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THE BERRY-ESSEEN bound AND LIL PP CM STATISTIC TESTING UNIFORM DISTRIBUTION ON SPHERE ABOUT DIMENSION AND SAMPLE SIZE

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Systems Science and Mathematical Sciences 2000年第2期13卷 136-145页

作者： LIU Yixing CHENG Ping (Institute of Systems Science, Academia Sinica, Beijing 100080, China) 中科院系统科学所北京 100080 中科院系统科学所北京

Cheng[1] gave the limit distribution of weighted PP Cramer-Von Mises test statistic when dimension and sample size tend to infinity simultaneously under the underlying distribution being uniform distribution on SP-1 = {a: ||a|| = 1, a SP-1 }; this limit distribution is standard normal distribution N(0, 1). In this paper, we give the Berry- Esseen bound of this statistic converging to normal distribution and the law of iterated logarithm.

关键词： PP CM statistic Berry-Esseen bound law of iterated logarithm large sample size.

Brauer Upper bound for the Z-Spectral Radius of Nonnegative Tensors

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Journal of Mathematical Research with Applications 2019年第4期39卷 353-360页

作者： Jun HE Hua KE Yanmin LIU Junkang TIAN School of Mathematics Zunyi Normal College

In this paper, we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which is called the Brauer upper bound:■where■ As applications, a bound on the Z... 详细信息

关键词： bound nonnegative tensor Z-eigenvalue hypergraph

POLYTOPIC PERTURBATION bound FOR STABILITY OF POLYNOMIALS

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Systems Science and Mathematical Sciences 1995年第2期8卷 134-143页

作者： AN Senjian WANG Enping (Institute of Systems Science, Academia Sinica, Beijing 100080,China) 中科院系统科学所北京

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关键词： Parametric uncertainty stability robustness edgewise-perturbed bound polytopic perturbation bound edge theorem

Improved generation of correlated photon pairs from monolayer WS_2 based on bound states in the continuum

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Photonics Research 2019年第3期7卷 341-350页

作者： TIECHENG WANG ZHIXIN LI XIANGDONG ZHANG Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems School of Physics Beijing Institute of Technology

Entangled photons are the fundamental resource in quantum information processing. How to produce them efficiently has always been a matter of concern. Here we propose a new way to produce correlated photons efficiently from monolayer WS_2 based on bound states in the continuum(BICs). The BICs of radiation modes in the monolayer WS_2 are realized by designing the photonic crystal slab-WS_2-slab structure. The generation efficiency of correlated photon pairs from such a structure has been studied by using a rigorous quantum model of spontaneous parametric down-conversion with the plane wave expansion method. It is found that the generation efficiency of correlated photon pairs is greatly improved if the signal and idler fields are located at the BICs determined by the inverse scattering matrix of the structure. This is in contrast to the parametric down-conversion process for the enhanced generation of nonlinear waves if the pump field is located at the BICs determined by the scattering matrix of the structure. The generation rate of the correlated photon pairs can be improved by 7 orders of magnitude in some designed structures. The generated quantum signals are sensitive to the wavelength and exhibit narrowed relative line width, which is very beneficial for quantum information processing.

关键词： correlated photon pairs monolayer WS2 based bound states

bound states in the continuum and high-Q resonances supported by a dielectric ridge on a slab waveguide

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Photonics Research 2018年第11期6卷 1084-1093页

作者： EVGENI A.BEZUS DMITRY A.BYKOV LEONID L.DOSKOLOVICH Image Processing Systems Institute-Branch of the Federal Scientific Research Centre“Crystallography and Photonics”of the Russian Academy of Sciences 151 Molodogvardeyskaya St.Samara 443001Russia Samara National Research University 34 Moskovskoe ShosseSamara 443086Russia

We investigate the diffraction of the guided modes of a dielectric slab waveguide on a simple integrated structure consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic rigorous coupled-wave analysis demonstrate the existence of sharp resonant features and bound states in the continuum(BICs) in the reflectance and transmittance spectra occurring at the oblique incidence of a transverseelectric(TE)-polarized guided mode on the ridge. Using the effective index method, we explain the resonances by the excitation of cross-polarized modes of the ridge. Formation of the BICs are confirmed using a theoretical model based on coupled-wave theory. The model suggests that the BICs occur due to the coupling of quasi-TE and quasi-transverse-magnetic modes of the structure. Simple analytical expressions for the angle of incidence and the ridge width predicting the location of the BICs are obtained. The existence of high-Q resonances and BICs enables using the considered integrated structure for sensing, transformation of optical signals, and enhancing nonlinear light–matter interactions. Due to the Lorentzian line shape of the resonances near the BICs, the structure is also promising for filtering applications.

