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## 1. chinaXiv:202105.00070 [pdf]

Subjects: Statistics >> Mathematical Statistics
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性表示的理论工具，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，概述了其基本概念和定理，以及估计方法。介绍了Copula熵研究的最新进展，包括其在统计学四个基本问题（结构学习、关联发现、变量选择和时序因果发现等）上的理论应用。讨论了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的相关性度量框架进行了对比。简述了Copula熵在水文学、环境气象学、生态学、认知神经学、系统生物学、老年医学、公共卫生学，以及能源工程、制造工程和可靠性工程等领域的实际应用。

## 2. chinaXiv:202103.00132 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 " Dempster-Shafer evidence theory, as an extension of Probability theory, is widely used in the field of information fusion due to it satisfies weaker conditions than probability theory in dealing with uncertain information. Nevertheless , the description space of the current evidence theory is only a real space, and it cannot effectively describe and process the uncertain information in the face of multidimensional characteristic data and periodic data with phase angle changes. Based on this gap , in this paper, Dempster-Shafer evidence theory is extended to the complex Dempster-Shafer evidence theory. In complex Dempster-Shafer evidence theory, mass function that used to describe the uncertain information extends from the real space to the complex space, named as complex mass function, and the modulus of the mass function indicates the degree of support for the proposition. On this basis, other basic concepts used to describe uncertainty information are also defined and discussed, such as complex belief function, complex plausibility function, etc. In order to perfect the complex Dempster-Shafer evidence theory, the complex Dempster combination rule (CDCR) is supplemented. CDCR is an extension of Dempster combination rule (CDR), which satisfies the commutative and associative laws just as CDR does, and it can degenerate into CDR under certain condition. In addition, we propose a method to generate complex mass function and apply it to target recognition. The recognized results show that compared with the mass function of the real plane, the target recognition rate can be larger by using complex mass function to describe the uncertain information.

## 3. chinaXiv:202102.00009 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 系统性掌握黄河流域经济发展时空格局演变规律能为整个流域高质量发展提供重要决策依据。目前，GDP是衡量经济发展格局的主要参考依据，然而GDP统计数据存在口径不统一、空间分辨率低等缺点，难以精准刻画经济发展的时空演变格局特征。夜晚灯光数据以其相对客观的特征，对其进行有效反映。本文通过对1992-2013年全国夜晚灯光数据的校正和处理，获得全国及流域夜晚灯光数据影像，进行经济空间聚合分析，以及与相关因子进行对比分析。研究结果表明：经济空间聚合高的区域分布在黄河河道附近，从黄河上游到下游，热力强度逐渐增强，并且以省会城市为核心区，向外扩散，呈现了在老的聚合点聚合度加剧的情况下，聚合区域有向周边分散的趋势；夜晚灯光数据的变化趋势与GDP的变化趋势具有一定的相似性，并且与城镇化率、人口数量、第三产比例、人均公园绿地面积、流域发展指数（Basin Development Index, BDI）具有一定的相关性；流域9省的夜晚灯光数据整体变化趋势与全国灯光数据的变化趋势基本一致，呈稳定上升的趋势，但整体值均低于全国的夜晚灯光数据，并且差距有所扩大，黄河流域高质量发展迫在眉睫。

## 4. chinaXiv:202101.00002 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 本文基于邓熵提出了度量量子纠缠度的方法。分别计算纠缠态和解纠缠之后状态的最大邓熵，将两个熵之差作为纠缠度度量。用GHZ和W纠缠态作为算例给出了所提出方法的应用。