基于随机矩阵的金融网络模型

随机矩阵理论运用于金融领域中研究金融相关系数矩阵的相关性,相关系数矩阵是网络构建中的关键因素,本文将随机矩阵理论与网络构建相结合,研究基于随机矩阵的金融网络模型.本文选取上海证券市场的股票数据,将其中的股票数据分成四个阶段,基于随机矩阵理论,讨论金融相关系数矩阵和随机矩阵的特征值统计性质,并在此基础上对现有的去噪方法进行改进,建立更适合构建金融网络的相关系数矩阵,并构建金融网络模型.然后,基于随机矩阵理论和网络的关键节点分析比较去噪前后的金融网络以及噪声网络,发现对网络去噪后仍保留了原始网络的关键重要的信息,而噪声信息对应的是原始网络中度比较小的节点所代表的信息.最后,基于去噪网络,分析金融网络的拓扑结构,如最小生成树、模体和社团结构,发现改进后的金融网络的拓扑性质更加明显,结构更加紧密.     

量子不可积性和随机矩阵理论

本文概述了量子不可积性的拓扑观.按拓扑观点探讨了量子体系完全可积的条件,通向不可积的机制,以及在量子不可积条件下的能谱性质,从动力学角度阐明了随机矩阵理论的基础,还简要讨论了这些理论在核结构问题中的应用. Quantum nonintegrability is studied in a topological view.The condition for complete integrability of quantum systems and the mechanism leading to global nonintegrability are investigated.The basis of random matrix theory for describing energy spectra of nonintegrable quantum systems is clarified.Applications to nuclear structure are briefly discussed.     

随机矩阵理论在肺癌基因网络识别中的应用

利用随机矩阵理论（RMT）方法除去肺癌基因表达数据中的噪声,并将去噪后的数据分别用模块方法和等级聚类方法进行处理.比较两种方法处理后的结果,发现RMT-等级聚类方法不仅能给出模块,还能给出模块间的关联强度.研究表明,RMT-等级聚类方法是一种有效的识别基因网络的新方法. 关键词： 随机矩阵理论 等级聚类 基因网络 肺癌     

基于随机矩阵最大特征值分布的频谱感知算法

现有频谱感知算法在低信噪比时检测性能较低且受虚警概率影响大,针对此问题,提出了一种基于wishart矩阵样本协方差矩阵最大特征值的分布特性的频谱感知算法。该算法利用最大特征值与几何平均特征值的比值,不需要主用户的先验知识,不敏感于噪声,对相关信号和独立同分布信号均具有较高的检测性能。仿真结果表明,所提算法受虚警概率的影响较小,检测性能高,并且在采样点数、协作用户数、信噪比及虚警概率较小的情况下,也能获得较好的检测性能。     

基于局部轮廓和随机森林的人体行为识别

基于视频信息的人体行为识别得到了越来越多的关注。针对人体行为的局部表达,提出了一种新的局部轮廓特征来描述人体的外观姿势,可以同时利用水平和竖直方向上的轮廓变化信息。该特征能有效区分不同动作,与轮廓起始点无关,具有平移、尺度和旋转不变性。针对该特征,提出了一种基于随机森林的两阶段分类方法,使用随机森林分类器对行为视频的局部轮廓进行初分类,并根据每个局部轮廓对应决策类的分类树数目占总分类树数目的比例,提出了一种基于袋外(OOB)数据误差加权投票准则的行为视频分类算法。在测试数据集上的实验结果证实了该方法的有效性。     

CS-MRI 中评价随机欠采样矩阵的新方法

在压缩感知-磁共振成像(CS-MRI)中,随机欠采样矩阵与重建图像质量密切相关．而选取随机欠采样矩阵一般是通过计算点扩散函数(PSF),以可能产生的伪影的最大值为评价参数,评估欠采样对图像重建的影响,然而最大值只反应了伪影的最坏情况．该文引入了两种新的统计学评价参数平均值(MV)和标准差(SD),其中平均值评估了伪影的平均大小,标准差可以反映伪影的波动情况．该文分别使用这3种参数对小鼠和人体脑部MRI数据以不同的采样比率进行CS图像重建,实验结果表明,当采样比率不低于4倍稀疏度时,使用平均值获得了质量更优的重建图像．因此,通过稀疏度先验知识指导合理选取采样比率,并以平均值为评价参数选取随机欠采样矩阵,能够获得更优的CS-MRI重建图像．
     

基于混沌序列和RIPless理论的循环压缩测量矩阵的构造

压缩测量矩阵的构造是压缩感知的核心工作之一.循环矩阵由于其对应离散卷积且具有快速算法被广泛应用于压缩测量矩阵.本文力图将混沌的优点和循环矩阵的优点相结合,提出基于混沌序列的循环压缩测量矩阵.混沌循环测量矩阵元素的产生仅需要利用混沌的内在确定性,即利用混沌映射公式、初始值以及一定的采样间隔就可以产生独立同分布的随机序列;同时混沌序列的外在随机性可以满足压缩测量矩阵对随机性的要求.本文给出了使用Cat混沌映射时混沌循环测量矩阵的构造方法,以及该矩阵RIPless特性的检验.研究了采用构造的混沌循环测量矩阵对一维和二维信号进行压缩测量的效果,并与采用传统的循环测量矩阵的效果进行了比较.结果表明,混沌循环测量矩阵对于一维和二维信号都具有很好的恢复效果,且对二维信号的恢复性能要优于已有的循环矩阵.从相图角度分析了混沌循环测量矩阵优于已有的循环矩阵的机理,指出混沌的内在确定性和外在随机性的有机结合是所构造的混沌循环测量矩阵性能优于传统的循环矩阵的本质性原因.     

横向随机晶场Ising模型的相图和磁化行为研究

在有效场理论和切断近似框架内，选择自旋S=1的二维方格子，研究横向随机晶场Ising模型的相图和磁化行为，重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-D_x空间的相图和m-T空间的磁化图.在晶场稀疏情况下，负晶场方向存在临界温度的峰值，正方向可出现重入现象.晶场比率取+0.5和-0.5时，磁有序相范围缩小，特别是晶场比率取-0.5时，随晶场浓度的降低，临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值，不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较. 关键词： 横向随机晶场Ising模型 相图 磁化行为     

掺杂对随机分布团簇粒子缪勒矩阵的影响

文章分析了不同含量的杂质对随机分布团簇粒子缪勒矩阵的影响.利用Bruggeman有效介质理论得到了含有不同体积份额杂质的硅酸盐粒子的等效复折射率.采用离散偶极子近似方法对包含有不同化学成分的随机分布团簇粒子的缪勒矩阵进行了数值计算,给出了各个缪勒矩阵元素的散射角分布曲线,探讨了不同含量的杂质对随机分布团簇粒子缪勒矩阵的影响.研究表明,掺杂对随机分布团簇粒子的缪勒矩阵存在着不同程度的影响,并且此影响随着粒子尺度参数的变化而显著变化. 关键词： 团簇粒子 缪勒矩阵 Bruggeman有效介质理论 离散偶极子近似方法     

Centrality in High-Energy Nuclear Collisions and Random Matrix Theory.

I discuss the results from a study of the central ^12CC collisions at 4.2 A GeV/c. The data have been analyzed using a new method based on the Random Matrix Theory. The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses. I found that the behavior of the nearest neighbor spacing distribution for the protons, neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data. I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.     

Centrality of the collision and random matrix theory

I discuss the results from a study of the central 12CC collisions at 4.2 A GeV/c.The data have been analyzed using a new method based on the Random Matrix Theory.The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses.I found that the behavior of the nearest neighbor spacing distribution for the protons,neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data.I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.     

Renormalizing rectangles and other topics in random matrix theory

We consider random Hermitian matrices made of complex or realM×N rectangular blocks, where the blocks are drawn from various ensembles. These matrices haveN pairs of opposite real nonvanishing eigenvalues, as well asM–N zero eigenvalues (forM>N). These zero eigenvalues are kinematical in the sense that they are independent of randomness. We study the eigenvalue distribution of these matrices to leading order in the large-N, M limit in which the rectangularityr=M/N is held fixed. We apply a variety of methods in our study. We study Gaussian ensembles by a simple diagrammatic method, by the Dyson gas approach, and by a generalization of the Kazakov method. These methods make use of the invariance of such ensembles under the action of symmetry groups. The more complicated Wigner ensemble, which does not enjoy such symmetry properties, is studied by large-N renormalization techniques. In addition to the kinematical -function spike in the eigenvalue density which corresponds to zero eigenvalues, we find for both types of ensembles that if |r–1| is held fixed asN, theN nonzero eigenvalues give rise to two separated lobes that are located symmetrically with respect to the origin. This separation arises because the nonzero eigenvalues are repelled macroscopically from the origin. Finally, we study the oscillatory behavior of the eigenvalue distribution near the endpoints of the lobes, a behavior governed by Airy functions. Asr1 the lobes come closer, and the Airy oscillatory behavior near the endpoints that are close to zero breaks down. We interpret this breakdown as a signal thatr1 drives a crossover to the oscillation governed by Bessel functions near the origin for matrices made of square blocks.     

Intra-urban human mobility patterns: An urban morphology perspective

This paper provides a new perspective on human motion with an investigation of whether and how patterns of human mobility inside cities are affected by two urban morphological characteristics: compactness and size. Mobile phone data have been collected in eight cities in Northeast China and used to extract individuals’ movement trajectories. The massive mobile phone data provides a wide coverage and detailed depiction of individuals’ movement in space and time. Considering that most individuals’ movement is limited within particular urban areas, boundaries of urban agglomerations are demarcated based on the spatial distribution of mobile phone base towers. Results indicate that the distribution of human’s intra-urban travel in general follows the exponential law. The exponents, however, vary from city to city and indicate the impact of city sizes and shapes. Individuals living in large or less compact cities generally need to travel farther on a daily basis, and vice versa. A Monte Carlo simulation analysis based on Levy flight is conducted to further examine and validate the relation between intra-urban human mobility and urban morphology.     

Dynamics of implied volatility surfaces from random matrix theory

We analyze the dynamics of the implied volatility surface of KOSPI 200 futures options from random matrix theory. To extract the informative data, we use random matrix criteria. Implied volatility data have a colossal eigenvalue, and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction. We discern the marketwide knowledge of the implied volatility surface movement such as the level, skew, and smile effect. These dynamics has the ergodic property and long range autocorrelation. We also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics, and confirm the existence of leverage effect even in the short time interval.     

Inverse spectral theory for random Jacobi matrices

We give necessary and sufficient conditions for a Herglotz function to be thew-function of a random stationary Jacobi matrix.This paper is dedicated to the memory of Mark Kac.     

Exploring space-time structure of human mobility in urban space

Understanding of human mobility in urban space benefits the planning and provision of municipal facilities and services. Due to the high penetration of cell phones, mobile cellular networks provide information for urban dynamics with a large spatial extent and continuous temporal coverage in comparison with traditional approaches. The original data investigated in this paper were collected by cellular networks in a southern city of China, recording the population distribution by dividing the city into thousands of pixels. The space-time structure of urban dynamics is explored by applying Principal Component Analysis (PCA) to the original data, from temporal and spatial perspectives between which there is a dual relation. Based on the results of the analysis, we have discovered four underlying rules of urban dynamics: low intrinsic dimensionality, three categories of common patterns, dominance of periodic trends, and temporal stability. It implies that the space-time structure can be captured well by remarkably few temporal or spatial predictable periodic patterns, and the structure unearthed by PCA evolves stably over time. All these features play a critical role in the applications of forecasting and anomaly detection.