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An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

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Chinese Physics B 2024年第7期33卷 117-124页

作者：魏姣耿献国王鑫 School of Mathematics and statistics Zhengzhou UniversityZhengzhou 450001China School of Mathematics and information Science Zhongyuan University of TechnologyZhengzhou 450007China

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

关键词： Darboux transformation soliton solutions generalized Fokas–Lenells equation

Applying Machine Learning Approach to Explore Childhood Circumstances and Self-Rated health in Old Age-China and the US,2020-2021

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China CDC weekly 2024年第11期6卷 213-218,I0008-I0013页

作者： Shutong Huo Derek Feng Thomas M.Gill Xi Chen department of health Society&BehaviorPublic HealthUniversity of CaliforniaIrvineCAUSA department of statistics and Data Science Yale UniversityNew HavenCTUS department of Internal Medicine Yale School of MedicineNew HavenCTUS department of health Policy and Management Yale School of Public HealthNew HavenCTUS department of Economics Yale UniversityNew HavenCTUS.

Introduction:Childhood circumstances impact senior health,prompting the introduction of machine learning methods to assess their individual and collective contributions to senior ***:Using health and retirement study(HRS)and China health and Retirement Longitudinal Study(CHARLS),we analyzed 2,434 American and 5,612 Chinese participants aged 60 and *** inference trees and forests were employed to estimate the influence of childhood circumstances on self-rated health(SRH).Results:The conventional method estimated higher inequality of opportunity(IOP)values in both China(0.039,accounting for 22.67%of the total Gini coefficient 0.172)and the US(0.067,accounting for 35.08%of the total Gini coefficient 0.191).In contrast,the conditional inference tree yielded lower estimates(China:0.022,accounting for 12.79%of 0.172;US:0.044,accounting for 23.04%of 0.191),as did the forest(China:0.035,accounting for 20.35%of 0.172;US:0.054,accounting for 28.27%of 0.191).Childhood health,financial status,and regional differences were key determinants of senior *** conditional inference forest consistently outperformed others in predictive accuracy,as demonstrated by lower out-of-sample mean squared error(MSE).Discussion:The findings emphasize the need for early-life interventions to promote health equity in aging *** learning showcases the potential in identifying contributing factors.

关键词： collective inequality estimates

Construction of Optimal Mixed-Level Uniform Designs

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Journal of Systems Science & Complexity 2024年第2期37卷 841-862页

作者： CHATTERJEE Kashinath LIU Min-Qian QIN Hong YANG Liuqing department of Population health Sciences Division of Biostatistics and Data ScienceAugusta UniversityGA 30912USA NITFID LPMC&KLMDASRSchool of Statistics and Data ScienceNankai UniversityTianjin 300071China School of statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

The theory of uniform design has received increasing interest because of its wide application in the field of computer *** generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial *** this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower *** methods are all deterministic construction methods which can avoid the complexity of stochastic *** saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these ***,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.

关键词： Generalized discrete discrepancy Hadamard matrix mixed-level design orthogonal array supersaturated design

Character Sheaves for Classical Graded Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第3期40卷 870-884页

作者： Ting XUE School of Mathematics and statistics University of MelbourneVIC 3010Australia department of Mathematics and statistics University of HelsinkiHelsinki 00014Finland

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

关键词： Graded Lie algebras character sheaves Fourier transform nilpotent orbits

Curve Classification Based onMean-Variance Feature Weighting and Its Application

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Computers, Materials & Continua 2024年第5期79卷 2465-2480页

作者： Zewen Zhang Sheng Zhou Chunzheng Cao School of Mathematics and statistics Nanjing University of Information Science and TechnologyNanjing210044China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and TechnologyNanjing210044China

The classification of functional data has drawn much attention in recent *** main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification *** this paper,we propose a mean-variance-based(MV)feature weighting method for classifying functional data or functional *** the feature extraction stage,each sample curve is approximated by B-splines to transfer features to the coefficients of the spline *** that,a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the *** also introduce a scaling parameter to adjust the gap between the weights of *** new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing *** algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both ***,the new approach can be well integrated into existing functional data classifiers,such as the generalized functional linear model and functional linear discriminant analysis,resulting in a more accurate *** performance of the mean-variance-based classifiers is evaluated by simulation studies and real *** results show that the newfeatureweighting approach significantly improves the classification accuracy for complex functional data.

关键词： Functional data analysis classification feature weighting B-splines

Berry-Esseen bounds for self-normalized sums of locally dependent random variables

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Science China Mathematics 2024年第11期67卷 2629-2652页

作者： Zhuo-Song Zhang department of statistics and Data Science Southern University of Science and Technology

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal *** this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment *** proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other *** main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

关键词： Berry-Esseen bounds self-normalized sums localdependence $m$-dependence graph dependency

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Double Moving Extremes Ranked Set Sampling Design

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 75-90页

作者： Meng Chen Wang-xue Chen Rui Yang department of Mathematics and statistics Jishou UniversityJishou416000China

The traditional simple random sampling(SRS)design method is inefficient in many *** proposed some new designs to increase *** this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are *** turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population ***,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.

关键词： double moving extremes ranked set sampling symmetric distribution efficiency

Robust Inference for Censored Quantile Regression

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Journal of Systems Science & Complexity 2024年

作者： TANG Yuanyuan WANG Xiaorui ZHU Jianming LIN Hongmei TANG Yanlin TONG Tiejun School of statistics and information Shanghai University of International Business and Economics department of statistics and Data Science Southern University of Science and Technology School of statistics KLATASDS-MOE East China Normal University department of Mathematics Hong Kong Baptist University

In various fields such as medical science and finance, it is not uncommon that the data are heavy-tailed and/or not fully observed, calling for robust inference methods that can deal with the outliers and incompleteness efficiently. In this paper, the authors propose a rank score test for quantile regression with fixed censored responses, based on the standard quantile regression in an informative subset which is computationally efficient and robust. The authors further select the informative subset by the multiply robust propensity scores, and then derive the asymptotic properties of the proposed test statistic under both the null and local alternatives. Moreover, the authors conduct extensive simulations to verify the validity of the proposed test, and apply it to a human immunodeficiency virus data set to identify the important predictors for the conditional quantiles of the censored viral load.

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A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational Mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao Xia Liu Xiaoli Huang School of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China School of Mathematics and information Science North Minzu UniversityYinchuan 750021China Ningxia Province Key Laboratory of Intelligent information and Data Processing Yinchuan 750021China School of Mathematics and statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming