Denoising Data with Random Matrix Theory

Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries, the introduction of noise, and the size of the matrix, the resulting eigenvalue and eigenvector distributions remain relatively unchanged. However, when there are certain anomalous eigenvalues and their corresponding eigenvectors that do not follow the predicted distributions, it could indicate that there’s an underlying non-random signal inside the data. As data and matrices become more important in the sciences and computing, so too will the importance of processing them with the principles of random matrix theory.

Corrigendum to“Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world”

The signs of the electric field markers in Figs.2 and 4 of the paper[Chin.Phys.B 32104211(2023)]have been corrected.These modifications do not affect the results derived in the paper.

The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Label-Free Microscopic Imaging Based on the Random Matrix Theory in Wavefront Shaping

Wavefront shaping technology has mainly been applied to microscopic fluorescence imaging through turbid media,with the advantages of high resolution and imaging depth beyond the ballistic regime. However, fluorescence needs to be introduced extrinsically and the field of view is limited by memory effects. Here we propose a new method for microscopic imaging light transmission through turbid media, which has the advantages of label-free and discretional field of view size, based on transmission-matrix-based wavefront shaping and the random matrix theory. We also verify that a target of absorber behind the strong scattering media can be imaged with high resolution in the experiment. Our method opens a new avenue for the research and application of wavefront shaping.

COOPERATIVE MIMO SPECTRUM SENSING BASED ON RANDOM MATRIX THEORY

Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.

Cross Correlation of Intra-day Stock Prices in Comparison to Random Matrix Theory

We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fact that the major part of the time series is random, and compare the eigenvalue spectrum of cross correlation matrix of a large set of random time series, to the spectrum derived by the random matrix theory (RMT) at the limit of large dimension (the number of independent time series) and long enough length of time series. We test this algorithm on the real tick data of American stocks at different years between 1994 and 2002 and show that the extracted principal components indeed reflects the change of leading stock sectors during this period.

An optimized cluster density matrix embedding theory

We propose an optimized cluster density matrix embedding theory(CDMET).It reduces the computational cost of CDMET with simpler bath states.And the result is as accurate as the original one.As a demonstration,we study the distant correlations of the Heisenberg J_(1)-J_(2)model on the square lattice.We find that the intermediate phase(0.43≤sssim J_(2)≤sssim 0.62)is divided into two parts.One part is a near-critical region(0.43≤J_(2)≤0.50).The other part is the plaquette valence bond solid(PVB)state(0.51≤J_(2)≤0.62).The spin correlations decay exponentially as a function of distance in the PVB.

Verification of the Validity of the NPT Treatment in Hereditary Spastic Paraplegia: An Investigation Performed by Application of Random Matrix Theory

We have applied the Random Matrix Theory in order to examine the validity of the NPT treatment in HSP. We have investigated the pathology examining the sEMG recorded signal for about eight minutes. We have performed standard electromyographic investigations as well as we have applied the RMT method of analysis. We have investigated the sEMG signals before and after the NPT treatment. The application of a so robust method as the RMT evidences that the NPT treatment was able to induce a net improvement of the disease respect to the pathological status before NPT.

Research on Power Quality Disturbance Signal Classification Based on Random Matrix Theory

In this paper, a method of power quality disturbance classification based on random matrix theory (RMT) is proposed. The method utilizes the power quality disturbance signal to construct a random matrix. By analyzing the mean spectral radius (MSR) variation of the random matrix, the type and time of occurrence of power quality disturbance are classified. In this paper, the random matrix theory is used to analyze the voltage sag, swell and interrupt perturbation signals to classify the occurrence time, duration of the disturbance signal and thedepth of voltage sag or swell. Examples show that the method has strong anti-noise ability.

A General(k,n)Threshold Secret Image Sharing Construction Based on Matrix Theory

Shamir proposed a classic polynomial-based secret sharing(SS)scheme,which is also widely applied in secret image sharing(SIS).However,the following researchers paid more attention to the development of properties,such as lossless recovery,rather than the principle of Shamir’s polynomial-based SS scheme.In this paper,we introduce matrix theory to analyze Shamir’s polynomial-based scheme as well as propose a general(k,n)threshold SIS construction based on matrix theory.Besides,it is proved that Shamir’s polynomial-based SS scheme is a special case of our construction method.Both experimental results and analyses are given to demonstrate the effectiveness of the proposed construction method.

