Search results for: optimal homotopy asymptotic method

Authors: Mahdieh Khalilinezhad, Silvana Dellepiane, Gianni Vernazza

Abstract:

The aim of this work is to build a model based on tissue characterization that is able to discriminate pathological and non-pathological regions from three-phasic CT images. With our research and based on a feature selection in different phases, we are trying to design a neural network system with an optimal neuron number in a hidden layer. Our approach consists of three steps: feature selection, feature reduction, and classification. For each region of interest (ROI), 6 distinct sets of texture features are extracted such as: first order histogram parameters, absolute gradient, run-length matrix, co-occurrence matrix, autoregressive model, and wavelet, for a total of 270 texture features. When analyzing more phases, we show that the injection of liquid cause changes to the high relevant features in each region. Our results demonstrate that for detecting HCC tumor phase 3 is the best one in most of the features that we apply to the classification algorithm. The percentage of detection between pathology and healthy classes, according to our method, relates to first order histogram parameters with accuracy of 85% in phase 1, 95% in phase 2, and 95% in phase 3.

Keywords: Feature selection, Multi-phasic liver images, Neural network, Texture analysis.

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Authors: Raja Muhammad Asif Zahoor, Junaid Ali Khan, I. M. Qureshi

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In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati differential equations. The strength of proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Comparison of the method has been made with standard numerical techniques as well as the analytic solutions. It is found that the designed method can provide the solution to the equation with better accuracy than its counterpart deterministic approaches. Another advantage of the given approach is to provide results on entire finite continuous domain unlike other numerical methods which provide solutions only on discrete grid of points.

Keywords: Riccati Equation, Non linear ODE, Fractional differential equation, Genetic algorithm.

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Authors: M. Sasajima, M. Watanabe, T. Yamaguchi, Y. Kurosawa, Y. Koike

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Sound pathways in the enclosures of small earphones are very narrow. In such narrow pathways, the speed of sound propagation and the phase of sound waves change because of the air viscosity. We have developed a new finite element method that includes the effects of damping due to air viscosity for modeling the sound pathway. This method is developed as an extension of the existing finite element method for porous sound-absorbing materials. The numerical calculation results using the proposed finite element method are validated against the existing calculation methods.

Keywords: Simulation, FEM, air viscosity, damping.

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Authors: Yael Dubinsky, Orit Hazzan

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There is a constant need for hi-tech innovation to be decentralized to peripheral regions. This work describes how we applied Design Science Research (DSR) principles to define what we refer to as the Sea of Galilee (SoG) method. The goal of the SoG method is to harness existing and new technological initiatives in peripheral regions to create a socio-technological network that can initiate and maintain hi-tech activities. The SoG method consists of a set of principles, a stakeholder network, and actual hi-tech business initiatives, including their infrastructure and practices. The three cycles of DSR, the Relevance, Design, and Rigor cycles, lay out a research framework to sharpen the requirements, collect data from case studies, and iteratively refine the SoG method based on the existing knowledge base. We propose that the SoG method can be deployed by regional authorities that wish to be considered as smart regions (an extension of the notion of smart cities).

Keywords: Design Science Research, socio-technological initiatives, Sea of Galilee method, periphery stakeholder network, hi-tech initiatives.

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Authors: Amir Hossein Pakshir, A. Hossein Pour, N. Jahandar, Ali Paydar

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Roundabout work on the principle of circulation and entry flows, where the maximum entry flow rates depend largely on circulating flow bearing in mind that entry flows must give away to circulating flows. Where an existing roundabout has a road hump installed at the entry arm, it can be hypothesized that the kinematics of vehicles may prevent the entry arm from achieving optimum performance. Road humps are traffic calming devices placed across road width solely as speed reduction mechanism. They are the preferred traffic calming option in Malaysia and often used on single and dual carriageway local routes. The speed limit on local routes is 30mph (50 km/hr). Road humps in their various forms achieved the biggest mean speed reduction (based on a mean speed before traffic calming of 30mph) of up to 10mph or 16 km/hr according to the UK Department of Transport. The underlying aim of reduced speed should be to achieve a 'safe' distribution of speeds which reflects the function of the road and the impacts on the local community. Constraining safe distribution of speeds may lead to poor drivers timing and delayed reflex reaction that can probably cause accident. Previous studies on road hump impact have focused mainly on speed reduction, traffic volume, noise and vibrations, discomfort and delay from the use of road humps. The paper is aimed at optimal entry and circulating flow induced by road humps. Results show that roundabout entry and circulating flow perform better in circumstances where there is no road hump at entrance.

Keywords: Road hump, Roundabout, Speed Reduction

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Authors: Marcin Sowa

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The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: Numerical method, SubIval, fractional calculus, numerical solver, circuit analysis.

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Li-Yeh Chuang, Yu-Jen Hou, Jr., Cheng-Hong Yang

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Single nucleotide polymorphisms (SNPs) hold much promise as a basis for disease-gene association. However, research is limited by the cost of genotyping the tremendous number of SNPs. Therefore, it is important to identify a small subset of informative SNPs, the so-called tag SNPs. This subset consists of selected SNPs of the genotypes, and accurately represents the rest of the SNPs. Furthermore, an effective evaluation method is needed to evaluate prediction accuracy of a set of tag SNPs. In this paper, a genetic algorithm (GA) is applied to tag SNP problems, and the K-nearest neighbor (K-NN) serves as a prediction method of tag SNP selection. The experimental data used was taken from the HapMap project; it consists of genotype data rather than haplotype data. The proposed method consistently identified tag SNPs with considerably better prediction accuracy than methods from the literature. At the same time, the number of tag SNPs identified was smaller than the number of tag SNPs in the other methods. The run time of the proposed method was much shorter than the run time of the SVM/STSA method when the same accuracy was reached.

Keywords: Genetic Algorithm (GA), Genotype, Single nucleotide polymorphism (SNP), tag SNPs.

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Authors: Tomas Luneckas, Dainius Udris

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In this paper a simple terrain evaluation method for hexapod robot is introduced. This method is based on feet coordinate evaluation when all are on the ground. Depending on the feet coordinate differences the local terrain evaluation is possible. Terrain evaluation is necessary for right gait selection and/or body position correction. For terrain roughness evaluation three planes are plotted: two of them as definition points use opposite feet coordinates, third coincides with the robot body plane. The leaning angle of body plane is evaluated measuring gravity force using three-axis accelerometer. Terrain roughness evaluation method is based on angle estimation between normal vectors of these planes. Aim of this work is to present a simple method for embedded robot controller, allowing to find the best further movement settings.

Keywords: Hexapod robot, pose estimation, terrain evaluation, terrain roughness.

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Authors: Muhammad Shafi, Paul W. H. Chung

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This paper proposes a hybrid method for eyes localization in facial images. The novelty is in combining techniques that utilise colour, edge and illumination cues to improve accuracy. The method is based on the observation that eye regions have dark colour, high density of edges and low illumination as compared to other parts of face. The first step in the method is to extract connected regions from facial images using colour, edge density and illumination cues separately. Some of the regions are then removed by applying rules that are based on the general geometry and shape of eyes. The remaining connected regions obtained through these three cues are then combined in a systematic way to enhance the identification of the candidate regions for the eyes. The geometry and shape based rules are then applied again to further remove the false eye regions. The proposed method was tested using images from the PICS facial images database. The proposed method has 93.7% and 87% accuracies for initial blobs extraction and final eye detection respectively.

Keywords: Erosion, dilation, Edge-density

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Authors: Yung-Ting Chang, Chung-You Tsai, Yu-Chuan Li

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Nosocomial (i.e., hospital-acquired) infections (NI) is a major cause of morbidity and mortality in hospitals. NI rate is higher in intensive care units (ICU) than in the general ward due to patients with severe symptoms, poor immunity, and accepted many invasive therapies. Contact behaviors between health caregivers and patients is one of the infect factors. It is difficult to obtain complete contact records by traditional method of retrospective analysis of medical records. This paper establishes a contact history inferential model (CHIM) intended to extend the use of Proximity Sensing of rapid frequency identification (RFID) technology to transferring all proximity events between health caregivers and patients into clinical events (close-in events, contact events and invasive events).The results of the study indicated that the CHIM can infer proximity care activities into close-in events and contact events. The infection control team could redesign and build optimal workflow in the ICU according to the patient-specific contact history which provided by our automatic tracing system.

Keywords: Active Radio Frequency Identification, Intensive Care Unit, Nosocomial Infections

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Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

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Authors: M. S. Annie Christi

Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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Authors: Ren Jian, Yang Shulin

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In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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Authors: Johan Segeborn, Johan S. Carlson, Robert Bohlin, Rikard Söderberg

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This paper presents a method to support dynamic packing in cases when no collision-free path can be found. The method, which is primarily based on path planning and shrinking of geometries, suggests a minimal geometry design change that results in a collision-free assembly path. A supplementing approach to optimize geometry design change with respect to redesign cost is described. Supporting this dynamic packing method, a new method to shrink geometry based on vertex translation, interweaved with retriangulation, is suggested. The shrinking method requires neither tetrahedralization nor calculation of medial axis and it preserves the topology of the geometry, i.e. holes are neither lost nor introduced. The proposed methods are successfully applied on industrial geometries.

