On the Split Reliability of Graphs

A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal reliability}) or that two specific vertices (or {\em terminals}) can communicate with each other ({\em two-terminal reliability}). A relatively new measure is {\em split reliability}, where for two fixed vertices $s$ and $t$, we consider the probability that every vertex communicates with one of $s$ or $t$, but not both. In this paper, we explore the existence for fixed numbers $n \geq 2$ and $m \geq n-1$ of an {\em optimal} connected $(n,m)$-graph $G_{n,m}$ for split reliability, that is, a connected graph with $n$ vertices and $m$ edges for which for any other such graph $H$, the split reliability of $G_{n,m}$ is at least as large as that of $H$, for {\em all} values of $p \in [0,1]$. Unlike the similar problems for all-terminal and two-terminal reliability, where only partial results are known, we completely solve the issue for split reliability, where we show that there is an optimal $(n,m)$-graph for split reliability if and only if $n\leq 3$, $m=n-1$, or $n=m=4$.Comment: 12 pages, 9 figure

J.S. Bell's Concept of Local Causality

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure

Binary orbits as the driver of γ-ray emission and mass ejection in classical novae

Classical novae are the most common astrophysical thermonuclear explosions, occurring on the surfaces of white dwarf stars accreting gas from companions in binary star systems. Novae typically expel �10,000 solar masses of material at velocities exceeding 1,000 km/s. However, the mechanism of mass ejection in novae is poorly understood, and could be dominated by the impulsive flash of the thermonuclear runaway, prolonged optically thick winds, or binary interaction with the nova envelope. Classical novae are now routinely detected in GeV gamma-rays, suggesting that relativistic particles are accelerated by strong shocks in nova ejecta. Here we present high-resolution imaging of the gamma-ray-emitting nova V959 Mon at radio wavelengths, showing that its ejecta were shaped by binary motion: some gas was expelled rapidly along the poles as a wind from the white dwarf, while denser material drifted out along the equatorial plane, propelled by orbital motion. At the interface between the equatorial and polar regions, we observe synchrotron emission indicative of shocks and relativistic particle acceleration, thereby pinpointing the location of gamma-ray production. Binary shaping of the nova ejecta and associated internal shocks are expected to be widespread among novae, explaining why many novae are gamma-ray emitters

Thinking about Later Life: Insights from the Capability Approach

A major criticism of mainstream gerontological frameworks is the inability of such frameworks to appreciate and incorporate issues of diversity and difference in engaging with experiences of aging. Given the prevailing socially structured nature of inequalities, such differences matter greatly in shaping experiences, as well as social constructions, of aging. I argue that Amartya Sen’s capability approach (2009) potentially offers gerontological scholars a broad conceptual framework that places at its core consideration of human beings (their values) and centrality of human diversity. As well as identifying these key features of the capability approach, I discuss and demonstrate their relevance to thinking about old age and aging. I maintain that in the context of complex and emerging identities in later life that shape and are shaped by shifting people-place and people-people relationships, Sen’s capability approach offers significant possibilities for gerontological research

Public service innovation and multiple institutional logics: the case of hybrid social enterprise providers of health and wellbeing

Public sector organisations are confronted with growing health and social care needs in combination with severe resource constraints, prompting interest in innovative responses to such challenges. Public service and social innovation is poorly understood, particularly where innovators must navigate between the norms, practices and logics of public, private and civil society sectors. We contribute to the understanding of how innovating hybrid organisations are able to creatively combine co-existing logics. Case study evidence from newly established social enterprise providers of health and wellbeing services in England is utilised to examine how innovations are shaped by (i) an incumbent state or public sector logic, and two ‘challenger’ logics relating to (ii) the market and increasing competition; and (iii) civil society, emphasising social value and democratic engagement with employees and service users. The analysis shows how a more fluid and creative interplay of logics can be observed in relation to specific strategies and practices. Within organisations, these strategies relate to the empowerment of staff to be creative, financial management, and knowledge sharing and protection. The interplay of logics shaping social innovation is also found in relationships with key stakeholders, notably public sector funders, service users and service delivery partners. Implications are drawn for innovation in public services and hybrid organisations more broadly

