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

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

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

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

Experimental field estimation of organic nitrogen formation in tree canopies

The content of organic N has been shown in many studies to increase during the passage of rain water through forest canopies. The source of this organic N is unknown, but generally assumed to come from canopy processing of wet or dry-deposited inorganic N. There have been very few experimental studies in the field to address the canopy formation or loss of organic N. We report two studies: a Scots pine canopy exposed to ammonia gas, and a Sitka spruce canopy exposed to ammonium and nitrate as wet deposition. In both cases, organic N deposition in throughfall was increased, but only represented a small fraction (<10%) of the additional inorganic N supplied, suggesting a limited capacity for net organic N production, similar in both conifer canopies under Scottish summertime conditions, of less than 1.6 mmol Nm2 mth1 (equivalent to 3 kg N ha1 y1)

"Sometimes it is difficult for us to stand up and change this": an analysis of power within priority-setting for health following devolution in Kenya

Background Practices of power lie at the heart of policy processes. In both devolution and priority-setting, actors seek to exert power through influence and control over material, human, intellectual and financial resources. Priority-setting arises as a consequence of the needs and demand exceeding the resources available, requiring some means of choosing between competing demands. This paper examines the use of power within priority-setting processes for healthcare resources at sub-national level, following devolution in Kenya. Methods We interviewed 14 national level key informants and 255 purposively selected respondents from across the health system in ten counties. These qualitative data were supplemented by 14 focus group discussions (FGD) involving 146 community members in two counties. We conducted a power analysis using Gaventa’s power cube and Veneklasen’s expressions of power to interpret our findings. Results We found Kenya’s transition towards devolution is transforming the former centralised balance of power, leading to greater ability for influence at the county level, reduced power at national and sub-county (district) levels, and limited change at community level. Within these changing power structures, politicians are felt to play a greater role in priority-setting for health. The interfaces and tensions between politicians, health service providers and the community has at times been felt to undermine health related technical priorities. Underlying social structures and discriminatory practices generally continue unchanged, leading to the continued exclusion of the most vulnerable from priority-setting processes. Conclusions Power analysis of priority-setting at county level after devolution in Kenya highlights the need for stronger institutional structures, processes and norms to reduce the power imbalances between decision-making actors and to enable community participation

Towards reviving post-Olympic Athens as a cultural destination

This paper examines the effects of global change on the status and qualities of the Greek national capital, Athens, focusing on how they affect the development of cultural tourism in the city. Although Athens constituted one of the most significant destinations for Greek tourism in the past, in recent years it started to weaken. Athens is characterised by a series of problems, among them are the degradation of its environment and quality of life and traffic congestion. However, in terms of tourism development, the Olympic Games helped in re-imaging the city and upgrading its infrastructure. This study based on semi-structured interviews with top officials reveals how global change has affected Athens’ socio-cultural/economic status, identity and image. Despite the tourism policy/planning responses to global changes, Athens’ tourism continues to decline leaving unexplored potential such as its rich cultural heritage, new multicultural identity and the New Acropolis Museum. The paper suggests that cultural elements of capital cities must be multidimensional including a variety of attractions and amenities. The use of cultural heritage assets needs to be in line with global developments in order for cities to effectively leverage heritage for cultural tourism