Information Geometry and Interior-Point Algorithms in Semidefinite Programs and Symmetric Cone Programs

We develop an information geometric approach to conic programming. Information geometry is a differential geometric framework specifically tailored to deal with convexity, naturally arising in information science including statistics, machine learning and signal processing etc. First we introduce an information geometric framework of conic programming. Then we focus on semidefinite and symmetric cone programs. Recently, we demonstrated that the number of iterations of Mizuno–Todd–Ye predictor–corrector primal–dual interior-point methods is (asymptotically) expressed with an integral over the central trajectory called “the curvature integral”. The number of iterations of the algorithm is approximated surprisingly well with the integral even for fairly large linear/semidefinite programs with thousands of variables. Here we prove that “the curvature integral” admits a rigorous differential geometric expression based on information geometry. We also obtain an interesting information geometric global theorem on the central trajectory for linear programs. Together with the numerical evidence in the aforementioned work, we claim that “the number of iterations of the interior-point algorithm is expressed as a differential geometric quantity.”     

Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains

In two-dimensional Euclidean space, a simply connected unbounded domain whose boundary is a Jordan curve is called an unbounded Jordan domain. In this article, we discuss a piecewise linear finite element approximation of conformal mappings from the unit disk of the plane to unbounded Jordan domains. Some convergence results and error analysis are presented. Numerical examples are also given.     

10 GHz, 2.4 ps pulse generation using a single-stage dual-drive Mach-Zehnder modulator

This Letter reports on picosecond pulse generation at a repetition of 10 GHz by using a single-stage electro-optic LiNbO(3) Mach-Zehnder modulator, stressing the simplicity of its setup. It is analytically and experimentally proved that dual-arm modulation with in-phase sinusoidal signals having slightly different amplitudes generated a highly coherent optical comb with a great spectral flatness and a parabolic phase relationship in its spectrum. The generated comb was Fourier synthesized and shaped into an ultrashort pulse train with an optical bandpass filter and a dispersive fiber. The pulse source was highly stable, exhibiting an ultralow timing jitter of less than 130 fs.     

Effects of excitation spectral width on decay profile of weakly confined excitons

We report the effect due to a simultaneous excitation of several exciton states on the radiative decay profiles on the basis of the nonlocal response of weakly confined excitons in GaAs thin films. In the case of excitation of single exciton state, the transient grating signal has two decay components. The fast decay component comes from nonlocal response, and the long-lived component is attributed to free exciton decay. With an increase of excitation spectral width, the nonlocal component becomes small in comparison with the long-lived component, and disappears under irradiation of a femtosecond-pulse laser with broader spectral width. The transient grating spectra clearly indicates the contribution of the weakly confined excitons to the signal, and the exciton line width hardly changes by excitation spectral width. From these results, we concluded that the change of decay profile is attributed not to the many-body effect but to the effect of simultaneous excitation of several exciton states.     

Long Pulse Operation of the THz Gyrotron with a Pulse Magnet

Long pulse operation up to 1 msec of a high frequency gyrotron with a pulse magnet has been successfully carried out in a frequency range including 1 THz. In the experiments, the timing of an electron beam pulse injection is adjusted at the top of the magnetic field pulse, where the variation of field intensity is negligible. The operation cavity modes seem to be TE_{1, 12} and TE_4,12 at the second harmonics. The corresponding frequencies are 903 GHz and 1,013 GHz, respectively. Additionally several features of radiation measurement results of the gyrotron are described and brief considerations are presented.     

Catalytic Hydroetherification of Unactivated Alkenes Enabled by Proton-Coupled Electron Transfer

We report a catalytic, light-driven method for the intramolecular hydroetherification of unactivated alkenols to furnish cyclic ether products. These reactions occur under visible-light irradiation in the presence of an Ir^III-based photoredox catalyst, a Brønsted base catalyst, and a hydrogen-atom transfer (HAT) co-catalyst. Reactive alkoxy radicals are proposed as key intermediates, generated by direct homolytic activation of alcohol O−H bonds through a proton-coupled electron-transfer mechanism. This method exhibits a broad substrate scope and high functional-group tolerance, and it accommodates a diverse range of alkene substitution patterns. Results demonstrating the extension of this catalytic system to carboetherification reactions are also presented.     

Flexible and Epitaxial Metal Oxide Thin Film Growth by Photoreaction Processing for Electrical and Optical Applications

This review summarizes the use of photoreactions that replace conventional heating processes for growing oxide thin films from chemical solutions. In particular, this review outlines key variables in photoreactions that affect epitaxial and polycrystalline thin film growth, including precursor materials, laser wavelength, laser fluence, and carbon. In addition, the features of the photoreaction process that can be controlled at a low temperature by oxygen non-stoichiometry are examined. Likewise, functions that are neither achieved by developing a gradient structure nor controlled by a thermal equilibrium reaction are detailed. Two new concepts are presented, known as photoreaction of nanoparticles (PRNP) and photoreaction of a hybrid solutions (PRHS), in which crystal nuclei are pre-dispersed in a metal–organic compound film. This method has successfully produced flexible phosphor films used as resistor or thermistor electronic components. Finally, thin film growth using different light sources such as flash lamps and femtosecond lasers (fs) is explored.     

A modified layered-step interior-point algorithm for linear programming

The layered-step interior-point algorithm was introduced by Vavasis and Ye. The algorithm accelerates the path following interior-point algorithm and its arithmetic complexity depends only on the coefficient matrixA. The main drawback of the algorithm is the use of an unknown big constant in computing the search direction and to initiate the algorithm. We propose a modified layered-step interior-point algorithm which does not use the big constant in computing the search direction. The constant is required only for initialization when a well-centered feasible solution is not available, and it is not required if an upper bound on the norm of a primal—dual optimal solution is known in advance. The complexity of the simplified algorithm is the same as that of Vavasis and Ye. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research supported in part by ONR contract N00014-94-C-0007 and the Grant-in-Aid for Scientific Research (C) 08680478 and the Grant-in-Aid for Encouragement of Young Scientists (A) 08780227 of the Ministry of Science, Education and Culture of Japan. This research was partially done while S. Mizuno and T. Tsuchiya were visiting IBM Almaden Research Center in the summer of 1995.