A Primal-Dual Quasi-Newton Method for Constrained Optimization

One of the most important developments in nonlinear constrained optimization in recent years has been the recursive quadratic programming (RQP) method suggested by Wilson, Han, Powell and many other researchers. It is clear that the role of the auxiliary quadratic programming problem is to calculate (implicitly) the inverse Hessian of the dual objective function. We describe the Hessian of the Lagrangian and that of the dual objective function as the primal Hessian and the dual Hessian, respectively. In this paper, a new method for constrained optimization, called the primal-dual quasi-Newton method, is proposed. The main feature of this method is that it improves (explicitly) both the primal Hessian and the dual Hessian using quasi-Newton methods. Several variants of the primal-dual quasi-Newton method are possible: the properties of these methods are described and the computational results obtained for some test problems are given

Superconductivity in metal rich Li-Pd-B ternary Boride

8K superconductivity was observed in the metal rich Li-Pd-B ternary system. Structural, microstructural, electrical and magnetic investigations for various compositions proved that Li2Pd3B compound, which has a cubic structure composed of distorted Pd6B octahedrons, is responsible for the superconductivity. This is the first observation of superconductivity in metal rich ternary borides containing alkaline metal and Pd as a late transition metal. The compound prepared by arc melting has high density, is stable in the air and has an upper critical field, Hc2(0), of 6T.Comment: 4 pages, 5 figur

Pressure-induced structural transitions in MgH2{_2}

The stability of MgH$_2$ has been studied up to 20~GPa using density-functional total-energy calculations. At ambient pressure $\alpha$-MgH${_2}$ takes a TiO$_2$-rutile-type structure. $\alpha$-MgH$_2$ is predicted to transform into $\gamma$-MgH${_2}$ at 0.39~GPa. The calculated structural data for $\alpha$- and $\gamma$-MgH${_2}$ are in very good agreement with experimental values. At equilibrium the energy difference between these modifications is very small, and as a result both phases coexist in a certain volume and pressure field. Above 3.84~GPa $\gamma$-MgH${_2}$ transforms into $\beta$-MgH${_2}$; consistent with experimental findings. Two further transformations have been identified at still higher pressure: i) $\beta$- to $\delta$-MgH${_2}$ at 6.73 GPa and (ii) $\delta$- to $\epsilon$-MgH${_2}$ at 10.26~GPa.Comment: 4 pages, 4 figure

Development and application of a Japanese model of the WHO fracture risk assessment tool (FRAX™)

SUMMARY: The present study estimated the 10-year probability using the Japanese version of WHO fracture risk assessment tool (FRAX) in order to determine fracture probabilities that correspond to intervention thresholds currently used in Japan and to resolve some issues for its use in Japan. INTRODUCTION: The objective of the present study was to evaluate a Japanese version of the WHO fracture risk assessment (FRAX) tool to compute 10-year probabilities of osteoporotic fracture in Japanese men and women. Since lumbar spine bone mineral density (BMD) is used preferentially as a site for assessment, and densitometers use Japanese reference data, a second aim was to investigate the suitability and impact of this practice in Japan. METHODS: Fracture probabilities were computed from published data on the fracture and death hazards in Japan. Probabilities took account of age, sex, the presence of clinical risk factors and femoral neck BMD. Fracture probabilities were determined that were equivalent to intervention thresholds currently used in Japan. The difference between T-scores derived from international reference data and that using Japanese-specific normal ranges was estimated from published sources. The gradient of risk of BMD for fracture in Japan was compared to that for BMD at the lumbar spine in the Hiroshima cohort. RESULTS: The 10-year probabilities of a major osteoporosis-related fracture that corresponded to current intervention thresholds ranged from approximately 5% at the age of 50 years to more than 20% at the age of 80 years. The use of femoral neck BMD predicts fracture as well as or better than BMD tests at the lumbar spine. There were small differences in T-scores between those used for the model and those derived from a Japanese reference population. CONCLUSIONS: The FRAX mark tool has been used to determine possible thresholds for therapeutic intervention, based on equivalence of risk with current guidelines. The approach will need to be supported by appropriate health economic analyses. Femoral neck BMD is suitable for the prediction of fracture risk among Japanese. However, when applying the FRAX model to Japan, T-scores and Z-scores should be converted to those derived from the international reference

123I-MIBG cardiac uptake and smell identification in parkinsonian patients with LRRK2 mutations

Reduced uptake of 123I- metaiodobenzylguanidine (MIBG) on cardiac gammagraphy and impaired odor identification are markers of neurodegenerative diseases with Lewy bodies (LB) as a pathological hallmark, such as idiopathic Parkinson’s disease (IPD). LRRK2 patients present with a clinical syndrome indistinguishable from IPD, but LB have not been found in some cases. Patients with such mutations could behave differently than patients with IPD with respect to MIBG cardiac uptake and olfaction. We studied 14 LRRK2 patients, 14 IPD patients matched by age, gender, disease duration and severity, and 13 age and gender matched control subjects. Olfaction was analyzed through the University of Pennsylvania Smell Identification Test (UPSIT). MIBG cardiac uptake was evaluated through the H/M ratio. The late H/M was 1.44 ± 0.31 for LRRK2 patients, 1.19 ± 0.15 for PD patients, and 1.67 ± 0.16 for control subjects. LRRK2 patients presented lower but not statistically significant MIBG cardiac uptake than controls (p = 0.08) and significant higher uptake than PD patients (p = 0.04). UPSIT mean scores were 21.5 ± 7.3 for LRRK2 patients, 18.7 ± 6.2 for IPD patients and 29.7 ± 5.7 for control subjects. UPSIT score was lower in both LRRK2 and PD than in controls. In LRRK2 patients a positive correlation was found between myocardial MIBG uptake and UPSIT scores, (R = 0.801, p < 0.001). In LRRK2 patients, MIBG cardiac uptake was less impaired than in PD; a positive correlation between MIBG cardiac uptake and UPSIT scores was observed. As MIBG cardiac reduced uptake and impaired odor identification are markers of LB pathology, this findings may represent neuropathological heterogeneity among LRRK2 patients