On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-hard, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.Comment: 25 pages, 4 figure

Coherent states for exactly solvable potentials

A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states, show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag

Risk stratified monitoring for methotrexate toxicity in immune mediated inflammatory diseases: prognostic model development and validation using primary care data from the UK.

OBJECTIVE: To develop and validate a prognostic model to inform risk stratified decisions on frequency of monitoring blood tests during long term methotrexate treatment. DESIGN: Retrospective cohort study. SETTING: Electronic health records within the UK's Clinical Practice Research Datalink (CPRD) Gold and CPRD Aurum. PARTICIPANTS: Adults (≥18 years) with a diagnosis of an immune mediated inflammatory disease who were prescribed methotrexate by their general practitioner for six months or more during 2007-19. MAIN OUTCOME MEASURE: Discontinuation of methotrexate owing to abnormal monitoring blood test result. Patients were followed-up from six months after their first prescription for methotrexate in primary care to the earliest of outcome, drug discontinuation for any other reason, leaving the practice, last data collection from the practice, death, five years, or 31 December 2019. Cox regression was performed to develop the risk equation, with bootstrapping used to shrink predictor effects for optimism. Multiple imputation handled missing predictor data. Model performance was assessed in terms of calibration and discrimination. RESULTS: Data from 13 110 (854 events) and 23 999 (1486 events) participants were included in the development and validation cohorts, respectively. 11 candidate predictors (17 parameters) were included. In the development dataset, the optimism adjusted R2 was 0.13 and the optimism adjusted Royston D statistic was 0.79. The calibration slope and Royston D statistic in the validation dataset for the entire follow-up period was 0.94 (95% confidence interval 0.85 to 1.02) and 0.75 (95% confidence interval 0.67 to 0.83), respectively. The prognostic model performed well in predicting outcomes in clinically relevant subgroups defined by age group, type of immune mediated inflammatory disease, and methotrexate dose. CONCLUSION: A prognostic model was developed and validated that uses information collected during routine clinical care and may be used to risk stratify the frequency of monitoring blood test during long term methotrexate treatment

During pregnancy, recreational drug-using women stop taking ecstasy (3,4-methylenedioxy-N-methylamphetamine) and reduce alcohol consumption but continue to smoke tobacco and cannabis

While recreational drug use in UK women is prevalent, to date there is little prospective data on patterns of drug use in recreational drug-using women immediately before and during pregnancy. A total of 121 participants from a wide range of backgrounds were recruited to take part in the longitudinal Development and Infancy Study (DAISY) study of prenatal drug use and outcomes. Eighty-six of the women were interviewed prospectively while pregnant and/or soon after their infant was born. Participants reported on use immediately before and during pregnancy and on use over their lifetime. Levels of lifetime drug use of the women recruited were high, with women reporting having used at least four different illegal drugs over their lifetime. Most users of cocaine, 3,4-methylenedioxy-N-methylamphetamine (MDMA) and other stimulants stopped using these by the second trimester and levels of use were low. However, in pregnancy, 64% of the sample continued to use alcohol, 46% tobacco and 48% cannabis. While the level of alcohol use reduced substantially, average tobacco and cannabis levels tended to be sustained at pre-pregnancy levels even into the third trimester (50 cigarettes and/or 11 joints per week). In sum, while the use of ‘party drugs’ and alcohol seems to reduce, levels of tobacco and cannabis use are likely to be sustained throughout pregnancy. The data provide polydrug profiles that can form the basis for the development of more realistic animal models

Information Needs of Hong Kong Chinese Patients Undergoing Surgery

BACKGROUND: The provision of information to patients is an important aspect of contemporary health care. Limitations in health resources necessitates that the provision of information is carefully planned and culturally specific to maximize the benefits to patients from the resources available. AIM AND OBJECTIVES: The purposes of the study were to recognize Chinese surgical patients' information needs on admission and ascertain why the information is important to assist in understanding how it is used and, therefore, its potential impact. METHODS: A descriptive study design was used. A convenience sample of 83 surgical patients took part comprising 51 men and 32 women. An eight-item questionnaire based on the right of patients to information as listed in the Patients' Charter in Hong Kong using a 5-point Likert scale and one open-ended question to comment on why the information was important to them was completed by patients on the day of admission. RESULTS: Patients rated highly the need for all types of information. They rated most highly the need for information about the signs and symptoms indicating postoperative complications and when to seek medical help. Patients did not rate as highly, information regarding why the doctor believes the surgery is important, treatment alternatives and explanation of the procedure. CONCLUSIONS: These findings indicate that Chinese patients are desirous of a range of relevant information. RELEVANCE TO PRACTICE: Nursing staff, in particular, need to consider the 'timeliness' of information and the cultural appropriateness of how information is delivered

