Worst-Case Violation of Sampled Convex Programs for Optimization with Uncertainty

A deterministic approach called robust optimization has been recently proposed to deal with optimization problems including inexact data, i.e., uncertainty. The basic idea of robust optimization is to seek a solution that is guaranteed to perform well in terms of feasibility and near-optimality for all possible realizations of the uncertain input data. To solve robust optimization problems, Calafiore and Campi have proposed a randomized approach based on sampling of constraints, where the number of samples is determined so that only a small portion of the original constraints is violated by the randomized solution. Our main concern is not only the probability of violation, but also the degree of violation, i.e., the worst-case violation. We derive an upper bound of the worst-case violation for the sampled convex programs and consider the relation between the probability of violation and the worst-case violation. The probability of violation and the degree of violation are simultaneously bounded by a prescribed value when the number of random samples is large enough. In addition, a confidence interval of the optimal value is obtained when the objective function includes uncertainty. Our method is applicable to not only a bounded uncertainty set but also an unbounded one. Hence, the scope of our method includes random sampling following an unbounded distribution such as the normal distribution.     

Three-dimensional electronic structure in highly doped NaxCoO2 studied by angle-resolved photoemission spectroscopy

We have investigated three-dimensional electronic structure for Na_xCoO₂ (x=0.77 and 0.65) by high-resolution angle-resolved photoemission spectroscopy to study the origin of antiferromagnetic (AF) transition of highly doped Na_xCoO₂(x>0.75). The a_1g large hole-like Fermi surface (FS) in x=0.77 shows distinct three-dimensionality along the k_z direction, and a three-dimensional small electron pocket appears around Γ point, indicating strong inter-layer electronic correlation. On the other hand, x=0.65 sample does not show three-dimensional behavior. This result indicates that transition of FS as a function of band filling is closely related to the occurrence of the magnetic transition in highly doped Na_xCoO₂.     

The Change of Grip Strength in a Patient with Congenital Myotonic Dystrophy Over a 4-year Period

Myotonic dystrophy (MyD) is a neuromuscular disease that is autosomal dominant and the most common form of muscular dystrophy affecting adults. The clinical features of MyD include a multisystemic disorder characterized by myotonia, progressive muscle weakness and wasting, cataracts, premature balding and mental retardation. The most severe type of MyD is classified as congenital MyD (CMyD). The muscle weakness in CMyD is very severe, but muscle development can be observed in the period of growth. However, no clinical case of this type has been reported yet. Therefore, we report on a girl with CMyD who had an increase in muscle strength over a four-year period. The girl with CMyD participated in this study from the age of 9 to the age of 12. The measurement of muscle strength was recorded as the maximum score of grip strength with the use of dynamometers. Grip strength was assessed once a year by the same two physical therapists. Grip strength of CMyD for each year was markedly weak when compared with the normal controls, but muscle strength changed within some specific growth areas. The muscle weakness in CMyD was remarkable, but the result showed that specific muscle strength of CMyD in childhood was actually increased.     

Arylmagnesiation of alkynes catalyzed cooperatively by iron and copper complexes

Iron and copper complexes cooperatively catalyzed the arylmagnesiation of unfunctionalized alkynes including dialkylacetylenes, where the presence of both iron and copper catalysts is essential for high yields of 2-aryl-1-alkenylmagnesium bromides.     

Synthesis of thiol-capped gold nanoparticle with a flow system using organosilane as a reducing agent

Synthesis of thiol-capped gold nanoparticle is carried out by mixing of a THF solution of HAuCl₄·4H₂O and ⁿC₁₂H₂₅SH with a THF solution of triethylsilane in a flow system that consists of polytetrafluoroethylene tubing. The effect of residence time and reaction temperature on the particle size is examined.     

Blue shift of the isolated CD stretching band of CH2DOH in water induced by changes in the hydrogen-bonding pattern

The wavenumber shift in the CD stretching (ν(CD)) band of the monodeuterated methanol (CH(2)DOH) has been monitored in water-methanol mixtures. For the pure liquid, two dominant bands are observed at 2148 and 2176 cm(-1) in the ν(CD) region. The matrix isolation technique and spectral simulation based on quantum chemical calculations have revealed that these two bands are categorized into the C(1) mode and originate from methanol molecules participating in different hydrogen(H)-bonding patterns. The simulation results for methanol clusters have suggested that the 2148 cm(-1) band is concerned with the end-donor species in the H-bonding network. The relative intensity of the band near 2148 cm(-1) decreases with increasing water concentration, indicating that the population of the end-donor species decreases by the addition of water. This spectral change causes the blue shift in the mean center of the ν(CD) band of CH(2)DOH in water.