Essential edges in Poisson random hypergraphs

Consider a random hypergraph on a set of N vertices in which, for k between 1 and N, a Poisson(N beta_k) number of hyperedges is scattered randomly over all subsets of size k. We collapse the hypergraph by running the following algorithm to exhaustion: pick a vertex having a 1-edge and remove it; collapse the hyperedges over that vertex onto their remaining vertices; repeat until there are no 1-edges left. We call the vertices removed in this process "identifiable". Also any hyperedge all of whose vertices are removed is called "identifiable". We say that a hyperedge is "essential" if its removal prior to collapse would have reduced the number of identifiable vertices. The limiting proportions, as N tends to infinity, of identifiable vertices and hyperedges were obtained by Darling and Norris. In this paper, we establish the limiting proportion of essential hyperedges. We also discuss, in the case of a random graph, the relation of essential edges to the 2-core of the graph, the maximal sub-graph with minimal vertex degree 2.Comment: 12 pages, 3 figures. Revised version with minor corrections/clarifications and slightly expanded introductio

Language and Ideology: A role for scientific metaphor

A number of prominent popular science writers have recently argued for the active appropriation of scientific language in the formulation of modern ideologies and ethical systems. A critical examination of scientific narratives in light of contemporary theories of metaphor and relevance suggests that scientific language indeed harbors the same emotive potential that is traditionally ascribed to religious language, and can exhibit potent transformative effects in shaping human thought. Also highlighted through this approach are the challenges of constructing scientific metaphors that are generally meaningful, accurate, and ethically responsible

A Compass in the Woods: Learning Through Grantmaking to Improve Impact

The field of philanthropy is under increasing pressure to produce – and be able to demonstrate – greater impact for its investments. A growing number of foundations are moving away from the traditional responsive banker model to becoming more thoughtful and engaged partners with their grantees in the business of producing outcomes. In the process, they are placing bigger bets on larger, more strategic programs and initiatives.  What the field is striving to do now is to ensure that this evolution is based on validated theory, not wishful thinking or shots in the dark. The larger the investment, the more skilled foundations must become at managing risk – making informed decisions, tracking progress, adjusting action and learning – throughout the life of a program, so that foreseeable and unforeseeable changes do not torpedo an otherwise worthy collective effort. The traditional grant?to?evaluation?to?adjustment cycle is very long. Because many traditional grantmaking practices are proving to be too slow to adapt, these foundations are striving to better integrate real?time evaluation and learning into their operations in order to become more adaptive; more innovative; more impactful.We undertook this research project to inform how the tools and practices that support Emergent   Learning (described in the next section) can best help foundations and their communities – grantees, intermediaries and other stakeholders – improve the way they learn in complex programs and initiatives

Complementary and alternative medicines for cancer treatment : a patient perspective : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Health Psychology with endorsement at Massey University, Palmerston North, New Zealand

Current research shows people diagnosed with cancer have a strong interest for complementary alternative medicine (CAM) to be an option for either sole treatment or used alongside conventional methods. This qualitative study aimed to investigate the attitudes of a sample of cancer patients to establish why they use CAM and explore their beliefs on the benefits (if any) they have from receiving this treatment. It is hoped that the current study will add to the limited CAM literature from Aotearoa. The findings presented in this study arise from the thematic analysis of semi-structured interviews with five participants. They included adults diagnosed with any type of cancer who were currently undergoing, or had undergone either CAM treatment or a combination of CAM and mainstream treatment. The interviewees openly discussed their cancer journey and from these deliberations the five main themes found were: decision; empowerment; holistic; wellbeing; and social harm. While there were similarities found with other studies regarding why patients chose CAM, the thesis also discovered the participants were now wanting to share their information and experience with others considering CAM for cancer treatment, but did not know how

The Hubble Expansion is Isotropic in the Epoch of Dark Energy

The isotropy of the universal Hubble expansion is a fundamental tenet of physical cosmology, but it has not been precisely tested during the current epoch, when dark energy is dominant. Anisotropic expansion will produce a shearing velocity field, causing objects to stream toward directions of faster expansion and away from directions of slower expansion. This work tests the basic cosmological assumption of isotropic expansion and thus the isotropy of dark energy. The simplest anisotropy will manifest as a quadrupolar curl-free proper motion vector field. We derive this theoretical signature using a tri-axial expanding metric with a flat geometry (Bianchi I model), generalizing and correcting previous work. We then employ the best current data, the Titov & Lambert (2013) proper motion catalog of 429 objects, to measure the isotropy of universal expansion. We demonstrate that the Hubble expansion is isotropic to 7% (1 $\sigma$), corresponding to streaming motions of 1 microarcsecond/yr, in the best-constrained directions (-19% and +17% in the least-constrained directions) and does not significantly deviate from isotropy in any direction. The Gaia mission, which is expected to obtain proper motions for 500,000 quasars, will likely constrain the anisotropy below 1%.Comment: 6 pages, 1 figure, 3 tables. Accepted for publication by MNRA