New Step-Size Criterion for the Steepest Descent based on Geometric Numerical Integration

This paper deals with unconstrained optimization problems based on numerical analysis of ordinary differential equations (ODEs). Although it has been known for a long time that there is a relation between optimization methods and discretization of ODEs, research in this direction has recently been gaining attention. In recent studies, the dissipation laws of ODEs have often played an important role. By contrast, in the context of numerical analysis, a technique called geometric numerical integration, which explores discretization to maintain geometrical properties such as the dissipation law, is actively studied. However, in research investigating the relationship between optimization and ODEs, techniques of geometric numerical integration have not been sufficiently investigated. In this paper, we show that a recent geometric numerical integration technique for gradient flow reads a new step-size criterion for the steepest descent method. Consequently, owing to the discrete dissipation law, convergence rates can be proved in a form similar to the discussion in ODEs. Although the proposed method is a variant of the existing steepest descent method, it is suggested that various analyses of the optimization methods via ODEs can be performed in the same way after discretization using geometric numerical integration

Sheet Dependence on Superconducting Gap in Oxygen-Deficient Iron-based Oxypnictide Superconductors NdFeAs0.85

Photoemission spectroscopy with low-energy tunable photons on oxygen-deficient iron-based oxypnictide superconductors NdFeAsO0.85 (Tc=52K) reveals a distinct photon-energy dependence of the electronic structure near the Fermi level (EF). A clear shift of the leading-edge can be observed in the superconducting states with 9.5 eV photons, while a clear Fermi cutoff with little leading-edge shift can be observed with 6.0 eV photons. The results are indicative of the superconducting gap opening not on the hole-like ones around Gamma (0,0) point but on the electron-like sheets around M(pi,pi) point.Comment: 8 pages, 3 figure

Cluster analysis after TAVR

Aims The aim of this study was to identify phenotypes with potential prognostic significance in aortic stenosis (AS) patients after transcatheter aortic valve replacement (TAVR) through a clustering approach. Methods and results This multi-centre retrospective study included 1365 patients with severe AS who underwent TAVR between January 2015 and March 2019. Among demographics, laboratory, and echocardiography parameters, 20 variables were selected through dimension reduction and used for unsupervised clustering. Phenotypes and outcomes were compared between clusters. Patients were randomly divided into a derivation cohort (n = 1092: 80%) and a validation cohort (n = 273: 20%). Three clusters with markedly different features were identified. Cluster 1 was associated predominantly with elderly age, a high aortic valve gradient, and left ventricular (LV) hypertrophy; Cluster 2 consisted of preserved LV ejection fraction, larger aortic valve area, and high blood pressure; and Cluster 3 demonstrated tachycardia and low flow/low gradient AS. Adverse outcomes differed significantly among clusters during a median of 2.2 years of follow-up (P < 0.001). After adjustment for clinical and echocardiographic data in a Cox proportional hazards model, Cluster 3 (hazard ratio, 4.18; 95% confidence interval, 1.76–9.94; P = 0.001) was associated with increased risk of adverse outcomes. In sequential Cox models, a model based on clinical data and echocardiographic variables (χ2 = 18.4) was improved by Cluster 3 (χ2 = 31.5; P = 0.001) in the validation cohort. Conclusion Unsupervised cluster analysis of patients after TAVR revealed three different groups for assessment of prognosis. This provides a new perspective in the categorization of patients after TAVR that considers comorbidities and extravalvular cardiac dysfunction

Ectopic adrenal adenoma causing gross hematuria: Steroidogenic enzyme profiling and literature review

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149375/1/iju512068.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149375/2/iju512068_am.pd