Keywords: Dynamic packing, path planning, shrinking.

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Authors: Michaela Vašková

Abstract:

The paper is focused on the application of the security audit method on the selected objects of the critical infrastructure. The emphasis is put on security audit method to find gaps in the critical infrastructure security. The theoretical part describes objects of the critical infrastructure. The practical part describes using of the security audit method. The main emphasis was put on the protection of the critical infrastructure in the Czech Republic.

Keywords: Crisis management, critical infrastructure, object of critical infrastructure, security audit, extraordinary event.

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Authors: Alessandro Barbiero

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This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.

Keywords: Approximation, asymmetry, experimental design, interference theory, Monte Carlo simulations.

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Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

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The problem of N cracks interaction in an isotropic elastic solid is decomposed into a subproblem of a homogeneous solid without crack and N subproblems with each having a single crack subjected to unknown tractions on the two crack faces. The unknown tractions, namely pseudo tractions on each crack are expanded into polynomials with unknown coefficients, which have to be determined by the consistency condition, i.e. by the equivalence of the original multiple cracks interaction problem and the superposition of the N+1 subproblems. In this paper, Kachanov-s approach of average tractions is extended into the method of moments to approximately impose the consistence condition. Hence Kachanov-s method can be viewed as the zero-order method of moments. Numerical results of the stress intensity factors are presented for interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks. As the order of moment increases, the accuracy of the method of moments improves.

Keywords: Crack interaction, stress intensity factor, multiplecracks, method of moments.

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Authors: Kyoungwoo Park, Byeong Sam Kim, Hyo-Jae Lim, Ji Won Han, Park Kyoun Oh, Juhee Lee, Keun-Yeol Yu

Abstract:

Predictions of flow and heat transfer characteristics and shape optimization in internally finned circular tubes have been performed on three-dimensional periodically fully developed turbulent flow and thermal fields. For a trapezoidal fin profile, the effects of fin height h, upper fin widths d1, lower fin widths d2, and helix angle of fin ? on transport phenomena are investigated for the condition of fin number of N = 30. The CFD and mathematical optimization technique are coupled in order to optimize the shape of internally finned tube. The optimal solutions of the design variables (i.e., upper and lower fin widths, fin height and helix angle) are numerically obtained by minimizing the pressure loss and maximizing the heat transfer rate, simultaneously, for the limiting conditions of d1 = 0.5~1.5 mm, d2 = 0.5~1.5 mm, h= 0.5~1.5mm, ? = 10~30 degrees. The fully developed flow and thermal fields are predicted using the finite volume method and the optimization is carried out by means of the multi-objective genetic algorithm that is widely used in the constrained nonlinear optimization problem.

Keywords: Computational fluid dynamics, Genetic algorithm, Internally finned tube with helix angle, Optimization.

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Authors: Young-Jae Kim, Young-Hwan You

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This paper presents a integer frequency offset (IFO) estimation scheme for the 3GPP long term evolution (LTE) downlink system. Firstly, the conventional joint detection method for IFO and sector cell index (CID) information is introduced. Secondly, an IFO estimation without explicit sector CID information is proposed, which can operate jointly with the proposed IFO estimation and reduce the time delay in comparison with the conventional joint method. Also, the proposed method is computationally efficient and has almost similar performance in comparison with the conventional method over the Pedestrian and Vehicular channel models.

Keywords: LTE, OFDMA, primary synchronization signal (PSS), IFO, CID

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Authors: Pinaki Pratim Acharjya, Dibyendu Ghoshal

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Image matching methods play a key role in deciding correspondence between two image scenes. This paper presents a method for the matching of digital images using mathematical morphology. The proposed method has been applied to real life images. The matching process has shown successful and promising results.

Keywords: Digital image, gradients, image matching, mathematical morphology.

