The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Current Management Strategies in Osgood Schlatter: A cross‐sectional mixed method study

AbstractBackground: Osgood Schlatter (OS) is the most common knee condition in adolescent athletes aged 9-16. Without evidence to guide clinical practice it is unclear how OS is managed. The aim of this study is to investigate how international healthcare professionals (General Practitioners, Physiotherapists, Rheumatologists, Sports and Exercise Medicine Doctors and Orthopaedic Surgeons) diagnose and manage OS.Methods: This mixed-method study used a convergent parallel design. A quantitative questionnaire and semi-structured interview covered prognosis, diagnosis, treatment, and return to play of adolescents with OS. For quantitative data those who reported likely/very likely considered 'for' and unlikely/very unlikely 'against' (for specific diagnostic/management strategy). Qualitative data analysis used a phenomenological approach.Results: Two hundred and fifty-one healthcare professionals completed the questionnaire. The most common diagnostic criterion was pain at the tibial tuberosity (97% for). The most common treatments were patient education (99%) and exercise therapy (92%). Other treatments options were more heterogeneous, e.g. pain medication (31% for, and 34% against). Managing training load (97%), pain intensity (87%) and psychological factors (86%) were considered the most important factors influencing the return to activities. Several themes emerged from the interviews (on N=20) including imaging, pain management, family, psychosocial factors influencing prognosis.Conclusion: Diagnosis criteria of OS was relatively well agreed upon, whereas triangulation of qualitative and quantitative data showed heterogeneity of treatments. Psychosocial factors including family were highlighted as critical in the management of OS.Keywords: Adolescents; Apophysitis; Musculoskeletal Pain; Osgood Schlatter; Osteochondrosis

Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Dilatonic Interpretation of the Quintessence?

We discuss the possibility that "quintessential effects", recently displayed by large scale observations, may be consistently described in the context of the low-energy string effective action, and we suggest a possible approach to the problem of the cosmic coincidence based on the link between the strength of the dilaton couplings and the cosmological state of our Universe.Comment: 6 pages, Revtex, four figures included using epsfig. To appear in Phys. Rev.

C-axis lattice dynamics in Bi-based cuprate superconductors

We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A2u eigenfrequencies and the experimental values of the c axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Gamma-point A1g symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is based on the published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.Comment: 29 pages, 13 figure

Validating epilepsy diagnoses in routinely collected data

Purpose: Anonymised, routinely-collected healthcare data is increasingly being used for epilepsy research. We validated algorithms using general practitioner (GP) primary healthcare records to identify people with epilepsy from anonymised healthcare data within the Secure Anonymised Information Linkage (SAIL) databank in Wales, UK. Method: A reference population of 150 people with definite epilepsy and 150 people without epilepsy was ascertained from hospital records and linked to records contained within SAIL (containing GP records for 2.4 million people). We used three different algorithms, using combinations of GP epilepsy diagnosis and anti-epileptic drug (AED) prescription codes, to identify the reference population. Results: Combining diagnosis and AED prescription codes had a sensitivity of 84% (95% ci 77–90) and specificity of 98% (95–100) in identifying people with epilepsy; diagnosis codes alone had a sensitivity of 86% (80–91) and a specificity of 97% (92–99); and AED prescription codes alone achieved a sensitivity of 92% (70–83) and a specificity of 73% (65–80). Using AED codes only was more accurate in children achieving a sensitivity of 88% (75–95) and specificity of 98% (88–100). Conclusion: GP epilepsy diagnosis and AED prescription codes can be confidently used to identify people with epilepsy using anonymised healthcare records in Wales, U

How to make complexity look simple? Conveying ecosystems restoration complexity for socio-economic research and public engagement

Ecosystems degradation represents one of the major global challenges at the present time, threating people’s livelihoods and well-being worldwide. Ecosystem restoration therefore seems no longer an option, but an imperative. Restoration challenges are such that a dialogue has begun on the need to re-shape restoration as a science. A critical aspect of that reshaping process is the acceptance that restoration science and practice needs to be coupled with socio-economic research and public engagement. This inescapably means conveying complex ecosystem’s information in a way that is accessible to the wider public. In this paper we take up this challenge with the ultimate aim of contributing to making a step change in science’s contribution to ecosystems restoration practice. Using peatlands as a paradigmatically complex ecosystem, we put in place a transdisciplinary process to articulate a description of the processes and outcomes of restoration that can be understood widely by the public. We provide evidence of the usefulness of the process and tools in addressing four key challenges relevant to restoration of any complex ecosystem: (1) how to represent restoration outcomes; (2) how to establish a restoration reference; (3) how to cope with varying restoration time-lags and (4) how to define spatial units for restoration. This evidence includes the way the process resulted in the creation of materials that are now being used by restoration practitioners for communication with the public and in other research contexts. Our main contribution is of an epistemological nature: while ecosystem services-based approaches have enhanced the integration of academic disciplines and non-specialist knowledge, this has so far only followed one direction (from the biophysical underpinning to the description of ecosystem services and their appreciation by the public). We propose that it is the mix of approaches and epistemological directions (including from the public to the biophysical parameters) what will make a definitive contribution to restoration practice

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure