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统计学中微分几何的两例应用

中国科学:数学 2025年第1期 169-182页

作者：彭捷 department of statistics University of California Davis

本文讨论两个统计问题,其中微分几何的概念和观念发挥了关键作用.第一个问题涉及函数型数据的主成分估计,其中一部分参数具有正交约束,因此寻找最大似然估计需要在Stiefel流形上进行优化.第二个问题涉及对从扩散磁共振成像数据中估计出... 详细信息

本文讨论两个统计问题,其中微分几何的概念和观念发挥了关键作用.第一个问题涉及函数型数据的主成分估计,其中一部分参数具有正交约束,因此寻找最大似然估计需要在Stiefel流形上进行优化.第二个问题涉及对从扩散磁共振成像数据中估计出来的扩散张量进行核平滑.由于这些张量是3×3的正定矩阵,所以平滑过程需要在3×3的正定矩阵空间上定义,并且依赖于这个空间上特定度量的选择.

关键词： Stiefel流形典型度量 Newton法函数型数据主成分分析自然约化齐性空间扩散张量核平滑

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Dynamic Multi-Graph Spatio-Temporal Graph Traffic Flow Prediction in Bangkok:An Application of a Continuous Convolutional Neural Network

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 579-607页

作者： Pongsakon Promsawat Weerapan Sae-dan Marisa Kaewsuwan Weerawat Sudsutad Aphirak Aphithana department of Civil Engineering Faculty of EngineeringRamkhamkaeng UniversityBangkok10240Thailand department of Computer Engineering Faculty of EngineeringRamkhamkaeng UniversityBangkok10240Thailand department of statistics Faculty of ScienceRamkhamkaeng UniversityBangkok10240Thailand

The ability to accurately predict urban traffic flows is crucial for optimising city ***,various methods for forecasting urban traffic have been developed,focusing on analysing historical data to understand complex mobility *** learning techniques,such as graph neural networks(GNNs),are popular for their ability to capture spatio-temporal ***,these models often become overly complex due to the large number of hyper-parameters *** this study,we introduce Dynamic Multi-Graph Spatial-Temporal Graph Neural Ordinary Differential Equation Networks(DMST-GNODE),a framework based on ordinary differential equations(ODEs)that autonomously discovers effective spatial-temporal graph neural network(STGNN)architectures for traffic prediction *** comparative analysis of DMST-GNODE and baseline models indicates that DMST-GNODE model demonstrates superior performance across multiple datasets,consistently achieving the lowest Root Mean Square Error(RMSE)and Mean Absolute Error(MAE)values,alongside the highest *** the BKK(Bangkok)dataset,it outperformed other models with an RMSE of 3.3165 and an accuracy of 0.9367 for a 20-min interval,maintaining this trend across 40 and 60 ***,on the PeMS08 dataset,DMST-GNODE achieved the best performance with an RMSE of 19.4863 and an accuracy of 0.9377 at 20 min,demonstrating its effectiveness over longer *** Los_Loop dataset results further emphasise this model’s advantage,with an RMSE of 3.3422 and an accuracy of 0.7643 at 20 min,consistently maintaining superiority across all time *** numerical highlights indicate that DMST-GNODE not only outperforms baseline models but also achieves higher accuracy and lower errors across different time intervals and datasets.

关键词： Graph neural networks convolutional neural network deep learning dynamic multi-graph spatio-temporal

Artificial Circulation System Algorithm:A Novel Bio-Inspired Algorithm

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 635-663页

作者： NerminÖzcan Semih Utku Tolga Berber department of Biomedical Technologies Dokuz Eylül UniversityIzmir35390Turkey department of Biomedical Engineering Iskenderun Technical UniversityIskenderun31200Turkey department of Computer Engineering Dokuz Eylül UniversityIzmir35390Turkey department of statistics and Computer Sciences Karadeniz Technical UniversityTrabzon61080Turkey

Metaheuristics are commonly used in various fields,including real-life problem-solving and engineering appli*** present work introduces a novel metaheuristic algorithm named the Artificial Circulatory System Algorithm(ACSA).The control of the circulatory system inspires it and mimics the behavior of hormonal and neural regulators involved in this *** work initially evaluates the effectiveness of the suggested approach on 16 two-dimensional test functions,identified as classical benchmark *** method was subsequently examined by application to 12 CEC 2022 benchmark problems of different ***,the paper evaluates ACSA in comparison to 64 metaheuristic methods that are derived from different approaches,including evolutionary,human,physics,and ***,a sequence of statistical tests was undertaken to examine the superiority of the suggested algorithm in comparison to the 7 most widely used algorithms in the existing *** results show that the ACSA strategy can quickly reach the global optimum,avoid getting trapped in local optima,and effectively maintain a balance between exploration and *** outperformed 42 algorithms statistically,according to post-hoc *** also outperformed 9 algorithms *** study concludes that ACSA offers competitive solutions in comparison to popüler methods.

关键词： Bio-inspired evolutionary heuristic metaheuristic optimization

Asymptotical p-moment stability of stochastic impulsive differential system and its application to chaos synchronization

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Chinese Physics B 2010年第3期19卷 176-181页

作者：牛玉俊徐伟陆朝阳 department of math and statistics Nanyang Normal University department of Applied math Northwestern Polytechnical University

In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.

