Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Linking routinely collected social work, education and health data to enable monitoring of the health and health care of school-aged children in state care (‘looked after children’) in Scotland: a national demonstration project

Background and objectives: Children in state care (‘looked after children’) have poorer health than children who are not looked after. Recent developments in Scotland and elsewhere have aimed to improve services and outcomes for looked after children. Routine monitoring of the health outcomes of looked after children compared to those of their non-looked after peers is currently lacking. Developing capacity for comparative monitoring of population based outcomes based on linkage of routinely collected administrative data has been identified as a priority. To our knowledge there are no existing population based data linkage studies providing data on the health of looked after and non-looked after children at national level. Smaller scale studies that are available generally provide very limited information on linkage methods and hence do not allow scrutiny of bias that may be introduced through the linkage process. Study design and methods: National demonstration project testing the feasibility of linking routinely collected looked after children, education, and health data. Participants: All children in publicly funded school in Scotland in 2011/12. Results: Linkage between looked after children data and the national pupil census classified 10,009 (1.5%) and 1,757 (0.3%) of 670,952 children as, respectively, currently and previously looked after. Recording of the unique pupil identifier (Scottish Candidate Number, SCN) on looked after children returns is incomplete, with 66% of looked after records for 2011/12 for children of possible school age containing a valid SCN. This will have resulted in some under-ascertainment of currently and, particularly, previously looked after children within the general pupil population. Further linkage of the pupil census to the NHS Scotland master patient index demonstrated that a safe link to the child’s unique health service (Community Health Index, CHI) number could be obtained for a very high proportion of children in each group (94%, 95%, and 95% of children classified as currently, previously, and non-looked after respectively). In general linkage rates were higher for older children and those living in more affluent areas. Within the looked after group, linkage rates were highest for children with the fewest placements and for those in permanent fostering. Conclusions: This novel data linkage demonstrates the feasibility of monitoring population based health outcomes of school aged looked after and non-looked after children using linked routine administrative data. Improved recording of the unique pupil identifier number on looked after data returns would be beneficial. Extending the range of personal identifiers on looked after children returns would enable linkage to health data for looked after children who are not in publicly funded schooling (i.e. those who are pre- or post-school, home schooled, or in independent schooling)

Inequalities in the dental health needs and access to dental services among looked after children in Scotland: a population data linkage study

Background: There is limited evidence on the health needs and service access among children and young people who are looked after by the state. The aim of this study was to compare dental treatment needs and access to dental services (as an exemplar of wider health and well-being concerns) among children and young people who are looked after with the general child population. Methods: Population data linkage study utilising national datasets of social work referrals for ‘looked after’ placements, the Scottish census of children in local authority schools, and national health service’s dental health and service datasets. Results: 633 204 children in publicly funded schools in Scotland during the academic year 2011/2012, of whom 10 927 (1.7%) were known to be looked after during that or a previous year (from 2007–2008). The children in the looked after children (LAC) group were more likely to have urgent dental treatment need at 5 years of age: 23%vs10% (n=209/16533), adjusted (for age, sex and area socioeconomic deprivation) OR 2.65 (95% CI 2.30 to 3.05); were less likely to attend a dentist regularly: 51%vs63% (n=5519/388934), 0.55 (0.53 to 0.58) and more likely to have teeth extracted under general anaesthesia: 9%vs5% (n=967/30253), 1.91 (1.78 to 2.04). Conclusions: LAC are more likely to have dental treatment needs and less likely to access dental services even when accounting for sociodemographic factors. Greater efforts are required to integrate child social and healthcare for LAC and to develop preventive care pathways on entering and throughout their time in the care system

Rigid ball-polyhedra in Euclidean 3-space

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is locally rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles.Comment: 11 pages, 2 figure

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Excitation cross section of erbium-doped GaN waveguides under 980 nm optical pumping

This is the published version. Copyright 2015 American Institute of PhysicsExcitation cross section of erbium-doped GaN waveguides is measured to be approximately 2.2×10−21cm2 at 980 nm pumping wavelength. This cross section value is found relatively insensitive to the crystalline quality of epilayers. However, spontaneous emission carrier lifetimes in these waveguides are directly related to both the crystalline quality and the optical loss, and thus can be used as a material quality indicator

Experiences of refugees and asylum seekers in general practice: a qualitative study

Background: There has been much debate regarding the refugee health situation in the UK. However most of the existing literature fails to take account of the opinions of refugees themselves. This study was established to determine the views of asylum seekers and refugees on their overall experiences in primary care and to suggest improvements to their care. Methods: Qualitative study of adult asylum seekers and refugees who had entered the UK in the last 10 years. The study was set in Barnet Refugee Walk in Service, London. 11 Semi structured interviews were conducted and analysed using framework analysis. Results: Access to GPs may be more difficult for failed asylum seekers and those without support from refugee agencies or family. There may be concerns amongst some in the refugee community regarding the access to and confidentiality of professional interpreters. Most participants stated their preference for GPs who offered advice rather than prescriptions. The stigma associated with refugee status in the UK may have led to some refugees altering their help seeking behaviour. Conclusion: The problem of poor access for those with inadequate support may be improved by better education and support for GPs in how to provide for refugees. Primary Care Trusts could also supply information to newly arrived refugees on how to access services. GPs should be aware that, in some situations, professional interpreters may not always be desired and that instead, it may be advisable to reach a consensus as to who should be used as an interpreter. A better doctor-patient experience resulting from improvements in access and communication may help to reduce the stigma associated with refugee status and lead to more appropriate help seeking behaviour. Given the small nature of our investigation, larger studies need to be conducted to confirm and to quantify these results

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.Comment: 10 pages, 13 figure

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face