• Title/Summary/Keyword: Random matrix theory

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A Random Matrix Theory approach to correlation matrix in Korea Stock Market (확률행렬이론을 이용한 한국주식시장의 상관행렬 분석)

  • Kim, Geon-Woo;Lee, Sung-Chul
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.4
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    • pp.727-733
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    • 2011
  • To understand the stock market structure it is very important to extract meaningful information by analyzing the correlation matrix between stock returns. Recently there has been many studies on the correlation matrix using the Random Matrix Theory. In this paper we adopt this random matrix methodology to a single-factor model and we obtain meaningful information on the correlation matrix. In particular we observe the analysis of the correlation matrix using the single-factor model explains the real market data and as a result we confirm the usefulness of the single-factor model.

Uncertainty reaction force model of ship stern bearing based on random theory and improved transition matrix method

  • Zhang, Sheng dong;Liu, Zheng lin
    • Ocean Systems Engineering
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    • v.6 no.2
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    • pp.191-201
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    • 2016
  • Stern bearing is a key component of marine propulsion plant. Its environment is diverse, working condition changeable, and condition severe, so that stern bearing load is of strong time variability, which directly affects the safety and reliability of the system and the normal navigation of ships. In this paper, three affecting factors of the stern bearing load such as hull deformation, propeller hydrodynamic vertical force and bearing wear are calculated and characterized by random theory. The uncertainty mathematical model of stern bearing load is established to research the relationships between factors and uncertainty load of stern bearing. The validity of calculation mathematical model and results is verified by examples and experiment yet. Therefore, the research on the uncertainty load of stern bearing has important theoretical significance and engineering practical value.

ASSVD: Adaptive Sparse Singular Value Decomposition for High Dimensional Matrices

  • Ding, Xiucai;Chen, Xianyi;Zou, Mengling;Zhang, Guangxing
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.14 no.6
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    • pp.2634-2648
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    • 2020
  • In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

Applying the Nash Equilibrium to Constructing Covert Channel in IoT

  • Ho, Jun-Won
    • International Journal of Internet, Broadcasting and Communication
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    • v.13 no.1
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    • pp.243-248
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    • 2021
  • Although many different types of covert channels have been suggested in the literature, there are little work in directly applying game theory to building up covert channel. This is because researchers have mainly focused on tailoring game theory for covert channel analysis, identification, and covert channel problem solving. Unlike typical adaptation of game theory to covert channel, we show that game theory can be utilized to establish a new type of covert channel in IoT devices. More specifically, we propose a covert channel that can be constructed by utilizing the Nash Equilibrium with sensor data collected from IoT devices. For covert channel construction, we set random seed to the value of sensor data and make payoff from random number created by running pseudo random number generator with the configured random seed. We generate I × J (I ≥ 2, J ≥ 2) matrix game with these generated payoffs and attempt to obtain the Nash Equilibrium. Covert channel construction method is distinctly determined in accordance with whether or not to acquire the Nash Equilibrium.

3D Beamforming Techniques in Multi-Cell MISO Downlink Active Antenna Systems for Large Data Transmission (대용량 데이터 전송을 위한 다중 셀 MISO 하향 능동 안테나 시스템에서 3D 빔포밍 기법)

  • Kim, Taehoon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.40 no.11
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    • pp.2298-2304
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    • 2015
  • In this paper, we provide a new approach which optimizes the vertical tilting angle of the base station for multi-cell multiple-input single-output (MISO) downlink active antenna systems (AAS). Instead of the conventional optimal algorithm which requires an exhaustive search, we propose simple and near optimal algorithms. First, we represent a large system approximation based vertical beamforming algorithm which is applied to the average sum rate by using the random matrix theory. Next, we suggest a signal-to-leakage-and-noise ratio (SLNR) based vertical beamforming algorithm which simplifies the optimization problem considerably. In the simulation results, we demonstrate that the performance of the proposed algorithms is near close to the exhaustive search algorithm with substantially reduced complexity.

Predicting stock movements based on financial news with systematic group identification (시스템적인 군집 확인과 뉴스를 이용한 주가 예측)

  • Seong, NohYoon;Nam, Kihwan
    • Journal of Intelligence and Information Systems
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    • v.25 no.3
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    • pp.1-17
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    • 2019
  • Because stock price forecasting is an important issue both academically and practically, research in stock price prediction has been actively conducted. The stock price forecasting research is classified into using structured data and using unstructured data. With structured data such as historical stock price and financial statements, past studies usually used technical analysis approach and fundamental analysis. In the big data era, the amount of information has rapidly increased, and the artificial intelligence methodology that can find meaning by quantifying string information, which is an unstructured data that takes up a large amount of information, has developed rapidly. With these developments, many attempts with unstructured data are being made to predict stock prices through online news by applying text mining to stock price forecasts. The stock price prediction methodology adopted in many papers is to forecast stock prices with the news of the target companies to be forecasted. However, according to previous research, not only news of a target company affects its stock price, but news of companies that are related to the company can also affect the stock price. However, finding a highly relevant company is not easy because of the market-wide impact and random signs. Thus, existing studies have found highly relevant companies based primarily on pre-determined international industry classification standards. However, according to recent research, global industry classification standard has different homogeneity within the sectors, and it leads to a limitation that forecasting stock prices by taking them all together without considering only relevant companies can adversely affect predictive performance. To overcome the limitation, we first used random matrix theory with text mining for stock prediction. Wherever the dimension of data is large, the classical limit theorems are no longer suitable, because the statistical efficiency will be reduced. Therefore, a simple correlation analysis in the financial market does not mean the true correlation. To solve the issue, we adopt random matrix theory, which is mainly used in econophysics, to remove market-wide effects and random signals and find a true correlation between companies. With the true correlation, we perform cluster analysis to find relevant companies. Also, based on the clustering analysis, we used multiple kernel learning algorithm, which is an ensemble of support vector machine to incorporate the effects of the target firm and its relevant firms simultaneously. Each kernel was assigned to predict stock prices with features of financial news of the target firm and its relevant firms. The results of this study are as follows. The results of this paper are as follows. (1) Following the existing research flow, we confirmed that it is an effective way to forecast stock prices using news from relevant companies. (2) When looking for a relevant company, looking for it in the wrong way can lower AI prediction performance. (3) The proposed approach with random matrix theory shows better performance than previous studies if cluster analysis is performed based on the true correlation by removing market-wide effects and random signals. The contribution of this study is as follows. First, this study shows that random matrix theory, which is used mainly in economic physics, can be combined with artificial intelligence to produce good methodologies. This suggests that it is important not only to develop AI algorithms but also to adopt physics theory. This extends the existing research that presented the methodology by integrating artificial intelligence with complex system theory through transfer entropy. Second, this study stressed that finding the right companies in the stock market is an important issue. This suggests that it is not only important to study artificial intelligence algorithms, but how to theoretically adjust the input values. Third, we confirmed that firms classified as Global Industrial Classification Standard (GICS) might have low relevance and suggested it is necessary to theoretically define the relevance rather than simply finding it in the GICS.

