Search results for: Vector Differential Equation.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2324

Search results for: Vector Differential Equation.

1904 Bone Proteome Study in Ovariectomised Rats Supplemented with Palm Vitamin E

Authors: Patrick Nwabueze Okechukwu, Ima Nirwana Soelaiman, Gabriele Anisah Ruth Froemming, Mohd Yusri Idorus, Norazlina Mohamed

Abstract:

Supplementation of palm vitamin E has been reported to prevent loss of bone density in ovariectomised female rats. The mechanism by which palm vitamin E exerts these effects is still unknown. We hypothesized that palm vitamin E may act by preventing the protein expression changes. Two dimensional poly acyrilamide gel electrophoresis (2-D PAGE) and PD Quest software genomic solutions Investigator (proteomics) was used to analyze the differential protein expression profile in femoral and humeri bones harvested from three groups of rats; sham-operated rats (SO), ovariectomised rats (Ovx) and ovariectomised rats supplemented for 2 months with palm vitamin E. The results showed that there were over 300 valued spot on each of the groups PVE and OVX as compared to about 200 in SO. Comparison between the differential protein expression between OVX and PVE groups showed that ten spots were down –regulated in OVX but up-regulated in PVE. The ten differential spots were separately named P1-P10. The identification and understanding of the pathway of the differential protein expression among the groups is ongoing and may account for the molecular mechanism through which palm vitamin E exert its anti-osteoporotic effect.

Keywords: Palm vitamin E, ovariectomised, osteoporosis protein expression, 2-d-page.

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1903 Space Vector PWM Simulation for Three Phase DC/AC Inverter

Authors: M. Kubeitari, A. Alhusayn, M. Alnahar

Abstract:

Space Vector Pulse Width Modulation SVPWM is one of the most used techniques to generate sinusoidal voltage and current due to its facility and efficiency with low harmonics distortion. This algorithm is specially used in power electronic applications. This paper describes simulation algorithm of SVPWM & SPWM using MatLab/simulink environment. It also implements a closed loop three phases DC-AC converter controlling its outputs voltages amplitude and frequency using MatLab. Also comparison between SVPWM & SPWM results is given.

Keywords: DC-AC Converter, MatLab, SPWM, SVPWM, Vref - rotating frame.

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1902 One-Class Support Vector Machines for Protein-Protein Interactions Prediction

Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

Predicting protein-protein interactions represent a key step in understanding proteins functions. This is due to the fact that proteins usually work in context of other proteins and rarely function alone. Machine learning techniques have been applied to predict protein-protein interactions. However, most of these techniques address this problem as a binary classification problem. Although it is easy to get a dataset of interacting proteins as positive examples, there are no experimentally confirmed non-interacting proteins to be considered as negative examples. Therefore, in this paper we solve this problem as a one-class classification problem using one-class support vector machines (SVM). Using only positive examples (interacting protein pairs) in training phase, the one-class SVM achieves accuracy of about 80%. These results imply that protein-protein interaction can be predicted using one-class classifier with comparable accuracy to the binary classifiers that use artificially constructed negative examples.

Keywords: Bioinformatics, Protein-protein interactions, One-Class Support Vector Machines

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1901 Pattern Recognition as an Internalized Motor Programme

Authors: M. Jändel

Abstract:

A new conceptual architecture for low-level neural pattern recognition is presented. The key ideas are that the brain implements support vector machines and that support vectors are represented as memory patterns in competitive queuing memories. A binary classifier is built from two competitive queuing memories holding positive and negative valence training examples respectively. The support vector machine classification function is calculated in synchronized evaluation cycles. The kernel is computed by bisymmetric feed-forward networks feed by sensory input and by competitive queuing memories traversing the complete sequence of support vectors. Temporary summation generates the output classification. It is speculated that perception apparatus in the brain reuses structures that have evolved for enabling fluent execution of prepared action sequences so that pattern recognition is built on internalized motor programmes.

Keywords: Competitive queuing model, Olfactory system, Pattern recognition, Support vector machine, Thalamus

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1900 Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA

Authors: G. Parmar, R. Prasad, S. Mukherjee

Abstract:

The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

Keywords: Genetic algorithm, Integral square error, Orderreduction, Stability equation method.

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1899 Face Recognition with PCA and KPCA using Elman Neural Network and SVM

Authors: Hossein Esbati, Jalil Shirazi

Abstract:

In this paper, in order to categorize ORL database face pictures, principle Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) methods by using Elman neural network and Support Vector Machine (SVM) categorization methods are used. Elman network as a recurrent neural network is proposed for modeling storage systems and also it is used for reviewing the effect of using PCA numbers on system categorization precision rate and database pictures categorization time. Categorization stages are conducted with various components numbers and the obtained results of both Elman neural network categorization and support vector machine are compared. In optimum manner 97.41% recognition accuracy is obtained.

Keywords: Face recognition, Principal Component Analysis, Kernel Principal Component Analysis, Neural network, Support Vector Machine.

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1898 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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1897 An Exact Solution to Support Vector Mixture

Authors: Monjed Ezzeddinne, Nicolas Lefebvre, Régis Lengellé

Abstract:

This paper presents a new version of the SVM mixture algorithm initially proposed by Kwok for classification and regression problems. For both cases, a slight modification of the mixture model leads to a standard SVM training problem, to the existence of an exact solution and allows the direct use of well known decomposition and working set selection algorithms. Only the regression case is considered in this paper but classification has been addressed in a very similar way. This method has been successfully applied to engine pollutants emission modeling.

Keywords: Identification, Learning systems, Mixture ofExperts, Support Vector Machines.

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1896 Dissolved Oxygen Prediction Using Support Vector Machine

Authors: Sorayya Malek, Mogeeb Mosleh, Sharifah M. Syed

Abstract:

In this study, Support Vector Machine (SVM) technique was applied to predict the dichotomized value of Dissolved oxygen (DO) from two freshwater lakes namely Chini and Bera Lake (Malaysia). Data sample contained 11 parameters for water quality features from year 2005 until 2009. All data parameters were used to predicate the dissolved oxygen concentration which was dichotomized into 3 different levels (High, Medium, and Low). The input parameters were ranked, and forward selection method was applied to determine the optimum parameters that yield the lowest errors, and highest accuracy. Initial results showed that pH, Water Temperature, and Conductivity are the most important parameters that significantly affect the predication of DO. Then, SVM model was applied using the Anova kernel with those parameters yielded 74% accuracy rate. We concluded that using SVM models to predicate the DO is feasible, and using dichotomized value of DO yields higher prediction accuracy than using precise DO value.

Keywords: Dissolved oxygen, Water quality, predication DO, Support Vector Machine.

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1895 Impact of Exchange Rate on Macroeconomic Indicators

Authors: Aleksandre Ergeshidze

Abstract:

The exchange rate is a pivotal pricing instrument that simultaneously impacts various components of the economy. Depreciation of nominal exchange rate is export promoting, which might be a desired export-led growth policy, and particularly critical to closing-down the widening current account imbalance. However, negative effects resulting from high dollarization and high share of imported intermediate inputs can outweigh positive effect. The aim of this research is to quantify impact of change in nominal exchange rate and test contractionary depreciation hypothesis on Georgian economy using structural and Bayesian vector autoregression. According to the acquired results, appreciation of nominal exchange rate is expected to decrease inflation, monetary policy rate, interest rate on domestic currency loans and economic growth in the medium run; however, impact on economic growth in the short run is statistically not significant.

Keywords: Bayesian vector autoregression, contractionary depreciation, dollarization, nominal exchange rate, structural vector autoregression.

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1894 Comparison of Domain and Hydrophobicity Features for the Prediction of Protein-Protein Interactions using Support Vector Machines

Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

The protein domain structure has been widely used as the most informative sequence feature to computationally predict protein-protein interactions. However, in a recent study, a research group has reported a very high accuracy of 94% using hydrophobicity feature. Therefore, in this study we compare and verify the usefulness of protein domain structure and hydrophobicity properties as the sequence features. Using the Support Vector Machines (SVM) as the learning system, our results indicate that both features achieved accuracy of nearly 80%. Furthermore, domains structure had receiver operating characteristic (ROC) score of 0.8480 with running time of 34 seconds, while hydrophobicity had ROC score of 0.8159 with running time of 20,571 seconds (5.7 hours). These results indicate that protein-protein interaction can be predicted from domain structure with reliable accuracy and acceptable running time.

Keywords: Bioinformatics, protein-protein interactions, support vector machines, protein features.

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1893 Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme

Authors: David J. Robbins, R. Stewart Cant, Lynn F. Gladden

Abstract:

A robust AUSM+ upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of state with respect to the IAPWS-IF97 equation of state for water. The algorithm demonstrates a combination of robustness and accuracy over a range of flow conditions, with the stiffened-gas equation tending to overestimate liquid temperature and density profiles.

Keywords: Multiphase flow, AUSM+ scheme, liquid EOS, low Mach number models

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1892 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions

Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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1891 Development of Variable Stepsize Variable Order Block Method in Divided Difference Form for the Numerical Solution of Delay Differential Equations

Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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1890 Addressing Scalability Issues of Named Entity Recognition Using Multi-Class Support Vector Machines

Authors: Mona Soliman Habib

Abstract:

This paper explores the scalability issues associated with solving the Named Entity Recognition (NER) problem using Support Vector Machines (SVM) and high-dimensional features. The performance results of a set of experiments conducted using binary and multi-class SVM with increasing training data sizes are examined. The NER domain chosen for these experiments is the biomedical publications domain, especially selected due to its importance and inherent challenges. A simple machine learning approach is used that eliminates prior language knowledge such as part-of-speech or noun phrase tagging thereby allowing for its applicability across languages. No domain-specific knowledge is included. The accuracy measures achieved are comparable to those obtained using more complex approaches, which constitutes a motivation to investigate ways to improve the scalability of multiclass SVM in order to make the solution more practical and useable. Improving training time of multi-class SVM would make support vector machines a more viable and practical machine learning solution for real-world problems with large datasets. An initial prototype results in great improvement of the training time at the expense of memory requirements.

Keywords: Named entity recognition, support vector machines, language independence, bioinformatics.

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1889 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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1888 The Use Support Vector Machine and Back Propagation Neural Network for Prediction of Daily Tidal Levels along the Jeddah Coast, Saudi Arabia

Authors: E. A. Mlybari, M. S. Elbisy, A. H. Alshahri, O. M. Albarakati

Abstract:

Sea level rise threatens to increase the impact of future  storms and hurricanes on coastal communities. Accurate sea level  change prediction and supplement is an important task in determining  constructions and human activities in coastal and oceanic areas. In  this study, support vector machines (SVM) is proposed to predict  daily tidal levels along the Jeddah Coast, Saudi Arabia. The optimal  parameter values of kernel function are determined using a genetic  algorithm. The SVM results are compared with the field data and  with back propagation (BP). Among the models, the SVM is superior  to BPNN and has better generalization performance.

 

Keywords: Tides, Prediction, Support Vector Machines, Genetic Algorithm, Back-Propagation Neural Network, Risk, Hazards.

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1887 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory

Authors: Ping Liu, Yongkun Li

Abstract:

This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.

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1886 Transformer Top-Oil Temperature Modeling and Simulation

Authors: T. C. B. N. Assunção, J. L. Silvino, P. Resende

Abstract:

The winding hot-spot temperature is one of the most critical parameters that affect the useful life of the power transformers. The winding hot-spot temperature can be calculated as function of the top-oil temperature that can estimated by using the ambient temperature and transformer loading measured data. This paper proposes the estimation of the top-oil temperature by using a method based on Least Squares Support Vector Machines approach. The estimated top-oil temperature is compared with measured data of a power transformer in operation. The results are also compared with methods based on the IEEE Standard C57.91-1995/2000 and Artificial Neural Networks. It is shown that the Least Squares Support Vector Machines approach presents better performance than the methods based in the IEEE Standard C57.91-1995/2000 and artificial neural networks.

Keywords: Artificial Neural Networks, Hot-spot Temperature, Least Squares Support Vector, Top-oil Temperature.

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1885 Road Accidents Bigdata Mining and Visualization Using Support Vector Machines

Authors: Usha Lokala, Srinivas Nowduri, Prabhakar K. Sharma

Abstract:

Useful information has been extracted from the road accident data in United Kingdom (UK), using data analytics method, for avoiding possible accidents in rural and urban areas. This analysis make use of several methodologies such as data integration, support vector machines (SVM), correlation machines and multinomial goodness. The entire datasets have been imported from the traffic department of UK with due permission. The information extracted from these huge datasets forms a basis for several predictions, which in turn avoid unnecessary memory lapses. Since data is expected to grow continuously over a period of time, this work primarily proposes a new framework model which can be trained and adapt itself to new data and make accurate predictions. This work also throws some light on use of SVM’s methodology for text classifiers from the obtained traffic data. Finally, it emphasizes the uniqueness and adaptability of SVMs methodology appropriate for this kind of research work.

Keywords: Road accident, machine learning, support vector machines.

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1884 About the Instability Modes of Current Sheet in Wide Range of Frequencies

Authors: V. V. Lyahov, V. M. Neshchadim

Abstract:

We offer a new technique for research of stability of current sheaths in space plasma taking into account the effect of polarization. At the beginning, the found perturbation of the distribution function is used for calculation of the dielectric permeability tensor, which simulates inhomogeneous medium of a current sheath. Further, we in the usual manner solve the system of Maxwell's equations closed with the material equation. The amplitudes of Fourier perturbations are considered to be exponentially decaying through the current sheath thickness. The dispersion equation follows from the nontrivial solution requirement for perturbations of the electromagnetic field. The resulting dispersion equation allows one to study the temporal and spatial characteristics of instability modes of the current sheath (within the limits of the proposed model) over a wide frequency range, including low frequencies.

Keywords: Current sheath, distribution function, effect of polarization, instability modes, low frequencies, perturbation of electromagnetic field dispersion equation, space plasma, tensor of dielectric permeability.

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1883 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation

Authors: Mohammad Najafi, Ali Jamshidi

Abstract:

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.

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1882 On the Approximate Solution of a Nonlinear Singular Integral Equation

Authors: Nizami Mustafa, C. Ardil

Abstract:

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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1881 Synthesis of a Control System of a Deterministic Chaotic Process in the Class of Two-Parameter Structurally Stable Mappings

Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva

Abstract:

In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.

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1880 Alternating Implicit Block FDTD Method For Scalar Wave Equation

Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

Abstract:

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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1879 Cardiac Disorder Classification Based On Extreme Learning Machine

Authors: Chul Kwak, Oh-Wook Kwon

Abstract:

In this paper, an extreme learning machine with an automatic segmentation algorithm is applied to heart disorder classification by heart sound signals. From continuous heart sound signals, the starting points of the first (S1) and the second heart pulses (S2) are extracted and corrected by utilizing an inter-pulse histogram. From the corrected pulse positions, a single period of heart sound signals is extracted and converted to a feature vector including the mel-scaled filter bank energy coefficients and the envelope coefficients of uniform-sized sub-segments. An extreme learning machine is used to classify the feature vector. In our cardiac disorder classification and detection experiments with 9 cardiac disorder categories, the proposed method shows significantly better performance than multi-layer perceptron, support vector machine, and hidden Markov model; it achieves the classification accuracy of 81.6% and the detection accuracy of 96.9%.

Keywords: Heart sound classification, extreme learning machine

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1878 Face Recognition Based On Vector Quantization Using Fuzzy Neuro Clustering

Authors: Elizabeth B. Varghese, M. Wilscy

Abstract:

A face recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame. A lot of algorithms have been proposed for face recognition. Vector Quantization (VQ) based face recognition is a novel approach for face recognition. Here a new codebook generation for VQ based face recognition using Integrated Adaptive Fuzzy Clustering (IAFC) is proposed. IAFC is a fuzzy neural network which incorporates a fuzzy learning rule into a competitive neural network. The performance of proposed algorithm is demonstrated by using publicly available AT&T database, Yale database, Indian Face database and a small face database, DCSKU database created in our lab. In all the databases the proposed approach got a higher recognition rate than most of the existing methods. In terms of Equal Error Rate (ERR) also the proposed codebook is better than the existing methods.

Keywords: Face Recognition, Vector Quantization, Integrated Adaptive Fuzzy Clustering, Self Organization Map.

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1877 Numerical Solution for Elliptical Crack with Developing Cusps Subject to Shear Loading

Authors: Nik Mohd Asri Nik Long, Koo Lee Feng, Zainidin K. Eshkuvatov, A. A. Khaldjigitov

Abstract:

This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.

Keywords: Elliptical crack, stress intensity factors, hyper singular integral equation, shear loading, conformal mapping.

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1876 Comparative Analysis of Geographical Routing Protocol in Wireless Sensor Networks

Authors: Rahul Malhotra

Abstract:

The field of wireless sensor networks (WSN) engages a lot of associates in the research community as an interdisciplinary field of interest. This type of network is inexpensive, multifunctionally attributable to advances in micro-electromechanical systems and conjointly the explosion and expansion of wireless communications. A mobile ad hoc network is a wireless network without fastened infrastructure or federal management. Due to the infrastructure-less mode of operation, mobile ad-hoc networks are gaining quality. During this work, we have performed an efficient performance study of the two major routing protocols: Ad hoc On-Demand Distance Vector Routing (AODV) and Dynamic Source Routing (DSR) protocols. We have used an accurate simulation model supported NS2 for this purpose. Our simulation results showed that AODV mitigates the drawbacks of the DSDV and provides better performance as compared to DSDV.

Keywords: Routing protocols, mobility, Mobile Ad-hoc Networks, Ad-hoc On-demand Distance Vector, Dynamic Source Routing, Destination Sequence Distance Vector, Quality of Service.

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1875 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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