摘要翻译:
复杂系统通常由大量的观测集合来表示。相关矩阵提供了一个有效的形式框架来从这些多元集合中提取信息,并以可量化的方式识别与通常由随机矩阵提供的作为基本参考的参考机会概率相比以统计显著的频率可复制的活动模式。问题的性质,特别是所涉及的对称性,必须指导随机矩阵的选择,以用于基线参考的定义。对于标准相关矩阵,这是对称随机矩阵的Wishart系综。然而,现实世界的复杂性往往表现出不对称的信息流,因此需要更通用的相关矩阵来充分捕捉不对称性。这里我们首先对相关的理论概念进行概述。然后,我们给出了一些人脑活动的例子,在这些例子中,不对称的时滞相关性是明显的,因此突出了进一步理论发展的必要性。
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英文标题:
《Asymmetric random matrices: What do we need them for?》
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作者:
Stanislaw Drozdz, Jaroslaw Kwapien, Andreas A. Ioannides
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最新提交年份:
2011
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分类信息:
一级分类:Physics 物理学
二级分类:Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述:Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件:数据处理与存储;测量方法;统计和数学方面,如参数化和不确定性。
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一级分类:Computer Science 计算机科学
二级分类:Computational Engineering, Finance, and Science 计算工程、金融和科学
分类描述:Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的,集中在技术和工具,使挑战性的计算模拟能够执行,其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4(经济学)中的材料。
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一级分类:Quantitative Finance 数量金融学
二级分类:Statistical Finance 统计金融
分类描述:Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要:
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared to a reference chance probability, usually provided by random matrices as fundamental reference. The character of the problem and especially the symmetries involved must guide the choice of random matrices to be used for the definition of a baseline reference. For standard correlation matrices this is the Wishart ensemble of symmetric random matrices. The real world complexity however often shows asymmetric information flows and therefore more general correlation matrices are required to adequately capture the asymmetry. Here we first summarize the relevant theoretical concepts. We then present some examples of human brain activity where asymmetric time-lagged correlations are evident and hence highlight the need for further theoretical developments.
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PDF链接:
https://arxiv.org/pdf/1106.0390