Random Matrix Theory 방법에 의하여 분해된 상관행렬의 속성 연구: 주식 네트워크와의 결합.검증

  • Eom, Cheol-Jun;O, Gap-Jin;Park, Jong-Won
    • The Korean Journal of Financial Studies
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    • v.14 no.1
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    • pp.83-96
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    • 2008
  • 본 연구는 Random Matrix Theory(RMT)방법에 의하여 분해된 상관행렬이 원래 주식간 상호작용을 충분히 반영하고 있는지 여부를 Mantegna(1999)에 의하여 제안된 주식 네트워크와 실증적으로 결합 검증하였다. 분석결과에 의하면, RMT 방법으로 분해된 상관행렬을 주식 네트워크와 결합하였을 때, 분해된 상관행렬은 주식간 상호작용에서 의미 있는 요인들의 속성을 적절히 반영하고 있다는 것을 실증적으로 확인할 수 있었다. 이러한 결과를 통하여, 주식간 상호작용을 계량화한 상관행렬을 RMT방법에 의하여 특정 속성을 갖는 상관행렬로 분해하여 재무이론과 결합 검증한다면, 주식간 상호작용을 보다 잘 이해하는데 유용한 방법이 될 수 있음을 확인하였다.

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HAMILTONIANS IN STEINHAUS GRAPHS

  • Lim, Dae-Keun;Kim, Hye-Kyung
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1137-1145
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    • 1996
  • A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

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Numerical and statistical analysis of permeability of concrete as a random heterogeneous composite

  • Zhou, Chunsheng;Li, Kefei
    • Computers and Concrete
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    • v.7 no.5
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    • pp.469-482
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    • 2010
  • This paper investigates the concrete permeability through a numerical and statistical approach. Concrete is considered as a random heterogeneous composite of three phases: aggregates, interfacial transition zones (ITZ) and matrix. The paper begins with some classical bound and estimate theories applied to concrete permeability and the influence of ITZ on these bound and estimate values is discussed. Numerical samples for permeability analysis are established through random aggregate structure (RAS) scheme, each numerical sample containing randomly distributed aggregates coated with ITZ and dispersed in a homogeneous matrix. The volumetric fraction of aggregates is fixed and the size distribution of aggregates observes Fuller's curve. Then finite element method is used to solve the steady permeation problem on 2D numerical samples and the overall permeability is deduced from flux-pressure relation. The impact of ITZ on overall permeability is analyzed in terms of ITZ width and contrast ratio between ITZ and matrix permeabilities. Hereafter, 3680 samples are generated for 23 sample sizes and 4 contrast ratios, and statistical analysis is performed on the permeability dispersion in terms of sample size and ITZ characteristics. By sample theory, the size of representative volume element (RVE) for permeability is then quantified considering sample realization number and expected error. Concluding remarks are provided for the impact of ITZ on concrete permeability and its statistical characteristics.

Using 3D theory of elasticity for free vibration analysis of functionally graded laminated nanocomposite shells

  • R. Bina;M. Soltani Tehrani;A. Ahmadi;A. Ghanim Taki;R. Akbarian
    • Steel and Composite Structures
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    • v.52 no.4
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    • pp.487-499
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    • 2024
  • The primary objective of this study is to analyze the free vibration behavior of a sandwich cylindrical shell with a defective core and wavy carbon nanotube (CNT)-enhanced face sheets, utilizing the three-dimensional theory of elasticity. The intricate equations of motion for the structure are solved semi-analytically using the generalized differential quadrature method. The shell structure consists of a damaged isotropic core and two external face sheets. The distributions of CNTs are either functionally graded (FG) or uniform across the thickness, with their mechanical properties determined through an extended rule of mixture. In this research, the conventional theory regarding the mechanical effectiveness of a matrix embedding finite-length fibers has been enhanced by introducing tube-to-tube random contact. This enhancement explicitly addresses the progressive reduction in the tubes' effective aspect ratio as the filler content increases. The study investigates the influence of a damaged matrix, CNT distribution, volume fraction, aspect ratio, and waviness on the free vibration characteristics of the sandwich cylindrical shell with wavy CNT-reinforced face sheets. Unlike two-dimensional theories such as classical and the first shear deformation plate theories, this inquiry is grounded in the three-dimensional theory of elasticity, which comprehensively accounts for transverse normal deformations.