Search results for: large sparse parameter–dependent matrices

Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: Gülnihal Meral

Abstract:

In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.

Keywords: Density Dependent Nonlinear Reaction-Diffusion Equation, Differential Quadrature Method, Implicit Euler Method.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

Abstract:

A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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Authors: Jin Sung Kim, Hoon Huh

Abstract:

The material properties of OFHC copper film was investigated with the High-Speed Material Micro Testing Machine (HSMMTM) at the high strain rates. The rate-dependent stress-strain curves from the experiment and the Johnson−Cook curve fitting showed large discrepancies as the plastic strain increases since the constitutive model implies no rate-dependent strain hardening effect. A new constitutive model was proposed in consideration of rate-dependent strain hardening effect. The strain rate hardening term in the new constitutive model consists of the strain rate sensitivity coefficients of the yield strength and strain hardening.

Keywords: Rate dependent material properties, Dynamic constitutive model, OFHC copper film, Strain rate.

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Authors: Fanqiang Kong, Chending Bian

Abstract:

In this work, we exploit two assumed properties of the abundances of the observed signatures (endmembers) in order to reconstruct the abundances from hyperspectral data. Joint-sparsity is the first property of the abundances, which assumes the adjacent pixels can be expressed as different linear combinations of same materials. The second property is rank-deficiency where the number of endmembers participating in hyperspectral data is very small compared with the dimensionality of spectral library, which means that the abundances matrix of the endmembers is a low-rank matrix. These assumptions lead to an optimization problem for the sparse unmixing model that requires minimizing a combined l_2,p-norm and nuclear norm. We propose a variable splitting and augmented Lagrangian algorithm to solve the optimization problem. Experimental evaluation carried out on synthetic and real hyperspectral data shows that the proposed method outperforms the state-of-the-art algorithms with a better spectral unmixing accuracy.

Keywords: Hyperspectral unmixing, joint-sparse, low-rank representation, abundance estimation.

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Authors: Yoonsuh Jung

Abstract:

As DNA microarray data contain relatively small sample size compared to the number of genes, high dimensional models are often employed. In high dimensional models, the selection of tuning parameter (or, penalty parameter) is often one of the crucial parts of the modeling. Cross-validation is one of the most common methods for the tuning parameter selection, which selects a parameter value with the smallest cross-validated score. However, selecting a single value as an ‘optimal’ value for the parameter can be very unstable due to the sampling variation since the sample sizes of microarray data are often small. Our approach is to choose multiple candidates of tuning parameter first, then average the candidates with different weights depending on their performance. The additional step of estimating the weights and averaging the candidates rarely increase the computational cost, while it can considerably improve the traditional cross-validation. We show that the selected value from the suggested methods often lead to stable parameter selection as well as improved detection of significant genetic variables compared to the tradition cross-validation via real data and simulated data sets.

Keywords: Cross Validation, Parameter Averaging, Parameter Selection, Regularization Parameter Search.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

The effect of different combinations of response feedback on the performance of active control system on nonlinear frames has been studied in this paper. To this end different feedback combinations including displacement, velocity, acceleration and full response feedback have been utilized in controlling the response of an eight story bilinear hysteretic frame which has been subjected to a white noise excitation and controlled by eight actuators which could fully control the frame. For active control of nonlinear frame Newmark nonlinear instantaneous optimal control algorithm has been used which a diagonal matrix has been selected for weighting matrices in performance index. For optimal design of active control system while the objective has been to reduce the maximum drift to below the yielding level, Distributed Genetic Algorithm (DGA) has been used to determine the proper set of weighting matrices. The criteria to assess the effect of each combination of response feedback have been the minimum required control force to reduce the maximum drift to below the yielding drift. The results of numerical simulation show that the performance of active control system is dependent on the type of response feedback where the velocity feedback is more effective in designing optimal control system in comparison with displacement and acceleration feedback. Also using full feedback of response in controller design leads to minimum control force amongst other combinations. Also the distributed genetic algorithm shows acceptable convergence speed in solving the optimization problem of designing active control systems.

Keywords: Active control, Distributed genetic algorithms, Response feedback, Weighting matrices.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: D. Mirauda, M. Greco, A. Volpe Plantamura

Abstract:

The necessity of updating the numerical models inputs, because of geometrical and resistive variations in rivers subject to solid transport phenomena, requires detailed control and monitoring activities. The human employment and financial resources of these activities moves the research towards the development of expeditive methodologies, able to evaluate the outflows through the measurement of more easily acquirable sizes. Recent studies highlighted the dependence of the entropic parameter on the kinematical and geometrical flow conditions. They showed a meaningful variability according to the section shape, dimension and slope. Such dependences, even if not yet well defined, could reduce the difficulties during the field activities, and also the data elaboration time. On the basis of such evidences, the relationships between the entropic parameter and the geometrical and resistive sizes, obtained through a large and detailed laboratory experience on steady free surface flows in conditions of macro and intermediate homogeneous roughness, are analyzed and discussed.

Keywords: Froude number, entropic parameter, roughness, water discharge.

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Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang

Abstract:

In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.

Keywords: Quaternionic matrix, left spectrum, linear preserver map.

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Pan Long, Bi Dongjie, Li Xifeng, Xie Yongle

Abstract:

The near-field synthetic aperture radar (SAR) imaging is an advanced nondestructive testing and evaluation (NDT&E) technique. This paper investigates the complex-valued signal processing related to the near-field SAR imaging system, where the measurement data turns out to be noncircular and improper, meaning that the complex-valued data is correlated to its complex conjugate. Furthermore, we discover that the degree of impropriety of the measurement data and that of the target image can be highly correlated in near-field SAR imaging. Based on these observations, A modified generalized sparse Bayesian learning algorithm is proposed, taking impropriety and noncircularity into account. Numerical results show that the proposed algorithm provides performance gain, with the help of noncircular assumption on the signals.

Keywords: Complex-valued signal processing, synthetic aperture radar (SAR), 2-D radar imaging, compressive sensing, Sparse Bayesian learning.

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

Abstract:

Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals.

Keywords: Compressed sensing, Lest Support Orthogonal Matching Pursuit, Partial Knowing Support, Restricted isometry property, signal reconstruction.

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Authors: Razvan Bocu, Dr Sabin Tabirca

Abstract:

The study of proteomics reached unexpected levels of interest, as a direct consequence of its discovered influence over some complex biological phenomena, such as problematic diseases like cancer. This paper presents the latest authors- achievements regarding the analysis of the networks of proteins (interactome networks), by computing more efficiently the betweenness centrality measure. The paper introduces the concept of betweenness centrality, and then describes how betweenness computation can help the interactome net- work analysis. Current sequential implementations for the between- ness computation do not perform satisfactory in terms of execution times. The paper-s main contribution is centered towards introducing a speedup technique for the betweenness computation, based on modified shortest path algorithms for sparse graphs. Three optimized generic algorithms for betweenness computation are described and implemented, and their performance tested against real biological data, which is part of the IntAct dataset.

Keywords: Betweenness centrality, interactome networks, protein-protein interactions, sub-communities, sparse networks, speedup tech-nique, IntAct.

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.

The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.

To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.

Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.

The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.

The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: Buckling, Finite Strip, Different Sides Support, Plates on Foundation.

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Authors: L. Nguyen, V. Golubev, R. Mankbadi

Abstract:

We consider here the subsonic impinging jet representing the flow field of a vertical take-off aircraft or the initial stage of rocket launching. Implicit Large-Eddy Simulation (ILES) is used to calculate the time-dependent flow field and the radiate sound pressure associated with jet impinging. With proper boundary treatments and high-order numerical scheme, the near field sound pressure is successfully obtained. Results are presented for both a rectangular as well a circular jet.

Keywords: Aeroacoustics, Large-Eddy Simulations, Jets, Fluid Dynamics.

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Authors: Corné J. Coetzee, Etienne Horn

Abstract:

One of the main challenges in using the Discrete Element Method (DEM) is to specify the correct input parameter values. In general, the models are sensitive to the input parameter values and accurate results can only be achieved if the correct values are specified. For the linear contact model, micro-parameters such as the particle density, stiffness, coefficient of friction, as well as the particle size and shape distributions are required. There is a need for a procedure to accurately calibrate these parameters before any attempt can be made to accurately model a complete bulk materials handling system. Since DEM is often used to model applications in the mining and quarrying industries, a calibration procedure was developed for materials that consist of relatively large (up to 40 mm in size) particles. A coarse crushed aggregate was used as the test material. Using a specially designed large shear box with a diameter of 590 mm, the confined Young’s modulus (bulk stiffness) and internal friction angle of the material were measured by means of the confined compression test and the direct shear test respectively. DEM models of the experimental setup were developed and the input parameter values were varied iteratively until a close correlation between the experimental and numerical results was achieved. The calibration process was validated by modelling the pull-out of an anchor from a bed of material. The model results compared well with experimental measurement.

Keywords: Discrete Element Method (DEM), calibration, shear box, anchor pull-out.

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Authors: Thi Nguyen, Lee Gordon-Brown, Jim Peterson, Peter Wheeler

Abstract:

An additive fuzzy system comprising m rules with n inputs and p outputs in each rule has at least t m(2n + 2 p + 1) parameters needing to be tuned. The system consists of a large number of if-then fuzzy rules and takes a long time to tune its parameters especially in the case of a large amount of training data samples. In this paper, a new learning strategy is investigated to cope with this obstacle. Parameters that tend toward constant values at the learning process are initially fixed and they are not tuned till the end of the learning time. Experiments based on applications of the additive fuzzy system in function approximation demonstrate that the proposed approach reduces the learning time and hence improves convergence speed considerably.

Keywords: Additive fuzzy system, improving convergence, parameter learning process, unsupervised learning.

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Authors: Young-Seok Choi

Abstract:

This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.

Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.

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Authors: Tatjana Eitrich, Bruno Lang

Abstract:

This work deals with aspects of support vector machine learning for large-scale data mining tasks. Based on a decomposition algorithm for support vector machine training that can be run in serial as well as shared memory parallel mode we introduce a transformation of the training data that allows for the usage of an expensive generalized kernel without additional costs. We present experiments for the Gaussian kernel, but usage of other kernel functions is possible, too. In order to further speed up the decomposition algorithm we analyze the critical problem of working set selection for large training data sets. In addition, we analyze the influence of the working set sizes onto the scalability of the parallel decomposition scheme. Our tests and conclusions led to several modifications of the algorithm and the improvement of overall support vector machine learning performance. Our method allows for using extensive parameter search methods to optimize classification accuracy.

Keywords: Support Vector Machine Training, Multi-ParameterKernels, Shared Memory Parallel Computing, Large Data

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Authors: N.Subramanian, C.Murugesan

Abstract:

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

Keywords: Fuzzy numbers, infinite matrix, Orlicz space, entiresequence.

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Authors: Kuo-Lung Wu

Abstract:

The weighting exponent m is called the fuzzifier that can have influence on the clustering performance of fuzzy c-means (FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this paper, we will discuss the robust properties of FCM and show that the parameter m will have influence on the robustness of FCM. According to our analysis, we find that a large m value will make FCM more robust to noise and outliers. However, if m is larger than the theoretical upper bound proposed by Yu et al. [14], the sample mean will become the unique optimizer. Here, we suggest to implement the FCM algorithm with mÎ[1.5,4] under the restriction when m is smaller than the theoretical upper bound.

Keywords: Fuzzy c-means, robust, fuzzifier.

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Authors: Yu-Ting Tsai, Yu-da Lee, Jin H. Huang

Abstract:

The nonlinear damping behavior is usually ignored in the design of a miniature moving-coil loudspeaker. But when the loudspeaker operated in air, the damping parameter varies with the voice-coil displacement corresponding due to viscous air flow. The present paper presents an identification model as inverse problem to identify the nonlinear damping parameter in the lumped parameter model for the loudspeaker. Theoretical results for the nonlinear damping are verified by using laser displacement measurement scanner. These results indicate that the damping parameter has the greatly different nonlinearity between in air and vacuum. It is believed that the results of the present work can be applied in diagnosis and sound quality improvement of a miniature loudspeaker.

Keywords: Miniature loudspeaker, non-linear damping, system identification, Lumped parameter model.

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Authors: Daniel I. Morariu, Lucian N. Vintan, Volker Tresp

Abstract:

Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, we present three feature selection methods: Information Gain, Support Vector Machine feature selection called (SVM_FS) and Genetic Algorithm with SVM (called GA_SVM). We show that the best results were obtained with GA_SVM method for a relatively small dimension of the feature vector.

Keywords: Feature Selection, Learning with Kernels, Support Vector Machine, Genetic Algorithm, and Classification.

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Authors: Daniel Morariu, Lucian N. Vintan, Volker Tresp

Abstract:

Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, three feature selection methods are evaluated: Random Selection, Information Gain (IG) and Support Vector Machine feature selection (called SVM_FS). We show that the best results were obtained with SVM_FS method for a relatively small dimension of the feature vector. Also we present a novel method to better correlate SVM kernel-s parameters (Polynomial or Gaussian kernel).

Keywords: Feature Selection, Learning with Kernels, SupportVector Machine, and Classification.

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Authors: Guangpu Chen

Abstract:

When the failure function is monotone, some monotonic reliability methods are used to gratefully simplify and facilitate the reliability computations. However, these methods often work in a transformed iso-probabilistic space. To this end, a monotonic simulator or transformation is needed in order that the transformed failure function is still monotone. This note proves at first that the output distribution of failure function is invariant under the transformation. And then it presents some conditions under which the transformed function is still monotone in the newly obtained space. These concern the copulas and the dependence concepts. In many engineering applications, the Gaussian copulas are often used to approximate the real word copulas while the available information on the random variables is limited to the set of marginal distributions and the covariances. So this note catches an importance on the conditional monotonicity of the often used transformation from an independent random vector into a dependent random vector with Gaussian copulas.

Keywords: Monotonic, Rosenblatt, Nataf transformation, dependence concepts, completely positive matrices, Gaussiancopulas

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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Authors: S. M. Ali, A. Salam Khan, A. U. Khan, M. Tariq, M. S. Hussain, B. A. Abbasi, I. Hussain, U. Farid

Abstract:

Environment and surrounding plays a pivotal rule in structuring life-style of the consumers. Living standards intern effect the energy consumption of the consumers. In smart grid paradigm, climate drifts, weather parameter and green environmental directly relates to the energy profiles of the various consumers, such as residential, commercial and industrial. Considering above factors helps policy in shaping utility load curves and optimal management of demand and supply. Thus, there is a pressing need to develop correlation models of load and weather parameters and critical analysis of the factors effecting energy profiles of smart grid consumers. In this paper, we elaborated various environment and weather parameter factors effecting demand of consumers. Moreover, we developed correlation models, such as Pearson, Spearman, and Kendall, an inter-relation between dependent (load) parameter and independent (weather) parameters. Furthermore, we validated our discussion with real-time data of Texas State. The numerical simulations proved the effective relation of climatic drifts with energy consumption of smart grid consumers.

Keywords: Climatic drifts, correlation analysis, energy consumption, smart grid, weather parameter.

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