Search results for: Elliptic Curve Discrete Logarithms.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 955

Search results for: Elliptic Curve Discrete Logarithms.

385 Blind Identification and Equalization of CDMA Signals Using the Levenvberg-Marquardt Algorithm

Authors: Mohammed Boutalline, Imad Badi, Belaid Bouikhalene, Said Safi

Abstract:

In this paper we describe the Levenvberg-Marquardt (LM) algorithm for identification and equalization of CDMA signals received by an antenna array in communication channels. The synthesis explains the digital separation and equalization of signals after propagation through multipath generating intersymbol interference (ISI). Exploiting discrete data transmitted and three diversities induced at the reception, the problem can be composed by the Block Component Decomposition (BCD) of a tensor of order 3 which is a new tensor decomposition generalizing the PARAFAC decomposition. We optimize the BCD decomposition by Levenvberg-Marquardt method gives encouraging results compared to classical alternating least squares algorithm (ALS). In the equalization part, we use the Minimum Mean Square Error (MMSE) to perform the presented method. The simulation results using the LM algorithm are important.

Keywords: Identification and equalization, communication channel, Levenvberg-Marquardt, tensor decomposition

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384 Optimal Location of the I/O Point in the Parking System

Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.

Keywords: Parking system, optimal location, response time, S/R machine.

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383 Effect of Sand Particle Transportation in Oil and Gas Pipeline Erosion

Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

Abstract:

Erosion in a pipe bends caused by particles is a major concern in the oil and gas fields and might cause breakdown to production equipment. This work investigates the effect of sand particle transport in an elbow using computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model is employed to calculate the air/solid particle flow in the elbow. Generic erosion model in Ansys fluent and three particle rebound models are used to predict the erosion rate on the 90° elbows. The model result is compared with experimental data from the open literature validating the CFD-based predictions which reveals that due to the sand particles impinging on the wall of the elbow at high velocity, a point on the pipe elbow were observed to have started turning red due to velocity increase and the maximum erosion locations occur at 48°.

Keywords: Erosion, prediction, elbow, computational fluid dynamics, CFD.

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382 Transmission Expansion Planning Considering Network Adequacy and Investment Cost Limitation using Genetic Algorithm

Authors: M. Mahdavi, E. Mahdavi

Abstract:

In this research, STNEP is being studied considering network adequacy and limitation of investment cost by decimal codification genetic algorithm (DCGA). The goal is obtaining the maximum of network adequacy with lowest expansion cost for a specific investment. Finally, the proposed idea is applied to the Garvers 6-bus network. The results show that considering the network adequacy for solution of STNEP problem is caused that among of expansion plans for a determined investment, configuration which has relatively lower expansion cost and higher adequacy is proposed by GA based method. Finally, with respect to the curve of adequacy versus expansion cost it can be said that more optimal configurations for expansion of network are obtained with lower investment costs.

Keywords: TNEP, Network Adequacy, Investment Cost, GA

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381 A Strategy for a Robust Design of Cracked Stiffened Panels

Authors: Francesco Caputo, Giuseppe Lamanna, Alessandro Soprano

Abstract:

This work is focused on the numerical prediction of the fracture resistance of a flat stiffened panel made of the aluminium alloy 2024 T3 under a monotonic traction condition. The performed numerical simulations have been based on the micromechanical Gurson-Tvergaard (GT) model for ductile damage. The applicability of the GT model to this kind of structural problems has been studied and assessed by comparing numerical results, obtained by using the WARP 3D finite element code, with experimental data available in literature. In the sequel a home-made procedure is presented, which aims to increase the residual strength of a cracked stiffened aluminum panel and which is based on the stochastic design improvement (SDI) technique; a whole application example is then given to illustrate the said technique.

Keywords: Residual strength, R-Curve, Gurson model, SDI.

