Correlative Sparsity in Primal-Dual Interior-Point Methods for LP,SDP, and SOCP

Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation which is determined by the sparsity of an optimization problem (linear program, semidefinite program or second-order cone program). We show if an optimization problem is correlatively sparse, then the coefficient matrix of the Schur complement equation inherits the sparsity, and a sparse Cholesky factorization applied to the matrix results in no fill-in. S. Kim’s research was supported by Kosef R01-2005-000-10271-0 and KRF-2006-312-C00062.     

Electrophilic glycosidation employing 3,5-O-(di-tert-butylsilylene)-erythro-furanoid glycal leads to exclusive formation of the β-anomer: synthesis of 2′-deoxynucleosides and its 1′-branched analogues

Stereoselectivity in N-iodosuccimide (NIS)-mediated electrophilic glycosidation was examined by employing 2,4-bis-O-(trimethylsilyl)thymine and three different silyl-protected erythro-furanoid glycals 12, 16, and 18. As a result, it was found that 3,5-O-(di-t-butylsilylene)-protected 18 gave only the β-anomer (21). The remarkable stereoselectivity observed by employing 18 is discussed on the basis of its X-ray crystallographic analysis. 1-Substituted glycals gave the corresponding β-anomer, again exclusively, to provide access to 1′-branched 2′-deoxynucleosides.     

Preparation of 2,2-disubstituted 1,2-dihydro-3H-indol-3-ones via oxidation of 2-substituted indoles and Mannich-type reaction

A novel preparative method for 2,2-disubstituted 1,2-dihydro-3H-indol-3-ones through the oxidation of 2-arylindoles followed by a Mannich-type reaction with carbon nucleophiles is described.     

Characterization of Ultra‐Thin Temperature‐Responsive Polymer Layer and Its Polymer Thickness Dependency on Cell Attachment/Detachment Properties

Ultra thin poly(N‐isopropylacrylamide) (PIPAAm) modified glass coverslips (PIAPAm‐CS) using electron beam irradiation exhibited a clear relationship between the polymer thickness and thermal cell adhesion/detachment behavior. The polymer thickness dependency and the characteristic of ultra thin PIPAAm layer, has been illustrated in terms of the molecular motion of the modified PIPAAm chains. PIPAAm‐CSs surfaces with various area‐polymer densities and thicknesses were characterized by AFM and protein adsorption assay. The newly obtained results gave a further insight into the illustration. Finally, the future application of intelligent surfaces was discussed for fabricating tissue and organ.

     

Optimum packing density and crystal structure of tin-doped indium oxide thin films for high-temperature annealing processes

The influence of high-temperature annealing on the electrical properties and microstructure of tin-doped indium oxide (ITO) thin films was investigated as a function of oxygen gas flow ratio to argon gas during the sputtering deposition. The ITO thin films were annealed at 500 °C in air after the deposition. It was found that the ITO thin films, which were deposited in relatively low oxygen gas flow ratio, exhibited high Hall mobility and low-resistivity after the annealing. Furthermore, the X-ray reflectivity and diffraction measurement revealed that the ITO thin film with low-resistivity after annealing exhibited high packing density, smooth surface and low crystallization degree. It can be considered that the carrier electron scattering was suppressed with increasing in the packing density of the ITO thin film; as a result, the Hall mobility and resistivity were improved.     

A case of Budd-Chiari syndrome: Gd-EOB-DTPA-enhanced MR findings

Budd-Chiari syndrome (BCS) is a rare disorder caused by the obstruction of hepatic venous outflow, leading to sinusoidal congestion, ischemic injury to liver cells and portal hypertension. Long-term survival largely depends on whether hepatocellular carcinoma occurs. A recently available liver-specific contrast medium, gadolinium-ethoxybenzyl-diethylenetriamine penta-acetic acid (Gd-EOB-DTPA), reportedly has high diagnostic capability for detection of malignant liver tumors. However, there has been no report of the sue of Gd-EOB-DTPA-enhanced magnetic resonance imaging (MRI) for BCS. We present a case of chronic BCS who underwent both gadopentetate dimeglumine (Gd-DTPA) and Gd-EOB-DTPA-enhanced MRI. Hepatic congestion and edema were seen as slightly hypointense areas on Gd-EOB-DTPA-enhanced hepatobiliary-phase images, although these areas were observed as slightly hyperintense on previously obtained Gd-DTPA-enhanced delayed-phase image. Reduced uptake of Gd-EOB-DTPA by hepatocytes in the region of congestion or edema may account for this difference, which should be recognized in image interpretations.     

Jensen’s inequality on convex spaces

We prove a Jensen’s inequality on $p$ -uniformly convex space in terms of $p$ -barycenters of probability measures with $(p-1)$ -th moment with $p\in ]1,\infty [$ under a geometric condition, which extends the results in Kuwae (Jensen’s inequality over CAT $(\kappa )$ -space with small diameter. In: Proceedings of Potential Theory and Stochastics, Albac Romania, pp. 173–182. Theta Series in Advanced Mathematics, vol. 14. Theta, Bucharest, 2009) , Eells and Fuglede (Harmonic maps between Riemannian polyhedra. In: Cambridge Tracts in Mathematics, vol. 142. Cambridge University Press, Cambridge, 2001) and Sturm (Probability measures on metric spaces of nonpositive curvature. Probability measures on metric spaces of nonpositive curvature. In: Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002), pp. 357–390. Contemporary Mathematics, vol. 338. American Mathematical Society, Providence, 2003). As an application, we give a Liouville’s theorem for harmonic maps described by Markov chains into $2$ -uniformly convex space satisfying such a geometric condition. An alternative proof of the Jensen’s inequality over Banach spaces is also presented.     

Curdlan as a Polymeric Starting Material to Access C6-Modified Glucose Derivatives

We evaluated the potential of a linear β-1,3-glucan (curdlan) as a starting material to access C6-modified glucose derivatives and found that 6-bromo-6-deoxyglucose, 6-azide-6-deoxyglucose, and 6-acetamido-6-deoxyglucose could be readily prepared from curdlan through its C6-selective and quantitative modifications and subsequent acid-catalyzed hydrolysis.