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.

     

Regulation of lithospermic acid B and shikonin production in Lithospermum erythrorhizon cell suspension cultures

Cell suspension cultures of Lithospermum erythrorhizon produced a large amount of lithospermic acid B, a caffeic acid tetramer, as well as shikonin derivatives (each ca. 10% of dry wt.) when cultured in shikonin production medium M-9. Various culture factors for increasing the production of lithospermic acid B were investigated. Lithospermic acid B production was inhibited by 2, 4-D or NH4+, whereas it was stimulated by Cu2+. These regulatory patterns were similar to those for the production of shikonin derivatives in these cell cultures, suggestive of close relations and similar metabolic regulation between the production of these compounds. Cultivation under light illumination, however, showed that these metabolisms were independently regulated. In particular, blue light showed a stimulatory effect on lithospermic acid B production, while shikonin production was strongly inhibited, indicative of an effective condition for lithospermic acid B production.     

Synthesis of bridged heteroaromatic compounds as reference standards for coal degradation products

The synthesis of 2-naphthyl 2′-dibenzothienyl ether, 1-(1′-naphthyl)-2-(4″-acridinyl)ethane and a series of naphthylethyldibenzothiophenes is reported.     

Syntheses of 1-, 2-, 3- and 4-acridinecarbaldehydes

The four acridinecarbaldehydes, namely, acridine-1-carbaldehyde, acridine-2-carbaldehyde, acridine-3-carbaldehyde, and acridine-4-carbaldehyde have been synthesized for the first time.     

Sulfur nitride in organic chemistry. 9. The reaction of tetrasulfur tetranitride with benzyl ketones. Preparation of 3,4-disubstituted-1,2,5-thiadiazoles

The reaction of tetrasulfur tetranitride ( 1 ) with various aryl and alkyl benzyl ketones ( 2a-o ), oxindole ( 11 ), benzyl α-pyridyl ketone ( 12 ) and α-phenacylpyridine ( 13 ) afforded the corresponding 1,2,5-thiadiazoles ( 3a-n, 11 and 14 ). The scope and limitations of the above reaction were investigated and the evidences suggesting the radical anion mechanism are presented.     

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.     

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.     

Macroscopic wall number analysis of single-walled, double-walled, and few-walled carbon nanotubes by X-ray diffraction

The layer number is of great importance for nanocarbon materials, such as carbon nanotubes (CNTs) and graphene. While simple optical methods exist to evaluate few-layer graphene, equivalent analysis for CNTs is limited to transmission electron microscopy. We present a simple macroscopic method based on the (002) X-ray diffraction peak to evaluate the average wall number of CNTs in the range from single- to few-walled. The key was the finding that the (002) peak could be decomposed into two basic components: the intertube structure (outer-wall contacts) and the intratube structure (concentric shells). Decomposition of the peaks revealed a linear relationship between the average wall number and the ratio of the intertube and intratube contributions to the (002) peak. Good agreement with CNTs having average wall numbers ranging from 1 to ～5 demonstrated this as a macroscopic method for average wall number analysis.     

On the approximation of eigenvalues associated with functional differential equations

In this paper an approximation method based upon spline functions is developed for the eigenvalue problem associated with functional differential equations. Convergence results are established and the rate of convergence is investigated. Numerical results for cubic and quintic spline based methods are given. The paper concludes with a brief discussion of other possible approximation methods.     

Prospective trial of a navigator setting under left hepatic lobe on magnetic resonance cholangiopancreatography using a free-breathing prospective acquisition correction technique

PURPOSE: To prospectively compare the image acquisition time and image quality obtained by navigator setting under the left hepatic lobe vs. on the right diaphragm on magnetic resonance cholangiopancreatography (MRCP) using a free-breathing navigator-triggered prospective acquisition correction technique (PACE). MATERIALS AND METHODS: Fifty consecutive patients prospectively underwent three-dimensional T2-weighted turbo spin-echo MRCP using PACE with the navigator randomly set either under the left hepatic lobe or on top of the right diaphragm. Image acquisition time and subjective image quality were compared on a five-point scale using Student's t-test and Mann-Whitney's U test, respectively. RESULTS: There was no significant difference for mean acquisition time (6.1+/-1.6 vs. 6.3+/-1.2 min, P=.689) between the left hepatic lobe group and right diaphragm group. Mean subjective image quality was significantly worse in the left hepatic lobe group than in the right diaphragm group (4.1 vs. 4.7, P=.044). CONCLUSION: Setting the navigator under the left hepatic lobe for MRCP using PACE causes the data processing to be more difficult. As well, under current circumstances, it does not contribute to reducing acquisition time or improving the image quality.