Graph Theory and Matrix Approach(GTMA)Model for the Selec­tion of the Femoral-Component of Total Knee Joint Replacement

Total Knee Replacement(TKR)is the increasing trend now a day,in revision surgery which is associated with aseptic loosening,which is a challenging research for the TKR component.The selection of optimal material loosening can be controlled at some limits.This paper is going to consider the best material selected among a number of alternative materials for the femoral component(FC)by using Graph Theory.Here GTMA process used for optimization of material and a systematic technique introduced through sensitivity analysis to find out the more reliable result.Obtained ranking suggests the use of optimized material over the other existing material.By following GTMA Co_Cr-alloys(wrought-Co-Ni-Cr-Mo)and Co_Cr-alloys(cast-able-Co-Cr-Mo)are on the 1st and 2nd position respectively.

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory

Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.

Compressive Wideband Spectrum Sensing Based on Random Matrix Theory

Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.

Test of Resource Competition Theory Between Microalga and Macroalga Under Phosphate Limitation

Short_term batch cultures were used to measure the phosphate_dependent growth kinetics for a marine microalga, Tetraselmis subcordiformis (Wille) Hazen, and a marine macroalga, Ulva pertusa Kjellm. Results were fitted to the Monod model. U. pertusa had a lower half_saturation constant and maximum growth rate, which were 0.016 μmol/L and 0.16 d -1 respectively, while the growth kinetics of T. subcordiformis were 0.021 μmol/L and 0.83 d -1 . Long_term semicontinuous nutrient competition experiments were performed between T. subcordiformis and U. pertusa under phosphate limitation in laboratory. Loss rates were manipulated to get the same or different resource requirement values ( R * ) of the two species. Comparison between the theoretical predictions derived from Monod kinetics and the outcome of competition experiments indicated that the Monod model could predict the results only when the R * values of the two species were significantly different, and T. subcordiformis displaced U. pertusa when they had the same resource requirements. The Monod model can only partly predict the competition results between microalga and macroalga.

基于TRIZ冲突解决理论的老年用品可用性设计方法

为有效解决老年用品可用性设计中的冲突问题,将可用性与冲突解决理论融合,提出一种老年用品可用性设计方法。由于传统TRIZ参数对老年用品的不适用和模糊性,在老年用品的可用性设计中难以获得解决方案。从老年用品的可用性设计冲突入手,将TRIZ的工程参数筛选出老年可用性设计领域的26个专属可用性参数,采用灰色关联分析法对参数进行可用性分类,从感知层、认知层和执行层进行冲突矩阵的重构;建立了基于冲突解决理论的老年用品可用性设计过程模型,并应用于老年药盒的可用性设计实例。结果表明:文中方法能系统化地解决老年用品可用性设计中的冲突问题,使老年用品可用性设计方法和TRIZ的应用领域得到进一步拓展。

Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

基于RMT-CNN的电网短路故障定位研究

随着我国智能电网的快速发展,电网监测数据呈现多元化、高速化、海量化的趋势.为了充分挖掘电力大数据的潜在价值,实现电网内异常区域的自动识别与定位,本文研究了基于随机矩阵理论(random matrix theory,RMT)和卷积神经网络(convolutional neural networks,CNN)的电网异常事件定位方法.首先根据电网内部联系将电网划分为若干子系统,分区构建监测矩阵;然后采用RMT作为数据挖掘的特征提取方法,提取分区矩阵特征向量作为输入,根据电网监测数据和异常识别需求的特点搭建CNN模型;最后基于分区矩阵特征向量构建数据集,训练获得有效的异常事件自动定位CNN模型.以IEEE39节点电网模型三相短路故障为例,分析表明通过RMT提取特征向量的预处理方法能有效降低数据维度,提高CNN模型的故障定位准确率,分区RMT-CNN模型能有效定位电网内异常事件的发生地点,定位精度可达97.96%,精确率可达98.65%.

A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements.This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation.The graph framework of the synthesis approach is built firstly,and it involves:(1)the kinematic function units extracted from mechanisms;(2)the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain;(3)two graph representations,i.e.,walk representation and path representation,of design candidates;(4)a weighted matrix theorem that transforms the synthesis process into polynomial operation.Then,the formulas and algorithm to the polynomial operation are presented.Based on them,the computational flowchart to the synthesis approach is summarized.A design example is used to validate and illustrate the synthesis approach in detail.The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically,but also helpful to make that enumeration process computable.