1. chinaXiv:202105.00070 [pdf]

Copula熵：理论和应用

马健
Subjects: Statistics >> Mathematical Statistics
Subjects: Mathematics >> Statistics and Probability
Subjects: Computer Science >> Computer Application Technology
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

统计独立性是统计学和机器学习领域的基础性概念，如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具，而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用，概述了其基本概念定义、定理和性质，以及估计方法。介绍了Copula熵研究的最新进展，包括其在统计学的八个基本问题（结构学习、关联发现、变量选择、因果发现、系统辨识、时延估计、域自适应和正态性检验等）上的理论应用。讨论了前四个理论应用之间的关系，以及其对应的深层次的相关性和因果性概念之间的联系，并将Copula熵的（条件）独立性度量框架与基于核函数和距离相关的同类框架进行了理论对比，又通过仿真和实际数据实验评估验证了CE的实际优越性。简述了Copula熵在理论物理学、理论化学、化学信息学、水文学、气候学、气象学、环境学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、管理学、社会学、教育学、计算语言学、新闻传播学、法学、政治学、军事学，以及能源工程、食品工程、土木工程、交通工程、制造工程、可靠性工程、化学工程、航空航天、电子工程、通信工程、高性能计算、测绘遥感和金融工程等领域的实际应用。

submitted time 2023-05-19 Hits42933， Downloads6268， Comment 0

2. chinaXiv:202303.00200 [pdf]

最小妒忌公平性区位模型及案例分析

孔云峰; 翟石艳
Subjects: Geosciences >> Geography
Subjects: Mathematics >> Control and Optimization.

区位模型广泛应用于公共健康、义务教育、应急管理和物流配送等领域。然而，主流区位问题多以服务效率为目标，注重设施成本、距离成本、覆盖客户数量等指标，未考虑服务公平性。部分区位模型考虑服务空间公平性，但存在公平指标多且选择使用缺乏共识、公平指标会严重扭曲效率指标、模型针对简单应用场景和缺乏通用性等局限。本文创新性地引入空间妒忌这一概念，构建公共服务最小嫉妒目标函数，并将其整合在容量约束P中值问题(Capacitated P-Median Problem, CPMP)模型目标函数中，形成最小妒忌公平性区位模型(CPMP-envy)。新模型克服了最小方差目标会扭曲效率指标的局限，实现公平指标与效率指标相兼容。本文考虑城市和农村地区人口空间分布特征，以及数据规模等因素，使用三个典型区域数据探索经典区位模型和公平性区位模型的基本特征。案例实验表明：最小妒忌目标能够显著地改进设施区位空间公平性指标，特别是设施数量较少时，公平性指标能够得到较大幅度改进。最小妒忌目标在公共服务设施布局规划中具有实用性，对于构建公平性区位模型具有理论价值。

submitted time 2023-05-13 Hits903， Downloads184， Comment 0

3. chinaXiv:202304.01057 [pdf]

The Modeling and Optimization of Building the Multi-dam System on Zambezi River

Xie,Pengcheng
Subjects: Mathematics >> Mathematics （General）
Subjects: Hydraulic Engineering >> Basic Disciplines of Hydraulic Engineering

In this paper, we mainly provide a proper maintenance plan for the Kariba Dam in Africa which falls into disrepair and is facing to collapse. Firstly, we make a threshold analysis of the three options about their costs which include people’s moving, old dam’s removing, new dams’ building, later repairing, ecological destruction and their incomes which include generation energy, avoiding of flood disasters’ loss, providing employment, tourism resources and ecological protection. Then we get the specific relationship between benefits and years with some collected data. Both of the results show that the third option is the best choice from the economic view. And the result is completely as same as the conclusion we get after studying deeply on Option 3. Secondly, we regard water management capabilities as the safety coefficient of dams. We select 30 seed points along the riverbank for preparing the establishment of dams. With flow-between-riverway model, Manning equations, large Cauchy distribute function we get the scores of the seed points. We give an advice that the number of dams should be more and the positions of dams should be well-distributed. Then, we build an assessment model by analytic hierarchy process. We select three factors among all the factors, safety, economy and population. After testing the consistency, we get the weights of each factor: 0.6442, 0.2705, 0.0852. Then we value the factors and get an optimal scheme during the assessment with 0-1 integer programming: the number of dams is 17 and the longitude and latitude of them are shown in Table 17. The sensitivity of the result is tested as well. We also provide some strategies for the managers of ZRA to use. We suggest that they should use the dams normally in general. With the Dam-break model, we find 13 points among 17 points which are shown in Table 20. The dams at the 13 points need to be closed when there is a flood and it is just the opposite when the drought happens. For the extreme water flow, we assume an ideal water flow at first. The extreme water flow has to be adjusted to satisfy the ideal one. As for the restrictions in extreme conditions, the biggest impact happens at the 8th point among the 17 points. If the duration of maximum flow is t0, the drainage time t to make the water flow return to the normal level equals to 4.95t0.

submitted time 2023-04-28 Hits769， Downloads75， Comment 0

4. chinaXiv:202304.01048 [pdf]

A Note on the Invariant Distribution of a Stochastic Dynamical System

Xie,Pengcheng
Subjects: Mathematics >> Mathematics （General）

This paper demonstrates the invariant distribution of a stochastic dynamical system. We give the invariant distribution and numerical examples. We also present a further discussion on the computation details.

submitted time 2023-04-27 Hits769， Downloads83， Comment 0

5. chinaXiv:202304.00998 [pdf]

代数上的拓扑结构及其完备化

刘雨喆
Comment：对于给定的Abel群或交换Noether环，可以通过上面的正规子群降链或理想降链分别建立Abel群或交换Noether环上的拓扑结构，使得可以对它们进行完备化。这篇初稿考虑在k-代数上建立类似的结构，并从射影极限的角度对该结构进行解释。我们后续还会利用箭图等方法对这些内容进行深入研究。
Subjects: Mathematics >> Algebra and Number Theory

本文以拓扑Abel群的完备化为基础, 定义了拓扑$k$-代数及其完备化, 并从射影极限的角度对完备化的进行了代数解释.

submitted time 2023-04-21 Hits982， Downloads208， Comment 0

6. chinaXiv:202304.00993 [pdf]

Parareal algorithm via Chebyshev-Gauss spectral collocation method

Zhou, Quan; Liu, Yicheng; Wu Shu-Lin
Subjects: Mathematics >> Computational Mathematics.

