All-Optical Spin–Orbit Coupling of Light in Coherent Media Using Rotating Image

The possibility of all-optical spin–orbit coupling (SOC) of light is investigated based on a rotating spinor image traveling through an electromagnetically induced transparency (EIT) medium. It is shown that the paraxial evolution of the spinor image composed of two Laguerre–Gaussian (LG) modes with different frequencies can be analogous with the quantum dynamics of a spin-1/2 particle with strong and tunable SOC governed by the Pauli equation, where the spin-up and -down states have different effective masses. Using realistic EIT parameters with cold atoms, both the radial inhomogeneity of the strong control field and the atomic density distribution with comparable size are considered. The results confirm that the large group refractive index varying in the radial dimension mimicking the central potential can greatly enhance the spin–orbit interaction, leading to visible spatial quantization of the oppositely oriented spin states, equivalent to the two LG modes.     

Portrait Segmentation Using Ensemble of Heterogeneous Deep-Learning Models

Image segmentation plays a central role in a broad range of applications, such as medical image analysis, autonomous vehicles, video surveillance and augmented reality. Portrait segmentation, which is a subset of semantic image segmentation, is widely used as a preprocessing step in multiple applications such as security systems, entertainment applications, video conferences, etc. A substantial amount of deep learning-based portrait segmentation approaches have been developed, since the performance and accuracy of semantic image segmentation have improved significantly due to the recent introduction of deep learning technology. However, these approaches are limited to a single portrait segmentation model. In this paper, we propose a novel approach using an ensemble method by combining multiple heterogeneous deep-learning based portrait segmentation models to improve the segmentation performance. The Two-Models ensemble and Three-Models ensemble, using a simple soft voting method and weighted soft voting method, were experimented. Intersection over Union (IoU) metric, IoU standard deviation and false prediction rate were used to evaluate the performance. Cost efficiency was calculated to analyze the efficiency of segmentation. The experiment results show that the proposed ensemble approach can perform with higher accuracy and lower errors than single deep-learning-based portrait segmentation models. The results also show that the ensemble of deep-learning models typically increases the use of memory and computing power, although it also shows that the ensemble of deep-learning models can perform more efficiently than a single model with higher accuracy using less memory and less computing power.     

Analytical methods for perfect wedge diffraction: A review

The subject of diffraction of waves by sharp boundaries has been studied intensively for well over a century, initiated by groundbreaking mathematicians and physicists including Sommerfeld, Macdonald and Poincaré. The significance of such canonical diffraction models, and their analytical solutions, was recognised much more broadly thanks to Keller, who introduced a geometrical theory of diffraction (GTD) in the middle of the last century, and other important mathematicians such as Fock and Babich. This has led to a very wide variety of approaches to be developed in order to tackle such two and three dimensional diffraction problems, with the purpose of obtaining elegant and compact analytic solutions capable of easy numerical evaluation.The purpose of this review article is to showcase the disparate mathematical techniques that have been proposed. For ease of exposition, mathematical brevity, and for the broadest interest to the reader, all approaches are aimed at one canonical model, namely diffraction of a monochromatic scalar plane wave by a two-dimensional wedge with perfect Dirichlet or Neumann boundaries. The first three approaches offered are those most commonly used today in diffraction theory, although not necessarily in the context of wedge diffraction. These are the Sommerfeld–Malyuzhinets method, the Wiener–Hopf technique, and the Kontorovich–Lebedev transform approach. Then follows three less well-known and somewhat novel methods, which would be of interest even to specialists in the field, namely the embedding method, a random walk approach, and the technique of functionally-invariant solutions.Having offered the exact solution of this problem in a variety of forms, a numerical comparison between the exact solution and several powerful approximations such as GTD is performed and critically assessed.     

On symplectic transformations

This is an English translation¹ of the Ph.D. thesis ‘Over symplectische transformaties’ that Tonny Albert Springer, ‘born in’s-Gravenhage in 1926’, submitted as thesis for – as is stated on the original frontispiece – the degree of doctor in mathematics and physics at Leiden University on the authority of the rector magnificus Dr. J.H. Boeke, professor in the faculty of law, to be defended against the objections of the Faculty of Mathematics and Physics on Wednesday October 17 1951 at 4 p.m., with promotor Prof. dr. H. D. Kloosterman.     

CANONICAL CORRELATION EQUATIONS AND THEIR EXTREMAL PROPERTIES

The canonical variables and canonical correlation coefficients satisfy a matrix equation which is called the canonical correlation equation. There are some different forms of the canonical correlation e-quations given in the literature. In this paper, we discuss four different forms of the canonical correlation equations. The purpose of this paper is to give extremal properties of the solutions of the canonical correlation equations. The results show that canonical variables maximize the determinant of the dispersion matrix of the transformed variables.     

Regular canonical covers

We construct three sequences of regular surfaces of general type with unbounded numerical invariants whose canonical map is 2–to–1 onto a canonically embedded surface. Only sporadic examples of surfaces with these properties were previously known.     

上市公司经营绩效评价方法的典型相关分析

本文介绍了上市公司经营绩效的传统评价方法和EVA、MVA方法,并对几种方法进行了比较,采用典型相关分析方法,以沪市180指标股的相关数据进行了实证研究。我们发现EVA类指标与传统财务评价指标的结论是相一致的,都是公司经营绩效的有效反映。     

Canonical basis linearity regions arising from quiver representations

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author [Math. Z. 237 (2001) 639] arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large cone by linear functions arising from these monomial bases for a quantized enveloping algebra.     

On Some Tests of the Covariance Matrix Under General Conditions

We consider the problem of testing the hypothesis about the covariance matrix of random vectors under the assumptions that the underlying distributions are nonnormal and the sample size is moderate. The asymptotic expansions of the null distributions are obtained up to n ^−1/2. It is found that in most cases the null statistics are distributed as a mixture of independent chi-square random variables with degree of freedom one (up to n ^−1/2) and the coefficients of the mixtures are functions of the fourth cumulants of the original random variables. We also provide a general method to approximate such distributions based on a normalization transformation.