Constrained principal component analysis of standardized data for biplots with unit-length variable vectors

Principal component analysis (PCA) of an objects ×  variables data matrix is used for obtaining a low-dimensional biplot configuration, where data are approximated by the inner products of the vectors corresponding to objects and variables. Borg and Groenen (Modern multidimensional scaling. Springer, New York, 1997) have suggested another biplot procedure which uses a technique for approximating data by projections of object vectors on variable vectors. This technique is formulated as constraining the variable vectors in PCA to be of unit length and can be called unit-length vector analysis (UVA). However, an algorithm for UVA has not yet been developed. In this paper, we present such an algorithm, discuss the properties of UVA solutions, and demonstrate the advantage of UVA in biplots for standardized data with homogeneous variances among variables. The advantage of UVA-based biplots is that the projections of object vectors onto variable vectors express the approximation of data in an easy way, while in PCA-based biplots we must consider not only the projections, but also the lengths of variable vectors in order to visualize approximations.     

Cooling dynamics of self‐assembled monolayer coating for integrated gold nanocrystals on a glass substrate

Picosecond time‐resolved X‐ray diffraction has been used to study the nanoscale thermal transportation dynamics of bare gold nanocrystals and thiol‐based self‐assembled monolayer (SAM)‐coated integrated gold nanocrystals on a SiO₂ glass substrate. A temporal lattice expansion of 0.30–0.33% was observed in the bare and SAM‐coated nanocrystals on the glass substrate; the thermal energy inside the gold nanocrystals was transported to the contacted substrate through the gold–SiO₂ interface. The interfacial thermal conductivity between the single‐layered gold nanocrystal film and the SiO₂ substrate is estimated to be 45 MW m^?2 K^?1 from the decay of the Au 111 peak shift, which was linearly dependent on the transient temperature. For the SAM‐coated gold nanocrystals, the thermal dissipation was faster than that of the bare gold nanocrystal film. The thermal flow from the nanocrystals to the SAM‐coated molecules promotes heat dissipation from the laser‐heated SAM‐coated gold nanocrystals. The thermal transportation of the laser‐heated SAM‐coated gold nanocrystal film was analyzed using the bidirectional thermal dissipation model.     

Synthesis of Sialyl Lewis X Ganglioside Analogs Containing A Variable Length Spacer Between the Sugar and Lipophilic Moieties 1

Abstract

Five sialyl Lew is X ganglioside analogs containing 4-(2-tetradecylhexadecanoylamino)benzyl group in place of ceramide and a variety of lengths of ethylene glycol chains as the spacer, have been synthesized. Glycosidation of O-(methyl 5-acetamido-4,7,8,9-tetra-O-acetyl-3,5-dideoxy-D-glycero-α-D-glacto-2-nonulopyranosylonate)-(2→3)-O-(4-O-acetyl-2,6-di-O-benzoyl-β-D-galactopyranosyl)-(1→4)-O-[(2,3,4-tri-O-acetylα-L-fucopyranosyl)-(1→3)]-2,4-di-O-benzoyl-α-D-glucopyranosyl trichloroacetimidate (13) with oligo ethyleneglycol monobenzyl ether derivatives 9, 10, 11 and 12, prepared from the corresponding oligo ethyleneglycols by 4-nitrobenzylation, reduction and N-acylation with 2-tetradecylhexadecanoic acid, using boron trifluoride etherate gave the corresponding glycolipid derivatives 14, 15, 16 and 17. A similar glycosidation of 13 with 4-nitrobenzyl alcohol gave the 4-nitrobenzyl glycoside 18, which was converted via reduction of nitro group and N-acylation into the corresponding glycolipid derivative 19. Compounds 14-17 and 19 were transformed into the title compounds by O-deacylation and hydrolysis of methyl ester group in good yields.

