The Fokker-Planck equation for bistable potential in the optimized expansion

The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to agree well with the exact solution of the Fokker-Planck equation. Even for a bistable system the whole period of evolution to equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an

Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals

We advocate a method to improve systematically the self-consistent harmonic approximation (or the Gaussian approximation), which has been employed extensively in condensed matter physics and statistical mechanics. We demonstrate the {\em convergence} of the method in a model obtained from dimensional reduction of SU($N$) Yang-Mills theory in $D$ dimensions. Explicit calculations have been carried out up to the 7th order in the large-N limit, and we do observe a clear convergence to Monte Carlo results. For $D \gtrsim 10$ the convergence is already achieved at the 3rd order, which suggests that the method is particularly useful for studying the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory.Comment: LaTeX, 4 pages, 5 figures; title slightly changed, explanations added (16 pages, 14 figures), final version published in JHE

American Orthopaedic Foot and Ankle Society (AOFAS) Ankle-Hindfoot Score: A study protocol for the translation and validation of the Dutch language version

Introduction: The American Orthopaedic Foot and Ankle Society (AOFAS) Ankle-Hindfoot Score is among the most commonly used instruments for measuring the outcome of treatment in patients who sustained a complex ankle or hindfoot injury. It combines a clinician-reported and a patient-reported part. A valid Dutch version of this instrument is currently not available. Such a translated and validated instrument would allow objective comparison across hospitals or between patient groups, and with shown validity and reliability it may become a quality of care indicator in future. The main aims of this study are to translate and culturally adapt the AOFAS Ankle-Hindfoot Score questionnaire into Dutch according to international guidelines, and to evaluate the measurement properties of the AOFAS Ankle-Hindfoot Score-Dutch language version (DLV) in patients with a unilateral ankle or hindfoot fracture. Methods and analysis: The design of the study will be a multicentre prospective observational study (case series) in patients who presented to the emergency department with a unilateral ankle or hindfoot fracture or (fracture) dislocation. A research physician or research assistant will complete the AOFAS Ankle-Hindfoot Score-DLV based on interview for the subjective part and a physical examination for the objective part. In addition, patients will be asked to complete the Foot Function Index (FFI) and the Short Form-36 (SF-36). Descriptive statistics (including floor and ceiling effects), internal consistency, construct validity, reproducibility (ie, test-retest reliability, agreement and smallest detectable change) and responsiveness will be assessed for the AOFAS DLV. Ethics and dissemination: This study has been exempted by the Medical Research Ethics Committee (MREC) Erasmus MC (Rotterdam, the Netherlands). Each participant will provide written consent to participate and remain anonymised during the study. The results of the study are planned to be published in an international, peer-reviewed journal. Trial registration number: NTR5613. pre-result

The American Orthopaedic Foot and Ankle Society Ankle-Hindfoot Scale; Translation and validation of the Dutch language version for ankle fractures

Objectives The American Orthopaedic Foot and Ankle Society (AOFAS) Ankle-Hindfoot Scale is among the most commonly used instruments for measuring outcome of treatment in patients who sustained a complex ankle or hindfoot injury. It consists of a patient-reported and a physician-reported part. A validated, Dutch version of this instrument is currently not available. The aim of this study was to translate the instrument into Dutch and to determine the measurement properties of the AOFAS Ankle-Hindfoot Scale Dutch language version (DLV) in patients with a unilateral ankle fracture. Setting Multicentre (two Dutch hospitals), prospective observational study. Participants In total, 142 patients with a unilateral ankle fracture were included. Ten patients were lost to follow-up. Primary and secondary outcome measures Patients completed the subjective (patient-reported) part of the AOFAS Ankle-Hindfoot Scale-DLV. A physician or trained physician-assistant completed the physician-reported part. For comparison and evaluation of the measuring characteristics, the Foot Function Index and the Short Form-36 were completed by the patient. Descriptive statistics (including floor and ceiling effects), reliability (ie, internal consistency), construct validity, reproducibility (ie, test-retest reliability, agreement and smallest detectable change) and responsiveness were determined. Results The AOFAS-DLV and its subscales showed good internal consistency (Cronbach's α >0.90). Construct validity and longitudinal validity were proven to be adequate (76.5% of predefined hypotheses were confirmed). Floor effects were not present. Ceiling effects were present from 6 months onwards, as expected. Responsiveness was adequate, with a smallest detectable change of 12.0 points. Conclusions The AOFAS-DLV is a reliable, valid and responsive measurement instrument for evaluating functional outcome in patients with a unilateral ankle fracture. This implies that the questionnaire is suitable to compare different treatment modalities within this population or to compare outcome across hospitals. Trial registration The Netherlands Trial Register (NTR5613

Testing the Gaussian expansion method in exactly solvable matrix models

The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.Comment: 30 pages, 15 figures, LaTeX; added references for section

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Validation of the American Orthopaedic Foot and Ankle Society Ankle-Hindfoot Scale Dutch language version in patients with hindfoot fractures

OBJECTIVES: The American Orthopaedic Foot and Ankle Society (AOFAS) Ankle-Hindfoot Scale is among the most used questionnaires for measuring functional recovery after a hindfoot injury. Recently, this instrument was translated and culturally adapted into a Dutch version. In this study, the measurement properties of the Dutch language version (DLV) were investigated in patients with a unilateral hindfoot fracture.DESIGN: Multicentre, prospective observational study. SETTING: This multicentre study was conducted in three Dutch hospitals. PARTICIPANTS: In total, 118 patients with a unilateral hindfoot fracture were included. Three patients were lost to follow-up. PRIMARY AND SECONDARY OUTCOME MEASURES: Patients were asked to complete the AOFAS-DLV, the Foot Function Index and the Short Form-36 on three occasions. Descriptive statistics (including floor and ceiling effects), reliability (ie, internal consistency), construct validity, reproducibility (ie, test-retest reliability, agreement and smallest detectable change (SDC)) and responsiveness were determined. RESULTS: Internal consistency was inadequate for the AOFAS-DLV total scale (α=0.585), but adequate for the function subscale (α=0.863). The questionnaire had adequate construct validity (82.4% of predefined hypotheses were confirmed), but inadequate longitudinal validity (70.6%). No floor effects were found, but ceiling effects were present in all AOFAS-DLV (sub)scales, most pronounced from 6 to 24 months after trauma onwards. Responsiveness was only adequate for the pain and alignment subscales, with a SDC of 1.7 points. CONCLUSIONS: The AOFAS Ankle-Hindfoot Scale DLV has adequate construct validity and is reliable, making it a suitable instrument for cross-sectional studies investigating functional outcome in patients with a hindfoot fracture. The inadequate longitudinal validity and responsiveness, however, hamper the use of the questionnaire in longitudinal studies and for assessing long-term functional outcome. TRIAL REGISTRATION NUMBER: NTR5613; Post-results

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students