Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Adaption to water shortage through the implementation of a unique pipeline system in Victoria, Australia

Abstract Water resource development has played a crucial role in the Grampians, Wimmera and Mallee regions of Australia, with the main source of surface water located in several reservoirs in the Grampians mountain ranges. Historically, water was delivered by gravity through a vast 19 500 km earthen channel system from the reservoirs to the townships and farms. As a result of the severe and protracted drought experienced in the region over the past 13 years and the projected drying climate, there have been fundamental changes made to the management of water in order to better cope with water scarcity. The primary strategic effort to sustainably manage water resources was by removing the unsustainable transport of water via the open channels which resulted in very high losses through seepage and evaporation. This inefficient system has been replaced by a pressurised pipeline, the largest geographical water infrastructure project of its type in Australia, spreading across an area of approximately 20 000 km2. To manage the change in water balance as a result of the pipeline and drying climate, the regions water corporations and environmental agencies have designed a scheme for water allocations intended to sustain local communities, allow for regional development and improve environmental conditions. This paper describes the unique pipeline system recently completed, provides a brief summary of water sharing arrangements and introduces the research program currently underway to optimise the performance of the pipeline system

Validation of the western ontario rotator cuff index in patients with arthroscopic rotator cuff repair: A study protocol

<p>Abstract</p> <p>Background</p> <p>Arthroscopic rotator cuff repair is described as being a successful procedure. These results are often derived from clinical general shoulder examinations, which are then classified as 'excellent', 'good', 'fair' or 'poor'. However, the cut-off points for these classifications vary and sometimes modified scores are used.</p> <p>Arthroscopic rotator cuff repair is performed to improve quality of life. Therefore, disease specific health-related quality of life patient-administered questionnaires are needed. The WORC is a quality of life questionnaire designed for patients with disorders of the rotator cuff. The score is validated for rotator cuff disease, but not for rotator cuff repair specifically.</p> <p>The aim of this study is to investigate reliability, validity and responsiveness of WORC in patients undergoing arthroscopic rotator cuff repair.</p> <p>Methods/Design</p> <p>An approved translation of the WORC into Dutch is used. In this prospective study three groups of patients are used: 1. Arthroscopic rotator cuff repair; 2. Disorders of the rotator cuff without rupture; 3. Shoulder instability.</p> <p>The WORC, SF-36 and the Constant Score are obtained twice before therapy is started to measure reliability and validity. Responsiveness is tested by obtaining the same tests after therapy.</p

Multi-messenger Observations of a Binary Neutron Star Merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ∼ 1.7 {{s}} with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of {40}-8+8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 {M}⊙ . An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ∼ 40 {{Mpc}}) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ∼10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position ∼ 9 and ∼ 16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.The AST3 project is supported by the National Basic Research Program (973 Program) of China (Grant Nos. 2013CB834901, 2013CB834900, 2013CB834903), and the Chinese Polar Environment Comprehensive Investigation & Assessment Program (grant No. CHINARE2016-02-03-05). The construction of the AST3 telescopes has received fundings from Tsinghua University, Nanjing University, Beijing Normal University, University of New South Wales, and Texas A&M University, the Australian Antarctic Division, and the National Collaborative Research Infrastructure Strategy (NCRIS) of Australia. It has also received funding from Chinese Academy of Sciences through the Center for Astronomical Mega-Science and National Astronomical Observatory of China (NAOC).The collaboration between LIGO/Virgo and EVN/e-MERLIN is part of a project that has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No. 653477.B.C., V.C., A.G., and W.S.P. gratefully acknowledge NASA funding through contract NNM13AA43C. M.S.B., R.H., P.J., C.A.M., S.P., R.D.P., M.S., and P.V. gratefully acknowledge NASA funding from cooperative agreement NNM11AA01A. E.B. is supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Universities Space Research Association under contract with NASA. D.K., C.A.W.H., C.M. H., and J.R. gratefully acknowledge NASA funding through the Fermi-GBM project. Support for the German contribution to GBM was provided by the Bundesministerium für Bildung und Forschung (BMBF) via the Deutsches Zentrum für Luft und Raumfahrt (DLR) under contract number 50 QV 0301. A. v.K. was supported by the Bundesministeriums für Wirtschaft und Technologie (BMWi) through DLR grant 50 OG 1101. S. M.B. acknowledges support from Science Foundation Ireland under grant 12/IP/1288.Part of the funding for GROND was generously granted from the Leibniz-Prize to Prof. G. Hasinger (DFG grant HA 1850/28-1). “We acknowledge the excellent help in obtaining GROND data from Angela Hempel, Markus Rabus and Régis Lachaume on La Silla.

Comprehensive Rare Variant Analysis via Whole-Genome Sequencing to Determine the Molecular Pathology of Inherited Retinal Disease

Inherited retinal disease is a common cause of visual impairment and represents a highly heterogeneous group of conditions. Here, we present findings from a cohort of 722 individuals with inherited retinal disease, who have had whole-genome sequencing (n = 605), whole-exome sequencing (n = 72), or both (n = 45) performed, as part of the NIHR-BioResource Rare Diseases research study. We identified pathogenic variants (single-nucleotide variants, indels, or structural variants) for 404/722 (56%) individuals. Whole-genome sequencing gives unprecedented power to detect three categories of pathogenic variants in particular: structural variants, variants in GC-rich regions, which have significantly improved coverage compared to whole-exome sequencing, and variants in non-coding regulatory regions. In addition to previously reported pathogenic regulatory variants, we have identified a previously unreported pathogenic intronic variant in $\textit{CHM}$ in two males with choroideremia. We have also identified 19 genes not previously known to be associated with inherited retinal disease, which harbor biallelic predicted protein-truncating variants in unsolved cases. Whole-genome sequencing is an increasingly important comprehensive method with which to investigate the genetic causes of inherited retinal disease.This work was supported by The National Institute for Health Research England (NIHR) for the NIHR BioResource – Rare Diseases project (grant number RG65966). The Moorfields Eye Hospital cohort of patients and clinical and imaging data were ascertained and collected with the support of grants from the National Institute for Health Research Biomedical Research Centre at Moorfields Eye Hospital, National Health Service Foundation Trust, and UCL Institute of Ophthalmology, Moorfields Eye Hospital Special Trustees, Moorfields Eye Charity, the Foundation Fighting Blindness (USA), and Retinitis Pigmentosa Fighting Blindness. M.M. is a recipient of an FFB Career Development Award. E.M. is supported by UCLH/UCL NIHR Biomedical Research Centre. F.L.R. and D.G. are supported by Cambridge NIHR Biomedical Research Centre

Bi-allelic Loss-of-Function CACNA1B Mutations in Progressive Epilepsy-Dyskinesia.

The occurrence of non-epileptic hyperkinetic movements in the context of developmental epileptic encephalopathies is an increasingly recognized phenomenon. Identification of causative mutations provides an important insight into common pathogenic mechanisms that cause both seizures and abnormal motor control. We report bi-allelic loss-of-function CACNA1B variants in six children from three unrelated families whose affected members present with a complex and progressive neurological syndrome. All affected individuals presented with epileptic encephalopathy, severe neurodevelopmental delay (often with regression), and a hyperkinetic movement disorder. Additional neurological features included postnatal microcephaly and hypotonia. Five children died in childhood or adolescence (mean age of death: 9 years), mainly as a result of secondary respiratory complications. CACNA1B encodes the pore-forming subunit of the pre-synaptic neuronal voltage-gated calcium channel Cav2.2/N-type, crucial for SNARE-mediated neurotransmission, particularly in the early postnatal period. Bi-allelic loss-of-function variants in CACNA1B are predicted to cause disruption of Ca2+ influx, leading to impaired synaptic neurotransmission. The resultant effect on neuronal function is likely to be important in the development of involuntary movements and epilepsy. Overall, our findings provide further evidence for the key role of Cav2.2 in normal human neurodevelopment.MAK is funded by an NIHR Research Professorship and receives funding from the Wellcome Trust, Great Ormond Street Children's Hospital Charity, and Rosetrees Trust. E.M. received funding from the Rosetrees Trust (CD-A53) and Great Ormond Street Hospital Children's Charity. K.G. received funding from Temple Street Foundation. A.M. is funded by Great Ormond Street Hospital, the National Institute for Health Research (NIHR), and Biomedical Research Centre. F.L.R. and D.G. are funded by Cambridge Biomedical Research Centre. K.C. and A.S.J. are funded by NIHR Bioresource for Rare Diseases. The DDD Study presents independent research commissioned by the Health Innovation Challenge Fund (grant number HICF-1009-003), a parallel funding partnership between the Wellcome Trust and the Department of Health, and the Wellcome Trust Sanger Institute (grant number WT098051). We acknowledge support from the UK Department of Health via the NIHR comprehensive Biomedical Research Centre award to Guy's and St. Thomas' National Health Service (NHS) Foundation Trust in partnership with King's College London. This research was also supported by the NIHR Great Ormond Street Hospital Biomedical Research Centre. J.H.C. is in receipt of an NIHR Senior Investigator Award. The research team acknowledges the support of the NIHR through the Comprehensive Clinical Research Network. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR, Department of Health, or Wellcome Trust. E.R.M. acknowledges support from NIHR Cambridge Biomedical Research Centre, an NIHR Senior Investigator Award, and the University of Cambridge has received salary support in respect of E.R.M. from the NHS in the East of England through the Clinical Academic Reserve. I.E.S. is supported by the National Health and Medical Research Council of Australia (Program Grant and Practitioner Fellowship)

Scenario archetypes:converging rather than diverging themes

Future scenarios provide challenging, plausible and relevant stories about how the future could unfold. Urban Futures (UF) research has identified a substantial set (>450) of seemingly disparate scenarios published over the period 1997–2011 and within this research, a sub-set of >160 scenarios has been identified (and categorized) based on their narratives according to the structure first proposed by the Global Scenario Group (GSG) in 1997; three world types (Business as Usual, Barbarization, and Great Transitions) and six scenarios, two for each world type (Policy Reform—PR, Market Forces—MF, Breakdown—B, Fortress World—FW, Eco-Communalism—EC and New Sustainability Paradigm—NSP). It is suggested that four of these scenario archetypes (MF, PR, NSP and FW) are sufficiently distinct to facilitate active stakeholder engagement in futures thinking. Moreover they are accompanied by a well-established, internally consistent set of narratives that provide a deeper understanding of the key fundamental drivers (e.g., STEEP—Social, Technological, Economic, Environmental and Political) that could bring about realistic world changes through a push or a pull effect. This is testament to the original concept of the GSG scenarios and their development and refinement over a 16 year period