Formaldehyde Densitometry of Galactic Star-Forming Regions Using the H2CO 3(12)-3(13) and 4(13)-4(14) Transitions

We present Green Bank Telescope (GBT) observations of the 3(12)-3(13) (29 GHz) and 4(13)-4(14) (48 GHz) transitions of the H2CO molecule toward a sample of 23 well-studied star-forming regions. Analysis of the relative intensities of these transitions can be used to reliably measure the densities of molecular cores. Adopting kinetic temperatures from the literature, we have employed a Large Velocity Gradient (LVG) model to derive the average hydrogen number density [n(H2)] within a 16 arcsecond beam toward each source. Densities in the range of 10^{5.5}--10^{6.5} cm^{-3} and ortho-formaldehyde column densities per unit line width between 10^{13.5} and 10^{14.5} cm^{-2} (km s^{-1})^{-1} are found for most objects, in general agreement with existing measurements. A detailed analysis of the advantages and limitations to this densitometry technique is also presented. We find that H2CO 3(12)-3(13)/4(13)-4(14) densitometry proves to be best suited to objects with T_K >~ 100 K, above which the H2CO LVG models become relatively independent of kinetic temperature. This study represents the first detection of these H2CO K-doublet transitions in all but one object in our sample. The ease with which these transitions were detected, coupled with their unique sensitivity to spatial density, make them excellent monitors of density in molecular clouds for future experiments. We also report the detection of the 9_2--8_1 A^- (29 GHz) transition of CH3OH toward 6 sources.Comment: 17 pages; 6 figures; Accepted by Ap

Antineutrophil cytoplasmic antibodies in myelodysplasia.

Antibodies to neutrophil cytoplasmic antigens (ANCA) are good serological markers for patients with mainly vasculitic conditions. Two main types of ANCAs have been detected, the first termed cytoplasmic antineutrophil cytoplasmic antibody (cANCA) are mainly associated with patients with Wegener's granulomatosis, the other termed perinuclear antineutrophil cytoplasmic antibody (pANCA) are mainly associated with patients with renal vasculitis, rheumatic and collagen disorders. These antibodies are against various constituents of neutrophil granules. In patients with myelodysplasia, defects in normal granulocyte development are seen. We report a series of twelve patients with myelodysplasia of whom at least four showed a low titre and one a high titre of pANCA. Two of these patients also had demonstrable activity against myeloperoxidase (MPO). None of these patients had any evidence of systemic or cutaneous vasculitis or of any autoimmune disorder. There was no pANCA positivity in an age matched control group

Detecting Weak Spectral Lines in Interferometric Data through Matched Filtering

Modern radio interferometers enable observations of spectral lines with unprecedented spatial resolution and sensitivity. In spite of these technical advances, many lines of interest are still at best weakly detected and therefore necessitate detection and analysis techniques specialized for the low signal-to-noise ratio (S/N) regime. Matched filters can leverage knowledge of the source structure and kinematics to increase sensitivity of spectral line observations. Application of the filter in the native Fourier domain improves S/N while simultaneously avoiding the computational cost and ambiguities associated with imaging, making matched filtering a fast and robust method for weak spectral line detection. We demonstrate how an approximate matched filter can be constructed from a previously observed line or from a model of the source, and we show how this filter can be used to robustly infer a detection significance for weak spectral lines. When applied to ALMA Cycle 2 observations of CH3OH in the protoplanetary disk around TW Hya, the technique yields a ≈53% S/N boost over aperture-based spectral extraction methods, and we show that an even higher boost will be achieved for observations at higher spatial resolution. A Python-based open-source implementation of this technique is available under the MIT license at http://github.com/AstroChem/VISIBLE