Machine learning methods, one type of methods used in artificial intelligence, are now widely used to analyze two-dimensional (2D) images in various fields. In these analyses, estimating the boundary between two regio...Machine learning methods, one type of methods used in artificial intelligence, are now widely used to analyze two-dimensional (2D) images in various fields. In these analyses, estimating the boundary between two regions is basic but important. If the model contains stochastic factors such as random observation errors, determining the boundary is not easy. When the probability distributions are mis-specified, ordinal methods such as probit and logit maximum likelihood estimators (MLE) have large biases. The grouping estimator is a semiparametric estimator based on the grouping of data that does not require specific probability distributions. For 2D images, the grouping is simple. Monte Carlo experiments show that the grouping estimator clearly improves the probit MLE in many cases. The grouping estimator essentially makes the resolution density lower, and the present findings imply that methods using low-resolution image analyses might not be the proper ones in high-density image analyses. It is necessary to combine and compare the results of high- and low-resolution image analyses. The grouping estimator may provide theoretical justifications for such analysis.展开更多
Orthorhombic copper polysilicate, CuSiO3, is isotypic to the spin-Peierls compound CuGeO3 and represents a further example of a quasi-one-dimensional spin = 1/2 antiferromagnetic Heisenberg chain system. This is a rep...Orthorhombic copper polysilicate, CuSiO3, is isotypic to the spin-Peierls compound CuGeO3 and represents a further example of a quasi-one-dimensional spin = 1/2 antiferromagnetic Heisenberg chain system. This is a representation of the first Raman and IR/FIR spectra for CuSiO3, measured at room temperature on polycrystalline samples. A comparison of the optical phonons, predicted by a factor group analysis, with those observed for the CuGeO3 prototype, is presented. A mode assignment for the silicate is given. Surface effects due to a very small crystallite size may cause additional broad bands observed in the Raman spectrum of CuSiO3. From the analysis of the Davydov doublet an intralayer-to-interlayer bond strength of about 40 is derived for the silicate, which is about 20% lower than for the isotypic germanate, allowing for different magnetic responses at low temperature.展开更多
文摘Machine learning methods, one type of methods used in artificial intelligence, are now widely used to analyze two-dimensional (2D) images in various fields. In these analyses, estimating the boundary between two regions is basic but important. If the model contains stochastic factors such as random observation errors, determining the boundary is not easy. When the probability distributions are mis-specified, ordinal methods such as probit and logit maximum likelihood estimators (MLE) have large biases. The grouping estimator is a semiparametric estimator based on the grouping of data that does not require specific probability distributions. For 2D images, the grouping is simple. Monte Carlo experiments show that the grouping estimator clearly improves the probit MLE in many cases. The grouping estimator essentially makes the resolution density lower, and the present findings imply that methods using low-resolution image analyses might not be the proper ones in high-density image analyses. It is necessary to combine and compare the results of high- and low-resolution image analyses. The grouping estimator may provide theoretical justifications for such analysis.
文摘Orthorhombic copper polysilicate, CuSiO3, is isotypic to the spin-Peierls compound CuGeO3 and represents a further example of a quasi-one-dimensional spin = 1/2 antiferromagnetic Heisenberg chain system. This is a representation of the first Raman and IR/FIR spectra for CuSiO3, measured at room temperature on polycrystalline samples. A comparison of the optical phonons, predicted by a factor group analysis, with those observed for the CuGeO3 prototype, is presented. A mode assignment for the silicate is given. Surface effects due to a very small crystallite size may cause additional broad bands observed in the Raman spectrum of CuSiO3. From the analysis of the Davydov doublet an intralayer-to-interlayer bond strength of about 40 is derived for the silicate, which is about 20% lower than for the isotypic germanate, allowing for different magnetic responses at low temperature.