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380 Self-Organization of Radiation Defects: Temporal Dissipative Structures

Authors: Pavlo Selyshchev

Abstract:

A theoretical approach to radiation damage evolution is developed. Stable temporal behavior taking place in solids under irradiation are examined as phenomena of self-organization in nonequilibrium systems. Experimental effects of temporal self-organization in solids under irradiation are reviewed. Their essential common properties and features are highlighted and analyzed. Dynamical model to describe development of self-oscillation of density of point defects under stationary irradiation is proposed. The emphasis is the nonlinear couplings between rate of annealing and density of defects that determine the kind and parameters of an arising self-oscillation. The field of parameters (defect generation rate and environment temperature) at which self-oscillations develop is found. Bifurcation curve and self-oscillation period near it is obtained.

Keywords: Irradiation, Point Defects, Solids, Temporal Selforganization.

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379 Estimating the Flow Velocity Using Flow Generated Sound

Authors: Saeed Hosseini, Ali Reza Tahavvor

Abstract:

Sound processing is one the subjects that newly attracts a lot of researchers. It is efficient and usually less expensive than other methods. In this paper the flow generated sound is used to estimate the flow speed of free flows. Many sound samples are gathered. After analyzing the data, a parameter named wave power is chosen. For all samples the wave power is calculated and averaged for each flow speed. A curve is fitted to the averaged data and a correlation between the wave power and flow speed is found. Test data are used to validate the method and errors for all test data were under 10 percent. The speed of the flow can be estimated by calculating the wave power of the flow generated sound and using the proposed correlation.

Keywords: Flow generated sound, sound processing, speed, wave power.

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378 A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations

Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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377 ANFIS Approach for Locating Faults in Underground Cables

Authors: Magdy B. Eteiba, Wael Ismael Wahba, Shimaa Barakat

Abstract:

This paper presents a fault identification, classification and fault location estimation method based on Discrete Wavelet Transform and Adaptive Network Fuzzy Inference System (ANFIS) for medium voltage cable in the distribution system.

Different faults and locations are simulated by ATP/EMTP, and then certain selected features of the wavelet transformed signals are used as an input for a training process on the ANFIS. Then an accurate fault classifier and locator algorithm was designed, trained and tested using current samples only. The results obtained from ANFIS output were compared with the real output. From the results, it was found that the percentage error between ANFIS output and real output is less than three percent. Hence, it can be concluded that the proposed technique is able to offer high accuracy in both of the fault classification and fault location.

Keywords: ANFIS, Fault location, Underground Cable, Wavelet Transform.

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376 DHT-LMS Algorithm for Sensorineural Loss Patients

Authors: Sunitha S. L., V. Udayashankara

Abstract:

Hearing impairment is the number one chronic disability affecting many people in the world. Background noise is particularly damaging to speech intelligibility for people with hearing loss especially for sensorineural loss patients. Several investigations on speech intelligibility have demonstrated sensorineural loss patients need 5-15 dB higher SNR than the normal hearing subjects. This paper describes Discrete Hartley Transform Power Normalized Least Mean Square algorithm (DHT-LMS) to improve the SNR and to reduce the convergence rate of the Least Means Square (LMS) for sensorineural loss patients. The DHT transforms n real numbers to n real numbers, and has the convenient property of being its own inverse. It can be effectively used for noise cancellation with less convergence time. The simulated result shows the superior characteristics by improving the SNR at least 9 dB for input SNR with zero dB and faster convergence rate (eigenvalue ratio 12) compare to time domain method and DFT-LMS.

Keywords: Hearing Impairment, DHT-LMS, Convergence rate, SNR improvement.

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375 Facial Expressions Animation and Lip Tracking Using Facial Characteristic Points and Deformable Model

Authors: Hadi Seyedarabi, Ali Aghagolzadeh, Sohrab Khanmohammadi

Abstract:

Face and facial expressions play essential roles in interpersonal communication. Most of the current works on the facial expression recognition attempt to recognize a small set of the prototypic expressions such as happy, surprise, anger, sad, disgust and fear. However the most of the human emotions are communicated by changes in one or two of discrete features. In this paper, we develop a facial expressions synthesis system, based on the facial characteristic points (FCP's) tracking in the frontal image sequences. Selected FCP's are automatically tracked using a crosscorrelation based optical flow. The proposed synthesis system uses a simple deformable facial features model with a few set of control points that can be tracked in original facial image sequences.

