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1. 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 Hits42Downloads137 Comment 0

2. 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、认知神经学、系统生物学、老年医学和能源工程等领域的实际应用。

submitted time 2021-05-21 Hits889Downloads218 Comment 0

3. 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 Hits632Downloads169 Comment 0

4. 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 Hits642Downloads149 Comment 0

5. 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 Hits20395Downloads2100 Comment 0

6. chinaXiv:202102.00079 [pdf]

均等分区问题模型、算法及应用

孔云峰
Subjects: Geosciences >> Geography

分区问题广泛应用于地理、经济、政治、商业、公共服务等领域。均等分区问题是其中一类问题,通常要求分区人口数量或任务量均等、几何形状紧凑和空间连续,应用于选区、销售区和巡逻区的划分。本文针对均等分区问题提出了一个混合整型线性规划模型,并设计了一个基于迭代局部搜索(ILS)的混合算法。该算法从三个方面扩展ILS:群解搜索、VND搜索及SPP模型改进。选择5个区域对模型和算法进行测试,结果表明:数学模型能够求解空间单元数量为324的案例;混合算法优化性能优异,鲁棒性强,计算效率较高。所提出的均等分区问题适用于政治分区等经典问题,在新冠疫情应急服务等领域也具有应用潜力。

submitted time 2021-02-24 Hits1532Downloads414 Comment 0

7. chinaXiv:202011.00118 [pdf]

A necessary and su#14;cient condition of positive definiteness for 4th order symmetric tensors defined in particle physics

宋义生; 祁力群
Subjects: Mathematics >> Mathematical Physics

In this paper, we mainly discuss analytical expressions of positive definiteness for a special 4th order 3-dimensional symmetric tensor defined by the constructed model for a physical phenomenon. Firstly, an analytically necessary and sufficient conditions of 4th order 2-dimensional symmetric tensors are given to test its positive definiteness. Furthermore, by means of such a result, a necessary and sufficient condition of positive definiteness is obtained for a special 4th order 3-dimensional symmetric tensor. Such an analytical conditions can be used for verifying the vacuum stability of general scalar potentials of two real singlet scalar fields and the Higgs boson. The positive semi-definiteness conclusions are presented too.

submitted time 2020-11-23 Hits3785Downloads568 Comment 0

8. chinaXiv:202010.00007 [pdf]

名字嵌入向量方法

何沧平; 许涛
Subjects: Mathematics >> Computational Mathematics.

在进入推荐系统之前,商品名、人名等实体名字需要嵌入低维向量。word2vec这样的流行嵌入算法的出发点是“相同语法位置上的词具有相似的向量”,而名字序列没有语法结构,导致名字向量的质量不高。 本文从“相邻的名字具有相似的向量”出发,提出一个称为名字嵌入的新方法。名字嵌入使用了一些新技巧:公式比word2vec更简单,向量模长固定为1、用相对权重处理低频名字、优化目标使用简单的均方差。 以名字相似度作为衡量标准,在NBA球队名人造集、球队名微博集和微博点赞集上,名字嵌入均显著优于word2vec。

submitted time 2020-10-19 Hits5906Downloads618 Comment 0

9. chinaXiv:202009.00004 [pdf]

一元半正定多项式降次平方和表示及其L-算法

黄勇; 曾振柄; 杨路; 饶永生
Subjects: Mathematics >> Theoretical Computer Science

本文给出一元半正定多项式一种降次平方和表示方法, 并给出从已知半正定多项式得到其降次平方和表示的算法. 在第四节, 我们把这种“降次平方和”表示思路和算法用到多元多项式上也取得成功.

submitted time 2020-10-10 Hits11004Downloads840 Comment 0

10. chinaXiv:202005.00043 [pdf]

DEED: A general quantization scheme for saving bits in communication

Tian Ye; Peijun Xiao; Ruoyu Sun
Subjects: Mathematics >> Control and Optimization.

Quantization is a popular technique to reduce communication in distributed optimization. Motivated by the classical work on inexact gradient descent (GD) \cite{bertsekas2000gradient}, we provide a general convergence analysis framework for inexact GD that is tailored for quantization schemes. We also propose a quantization scheme Double Encoding and Error Diminishing (DEED). DEED can achieve small communication complexity in three settings: frequent-communication large-memory, frequent-communication small-memory, and infrequent-communication (e.g. federated learning). More specifically, in the frequent-communication large-memory setting, DEED can be easily combined with Nesterov's method, so that the total number of bits required is $ \tilde{O}( \sqrt{\kappa} \log 1/\epsilon )$, where $\tilde{O}$ hides numerical constant and $\log \kappa $ factors. In the frequent-communication small-memory setting, DEED combined with SGD only requires $\tilde{O}( \kappa \log 1/\epsilon)$ number of bits in the interpolation regime. In the infrequent communication setting, DEED combined with Federated averaging requires a smaller total number of bits than Federated Averaging. All these algorithms converge at the same rate as their non-quantized versions, while using a smaller number of bits.

submitted time 2020-06-16 Hits12619Downloads1458 Comment 0

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