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High-dimensional large-scale mixed-type data imputation under missing at random

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Science China mathematics 2025年

作者： Wei Liu Guizhen Li Ling Zhou Lan Luo School of mathematics Sichuan University Center of Statistical Research and School of Statistics Southwestern University of Finance and Economics Department of Statistics and Actuarial Science University of Iowa

Missingness in mixed-type variables is commonly encountered in a variety of areas. The requirement of complete observations necessities data imputation when a moderate or large proportion of data is ***, inappropriate imputation would downgrade the performance of machine learning algorithms, leading to bad predictions and unreliable statistical inference. For high-dimensional large-scale mixed-type missing data, we develop a computationally efficient imputation method, missing value imputation via generalized factor models（MIG）, under missing at random. The proposed MIG method allows missing variables to be of different types,including continuous, binary, and count variables, and are scalable to both data size n and variable dimension p while existing imputation methods rely on restrictive assumptions such as the same type of missing variables,the low dimensionality of variables, and a limited sample size. We explicitly show that the imputation error of the proposed MIG method diminishes to zero with the rate Op(max{n-1/2, p-1/2}) as both n and p tend to infinity. Five real datasets demonstrate the superior empirical performance of the proposed MIG method over existing methods that the average normalized absolute imputation error is reduced by 5.3%–34.1%.

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Orbits of Jacobi forms and theta relations

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Science China mathematics 2025年

作者： Valery Gritsenko Haowu Wang Laboratoire Paul Painlevé Université de Lille International Laboratory for Mirror Symmetry and Automorphic Forms National Research University Higher School of Economics School of mathematics and Statistics Wuhan University

Jacobi theta functions with rational characteristics can be viewed as vector-valued Jacobi *** relations usually correspond to different constructions of certain Jacobi forms. From this observation, we extract a new approach, which is called orbits of Jacobi forms, to produce identities on Jacobi theta *** approach not only provides simple proofs of many known theta relations but also produces a large number of new identities, which can be considered as generalizations of Riemann’s theta relations.

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Accuracy and Consistency of the Explicit-Invariant Energy Quadratization Approach for the Cahn-Hilliard Equation

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Journal of Mathematical Research with Applications 2025年第1期 84-104页

作者： Jun ZHANG Fangying SONG Yu ZHANG Computational mathematics Research Center Guizhou University of Finance and Economics School of mathematics and statistics Guizhou University of Finance and Economics School of mathematics and Stastistics Fuzhou University

It is well known that the explicit-invariant energy quadratization (EIEQ) approach can generate fully decoupled, linear and unconditionally energy-stable numerical schemes, so it is favored by many researchers. However, the undeniable fact is that the numerical method obtained by EIEQ approach preserves the “modified” energy law instead of the original *** is mainly due to the introduction of some auxiliary variables in EIEQ scheme, and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation. The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation. We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ. The analysis results show that the newly constructed schemes are not only unconditionally energy stable, linear and fully decoupled, but also can effectively correct the errors introduced by auxiliary variables and follow the original energy ***, several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.

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A General Association Test for High-Dimensional Random Vectors

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Acta Mathematica Sinica,English Series 2025年

作者： Yongshuai Chen Peng Lin Baoxue Zhang School of Statistics Capital University of Economics and Business

Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications. In this paper, we propose a new test statistic based on the Frobenius norm and subtracting bias technique, which is generally applicable to high-dimensional data without restricting the distributional assumptions. The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation. Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions. To make the test statistic applicable, we introduce a wild bootstrap method and demonstrate its validity. The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests, even when the normal approximation is invalid. Real data analysis is devoted to illustrating the proposed test.

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Exit options sustain altruistic punishment and decrease the second-order free-riders, but it is not a panacea

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Science China(Information Sciences) 2025年第1期68卷 278-291页

作者： Chen SHEN Zhao SONG Lei SHI Jun TANIMOTO Zhen WANG Faculty of Engineering Sciences Kyushu University School of Statistics and mathematics Yunnan University of Finance and Economics School of Computing Engineering and Digital Technologies Teesside University School of Artificial Intelligence OPtics and Electro Nics (iOPEN) Northwestern Polytechnical University

Why do humans punish free riders at their own expense? This behavior represents an evolutionary puzzle in human societies. This study explores the role of exit strategies in fostering altruistic punishment within evolutionary game theory. We extend the traditional prisoner's dilemma model by incorporating exiters, players who opt out for a small payoff while nullifying their opponent's payoff, and altruistic punishers who cooperate and punish non-cooperators. Our findings indicate that in well-mixed populations, exiters destabilize defection but do not promote altruistic punishment. In social networks, however,exiters enable altruistic punishment via cyclic dominance among altruistic punishers, defectors, and exiters. Notably, this cyclic dominance is sensitive to exit payoffs; adjustments can lead to cyclic dominance of non-punishing cooperators, defectors, and exiters, or to a bi-stable state between these two types of cyclic dominance. These results highlight the nuanced impact of exiters on altruistic punishment, emphasizing the need for careful incentivization of exit behavior. While exiters can support altruistic punishment in networked populations, their effectiveness is not a panacea and is highly sensitive to exit payoffs, indicating limits to the voluntary participation mechanism.

关键词： evolutionary game theory altruistic punishment coexistence cyclic dominance bi-stable

Extensions and Deformations of 3-Lie Algebras with Higher Derivations

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Journal of Mathematical Research with Applications 2025年第1期 20-32页

作者： Shuangjian GUO School of mathematics and Statistics Guizhou University of Finance and Economics

In this paper, we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair. We introduce a cohomology theory of 3-LieHDer pairs. Next, we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions. Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.

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Sharp Bounds for Upper and Bottom Spectrum of Hermitizable Tridiagonal Matrices

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Journal of Mathematical Research with Applications 2025年第1期 125-132页

作者： Yueshuang LI Lingdi WANG School of Statistics Capital University of Economics and Business School of mathematics and Statistics Henan University

We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix. The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector) of tridiagonal matrices, isospectral transforms and sharp bounds for speed stability of birth-death processes.

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Improving the Position Accuracy and Computational Efficiency of UAV Terrain Aided Navigation Using a Two-Stage Hybrid Fuzzy Particle Filtering Method

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Computers, Materials & Continua 2025年第1期82卷 1193-1210页

作者： Sofia Yousuf Muhammad Bilal Kadri College of Engineering Karachi Institute of Economics&TechnologyKarachi75190Pakistan College of Computer and Information Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia

Terrain Aided Navigation(TAN)technology has become increasingly important due to its effectiveness in environments where Global Positioning System(GPS)is *** recent years,TAN systems have been extensively researched for both aerial and underwater navigation ***,many TAN systems that rely on recursive Unmanned Aerial Vehicle(UAV)position estimation methods,such as Extended Kalman Filters(EKF),often face challenges with divergence and instability,particularly in highly non-linear *** address these issues,this paper proposes and investigates a hybrid two-stage TAN positioning system for UAVs that utilizes Particle *** enhance the system’s robustness against uncertainties caused by noise and to estimate additional system states,a Fuzzy Particle Filter(FPF)is employed in the first *** approach introduces a novel terrain composite feature that enables a fuzzy expert system to analyze terrain non-linearities and dynamically adjust the number of particles in *** design allows the UAV to be efficiently localized in GPS-denied environments while also reducing the computational complexity of the particle filter in real-time *** the second stage,an Error State Kalman Filter(ESKF)is implemented to estimate the UAV’s *** ESKF is chosen over the conventional EKF method because it is more suitable for non-linear *** results demonstrate that the proposed fuzzy-based terrain composite method achieves high positional accuracy while reducing computational time and memory usage.

关键词： Sensor fusion fuzzy logic particle filter composite feature terrain aided navigation

Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

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Chinese Physics B 2023年第3期32卷 53-57页

作者：杜明婧孙宝军凯歌 School of Computer Information Management Inner Mongolia University of Finance and economics Hohhot 010070China School of Statistics and mathematics Inner Mongolia University of Finance and EconomicsHohhot 010070China

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial *** traditional reproducing kernel(RK)method which deals with this problem is very *** paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first *** method has three obvious advantages which are as ***,the piecewise number is ***,the calculation accuracy is ***,the waste time caused by too many fragments is *** four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the *** research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

关键词： time-fractional partial differential equation adaptive multi-step reproducing kernel method method numerical solution

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