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.

     

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N₂ atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Graphical Abstract

     

Synthetic studies toward swinhoeisterol A,a novel steroid with an unusual carbon skeleton

Swinhoeisterol A is a novel steroid with unusual 6/6/5/7 tetracyclic skeleton. The model compound with BCD rings is constructed by Friedel–Crafts acylation and an oxidative dearomatization as key steps.     

Extension of the LP-Newton method to conic programming problems via semi-infinite representation

Numerical Algorithms - The LP-Newton method solves linear programming (LP) problems by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the...     

Direct Introduction of a Dimesitylboryl Group Using Base‐Mediated Substitution of Aryl Halides with Silyldimesitylborane

The first dimesitylboryl substitution of aryl halides with a silylborane bearing a dimesitylboryl group in the presence of alkali‐metal alkoxides is described. The reactions of aryl bromides or iodides with Ph₂MeSi?BMes₂ and Na(OtBu) afforded the desired aryl dimesitylboranes in good to high yields and with high borylation/silylation ratios. Selective reaction of the sterically less‐hindered C?Br bond of dibromoarenes provided monoborylated products. This reaction was used to rapidly construct a D‐π‐A aryl dimesityl borane with a non‐symmetrical biphenyl spacer.     

9,10‐Diaminoanthracenes Revisited: The Influence of N‐Substituents on Their Electronic States

The electronic and molecular structures of 9,10‐diamino‐substituted anthracenes with different N‐substituents have been re‐examined. In particular, different N‐substituents influence both the electronic and molecular structures of the oxidized species of 9,10‐diaminoanthracenes. The anthrylene moiety of 9,10‐bis(N,N‐di(p‐anisyl)amino)anthracene retains its planarity during the course of two successive one‐electron oxidations, whereas 9,10‐bis(N,N‐dimethylamino)anthracene and 9,10‐bis(N‐p‐anisyl‐N‐methylamino)anthracene undergo a substantial structural change to a butterfly‐like structure through a two‐electron oxidation process. The structural changes observed for the oxidized states are ascribed to significant differences in the frontier molecular orbitals of the above‐mentioned three kinds of 9,10‐diaminoanthracenes due to different extents of mixing between the amine‐localized and anthrylene‐localized orbitals.     

Triply Linked Corrole Dimers

The oxidation of 10–10′ singly linked corrole dimers with DDQ at low concentration in CHCl₃ afforded meso–meso, β–β, β–β triply linked 2H‐corrole dimers (with two inner NH groups in each corrole unit), which exhibited characteristic ¹H NMR and absorption spectra attributable to their nonaromatic electronic networks. These 2H‐corrole dimers were reduced with NaBH₄ to aromatic 3H‐corrole dimers, which were unstable and easily oxidized back to the 2H‐corrole dimers upon exposure to air. Bis(zinc(II)) complexes of the 2H‐corrole dimers were synthesized and characterized as rare examples of nonaromatic zinc(II) corrole complexes.     

Total Synthesis and Structure Elucidation of JBIR‐39: A Linear Hexapeptide Possessing Piperazic Acid and γ‐Hydroxypiperazic Acid Residues

The total synthesis and stereochemical structural elucidation of JBIR‐39, containing four nonproteinogenic piperazic acid (Piz) residues, is reported. The synthesis includes Sc(OTf)₃‐catalyzed acylation of a Piz(γ‐OTBS) derivative with piperazic acid chloride, providing the desired Piz‐Piz(γ‐OTBS) dipeptide in high yield without epimerization. After assembling two additional Piz moieties and (S)‐isoleucic acid at the N‐terminus, amidation with the (R)‐α‐methylserine ester at the C‐terminus, and deprotection afforded the desired (2R,8S)‐hexapeptide, which is the assumed structure of JBIR‐39. Although the spectral data of the (2R,8S)‐hexapeptide was not identical to JBIR‐39, further synthesis of three stereoisomers confirmed the stereochemical structure of JBIR‐39 to be (2S,6S,8S,11R,16S,21R,26S,27S).