     

Observation of a resonancelike structure in the pi +- psi' mass distribution in exclusive B-->Kpi +- psi' decays

A distinct peak is observed in the pi +/- psi' invariant mass distribution near 4.43 GeV in B-->K pi +/- psi' decays. A fit using a Breit-Wigner resonance shape yields a peak mass and width of M=4433+/-4(stat)+/-2(syst) MeV and Gamma=45-13+18(stat)-13+30(syst) MeV. The product branching fraction is determined to be B(B 0-->K -/+Z+/-(4430)) x B(Z+/-(4430)-->pi+/-psi')=(4.1+/-1.0(stat)+/-1.4(syst)) x 10(-5), where Z+/-(4430) is used to denote the observed structure. The statistical significance of the observed peak is 6.5 sigma. These results are obtained from a 605 fb(-1) data sample that contains 657 x 10(6) BB pairs collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e+ e- collider.     

Search for B+-->D*+pi0 decay

We report on a search for the doubly Cabibbo suppressed decay B+-->D*+pi0, based on a data sample of 657x10(6) BB pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We find no significant signal and set an upper limit of B(B+-->D*+pi0)<3.6x10(-6) at the 90% confidence level. This limit can be used to constrain the ratio between suppressed and favored B-->D*pi decay amplitudes, r<0.051, at the 90% confidence level.     

Exact formula of the distribution of Schmidt eigenvalues for dynamical formation of entanglement in quantum chaos

The exact formula of the one-level distribution of the Schmidt eigenvalues is obtained for dynamical formation of entanglement in quantum chaos. The formula is based on the random matrix theory of the fixed-trace ensemble, and is derived using the theory of the holonomic system of differential equations. We confirm that the formula describes the universality of the distribution of the Schmidt eigenvalues in quantum chaos.     

Time-dependent CP-violating asymmetry in B0-->rho0gamma decays

We report the first measurement of CP-violation parameters in B0-->rho0gamma decays based on a data sample of 657x10(6)BB pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain the time-dependent and direct CP-violating parameters, Srho0gamma=-0.83+/-0.65(stat)+/-0.18(syst) and Arho0gamma=-0.44+/-0.49(stat)+/-0.14(syst), respectively.     

Measurement of time-dependent CP-violating parameters in B(0)-->K_(S)(0)K_(S)(0) decays

We report a measurement of the CP-violating parameters in B;{0}-->K_{S}{0}K_{S}{0} decays based on a data sample of 657x10{6} BB[over ] pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e;{+}e{-} collider. In this Letter, one neutral B meson is fully reconstructed in the B;{0}-->K_{S}{0}K_{S}{0} decay mode, and the flavor of the accompanying B meson is identified by its decay products. The CP-violating parameters are measured from the asymmetry in the distributions of the proper-time interval between the two B decays: S_K_{S}{0}K_{S}{0}}=-0.38_{-0.77}{+0.69}(stat)+/-0.09(syst) and A_{K_{S}{0}K_{S}{0}}=-0.38+/-0.38(stat)+/-0.05(syst).     

Relaxation of flexible chains in dilute and non‐dilute systems. Dynamic Monte Carlo results for linear and star chains

A dynamic Monte Carlo algorithm is employed to investigate the dynamics of flexible linear and star chains on a cubic lattice at different concentrations. Some results for similar systems are also obtained with an off‐lattice algorithm. Diffusion coefficient, relaxation times and mean size data are combined into friction‐independent ratios in good agreement with the theoretical predictions from the Rouse theory. The relaxation times and amplitudes corresponding to the Rouse normal modes are analyzed in terms of their variation with the mode order. The end‐to‐end vector correlation times obtained from the simulations for linear chains are compared with the theoretical expression obtained from the Rouse theory. Deviations from this theory are observed for the contribution of the different modes in the non‐dilute systems. Finally, the time correlation function corresponding to a subchain's end‐to‐end vector is investigated. The results also show deviations from the Rouse theory, which are in qualitative agreement with the features observed in data from dielectric relaxation experiments of block copolymers.