Regge and Okamoto symmetries

We will relate the surprising Regge symmetry of the Racah-Wigner 6j symbols to the surprising Okamoto symmetry of the Painleve VI differential equation. This then presents the opportunity to give a conceptual derivation of the Regge symmetry, as the representation theoretic analogue of the author's previous derivation of the Okamoto symmetry. [The resulting derivation is quite simple, so it would be surprising if it has not been previously observed. Any references would be appreciated!]Comment: 14 page

Categorical geometric skew Howe duality

We categorify the R-matrix isomorphism between tensor products of minuscule representations of U_q(sl(n)) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of U_q(sl(2)) which are related to representations of U_q(sl(n)) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometric categorification of Reshitikhin-Turaev tangle invariants developed by the first two authors.Comment: 31 page

Atlas of the OMERACT Heel Enthesitis MRI Scoring System (HEMRIS)

Objective: Assessment of enthesitis, a key feature in spondyloarthritis (SpA) and psoriatic arthritis (PsA), using objective and sensitive methods is pivotal in clinical trials. MRI allows detection of both soft tissue and intra-osseous changes of enthesitis. This article presents an atlas for the Outcome Measures in Rheumatology (OMERACT) Heel Enthesitis Magnetic Resonance ImagingMRI Scoring System (HEMRIS). Methods: Following a preliminary selection of potential examples of each grade, as per HEMRIS definitions, the images along with detailed definitions and reader rules were discussed at web-based, interactive meetings between the members of the OMERACT MRI in Arthritis Working Group. Results: Reference images of each grade of the MRI features to be assessed using HEMRIS, along with reader rules and recommended MRI sequences are depicted. Conclusion: The presented reference images can be used to guide scoring Achilles tendon and plantar fascia (plantar aponeurosis) enthesitis according to the OMERACT HEMRIS in clinical trials and cohorts in which MRI enthesitis is used as an outcome

Treatment of Truncal Incompetence and Varicose Veins with a Single Administration of a New Polidocanol Endovenous Microfoam Preparation Improves Symptoms and Appearance

ObjectiveThis multicenter, parallel group study was designed to determine if a single administration of ≤15 mL of pharmaceutical-grade polidocanol endovenous microfoam (PEM, now approved in the United States as Varithena [polidocanol injectable foam], BTG International Ltd.) could alleviate symptoms and improve appearance of varicose veins in a typical population of patients with moderate to very severe symptoms of superficial venous incompetence and visible varicosities of the great saphenous vein (GSV) system.MethodsThe primary endpoint was patient-reported venous symptom improvement measured by change from baseline to Week 8 in 7-day average VVSymQ score. Co-secondary endpoints measured improvement in appearance of visible varicose veins from baseline to Week 8, as measured by the Independent Photography Review–Visible Varicose Veins (IPR-V3) and Patient Self-assessment of Visible Varicose Veins (PA-V3) scores. Patients were randomized to five groups: PEM 0.125% (control), 0.5%, 1%, 2%, or placebo. Adverse events (AEs) were recorded at each study visit. Tertiary endpoints measured duplex ultrasound response, changes in venous clinical severity score, and the modified Venous Insufficiency Epidemiological and Economic Study–Quality of Life/Symptoms.ResultsAt Week 8, VVSymQ scores for the pooled PEM group (0.5% + 1% + 2%; p < .0001) and individual dose concentrations (p < .001) were significantly superior to placebo. Mean changes from baseline to Week 8 in IPR-V3 and PA-V3 scores were significantly greater for pooled PEM than for placebo (p < .0001). Most AEs were mild and resolved without sequelae. No pulmonary emboli were reported.ConclusionsThis study demonstrated that a single administration of up to 15 mL of PEM is a safe, effective, and convenient treatment for the symptoms of superficial venous incompetence and the appearance of visible varicosities of the GSV system. Doses of 0.5%, 1%, and 2% PEM appear to have an acceptable risk-benefit ratio

Meromorphic tensor equivalence for Yangians and quantum loop algebras

Let ${\mathfrak g}$ be a complex semisimple Lie algebra, and $Y_h({\mathfrak g})$, $U_q(L{\mathfrak g})$ the corresponding Yangian and quantum loop algebra, with deformation parameters related by $q=\exp(\pi i h)$. When $h$ is not a rational number, we constructed in arXiv:1310.7318 a faithful functor $\Gamma$ from the category of finite-dimensional representations of $Y_h ({\mathfrak g})$ to those of $U_q(L{\mathfrak g})$. The functor $\Gamma$ is governed by the additive difference equations defined by the commuting fields of the Yangian, and restricts to an equivalence on a subcategory of $Y_h({\mathfrak g})$ defined by choosing a branch of the logarithm. In this paper, we construct a tensor structure on $\Gamma$ and show that, if $|q|\neq 1$, it yields an equivalence of meromorphic braided tensor categories, when $Y_h({\mathfrak g})$ and $U_q(L{\mathfrak g})$ are endowed with the deformed Drinfeld coproducts and the commutative part of the universal $R$-matrix. This proves in particular the Kohno-Drinfeld theorem for the abelian $q$KZ equations defined by $Y_h({\mathfrak g})$. The tensor structure arises from the abelian $q$KZ equations defined by a appropriate regularisation of the commutative $R$-matrix of $Y_h({\mathfrak g})$.Comment: Title changed, details added. 67 pages, 1 figure. Final version, to appear in Publ. Math IHE

Numerical Weather Prediction (NWP) and hybrid ARMA/ANN model to predict global radiation

We propose in this paper an original technique to predict global radiation using a hybrid ARMA/ANN model and data issued from a numerical weather prediction model (ALADIN). We particularly look at the Multi-Layer Perceptron. After optimizing our architecture with ALADIN and endogenous data previously made stationary and using an innovative pre-input layer selection method, we combined it to an ARMA model from a rule based on the analysis of hourly data series. This model has been used to forecast the hourly global radiation for five places in Mediterranean area. Our technique outperforms classical models for all the places. The nRMSE for our hybrid model ANN/ARMA is 14.9% compared to 26.2% for the na\"ive persistence predictor. Note that in the stand alone ANN case the nRMSE is 18.4%. Finally, in order to discuss the reliability of the forecaster outputs, a complementary study concerning the confidence interval of each prediction is proposedComment: Energy (2012)

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page