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1. chinaXiv:202108.00116 [pdf]

Some discussions on Hausdorff metric

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we discuss the properties of functions generated using Hausdorff metric.

submitted time 2021-08-30 Hits390Downloads72 Comment 0

2. chinaXiv:202108.00117 [pdf]

如何使用神经网络研究认知

耿海洋; 李吉星
Subjects: Psychology >> Cognitive Psychology
Subjects: Biology >> Neurobiology

近年来,越来越多研究者使用神经网络研究认知和计算。由于研究背景和目的的差异,研究者使用神经网络的方式不尽相同。本文总结了几种“使用神经网络研究认知”的常见思路,并且列举了具体的实例,帮助大家对这些思路进行深入理解。同时,我们也探讨了每种研究思路需要研究者具备哪些能力。最后,对目前“神经网络研究认知”领域中所面临的问题以及如何建立通用人工智能,进行了简单探讨。

submitted time 2021-08-30 Hits3006Downloads469 Comment 0

3. chinaXiv:202105.00070 [pdf]

Copula熵:理论和应用

马健
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。

submitted time 2021-08-19 Hits7553Downloads897 Comment 0

4. chinaXiv:202108.00057 [pdf]

Properties of fuzzy set

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we give some properties related to platform points of a fuzzy set and their applications.

submitted time 2021-08-10 Hits1823Downloads215 Comment 0

5. chinaXiv:202107.00011 [pdf]

Properties of several fuzzy set spaces

Huan Huang
Subjects: Mathematics >> Mathematics (General)

This paper discusses the properties the spaces of fuzzy sets in a metric s- pace equipped with the endograph metric and the sendograph metric, re- spectively. We fist discuss the level characterizations of the Γ-convergence and the endograph metric, and point out the elementary relationships among Γ-convergence, endograph metric and the sendograph metric. On the basis of these results, we present the characterizations of total boundedness, rel- ative compactness and compactness in the space of compact positive α-cuts fuzzy sets equipped with the endograph metric, and in the space of com- pact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these two kinds of spaces, respectively.

submitted time 2021-08-01 Hits3937Downloads240 Comment 0

6. chinaXiv:202107.00070 [pdf]

A Note on the High-dimensional Sparse Fourier Transform in the Continuous Setting

陈亮
Subjects: Mathematics >> Theoretical Computer Science

In this paper, we theoretically propose a new hashing scheme to establish the sparse Fourier transform in high-dimensional space. The estimation of the algorithm complexity shows that this sparse Fourier transform can overcome the curse of dimensionality. To the best of our knowledge, this is the first polynomial-time algorithm to recover the high-dimensional continuous frequencies.

submitted time 2021-07-26 Hits1363Downloads104 Comment 0

7. chinaXiv:202105.00069 [pdf]

Copositivity for a class of fourth order symmetric tensors given by scalar dark matter

宋义生; 李旭东
Subjects: Mathematics >> Mathematical Physics

In this paper, we mainly discuss the copositivity of 4th order symmetric tensor defined by scalar dark matter stable under a $\mathbb{Z}_{3}$ discrete group, and obtain an analytically necessary and sufficient condition of the copositivity of such a class of tensors. Furthermore, this analytic expression may be used to verify the vacuum stability for $\mathbb{Z}_{3}$ scalar dark matter.

submitted time 2021-06-16 Hits5800Downloads412 Comment 0

8. chinaXiv:202105.00041 [pdf]

基于高阶AGO生成的GM(1,1)模型

倪嘉雨; 涂缘
Subjects: Mathematics >> Modeling and Simulation

近年来,灰色系统理论在各个领域中的应用愈发广泛.在灰色预测模型中,GM(1,1)模型最为核心与基础,但该模型对振荡序列难以进行模拟,且振荡序列往往无法通过准指数律检验,这削弱了GM(1,1)模型的应用范围.本文利用GM(1,1)模型对单调序列的模拟,对振荡序列的1-AGO序列建立 GM(1,1)模型.再通过引入修正项的IAGO操作,还原到对原振荡序列的模拟.建立了改进的GM(1,1)模型,弥补了传统GM(1,1)模型对振荡序列模拟的缺陷.

submitted time 2021-05-07 Hits4114Downloads425 Comment 0

9. chinaXiv:202104.00127 [pdf]

灰色系统GM(1,1)与三角函数耦合模型的研究

倪嘉雨; 叶林峰; 高德宏; 邓洋
Subjects: Mathematics >> Modeling and Simulation

灰色系统模型由于其具有简便、数学背景清晰等特点,在数学建模与近似计算等领域都有着十分广泛的应用。灰色系统模型的原理可以概括为利用时间响应函数来模拟数据序列的演化,而其中GM(1,1)模型作为最基础、最能体现灰色建模思想的一个模型,应用最广泛。传统的GM(1,1)模型的时间响应函数是以自然常数 的指数构造的函数,也正是由于这个特点,所以GM(1,1)模型具有较强的局限性,在实际应用中人们往往会将GM(1,1)模型的时间响应函数做一定的修正。其中,最重要的一种修正方法就是将原本的时间响应函数与其他能够描述数据序列性质的函数进行耦合,例如对于具有一定周期性或准周期性的数据序列,就可将原本的时间响应函数与三角函数耦合,构成GM(1,1)-三角函数耦合模型。本文便深入探讨了这种模型的可行性,提出了耦合模型时间响应函数中参数的估计方法,以及误差分析。

submitted time 2021-04-23 Hits4584Downloads397 Comment 0

10. chinaXiv:201705.00829 [pdf]

Entropy-partition of Complex Systems and Emergence of Human Brain’s Consciousness

Xi Guangcheng
Subjects: Mathematics >> Statistics and Probability

The three frameworks for theories of consciousness taken moust seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state. Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system in present article. Human brain’s system self-organizably and adaptively implements partition、aggregation and integration, and consciousness emerges.

submitted time 2021-02-28 Hits26932Downloads2275 Comment 0

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