Keywords: Deformable face model, facial animation, facialcharacteristic points, optical flow.

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374 Automated Java Testing: JUnit versus AspectJ

Authors: Manish Jain, Dinesh Gopalani

Abstract:

Growing dependency of mankind on software technology increases the need for thorough testing of the software applications and automated testing techniques that support testing activities. We have outlined our testing strategy for performing various types of automated testing of Java applications using AspectJ which has become the de-facto standard for Aspect Oriented Programming (AOP). Likewise JUnit, a unit testing framework is the most popular Java testing tool. In this paper, we have evaluated our proposed AOP approach for automated testing and JUnit on various parameters. First we have provided the similarity between the two approaches and then we have done a detailed comparison of the two testing techniques on factors like lines of testing code, learning curve, testing of private members etc. We established that our AOP testing approach using AspectJ has got several advantages and is thus particularly more effective than JUnit.

Keywords: Aspect oriented programming, AspectJ, Aspects, JUnit, software testing.

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373 Two-Stage Approach for Solving the Multi-Objective Optimization Problem on Combinatorial Configurations

Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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372 A Survey on Quasi-Likelihood Estimation Approaches for Longitudinal Set-ups

Authors: Naushad Mamode Khan

Abstract:

The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, over- and under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thus restricts the likelihood-based estimating methodology. The joint generalized quasi-likelihood approach (GQL-I) was instead considered but is rather computationally intensive and may not even estimate the regression effects due to a complex and frequently ill-conditioned covariance structure. This paper proposes a new GQL approach for estimating the regression parameters (GQL-III) that is based on a single score vector representation. The performance of GQL-III is compared with GQL-I and separate marginal GQLs (GQL-II) through some simulation experiments and is proved to yield equally efficient estimates as GQL-I and is far more computationally stable.

Keywords: Longitudinal, Com-Poisson, Ill-conditioned, INAR(1), GLMS, GQL.

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371 Qualitative Modelling for Ferromagnetic Hysteresis Cycle

Authors: M. Mordjaoui, B. Boudjema, M. Chabane, R. Daira

Abstract:

In determining the electromagnetic properties of magnetic materials, hysteresis modeling is of high importance. Many models are available to investigate those characteristics but they tend to be complex and difficult to implement. In this paper a new qualitative hysteresis model for ferromagnetic core is presented, based on the function approximation capabilities of adaptive neuro fuzzy inference system (ANFIS). The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach can restored the hysteresis curve with a little RMS error. The model accuracy is good and can be easily adapted to the requirements of the application by extending or reducing the network training set and thus the required amount of measurement data.

Keywords: ANFIS modeling technique, magnetic hysteresis, Jiles-Atherton model, ferromagnetic core.

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370 Aging Behaviour of 6061 Al-15 vol% SiC Composite in T4 and T6 Treatments

Authors: Melby Chacko, Jagannath Nayak

Abstract:

The aging behaviour of 6061 Al-15 vol% SiC composite was investigated using Rockwell B hardness measurement. The composite was solutionized at 350°C and quenched in water. The composite was aged at room temperature (T4 treatment) and also at 140°C, 160°C, 180°C and 200°C (T6 treatment). The natural and artificial aging behaviour of composite was studied using aging curves determined at different temperatures. The aging period for peak aging for different temperatures was identified. The time required for attaining peak aging decreased with increase in the aging temperature. The peak hardness was found to increase with increase with aging temperature and the highest peak hardness was observed at 180ºC. Beyond 180ºC the peak hardness was found to be decreasing.

Keywords: 6061 Al-SiC composite, Aging curve, Rockwell B hardness, T4, T6 treatments.

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369 Reliable Capacitated Facility Location Problem Considering Maximal Covering

Authors: Mehdi Seifbarghy, Sajjad Jalali, Seyed Habib A. Rahmati

Abstract:

This paper provides a framework in order to incorporate reliability issue as a sign of disruption in distribution systems and partial covering theory as a response to limitation in coverage radios and economical preferences, simultaneously into the traditional literatures of capacitated facility location problems. As a result we develop a bi-objective model based on the discrete scenarios for expected cost minimization and demands coverage maximization through a three echelon supply chain network by facilitating multi-capacity levels for provider side layers and imposing gradual coverage function for distribution centers (DCs). Additionally, in spite of objectives aggregation for solving the model through LINGO software, a branch of LP-Metric method called Min- Max approach is proposed and different aspects of corresponds model will be explored.

Keywords: Reliability Cost, Partial Covering, LP-Metric

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368 A Novel Compression Algorithm for Electrocardiogram Signals based on Wavelet Transform and SPIHT

Authors: Sana Ktata, Kaïs Ouni, Noureddine Ellouze

Abstract:

Electrocardiogram (ECG) data compression algorithm is needed that will reduce the amount of data to be transmitted, stored and analyzed, but without losing the clinical information content. A wavelet ECG data codec based on the Set Partitioning In Hierarchical Trees (SPIHT) compression algorithm is proposed in this paper. The SPIHT algorithm has achieved notable success in still image coding. We modified the algorithm for the one-dimensional (1-D) case and applied it to compression of ECG data. By this compression method, small percent root mean square difference (PRD) and high compression ratio with low implementation complexity are achieved. Experiments on selected records from the MIT-BIH arrhythmia database revealed that the proposed codec is significantly more efficient in compression and in computation than previously proposed ECG compression schemes. Compression ratios of up to 48:1 for ECG signals lead to acceptable results for visual inspection.

Keywords: Discrete Wavelet Transform, ECG compression, SPIHT.

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367 Reducing the Number of Constraints in Non Safe Petri Net

Authors: M. Zareiee, A. Dideban

Abstract:

This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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366 Phase Jitter Transfer in High Speed Data Links

Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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365 Heat Transfer and Friction Factor Study for Triangular Duct Solar Air Heater Having Discrete V-Shaped Ribs

Authors: Varun

Abstract:

Solar energy is a good option among renewable energy resources due to its easy availability and abundance. The simplest and most efficient way to utilize solar energy is to convert it into thermal energy and this can be done with the help of solar collectors. The thermal performance of such collectors is poor due to less heat transfer from the collector surface to air. In this work, experimental investigations of single pass solar air heater having triangular duct and provided with roughness element on the underside of the absorber plate. V-shaped ribs are used for investigation having three different values of relative roughness pitch (p/e) ranges from 4- 16 for a fixed value of angle of attack (α), relative roughness height (e/Dh) and a relative gap distance (d/x) values are 60°, 0.044 and 0.60 respectively. Result shows that considerable augmentation in heat transfer has been obtained by providing roughness.

Keywords: Artificial roughness, Solar Air heater, Triangular duct, V-Shaped Ribs.

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364 Low-Cost Inertial Sensors Modeling Using Allan Variance

Authors: A. A. Hussen, I. N. Jleta

Abstract:

Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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363 Ziegler Nichols Based Integral Proportional Controller for Superheated Steam Temperature Control System

Authors: Amil Daraz, Suheel Abdullah Malik, Tahir Saleem, Sajid Ali Bhati

Abstract:

In this paper, Integral Proportional (I-P) controller is employed for superheated steam temperature control system. The Ziegler-Nichols (Z-N) method is used for the tuning of I-P controller. The performance analysis of Z-N based I-P controller is assessed on superheated steam system of 500-MW boiler. The comparison of transient response parameters such as rise time, settling time, and overshoot is made with Z-N based Proportional Integral (PI) controller. It is observed from the results that Z-N based I-P controller completely eliminates the overshoot in the output response.

Keywords: Superheated steam, process reaction curve, PI and I-P controller, Ziegler-Nichols tuning.

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362 A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments

Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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361 Signature Identification Scheme Based on Iterated Function Systems

Authors: Nadia M. G. AL-Saidi

Abstract:

Since 1984 many schemes have been proposed for digital signature protocol, among them those that based on discrete log and factorizations. However a new identification scheme based on iterated function (IFS) systems are proposed and proved to be more efficient. In this study the proposed identification scheme is transformed into a digital signature scheme by using a one way hash function. It is a generalization of the GQ signature schemes. The attractor of the IFS is used to obtain public key from a private one, and in the encryption and decryption of a hash function. Our aim is to provide techniques and tools which may be useful towards developing cryptographic protocols. Comparisons between the proposed scheme and fractal digital signature scheme based on RSA setting, as well as, with the conventional Guillou-Quisquater signature, and RSA signature schemes is performed to prove that, the proposed scheme is efficient and with high performance.

Keywords: Digital signature, Fractal, Iterated function systems(IFS), Guillou-Quisquater (GQ) protocol, Zero-knowledge (ZK)

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360 Involving Action Potential Morphology on a New Cellular Automata Model of Cardiac Action Potential Propagation

Authors: F. Pourhasanzade, S. H. Sabzpoushan

Abstract:

Computer modeling has played a unique role in understanding electrocardiography. Modeling and simulating cardiac action potential propagation is suitable for studying normal and pathological cardiac activation. This paper presents a 2-D Cellular Automata model for simulating action potential propagation in cardiac tissue. We demonstrate a novel algorithm in order to use minimum neighbors. This algorithm uses the summation of the excitability attributes of excited neighboring cells. We try to eliminate flat edges in the result patterns by inserting probability to the model. We also preserve the real shape of action potential by using linear curve fitting of one well known electrophysiological model.

Keywords: Cellular Automata, Action Potential Propagation, cardiac tissue, Isotropic Pattern, accurate shape of cardiac actionpotential.

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359 Image Compression Using Multiwavelet and Multi-Stage Vector Quantization

Authors: S. Esakkirajan, T. Veerakumar, V. Senthil Murugan, P. Navaneethan

Abstract:

The existing image coding standards generally degrades at low bit-rates because of the underlying block based Discrete Cosine Transform scheme. Over the past decade, the success of wavelets in solving many different problems has contributed to its unprecedented popularity. Due to implementation constraints scalar wavelets do not posses all the properties such as orthogonality, short support, linear phase symmetry, and a high order of approximation through vanishing moments simultaneously, which are very much essential for signal processing. New class of wavelets called 'Multiwavelets' which posses more than one scaling function overcomes this problem. This paper presents a new image coding scheme based on non linear approximation of multiwavelet coefficients along with multistage vector quantization. The performance of the proposed scheme is compared with the results obtained from scalar wavelets.

Keywords: Image compression, Multiwavelets, Multi-stagevector quantization.

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358 Hybrid Fuzzy Selecting-Control-by- Range Controllers of a Servopneumatic Fatigue System

Authors: Marco Soares dos Santos, Jorge Augusto Ferreira, Camila Nicola Boeri, Fernando Neto da Silva

Abstract:

The present paper proposes high performance nonlinear force controllers for a servopneumatic real-time fatigue test machine. A CompactRIO® controller was used, being fully programmed using LabVIEW language. Fuzzy logic control algorithms were evaluated to tune the integral and derivative components in the development of hybrid controllers, namely a FLC P and a hybrid FLC PID real-time-based controllers. Their behaviours were described by using state diagrams. The main contribution is to ensure a smooth transition between control states, avoiding discrete transitions in controller outputs. Steady-state errors lower than 1.5 N were reached, without retuning the controllers. Good results were also obtained for sinusoidal tracking tasks from 1/¤Ç to 8/¤Ç Hz.

Keywords: Hybrid Fuzzy Selecting, Control, Range Controllers, Servopneumatic Fatigue System.

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357 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieh

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: Polynomial constitutive equation, solitary.

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356 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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