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Authors: Kholod M. Abu-Alnaja

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In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Kapse Swapnil, K. Shankar

Abstract:

Aiming at optimizing the weight and deflection of cantilever beam subjected to maximum stress and maximum deflection, Multi-objective Particle Swarm Optimization (MOPSO) with Utopia Point based local search is implemented. Utopia point is used to govern the search towards the Pareto Optimal set. The elite candidates obtained during the iterations are stored in an archive according to non-dominated sorting and also the archive is truncated based on least crowding distance. Local search is also performed on elite candidates and the most diverse particle is selected as the global best. This method is implemented on standard test functions and it is observed that the improved algorithm gives better convergence and diversity as compared to NSGA-II in fewer iterations. Implementation on practical structural problem shows that in 5 to 6 iterations, the improved algorithm converges with better diversity as evident by the improvement of cantilever beam on an average of 0.78% and 9.28% in the weight and deflection respectively compared to NSGA-II.

Keywords: Utopia point, multi-objective particle swarm optimization, local search, cantilever beam.

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Authors: Hae-Yeoun Lee, In-Koo Kang, Heung-Kyu Lee

Abstract:

This paper addresses an efficient technique to embed and detect digital fingerprint code. Orthogonal modulation method is a straightforward and widely used approach for digital fingerprinting but shows several limitations in computational cost and signal efficiency. Coded modulation method can solve these limitations in theory. However it is difficult to perform well in practice if host signals are not available during tracing colluders, other kinds of attacks are applied, and the size of fingerprint code becomes large. In this paper, we propose a hybrid modulation method, in which the merits of or-thogonal modulation and coded modulation method are combined so that we can achieve low computational cost and high signal efficiency. To analyze the performance, we design a new fingerprint code based on GD-PBIBD theory and modulate this code into images by our method using spread-spectrum watermarking on frequency domain. The results show that the proposed method can efficiently handle large fingerprint code and trace colluders against averaging attacks.

Keywords: Fingerprinting, GD-PBIBD theory, Hybrid modulationtechnique.

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Authors: Emiliano Matta

Abstract:

Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.

Keywords: Amplitude-independent damping, Homogeneous friction, Pendulum nonlinear dynamics, Structural control, Vibration resonant absorbers.

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Authors: Patsaraporn Somboonsak, Mud-Armeen Munlin

Abstract:

In April 2009, a new variant of Influenza A virus subtype H1N1 emerged in Mexico and spread all over the world. The influenza has three subtypes in human (H1N1, H1N2 and H3N2) Types B and C influenza tend to be associated with local or regional epidemics. Preliminary genetic characterization of the influenza viruses has identified them as swine influenza A (H1N1) viruses. Nucleotide sequence analysis of the Haemagglutinin (HA) and Neuraminidase (NA) are similar to each other and the majority of their genes of swine influenza viruses, two genes coding for the neuraminidase (NA) and matrix (M) proteins are similar to corresponding genes of swine influenza. Sequence similarity between the 2009 A (H1N1) virus and its nearest relatives indicates that its gene segments have been circulating undetected for an extended period. Nucleic acid sequence Maximum Likelihood (MCL) and DNA Empirical base frequencies, Phylogenetic relationship amongst the HA genes of H1N1 virus isolated in Genbank having high nucleotide sequence homology. In this paper we used 16 HA nucleotide sequences from NCBI for computing sequence relationships similarity of swine influenza A virus using the following method MCL the result is 28%, 36.64% for Optimal tree with the sum of branch length, 35.62% for Interior branch phylogeny Neighber – Join Tree, 1.85% for the overall transition/transversion, and 8.28% for Overall mean distance.

Keywords: Sequence DNA, Relationship of swine, Swineinfluenza, Sequence Similarity

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Authors: N.R.N. Idris

Abstract:

This study uses simulated meta-analysis to assess the effects of publication bias on meta-analysis estimates and to evaluate the efficacy of the trim and fill method in adjusting for these biases. The estimated effect sizes and the standard error were evaluated in terms of the statistical bias and the coverage probability. The results demonstrate that if publication bias is not adjusted it could lead to up to 40% bias in the treatment effect estimates. Utilization of the trim and fill method could reduce the bias in the overall estimate by more than half. The method is optimum in presence of moderate underlying bias but has minimal effects in presence of low and severe publication bias. Additionally, the trim and fill method improves the coverage probability by more than half when subjected to the same level of publication bias as those of the unadjusted data. The method however tends to produce false positive results and will incorrectly adjust the data for publication bias up to 45 % of the time. Nonetheless, the bias introduced into the estimates due to this adjustment is minimal

Keywords: Publication bias, Trim and Fill method, percentage relative bias, coverage probability

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Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

Abstract:

This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid

Abstract:

Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum error

Keywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise

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Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

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