Cutting A Pie Is Not A Piece Of Cake

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions

Shock and vibration tests of a SNAP-8 NaK pump

The pump used for reactor cooling in the SNAP 8 space power system was subjected to the expected vehicle launch vibration, and shock loading in accordance with the SNAP 8 environmental specification. Subsequent disassembly revealed damage to the thrust bearing pins, which should be redesigned and strengthened. The unit was operational, however, when run in a test loop after reassembly

Cutting a pie is not a piece of cake

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions.Fair division; cake-cutting; pie-cutting; divisible good; envy-freeness; allocative efficiency

Packing Rates Of Measures And A Conjecture For The Packing Density Of 2413

We give a new lower bound of 0.10472422757673209041 for the packing density of 2413, justify it by a construction, and conjecture that this value is actually equal to the packing density. Along the way we define the packing rate of a permutation with respect to a measure, and show that maximizing the packing rate of a pattern over all measures gives the packing density of the pattern

Gender equality and girls education: Investigating frameworks, disjunctures and meanings of quality education

The article draws on qualitative educational research across a diversity of low-income countries to examine the gendered inequalities in education as complex, multi-faceted and situated rather than a series of barriers to be overcome through linear input–output processes focused on isolated dimensions of quality. It argues that frameworks for thinking about educational quality often result in analyses of gender inequalities that are fragmented and incomplete. However, by considering education quality more broadly as a terrain of quality it investigates questions of educational transitions, teacher supply and community participation, and develops understandings of how education is experienced by learners and teachers in their gendered lives and their teaching practices. By taking an approach based on theories of human development the article identifies dynamics of power underpinning gender inequalities in the literature and played out in diverse contexts and influenced by social, cultural and historical contexts. The review and discussion indicate that attaining gender equitable quality education requires recognition and understanding of the ways in which inequalities intersect and interrelate in order to seek out multi-faceted strategies that address not only different dimensions of girls’ and women’s lives, but understand gendered relationships and structurally entrenched inequalities between women and men, girls and boys

Expanding the parameters of academia

This paper draws on qualitative data gathered from two studies funded by the UK Leadership Foundation for Higher Education to examine the expansion of academic identities in higher education. It builds on Whitchurch’s earlier work, which focused primarily on professional staff, to suggest that the emergence of broadly based projects such as widening participation, learning support and community partnership is also impacting on academic identities. Thus, academic as well as professional staff are increasingly likely to work in multi-professional teams across a variety of constituencies, as well as with external partners, and the binary distinction between ‘academic’ and ‘non-academic’ roles and activities is no longer clear-cut. Moreover, there is evidence from the studies of an intentionality about deviations from mainstream academic career routes among respondents who could have gone either way. Consideration is therefore given to factors that influence individuals to work in more project-oriented areas, as well as to variables that affect ways in which these roles and identities develop. Finally, three models of academically oriented project activity are identified, and the implications of an expansion of academic identities are reviewed

Population policies and education: exploring the contradictions of neo-liberal globalisation

The world is increasingly characterised by profound income, health and social inequalities (Appadurai, 2000). In recent decades development initiatives aimed at reducing these inequalities have been situated in a context of increasing globalisation with a dominant neo-liberal economic orthodoxy. This paper argues that neo-liberal globalisation contains inherent contradictions regarding choice and uniformity. This is illustrated in this paper through an exploration of the impact of neo-liberal globalisation on population policies and programmes. The dominant neo-liberal economic ideology that has influenced development over the last few decades has often led to alternative global visions being overlooked. Many current population and development debates are characterised by polarised arguments with strongly opposing aims and views. This raises the challenge of finding alternatives situated in more middle ground that both identify and promote the socially positive elements of neo-liberalism and state intervention, but also to limit their worst excesses within the population field and more broadly. This paper concludes with a discussion outling the positive nature of middle ground and other possible alternatives

Conceptualizing pathways linking women's empowerment and prematurity in developing countries.

BackgroundGlobally, prematurity is the leading cause of death in children under the age of 5. Many efforts have focused on clinical approaches to improve the survival of premature babies. There is a need, however, to explore psychosocial, sociocultural, economic, and other factors as potential mechanisms to reduce the burden of prematurity. Women's empowerment may be a catalyst for moving the needle in this direction. The goal of this paper is to examine links between women's empowerment and prematurity in developing settings. We propose a conceptual model that shows pathways by which women's empowerment can affect prematurity and review and summarize the literature supporting the relationships we posit. We also suggest future directions for research on women's empowerment and prematurity.MethodsThe key words we used for empowerment in the search were "empowerment," "women's status," "autonomy," and "decision-making," and for prematurity we used "preterm," "premature," and "prematurity." We did not use date, language, and regional restrictions. The search was done in PubMed, Population Information Online (POPLINE), and Web of Science. We selected intervening factors-factors that could potentially mediate the relationship between empowerment and prematurity-based on reviews of the risk factors and interventions to address prematurity and the determinants of those factors.ResultsThere is limited evidence supporting a direct link between women's empowerment and prematurity. However, there is evidence linking several dimensions of empowerment to factors known to be associated with prematurity and outcomes for premature babies. Our review of the literature shows that women's empowerment may reduce prematurity by (1) preventing early marriage and promoting family planning, which will delay age at first pregnancy and increase interpregnancy intervals; (2) improving women's nutritional status; (3) reducing domestic violence and other stressors to improve psychological health; and (4) improving access to and receipt of recommended health services during pregnancy and delivery to help prevent prematurity and improve survival of premature babies.ConclusionsWomen's empowerment is an important distal factor that affects prematurity through several intervening factors. Improving women's empowerment will help prevent prematurity and improve survival of preterm babies. Research to empirically show the links between women's empowerment and prematurity is however needed

Community-based rehabilitation and disability-inclusive development: On a winding path to an uncertain destination

The majority of people with disabilities who live in developing countries, predominantly in the global South, do not receive any formal disability or rehabilitation services. In those countries or regions where at least some disability services are provided, the community-based rehabilitation (CBR) approach, or some form of it, is likely to be the only approach available (Evans et al. 2001)