We present the Parareal-CG algorithm for time-dependent differential equations in this work. The algorithm is a parallel in time iteration algorithm utilizes Chebyshev-Gauss spectral collocation method for fine propagator F and backward Euler method for coarse propagator G. As far as we know, this is the first time that the spectral method used as the F propagator of the parareal algorithm. By constructing the stable function of the Chebyshev-Gauss spectral collocation method for the symmetric positive definite (SPD) problem, we find out that the Parareal-CG algorithm and the Parareal-TR algorithm, whose F propagator is chosen to be a trapezoidal ruler, converge similarly, i.e., the Parareal-CG algorithm converge as fast as Parareal-Euler algorithm with sufficient Chebyhsev-Gauss points in every coarse grid. Numerical examples including ordinary differential equations and time-dependent partial differential equations are given to illustrate the high efficiency and accuracy of the proposed algorithm.

submitted time 2023-04-20 Hits807， Downloads101， Comment 0

7. chinaXiv:202304.00964 [pdf]

单个率Meta分析中率的不同转换方法应用现状

曾治宇
Subjects: Medicine, Pharmacy >> Preclinical Medicine
Subjects: Mathematics >> Statistics and Probability

目的 考察当前单个率Meta分析的文献中对率的数据转换的实际使用情况。方法 在PubMed中检索2017年发表的单个率Meta分析的文献，从481条记录中筛选出145篇纳入分析。结果 在有全文的123篇文献中只有33篇（26.8%）文献交代了率的转换方法的使用，其中双重反正弦法20篇，logit转换8篇，平方根反正弦法3篇，对数转换1篇，直接使用原始率1篇。在这33篇文献中，率的转换方法的使用与汇总率的大小无关（P=0.217）。结论 单个率的Meta分析中率的转换方法是较为重要的因素，但各种转换方法的优劣尚无定论，发表的文献应加强对于率的数据转换等方法的说明。

submitted time 2023-04-19 Hits949， Downloads106， Comment 0

8. chinaXiv:202304.00965 [pdf]

单个率Meta分析中率的不同转换方法的比较

曾治宇
Subjects: Medicine, Pharmacy >> Preclinical Medicine
Subjects: Mathematics >> Statistics and Probability

目的 在单个率Meta分析中对率的不同转换方法进行比较。方法 构造两套模拟数据进行单个率的Meta分析，考察5种数据转换方法（不转换、对数转换、logit转换、平方根反正弦转换及双重反正弦转换）下的结果，兼顾固定效应模型和随机效应模型，及事件数为零时增加不同的固定值。计算汇总的率的均值（Mean），偏倚值（Bias）、偏倚率（Proportion Bias）、误差均方（Mean Squared Error, MSE）、误差均方百分比（Proportion MSE）及95%可信区间的覆盖率（Coverage）。结果 对基于二项分布的单个率进行Meta分析时，平方根反正弦转换总体表现最佳。当事件数为零时，增加不同的固定值对结果影响较大，但这种校正对不转换的策略没有帮助，甚至有损；对于对数转换和logit转换的改善也非常有限。总体率<0.05时，单个率Meta分析汇总的率偏倚较大。结论 单个率的Meta分析中平方根反正弦转换表现最佳。总体率<0.05时使用Meta分析宜谨慎。

submitted time 2023-04-19 Hits901， Downloads134， Comment 0

9. chinaXiv:202304.00967 [pdf]

单样本率比较（单组目标值法）的样本量计算确切概率法及R语言实现

曾治宇
Subjects: Medicine, Pharmacy >> Preclinical Medicine
Subjects: Mathematics >> Statistics and Probability

单样本率比较（单组目标值法）的样本量计算常见的方法为正态近似法，有时伴相应的数据转换如平方根反正弦转换，而确切概率法通常需要商业统计软件寻值或编程实现。本文利用免费软件R语言编程实现单样本率比较确切概率法计算样本量，并且考虑到了确切概率法计算时检验效能与样本量非单调递增的关系，直接给出计算结果，也可作图直观显示检验效能与样本量的关系，希望能有助于这类研究的有效开展。

submitted time 2023-04-19 Hits853， Downloads132， Comment 0

10. chinaXiv:202302.00246 [pdf]

Harmonic and biharmonic Riemannain submersions from Sol space

Wang, Zeping; Ou, Yelin; Liu, Qilong
Subjects: Mathematics >> Geometry and Topology

In this paper, we give a complete classifification of harmonic and biharmon#2; ic Riemannian submersions π : (R^3 , g_Sol) → (N^2 , h) from Sol space into a surface by proving that there is neither harmonic nor biharmonic Riemann#2; ian submersion π : (R^3 , g_Sol) → (N^2 , h) from Sol space no matter what the base space (N2 , h) is. We also prove that a Riemannian submersion π : (R^3 , g_Sol) → (N^2 , h) from Sol space exists only when the base space is a hyperbolic space form.

submitted time 2023-02-22 Hits3405， Downloads159， Comment 0