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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

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

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

Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

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Science China Mathematics 2024年第1期67卷 163-186页

作者： Yang Yang Shaoying Chen Kam Chuen Yuen School of statistics and Data Science Nanjing Audit UniversityNanjing 211815China department of statistics and Actuarial Science The University of Hong KongHong Kong 999077China

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually *** two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence *** applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

关键词： asymptotic joint tail behavior randomly weighted sum heavy-tailed distribution dependence insurance risk model

Quasi-periodically Forced Logistic Map with Weak Liouvillean Frequency

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2411-2435页

作者： Jin Hao LIANG Lin Lin FU department of Applied Mathematics Nanjing Forestry University School of Mathematics and statistics Shaoguan University

Consider a class of quasi-periodically forced logistic maps■whereωis an irrational frequency and c(θ) is a specific bimodal *** prove that under weak Liouvillean condition on frequency,the strange non-chaotic attra... 详细信息

关键词： 37C60 37C70 logistic map Lyapunov exponent Quasi-periodically forced strange non-chaotic attractor weak Liouvillean frequency

Sequential good lattice point sets for computer experiments

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Science China Mathematics 2024年第9期67卷 2153-2170页

作者： Xue-Ru Zhang Yong-Dao Zhou Min-Qian Liu Dennis K.J.Lin NITFID LPMC&KLMDASRSchool of Statistics and Data ScienceNankai UniversityTianjin 300071China department of statistics Purdue UniversityWest LafayetteIN 47907USA

Sequential Latin hypercube designs(SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point(SGLP) sets. Moreover, we provide efficient approaches for identifying the(nearly)optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability.

关键词： contracting space maximin distance nested Latin hypercube design sequential design space-fillingdesign

DiffGR:Detecting Differentially Interacting Genomic Regions from Hi-C Contact Maps

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Genomics, Proteomics & Bioinformatics 2024年第2期22卷 143-155页

作者： Huiling Liu Wenxiu Ma department of statistics University of California RiversideRiversideCA 92521USA

Recent advances in high-throughput chromosome conformation capture(Hi-C)techniques have allowed us to map genome-wide chromatin interactions and uncover higher-order chromatin structures,thereby shedding light on the principles of genome architecture and ***,statistical methods for detecting changes in large-scale chromatin organization such as topologically associating domains(TADs)are still ***,we proposed a new statistical method,DiffGR,for detecting differentially interacting genomic regions at the TAD level between Hi-C contact *** utilized the stratum-adjusted correlation coefficient to measure similarity of local TAD *** then developed a nonparametric approach to identify statistically significant changes of genomic interacting *** simulation studies,we demonstrated that DiffGR can robustly and effectively discover differential genomic regions under various ***,we successfully revealed cell type-specific changes in genomic interacting regions in both human and mouse Hi-C datasets,and illustrated that DiffGR yielded consistent and advantageous results compared with state-of-the-art differential TAD detection *** DiffGR R package is published under the GNU General Public License(GPL)≥2 license and is publicly available at https://***/wmalab/DiffGR.

关键词： Hi-C Differential analysis Topologically associating domain Stratum-adjusted correlation coefficient Nonparametric method

Automated Machine Learning Algorithm Using Recurrent Neural Network to Perform Long-Term Time Series Forecasting

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Computers, Materials & Continua 2024年第3期78卷 3529-3549页

作者： Ying Su Morgan C.Wang Shuai Liu department of statistics and Data Science University of Central FloridaOrlandoFL32816-2370USA School of Mathematics and statistics Beijing Technology and Business UniversityBeijing100048China

Long-term time series forecasting stands as a crucial research domain within the realm of automated machine learning(AutoML).At present,forecasting,whether rooted in machine learning or statistical learning,typically relies on expert input and necessitates substantial manual *** manual effort spans model development,feature engineering,hyper-parameter tuning,and the intricate construction of time series *** complexity of these tasks renders complete automation unfeasible,as they inherently demand human intervention at multiple *** surmount these challenges,this article proposes leveraging Long Short-Term Memory,which is the variant of Recurrent Neural Networks,harnessing memory cells and gating mechanisms to facilitate long-term time series ***,forecasting accuracy by particular neural network and traditional models can degrade significantly,when addressing long-term time-series ***,our research demonstrates that this innovative approach outperforms the traditional Autoregressive Integrated Moving Average(ARIMA)method in forecasting long-term univariate time *** is a high-quality and competitive model in time series prediction,and yet it requires significant preprocessing *** multiple accuracy metrics,we have evaluated both ARIMA and proposed method on the simulated time-series data and real data in both short and long ***,our findings indicate its superiority over alternative network architectures,including Fully Connected Neural Networks,Convolutional Neural Networks,and Nonpooling Convolutional Neural *** AutoML approach enables non-professional to attain highly accurate and effective time series forecasting,and can be widely applied to various domains,particularly in business and finance.

关键词： Automated machine learning autoregressive integrated moving average neural networks time series analysis

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem