A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

Cross‐sectional structural characterization of the surface of exfoliated HOPG using HRTEM‐EELS

We analyzed the surface atomic structure of highly oriented pyrolytic graphite (HOPG) substrate exfoliated with adhesive tape, using high‐resolution transmission electron microscopy and scanning transmission electron microscopy‐electron energy‐loss spectroscopy (STEM‐EELS). The surface step height of the exfoliated HOPG substrate was determined using high‐angle annular dark‐field‐scanning transmission electron microscopy (HAADF‐STEM) images and the depth profiles of the EELS spectra of a cross‐sectioned thin foil specimen prepared via focused ion beam milling. The exfoliated surface of the HOPG substrate presented disordered and curved graphene layers. The STEM‐EELS measurements indicated that upon exfoliation, the surface of the HOPG substrate reacted with atmospheric water and oxygen molecules.     

Revisiting the Rate-Limiting Step of the ANS–Protein Binding at the Protein Surface and Inside the Hydrophobic Cavity

8-Anilino-1-naphthalenesulfonic acid (ANS) is used as a hydrophobic fluorescence probe due to its high intensity in hydrophobic environments, and also as a microenvironment probe because of its unique ability to exhibit peak shift and intensity change depending on the surrounding solvent environment. The difference in fluorescence can not only be caused by the microenvironment but can also be affected by the binding affinity, which is represented by the binding constant (K). However, the overall binding process considering the binding constant is not fully understood, which requires the ANS fluorescence binding mechanism to be examined. In this study, to reveal the rate-limiting step of the ANS–protein binding process, protein concentration-dependent measurements of the ANS fluorescence of lysozyme and bovine serum albumin were performed, and the binding constants were analyzed. The results suggest that the main factor of the binding process is the microenvironment at the binding site, which restricts the attached ANS molecule, rather than the attractive diffusion-limited association. The molecular mechanism of ANS–protein binding will help us to interpret the molecular motions of ANS molecules at the binding site in detail, especially with respect to an equilibrium perspective.     

Freezing limit of water in a closed circular tube

This paper is concerned with the freezing of water in a closed metal tube by regarding the effect of volumetric change of water which is closely related with solidification. The pressure of unfrozen water in the tube increases gradually with increasing frozen layer, consequently the freezing temperature of the water decreases monotonically. It is found from the present results that the freezing limit of water corresponding to the cease of freezing caused by no temperature difference between environmental temperature and freezing point would exist. This remarkable phenomena are mainly attributed to the combined effect of environmental temperature and inner diameter of the tube.     

Chemiluminescence from singlet oxygen that was detected at two wavelengths and effects of biomolecules on it

We developed the detection apparatus that equipped with the two-photomultiplier tubes for chemiluminescence from singlet oxygen. Singlet oxygen was generated with reaction between sodium hypochlorite and hydrogen peroxide. The chemiluminescence from singlet oxygen, the dimol light emission (ca. 634 nm) and the monomol light emission (ca. 1270 nm), was observed simultaneously for the same reaction cell. The effects of sodium azide as an antioxidant, human serum albumin, and α-amino acids on the chemiluminescence based on the both emissions were examined; the observed chemiluminescence could provide direct information with regard to the reaction between singlet oxygen and antioxidant/biomolecules. The apparent rate constants for quenching singlet oxygen in the presence of human serum albumin were calculated to be ca. 3.3 × 10⁹ and ca. 8.8 × 10⁸ M⁻¹ s⁻¹ for the dimol and monomol light emissions, respectively, under the present conditions. The chemiluminescence intensities of the dimol emission decreased in the presence of His, Asp, Phe, Ser, and Tyr, and that of the monomol decreased in the presence of Cys and Trp. The chemiluminescence observed in the presence of biomolcules was discussed together with the reactivities of sodium hypochlorite and hydrogen peroxide to biomolecules.     

Relative contributions of porosity and mineralized matrix properties to the bulk axial ultrasonic wave velocity in human cortical bone

Velocity of ultrasound waves has proved to be a useful indicator of bone biomechanical competence. A detailed understanding of the dependence of ultrasound parameters such as velocity on bone characteristics is a key to the development of bone quantitative ultrasound (QUS). The objective of this study is to investigate the relative contributions of porosity and mineralized matrix properties to the bulk compressional wave velocity (BCV) along the long bone axis. Cross-sectional slabs from the diaphysis of four human femurs were included in the study. Seven regions of interest (ROIs) were selected in each slab. BCV was measured in through-transmission at 5 MHz. Impedance of the mineralized matrix (Z_m) and porosity (Por) were obtained from 50 MHz scanning acoustic microscopy. Por and Z_m had comparable effects on BCV along the bone axis (R = −0.57 and R = 0.72, respectively).     

Unnatural base pair systems toward the expansion of the genetic alphabet in the central dogma

Toward the expansion of the genetic alphabet of DNA, several artificial third base pairs (unnatural base pairs) have been created. Synthetic DNAs containing the unnatural base pairs can be amplified faithfully by PCR, along with the natural A-T and G-C pairs, and transcribed into RNA. The unnatural base pair systems now have high potential to open the door to next generation biotechnology. The creation of unnatural base pairs is a consequence of repeating "proof of concept" experiments. In the process, initially designed base pairs were modified to address their weak points. Some of them were artificially evolved to ones with higher efficiency and selectivity in polymerase reactions, while others were eliminated from the analysis. Here, we describe the process of unnatural base pair development, as well as the tests of their applications.(Communicated by Takao SEKIYA, M.J.A.).     

A new plane type sensor for concentration measurement in liquid

In this paper, we propose a new plane type sensor for measurement of the liquid. In the proposed sensor, the PVDF films with the transparent conductive electrodes are respectively arranged on the surface of a LED and a photodiode. The optical properties of the liquid are measured using the LED and the photodiode, and the electrical and ultrasonic properties are measured using the PVDF films on the surface of the LED and photodiode. Therefore, the optical, electrical and ultrasonic properties at same space are measured by the proposed sensor. Three parameters in the sample liquid were estimated by the proposed sensor.     

MTV-G experiment: Probing non-standard strong gravitational field at nuclear scale using geodetic precession

A new experiment named MTV-G, probing a large electron spin-precession due to a possible strong gravitational field, which predicted by large extra dimension model, is started at TRIUMF from 2011. In an electron-nuclear scattering experiment, a strong gravitational field is tested as a large spin precession effect caused by geodetic precession predicted by general relativity theory as a result of a warped space-time around nuclei. Experimental design using spin polarized electron source and Mott-spin analyzer, commissioning experiment and the preliminary results are described.     

Isolation and structure determination of six glucocerebrosides from the starfish Luidia maculata

Two new glucocerebrosides, luidiacerebroside A (2) and B (6), were isolated from the cerebroside molecular species obtained from the less polar fraction of the CHCl3/MeOH extract of the starfish Luidia maculata using HPLC. Four known cerebrosides, CE-2b (1), astrocerebroside B (3), acanthacerebroside B (4), and CE-3-2 (5) have also been isolated and characterized. The structures of these cerebrosides were determined on the basis of chemical and spectroscopic evidence. Mass spectrometry of dimethyl disulfide derivatives was useful for the determination of the double-bond position in the long-chain base.