Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4947

Search results for: correlation matrix

4947 Random Matrix Theory Analysis of Cross-Correlation in the Nigerian Stock Exchange

Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue


In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

Procedia PDF Downloads 256
4946 Efficient Antenna Array Beamforming with Robustness against Random Steering Mismatch

Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee


This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector

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4945 The Second Smallest Eigenvalue of Complete Tripartite Hypergraph

Authors: Alfi Y. Zakiyyah, Hanni Garminia, M. Salman, A. N. Irawati


In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.

Keywords: connectivity, graph, hypergraph, Laplacian matrix

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4944 Analysis of Cross-Correlations in Emerging Markets Using Random Matrix Theory

Authors: Thomas Chinwe Urama, Patrick Oseloka Ezepue, Peters Chimezie Nnanwa


This paper investigates the universal financial dynamics in two dominant stock markets in Sub-Saharan Africa, through an in-depth analysis of the cross-correlation matrix of price returns in Nigerian Stock Market (NSM) and Johannesburg Stock Exchange (JSE), for the period 2009 to 2013. The strength of correlations between stocks is known to be higher in JSE than that of the NSM. Particularly important for modelling Nigerian derivatives in the future, the interactions of other stocks with the oil sector are weak, whereas the banking sector has strong positive interactions with the other sectors in the stock exchange. For the JSE, it is the oil sector and beverages that have greater sectorial correlations, instead of the banks which have the weaker correlation with other sectors in the stock exchange.

Keywords: random matrix theory, cross-correlations, emerging markets, option pricing, eigenvalues eigenvectors, inverse participation ratios and implied volatility

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4943 Conditions on Expressing a Matrix as a Sum of α-Involutions

Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino


Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

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4942 Derivation of Bathymetry Data Using Worldview-2 Multispectral Images in Shallow, Turbid and Saline Lake Acıgöl

Authors: Muhittin Karaman, Murat Budakoglu


In this study, derivation of lake bathymetry was evaluated using the high resolution Worldview-2 multispectral images in the very shallow hypersaline Lake Acıgöl which does not have a stable water table due to the wet-dry season changes and industrial usage. Every year, a great part of the lake water budget has been consumed for the industrial salt production in the evaporation ponds, which are generally located on the south and north shores of Lake Acıgöl. Therefore, determination of the water level changes from a perspective of remote sensing-based lake water by bathymetry studies has a great importance in the sustainability-control of the lake. While the water table interval is around 1 meter between dry and wet season, dissolved ion concentration, salinity and turbidity also show clear differences during these two distinct seasonal periods. At the same time, with the satellite data acquisition (June 9, 2013), a field study was conducted to collect the salinity values, Secchi disk depths and turbidity levels. Max depth, Secchi disk depth and salinity were determined as 1,7 m, 0,9 m and 43,11 ppt, respectively. Eight-band Worldview-2 image was corrected for atmospheric effects by ATCOR technique. For each sampling point in the image, mean reflectance values in 1*1, 3*3, 5*5, 7*7, 9*9, 11*11, 13*13, 15*15, 17*17, 19*19, 21*21, 51*51 pixel reflectance neighborhoods were calculated separately. A unique image has been derivated for each matrix resolution. Spectral values and depth relation were evaluated for these distinct resolution images. Correlation coefficients were determined for the 1x1 matrix: 0,98, 0,96, 0,95 and 0,90 for the 724 nm, 831 nm, 908 nm and 659 nm, respectively. While 15x5 matrix characteristics with 0,98, 0,97 and 0,97 correlation values for the 724 nm, 908 nm and 831 nm, respectively; 51x51 matrix shows 0,98, 0,97 and 0,96 correlation values for the 724 nm, 831 nm and 659 nm, respectively. Comparison of all matrix resolutions indicates that RedEdge band (724 nm) of the Worldview-2 satellite image has the best correlation with the saline shallow lake of Acıgöl in-situ depth.

Keywords: bathymetry, Worldview-2 satellite image, ATCOR technique, Lake Acıgöl, Denizli, Turkey

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4941 Manufacturing and Characterization of Ni-Matrix Composite Reinforced with Ti3SiC2 and Ti2AlC; and Al-Matrix with Ti2SiC

Authors: M. Hadji, N. Chiker, Y. Hadji, A. Haddad


In this paper, we report for the first time on the synthesis and characterization of novel MAX phases (Ti3SiC2, Ti2AlC) reinforced Ni-matrix and Ti2AlC reinforced Al-matrix. The stability of MAX phases in Al-matrix and Ni-matrix at a temperature of 985°C has been investigated. All the composites were cold pressed and sintered at a temperature of 985°C for 20min in H2 environment, except (Ni/Ti3SiC2) who was sintered at 1100°C for 1h.Microstructure analysis by scanning electron microscopy and phase analysis by X-Ray diffraction confirmed that there was minimal interfacial reaction between MAX particles and Ni, thus Al/MAX samples shown that MAX phases was totally decomposed at 985°C.The Addition of MAX enhanced the Al-matrix and Ni-matrix.

Keywords: MAX phase, microstructures, composites, hardness, SEM

Procedia PDF Downloads 241
4940 Inverse Matrix in the Theory of Dynamical Systems

Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova


In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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4939 Choosing between the Regression Correlation, the Rank Correlation, and the Correlation Curve

Authors: Roger L. Goodwin


This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, "first-glance" correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve

Procedia PDF Downloads 365
4938 Testing the Change in Correlation Structure across Markets: High-Dimensional Data

Authors: Malay Bhattacharyya, Saparya Suresh


The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

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4937 Relationship between Matrix Metalloproteases and Tissue Inhibitor of Matrix Metalloproteinase Levels and Elastic Moduli of Ascending Aneurysms

Authors: Khalil Khanafer


The objective of this study is to determine if there is a correlation between the biological levels of matrix metalloproteinases and tissue inhibitor of matrix metalloproteinase (TIMP) and the elastic moduli of the ascending aortic wall in patients with ascending thoracic aortic aneurysms (ATAA). Methods: Circumferential specimens from twelve patients with ATAA were obtained from the greater curvature, and their tensile properties (maximum elastic modulus) were tested uniaxially. The levels of MMP2, 3, and 9, as well as TIMP1, were determined in these aortic wall specimens using MMP/TIMP antibodies array. Direct relations were found between MMP2 and the elastic modulus of the ascending aorta wall and between MMP9 and TIMP1.

Keywords: elastic modulus, MMPs/TIMPs levels, Ascending Thoracic Aortic Aneurysm

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4936 On Block Vandermonde Matrix Constructed from Matrix Polynomial Solvents

Authors: Malika Yaici, Kamel Hariche


In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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4935 Interaction of Vegetable Fillers with Polyethylene Matrix in Biocomposites

Authors: P. V. Pantyukhov, T. V. Monakhova, A. A. Popov


The paper studies the diffusion of low molecular weight components from vegetable fillers into polyethylene matrix during the preparation of biocomposites. In order to identify the diffusible substances a model experiment used where the hexadecane acted as a model of polyethylene. It was determined that polyphenolic compounds and chlorophyll penetrate from vegetable fillers to hexadecane to the maximum extent. There was found a correlation between the amount of polyphenolic compounds diffusible from the fillers to hexadecane and thermal oxidation kinetics of real biocomposites based on polyethylene and vegetable fillers. Thus, it has been assumed the diffusion of polyphenols and chlorophyll from vegetable fillers into polyethylene matrix during the preparation of biocomposites.

Keywords: biocomposite, composite, diffusion, polyethylene, vegetable filler

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4934 Spatial and Geostatistical Analysis of Surficial Soils of the Contiguous United States

Authors: Rachel Hetherington, Chad Deering, Ann Maclean, Snehamoy Chatterjee


The U.S. Geological Survey conducted a soil survey and subsequent mineralogical and geochemical analyses of over 4800 samples taken across the contiguous United States between the years 2007 and 2013. At each location, samples were taken from the top 5 cm, the A-horizon, and the C-horizon. Many studies have looked at the correlation between the mineralogical and geochemical content of soils and influencing factors such as parent lithology, climate, soil type, and age, but it seems little has been done in relation to quantifying and assessing the correlation between elements in the soil on a national scale. GIS was used for the mapping and multivariate interpolation of over 40 major and trace elements for surficial soils (0-5 cm depth). Qualitative analysis of the spatial distribution across the U.S. shows distinct patterns amongst elements both within the same periodic groups and within different periodic groups, and therefore with different behavioural characteristics. Results show the emergence of 4 main patterns of high concentration areas: vertically along the west coast, a C-shape formed through the states around Utah and northern Arizona, a V-shape through the Midwest and connecting to the Appalachians, and along the Appalachians. The Band Collection Statistics tool in GIS was used to quantitatively analyse the geochemical raster datasets and calculate a correlation matrix. Patterns emerged, which were not identified in qualitative analysis, many of which are also amongst elements with very different characteristics. Preliminary results show 41 element pairings with a strong positive correlation ( ≥ 0.75). Both qualitative and quantitative analyses on this scale could increase knowledge on the relationships between element distribution and behaviour in surficial soils of the U.S.

Keywords: correlation matrix, geochemical analyses, spatial distribution of elements, surficial soils

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4933 Adaptive Beamforming with Steering Error and Mutual Coupling between Antenna Sensors

Authors: Ju-Hong Lee, Ching-Wei Liao


Owing to close antenna spacing between antenna sensors within a compact space, a part of data in one antenna sensor would outflow to other antenna sensors when the antenna sensors in an antenna array operate simultaneously. This phenomenon is called mutual coupling effect (MCE). It has been shown that the performance of antenna array systems can be degraded when the antenna sensors are in close proximity. Especially, in a systems equipped with massive antenna sensors, the degradation of beamforming performance due to the MCE is significantly inevitable. Moreover, it has been shown that even a small angle error between the true direction angle of the desired signal and the steering angle deteriorates the effectiveness of an array beamforming system. However, the true direction vector of the desired signal may not be exactly known in some applications, e.g., the application in land mobile-cellular wireless systems. Therefore, it is worth developing robust techniques to deal with the problem due to the MCE and steering angle error for array beamforming systems. In this paper, we present an efficient technique for performing adaptive beamforming with robust capabilities against the MCE and the steering angle error. Only the data vector received by an antenna array is required by the proposed technique. By using the received array data vector, a correlation matrix is constructed to replace the original correlation matrix associated with the received array data vector. Then, the mutual coupling matrix due to the MCE on the antenna array is estimated through a recursive algorithm. An appropriate estimate of the direction angle of the desired signal can also be obtained during the recursive process. Based on the estimated mutual coupling matrix, the estimated direction angle, and the reconstructed correlation matrix, the proposed technique can effectively cure the performance degradation due to steering angle error and MCE. The novelty of the proposed technique is that the implementation procedure is very simple and the resulting adaptive beamforming performance is satisfactory. Simulation results show that the proposed technique provides much better beamforming performance without requiring complicated complexity as compared with the existing robust techniques.

Keywords: adaptive beamforming, mutual coupling effect, recursive algorithm, steering angle error

Procedia PDF Downloads 249
4932 A Comparative Study on Indian and Greek Cotton Fiber Properties Correlations

Authors: Md. Nakib Ul Hasan, Md. Ariful Islam, Md. Sumon Miah, Misbah Ul Hoque, Bulbul Ahmed


The variability of cotton fiber characteristics has always been influenced by origin, weather conditions, method of culturing, and harvesting. Spinners work tirelessly to ensure consistent yarn quality by using the different origins of fibers to maximizes the profit margin. Spinners often fail to select desired raw materials of various origins to achieve an appropriate mixing plan due to the lack of knowledge on the interrelationship among fiber properties. The purpose of this research is to investigate the correlations among dominating fiber properties such as micronaire, strength, breaking elongation, upper half mean length, length uniformity index, short fiber index, maturity, reflectance, and yellowness. For this purpose, fiber samples from 500 Indian cotton bales and 350 Greek cotton bales were collected and tested using the high volume instrument (HVI). The fiber properties dataset was then compiled and analyzed using python 3.7 to determine the correlations matrix. Results show that Indian cotton fiber have highest correlation between strength-mat = 0.84, followed by SFI-Unf =-0.83, and Neps-Unf = -0.72. Greek cotton fiber, in contrast, have highest correlation between SFI-Unf =-0.98, followed by SFI-Mat = 0.89, +b-Len = 0.84, and Str-Mat = 0.74. Overall, the Greek cotton fiber showed a higher correlational matrix than compared to that of Indian cotton fiber.

Keywords: cotton fiber, fiber properties correlation, Greek cotton, HVI, Indian cotton, spinning

Procedia PDF Downloads 72
4931 On Direct Matrix Factored Inversion via Broyden's Updates

Authors: Adel Mohsen


A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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4930 A Review on Aluminium Metal Matric Composites

Authors: V. Singh, S. Singh, S. S. Garewal


Metal matrix composites with aluminum as the matrix material have been heralded as the next great development in advanced engineering materials. Aluminum metal matrix composites (AMMC) refer to the class of light weight high performance material systems. Properties of AMMCs can be tailored to the demands of different industrial applications by suitable combinations of matrix, reinforcement and processing route. AMMC finds its application in automotive, aerospace, defense, sports and structural areas. This paper presents an overview of AMMC material systems on aspects relating to processing, types and applications with case studies.

Keywords: aluminum metal matrix composites, applications of aluminum metal matrix composites, lighting material processing of aluminum metal matrix composites

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4929 An Adaptive Dimensionality Reduction Approach for Hyperspectral Imagery Semantic Interpretation

Authors: Akrem Sellami, Imed Riadh Farah, Basel Solaiman


With the development of HyperSpectral Imagery (HSI) technology, the spectral resolution of HSI became denser, which resulted in large number of spectral bands, high correlation between neighboring, and high data redundancy. However, the semantic interpretation is a challenging task for HSI analysis due to the high dimensionality and the high correlation of the different spectral bands. In fact, this work presents a dimensionality reduction approach that allows to overcome the different issues improving the semantic interpretation of HSI. Therefore, in order to preserve the spatial information, the Tensor Locality Preserving Projection (TLPP) has been applied to transform the original HSI. In the second step, knowledge has been extracted based on the adjacency graph to describe the different pixels. Based on the transformation matrix using TLPP, a weighted matrix has been constructed to rank the different spectral bands based on their contribution score. Thus, the relevant bands have been adaptively selected based on the weighted matrix. The performance of the presented approach has been validated by implementing several experiments, and the obtained results demonstrate the efficiency of this approach compared to various existing dimensionality reduction techniques. Also, according to the experimental results, we can conclude that this approach can adaptively select the relevant spectral improving the semantic interpretation of HSI.

Keywords: band selection, dimensionality reduction, feature extraction, hyperspectral imagery, semantic interpretation

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4928 Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel

Authors: Seok Min Choi, Minho Bang, Seuong Yun Kim, Hyungmin Lee, Won-Gu Joo, Hyung Hee Cho


The matrix cooling channel was used for gas turbine blade cooling passage. The matrix cooling structure is useful for the structure stability however the cooling performance of internal cooling channel was not enough for cooling. Therefore, we designed the rib configurations in the matrix cooling channel to enhance the cooling performance. The numerical simulation was conducted to analyze cooling performance of rib configured matrix cooling channel. Three different rib configurations were used which are vertical rib, angled rib and c-type rib. Three configurations were adopted in two positions of matrix cooling channel which is one fourth and three fourth of channel. The result shows that downstream rib has much higher cooling performance than upstream rib. Furthermore, the angled rib in the channel has much higher cooling performance than vertical rib. This is because; the angled rib improves the swirl effect of matrix cooling channel more effectively. The friction factor was increased with the installation of rib. However, the thermal performance was increased with the installation of rib in the matrix cooling channel.

Keywords: matrix cooling, rib, heat transfer, gas turbine

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4927 Parallel Computation of the Covariance-Matrix

Authors: Claude Tadonki


We address the issues related to the computation of the covariance matrix. This matrix is likely to be ill conditioned following its canonical expression, thus consequently raises serious numerical issues. The underlying linear system, which therefore should be solved by means of iterative approaches, becomes computationally challenging. A huge number of iterations is expected in order to reach an acceptable level of convergence, necessary to meet the required accuracy of the computation. In addition, this linear system needs to be solved at each iteration following the general form of the covariance matrix. Putting all together, its comes that we need to compute as fast as possible the associated matrix-vector product. This is our purpose in the work, where we consider and discuss skillful formulations of the problem, then propose a parallel implementation of the matrix-vector product involved. Numerical and performance oriented discussions are provided based on experimental evaluations.

Keywords: covariance-matrix, multicore, numerical computing, parallel computing

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4926 Texture Analysis of Grayscale Co-Occurrence Matrix on Mammographic Indexed Image

Authors: S. Sushma, S. Balasubramanian, K. C. Latha


The mammographic image of breast cancer compressed and synthesized to get co-efficient values which will be converted (5x5) matrix to get ROI image where we get the highest value of effected region and with the same ideology the technique has been extended to differentiate between Calcification and normal cell image using mean value derived from 5x5 matrix values

Keywords: texture analysis, mammographic image, partitioned gray scale co-oocurance matrix, co-efficient

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4925 Redundancy Component Matrix and Structural Robustness

Authors: Xinjian Kou, Linlin Li, Yongju Zhou, Jimian Song


We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

Keywords: Structural Robustness, Structural Reliability, Redundancy Component, Redundancy Matrix

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4924 Multiple Images Stitching Based on Gradually Changing Matrix

Authors: Shangdong Zhu, Yunzhou Zhang, Jie Zhang, Hang Hu, Yazhou Zhang


Image stitching is a very important branch in the field of computer vision, especially for panoramic map. In order to eliminate shape distortion, a novel stitching method is proposed based on gradually changing matrix when images are horizontal. For images captured horizontally, this paper assumes that there is only translational operation in image stitching. By analyzing each parameter of the homography matrix, the global homography matrix is gradually transferred to translation matrix so as to eliminate the effects of scaling, rotation, etc. in the image transformation. This paper adopts matrix approximation to get the minimum value of the energy function so that the shape distortion at those regions corresponding to the homography can be minimized. The proposed method can avoid multiple horizontal images stitching failure caused by accumulated shape distortion. At the same time, it can be combined with As-Projective-As-Possible algorithm to ensure precise alignment of overlapping area.

Keywords: image stitching, gradually changing matrix, horizontal direction, matrix approximation, homography matrix

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4923 Matrix Method Posting

Authors: Varong Pongsai


The objective of this paper is introducing a new method of accounting posting which is called Matrix Method Posting. This method is based on the Matrix operation of pure Mathematics. Although, accounting field is classified as one of the social-science knowledge, many of accounting operations are placed by Mathematics sign and operation. Through the operation applying, it seems to be that the operations of Mathematics should be applied to accounting possibly. So, this paper tries to over-lap Mathematics logic to accounting logic smoothly. According to the context of discovery, deductive approach is employed to prove a simultaneously logical concept of both Mathematics and Accounting. The result proves that the Matrix can be placed to operate accounting perfectly, because Matrix and accounting logic also have a similarity concept which is balancing 2 sides during operations. Moreover, the Matrix posting also has a lot of benefit. It can help financial analyst calculating financial ratios comfortably. Furthermore, the matrix determinant which is a signature operation itself also helps auditors checking out the correction of clients’ recording. If the determinant is not equaled to 0, it will point out that the recording process of clients getting into the problem. Finally, the Matrix should be easily determining a concept of merger and consolidation far beyond the present day concept.

Keywords: matrix method posting, deductive approach, determinant, accounting application

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4922 Effects of the Mass and Damping Matrix Model in the Non-Linear Seismic Response of Steel Frames

Authors: Alfredo Reyes-Salazar, Mario D. Llanes-Tizoc, Eden Bojorquez, Federico Valenzuela-Beltran, Juan Bojorquez, Jose R. Gaxiola-Camacho, Achintya Haldar


Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated with lateral vibrations are commonly used to develop matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the non-linear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead of the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment-resisting steel frames and that the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: moment-resisting steel frames, consistent and concentrated mass matrices, non-linear seismic response, Rayleigh damping

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4921 Student Loan Debt among Students with Disabilities

Authors: Kaycee Bills


This study will determine if students with disabilities have higher student loan debt payments than other student populations. The hypothesis was that students with disabilities would have significantly higher student loan debt payments than other students due to the length of time they spend in school. Using the Bachelorette and Beyond Study Wave 2015/017 dataset, quantitative methods were employed. These data analysis methods included linear regression and a correlation matrix. Due to the exploratory nature of the study, the significance levels for the overall model and each variable were set at .05. The correlation matrix demonstrated that students with certain types of disabilities are more likely to fall under higher student loan payment brackets than students without disabilities. These results also varied among the different types of disabilities. The result of the overall linear regression model was statistically significant (p = .04). Despite the overall model being statistically significant, the majority of the significance values for the different types of disabilities were null. However, several other variables had statistically significant results, such as veterans, people of minority races, and people who attended private schools. Implications for how this impacts the economy, capitalism, and financial wellbeing of various students are discussed.

Keywords: disability, student loan debt, higher education, social work

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4920 Corrosion Characterization of Al6061, Quartz Metal Matrix Composites in Alkali Medium

Authors: Radha H. R., Krupakara P. V.


Metal matrix composites are attracting today's manufacturers of many automobile parts so that they lost longer and their properties can be tailored according to the requirement. In this paper an attempt has been made to study the corrosion characteristics of Aluminium 6061 / quartz metal matrix composites in alkali medium like sodium hydroxide solutions. Metal matrix composites are heterogeneous mixtures of a matrix and reinforcement. In this work the matrix selected is Aluminium 6061 alloy which is commercially available and the reinforcement selected is quartz particulates of 50-80 micron size which is available in plenty in and around Bangalore district, India. Composites containing Aluminium 6061 with 2, 4 and 6 weight percent of quartz are manufactured by liquid melt metallurgy technique using vortex method. Corrosion tests like static weight loss and open circuit potential tests are conducted in different concentrated solutions of sodium hydroxide. To compare the results the matrix Aluminium 6061 is also casted in the same way. Specimens for the test are prepared according to ASTM standards. In all the tests the metal matrix composites showed better corrosion resistance than matrix alloy.

Keywords: aluminium 6061, corrosion, quartz, vortex

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4919 Membership Surface and Arithmetic Operations of Imprecise Matrix

Authors: Dhruba Das


In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: imprecise number, imprecise vector, membership surface, imprecise matrix

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4918 Corrosion Characterization of Al6061 Hybrid Metal Matrix Composites in Acid Medium

Authors: P. V. Krupakara


This paper deals with the high corrosion resistance developed by the hybrid metal matrix composites when compared with that of matrix alloy. Matrix selected is Al6061. Reinforcements selected are graphite and red mud particulates. The composites are prepared using liquid melt metallurgy technique using vortex method. Metal matrix composites containing 2 percent graphite and 2 percent red mud, 2 percent graphite and 4 percent red mud, 2 percent graphite and 6 percent of red mud are prepared. Bar castings are cut into cylindrical discs of 20mm diameter and 20mm thickness. Corrosion tests were conducted at room temperature (230 °C) using conventional weight loss method according to ASTM G69-80. The corrodents used for the test were hydrochloric acid solution of different concentrations. Specimens were tested for every 24 hours interval up to 96 hours. Four specimens for each condition and time were immersed in corrodent. In each case the corrosion rate decreases with increase in exposure time for matrix and metal matrix composites whatever may be the concentration of hydrochloric acid. This may be due to aluminium, which may induce passivation due to development of non-porous layer. As red mud content increases the composites become corrosion resistant due to insulating nature of ceramic material red mud and less exposure of matrix alloy in those metal matrix composites.

Keywords: Al6061, graphite, passivation, red mud, vortex

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