al., 2003) and can be applied to other matrices such as blood and faeces. In this study GC/TOF-MS was used to identify metabolites within heathland plants, and to investigate which of these metabolites were present and absent within plasma and faeces from sheep consuming mixtures of these plants

Understanding of research, genetics and genetic research in a rapid ethical assessment in north west Cameroon

BACKGROUND There is limited assessment of whether research participants in low-income settings are afforded a full understanding of the meaning of medical research. There may also be particular issues with the understanding of genetic research. We used a rapid ethical assessment methodology to explore perceptions surrounding the meaning of research, genetics and genetic research in north west Cameroon. METHODS Eleven focus group discussions (including 107 adults) and 72 in-depth interviews were conducted with various stakeholders in two health districts in north west Cameroon between February and April 2012. RESULTS Most participants appreciated the role of research in generating knowledge and identified a difference between research and healthcare but gave varied explanations as to this difference. Most participants' understanding of genetics was limited to concepts of hereditary, with potential benefits limited to the level of the individual or family. Explanations based on supernatural beliefs were identified as a special issue but participants tended not to identify any other special risks with genetic research. CONCLUSION We demonstrated a variable level of understanding of research, genetics and genetic research, with implications for those carrying out genetic research in this and other low resource settings. Our study highlights the utility of rapid ethical assessment prior to complex or sensitive research