关键词： p-moment stability impulsive stochastic differential equations chaos synchronization

Practice patterns among ophthalmic surgeons in treating concomitant oculoplastic conditions in preoperative period:A questionnaire-based study

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World Journal of Clinical Cases 2025年第1期13卷 29-37页

作者： Bijnya Birajita Panda Chitaranjan Mishra Bhagabat Nayak Avik Kumar Roy Logesh Balakrishnan Priyadarshini Mishra department of Ophthalmology All India Institute of Medical SciencesBhubaneswar 751019OdishaIndia department of Vitreo-Retina Trilochan NetralayaSambalpur 768004India department of Glaucoma Services LV Prasad Eye InstituteBhubaneswar 751013India department of statistics Apollo HospitalsChennai 823104India

BACKGROUND Addressing oculoplastic conditions in the preoperative period ensures both the safety and functional success of any ophthalmic *** oculoplastic conditions,like nasolacrimal duct obstruction,have been extensively studied,whereas others,like eyelid malposition and thyroid eye disease,have received minimal or no *** To investigate the current practice patterns among ophthalmologists while treating concomitant oculoplastic conditions before any subspecialty ophthalmic *** A cross-sectional survey was disseminated among ophthalmologists all over *** survey included questions related to pre-operative evaluation,anaesthetic and surgical techniques preferred,post-operative care,the use of adjunctive therapies,and patient follow-up *** A total of 180 ophthalmologists responded to the *** practitioners(89%)felt that the ROPLAS test was sufficient during pre-operative evaluation before any subspecialty surgery was *** most common surgical techniques employed were lacrimal drainage procedures(Dacryocystorhinostomy)(63.3%),eyelid malposition repair(36.9%),and ptosis repair(58.7%).Post-operatively,47.7%of respondents emphasized that at least a 4-week gap should be maintained after lacrimal drainage procedures and eyelid ***-seven percent of ophthalmologists felt that topical anaesthetic procedures should be preferred while performing ocular surgeries in thyroid eye disease *** Approximately 50%of ophthalmologists handle prevalent oculoplastic issues themselves,seeking the expertise of an oculoplastic surgeon under particular *** ophthalmologists still favor using ROPLAS as a preliminary screening method before proceeding with cataract *** conditions and thyroid eye disease are not as commonly addressed before subspecialty procedures compared to issues like nasolacrimal duct obstruction and periocular infections.

关键词： Oculoplasty Ophthalmic plastic surgery Nasolacrimal duct obstruction Practice patterns Survey

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一类形变Lie代数的结构与表示

中国科学:数学 2025年第1期 3-14页

作者：陈洪佳郜云徐大树赵琦中国科学技术大学数学科学学院 department of mathematics and statistics York University

扭Heisenberg-Virasoro代数是复数域上一类重要的无限维Lie代数,它与一类曲线的模空间有关.本文对无中心扭Heisenberg-Virasoro代数的一族形变Lie代数Gβ的结构与表示展开研究.主要结果包括:（1）确定不同Gβ之间的同构关系;（2）刻画G... 详细信息

扭Heisenberg-Virasoro代数是复数域上一类重要的无限维Lie代数,它与一类曲线的模空间有关.本文对无中心扭Heisenberg-Virasoro代数的一族形变Lie代数Gβ的结构与表示展开研究.主要结果包括:（1）确定不同Gβ之间的同构关系;（2）刻画Gβ的导子Lie代数与泛中心扩张;（3）分类Gβ的U（CL0）秩1自由模,并给出这些模不可约的充分必要条件.在可约的情形下,本文确定了其唯一非零真子模.

关键词：扭Heisenberg-Virasoro代数导子Lie代数泛中心扩张不可约模秩1自由模

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Maximum Likelihood Estimator of the Parameter for a Continuous One-Parameter Exponential Family Under the Optimal Ranked Set Sampling

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Journal of Systems Science & Complexity 2017年第6期30卷 1350-1363页

作者： CHEN Wangxue TIAN Yi XIE Minyu department of mathematics and statistics Jishou University department of mathematics and statistics Central China Normal University

This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

关键词： Complete sufficient statistic continuous one-parameter exponential family maximum likelihood estimator ranked set sampling

A dynamic logistic regression for network link prediction

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Science China mathematics 2017年第1期60卷 165-176页

作者： ZHOU Jing HUANG DanYang WANG HanSheng department of statistics Renmin University of China department of statistics Peking University

In social network analysis, link prediction is a problem of fundamental importance. How to conduct a comprehensive and principled link prediction, by taking various network structure information into consideration,is of great interest. To this end, we propose here a dynamic logistic regression method. Specifically, we assume that one has observed a time series of network structure. Then the proposed model dynamically predicts future links by studying the network structure in the past. To estimate the model, we find that the standard maximum likelihood estimation(MLE) is computationally forbidden. To solve the problem, we introduce a novel conditional maximum likelihood estimation(CMLE) method, which is computationally feasible for large-scale networks. We demonstrate the performance of the proposed method by extensive numerical studies.

关键词： conditional likelihood dynamic logistic regression link prediction social networks

ESTIMATION OF A SUBSET OF REGRESSION COEFFICIENTS OF INTEREST IN A MODEL WITH NON-SPHERICAL DISTURBANCES

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Journal of Systems Science & Complexity 2013年第2期26卷 209-231页

作者： CHATURVEDI Anoop KESARWANI Suchita department of statistics University of Allahabad

This paper considers the estimation of a subset of regression coefficients in a linear regression model with non-spherical disturbances,when other regression coefficients are of no interest.A family of estimators is considered and its asymptotic distribution is *** proposed family of improved estimators is compared with the usual unrestricted FGLS estimator,and dominance conditions are obtained with respect to risk under quadratic loss as well as the Pitman nearness *** results of a numerical simulation are presented to illustrate the risk performance of various estimators.

关键词： Large sample asymptotic minimum mean square error non-spherical disturbances pitman nearness criterion quadratic loss risk.