关键词： bound states high-Q resonances slab waveguide TE BIC

Break Up of <i>N</i>-Soliton bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity

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Optics and Photonics Journal 2012年第3期2卷 178-184页

作者： Isnani Darti Suhariningsih Suhariningsih Marjono Marjono Agus Suryanto Department of Mathematics Faculty of Sciences Brawijaya University Malang Indonesia Department of Physics Faculty of Sciences and Technology Airlangga University Surabaya Indonesia

We study the propagation of N-soliton bound state in a triangular gradient refractive index waveguide with nonlocal nonlinearity. The study is based on the direct numerical solutions of the model and subsequent eigenvalues evolution of the corresponding Zakharov-Shabat spectral problem. In the waveguide with local nonlinearity, the velocity of a single soliton is found to be symmetric around zero and therefore the soliton oscillates periodically inside the waveguide. If the nonlocality is presence in the medium, the periodic motion of soliton is destroyed due to the soliton experiences additional positive acceleration induced by the nonlocality. In the waveguide with the same strength of nonlocality, a higher amplitude soliton experiences higher nonlocality effects, i.e. larger acceleration. Based on this soliton behavior we predict the break up of N-soliton bound state into their single-soliton constituents. We notice that the splitting process does not affect the amplitude of each soliton component.

关键词： N-Soliton bound State GRIN Waveguide Nonlocal Nonlinearity Conserved Implicit Crank-Nicolson Method Inverse Scattering Technique

A SUBSPACE PROJECTED CONJUGATE GRADIENT ALGORITHM FOR LARGE bound CONSTRAINED QUADRATIC PROGRAMMING

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1998年第1期7卷 51-60页

作者：倪勤

A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.

关键词： Projected search conjugate gradient method large problem bound constrained quadraic programming.

Inference and Properties of Mixture Two Extreme Lower bound Distributions

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Engineering（科研） 2017年第6期9卷 517-523页

作者： Fathy H. Riad Department of Mathematics Faculty of Science Minia University Minya Egypt Department of Mathematics Faculty of Sciences Aljouf University Sakakah KSA

In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown parameters via the EM algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation.

关键词： Mixture Extreme Lower bound Distribution Reliability Estimation EM Algorithm Monte Carlo Simulation

Transcription Factor bound Regions Prediction: Word2Vec Technique with Convolutional Neural Network

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Journal of Intelligent Learning Systems and Applications 2020年第1期12卷 1-13页

作者： Rixin Chen Ruoxi Dai Mingye Wang University of Electronic Science and Technology of China Chengdu China Northeastern University Shenyang China Sun Yat-sen University Guangzhou China

Genome-wide epigenomic datasets allow us to validate the biological function of motifs and understand the regulatory mechanisms more comprehensively. How different motifs determine whether transcription factors (TFs) can bind to DNA at a specific position is a critical research question. In this project, we apply computational techniques that were used in Natural Language Processing (NLP) to predict the Transcription Factor bound Regions (TFBRs) given motif instances. Most existing motif prediction methods using deep neural network apply base sequences with one-hot encoding as an input feature to realize TFBRs identification, contributing to low-resolution and indirect binding mechanisms. However, how the collective effect of motifs on binding sites is complicated to figure out. In our pipeline, we apply Word2Vec algorithm, with names of motifs as an input to predict TFBRs utilizing Convolutional Neural Network (CNN) to realize binary classification, based on the ENCODE dataset. In this regard, we consider different types of motifs as separate “words”, and their corresponding TFBR as the meanings of “sentences”. One “sentence” itself is merely the combination of these motifs, and all “sentences” compose of the whole “passage”. For each binding site, we do the binary classification within different cell types to show the performance of our model in different binding sites and cell types. Each “word” has a corresponding vector in high dimensions, and the distances between each vector can be figured out, so we can extract the similarity between each motif, and the explicit binding mechanism from our model. We apply Convolutional Neural Network (CNN) to extract features in the process of mapping and pooling from motif vectors extracted by Word2Vec Algorithm and gain the result of 87% accuracy at the peak.

关键词： Motifs bound Regions Word2Vec CNN