The Q2Q^2-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron

The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides a measurement of the generalised GDH integral covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing $Q^2$. The DIS contribution is sizeable over the full measured range, even down to the lowest measured $Q^2$. As expected, at higher $Q^2$ the data are found to be in agreement with previous measurements of the first moment of $g_1$. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton--neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at $Q^2 = 5$ GeV$^2$.Comment: 12 pages, 10 figure

Measurement of single-spin azimuthal asymmetries in semi-inclusive electroproduction of pions and kaons on a longitudinally polarised deuterium target

Single-spin asymmetries have been measured for semi-inclusive electroproduction of $\pi^+$, $\pi^-$, $\pi^0$ and $K^+$ mesons in deep-inelastic scattering off a longitudinally polarised deuterium target. The asymmetries appear in the distribution of the hadrons in the azimuthal angle $\phi$ around the virtual photon direction, relative to the lepton scattering plane. The corresponding analysing powers in the $\sin \phi$ moment of the cross section are $0.012 \pm 0.002 {(stat.)} \pm 0.002 {(syst.)}$ for $\pi^+$, $0.006 \pm 0.003 {(stat.)} \pm 0.002 {(syst.)}$ for $\pi^-$, $0.021 \pm 0.005 {(stat.)} \pm 0.003 {(syst.)}$ for $\pi^0$ and $0.013 \pm 0.006 {(stat.)} \pm 0.003 {(syst.)}$ for $K^+$. The $\sin 2\phi$ moments are compatible with zero for all particles.Comment: Revised version shortened 9 pages, 3 tables, 7 figure

Enhanced glycemic control with combination therapy for type 2 diabetes in primary care

Type 2 diabetes mellitus is an increasingly common medical problem for primary care clinicians to address. Treatment of diabetes has evolved from simple replacement of insulin (directly or through insulin secretagogs) through capture of mechanisms such as insulin sensitizers, alpha-glucosidase inhibitors, and incretins. Only very recently has recognition of the critical role of the gastrointestinal system as a major culprit in glucose dysregulation been established. Since glycated hemoglobin A1c reductions provide meaningful risk reduction as well as improved quality of life, it is worthwhile to explore evolving paths for more efficient use of the currently available pharmacotherapies. Because diabetes is a progressive disease, even transiently successful treatment will likely require augmentation as the disorder progresses. Pharmacotherapies with complementary mechanisms of action will be necessary to achieve glycemic goals. Hence, clinicians need to be well informed about the various noninsulin alternatives that have been shown to be successful in glycemic goal attainment. This article reviews the benefits of glucose control, the current status of diabetes control, pertinent pathophysiology, available pharmacological classes for combination, limitations of current therapies, and suggestions for appropriate combination therapies, including specific suggestions for thresholds at which different strategies might be most effectively utilized by primary care clinicians

Shell evolution approaching the N=20 island of inversion : Structure of 26Na

The levels in 26Na with single particle character have been observed for the first time using the d(25Na, pγ) reaction at 5 MeV/nucleon. The measured excitation energies and the deduced spectroscopic factors are in good overall agreement with (0+1)hω shell model calculations performed in a complete spsdfp basis and incorporating a reduction in the N=20 gap. Notably, the 1p3/2 neutron configuration was found to play an enhanced role in the structure of the low-lying negative parity states in 26Na, compared to the isotone 28Al. Thus, the lowering of the 1p3/2 orbital relative to the 0f7/2 occurring in the neighbouring Z=10 and 12 nuclei - 25,27Ne and 27,29Mg - is seen also to occur at Z=11 and further strengthens the constraints on the modelling of the transition into the island of inversion