Search results for: Mean Squared Error
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1285

Search results for: Mean Squared Error

745 Machine Learning Techniques for Short-Term Rain Forecasting System in the Northeastern Part of Thailand

Authors: Lily Ingsrisawang, Supawadee Ingsriswang, Saisuda Somchit, Prasert Aungsuratana, Warawut Khantiyanan

Abstract:

This paper presents the methodology from machine learning approaches for short-term rain forecasting system. Decision Tree, Artificial Neural Network (ANN), and Support Vector Machine (SVM) were applied to develop classification and prediction models for rainfall forecasts. The goals of this presentation are to demonstrate (1) how feature selection can be used to identify the relationships between rainfall occurrences and other weather conditions and (2) what models can be developed and deployed for predicting the accurate rainfall estimates to support the decisions to launch the cloud seeding operations in the northeastern part of Thailand. Datasets collected during 2004-2006 from the Chalermprakiat Royal Rain Making Research Center at Hua Hin, Prachuap Khiri khan, the Chalermprakiat Royal Rain Making Research Center at Pimai, Nakhon Ratchasima and Thai Meteorological Department (TMD). A total of 179 records with 57 features was merged and matched by unique date. There are three main parts in this work. Firstly, a decision tree induction algorithm (C4.5) was used to classify the rain status into either rain or no-rain. The overall accuracy of classification tree achieves 94.41% with the five-fold cross validation. The C4.5 algorithm was also used to classify the rain amount into three classes as no-rain (0-0.1 mm.), few-rain (0.1- 10 mm.), and moderate-rain (>10 mm.) and the overall accuracy of classification tree achieves 62.57%. Secondly, an ANN was applied to predict the rainfall amount and the root mean square error (RMSE) were used to measure the training and testing errors of the ANN. It is found that the ANN yields a lower RMSE at 0.171 for daily rainfall estimates, when compared to next-day and next-2-day estimation. Thirdly, the ANN and SVM techniques were also used to classify the rain amount into three classes as no-rain, few-rain, and moderate-rain as above. The results achieved in 68.15% and 69.10% of overall accuracy of same-day prediction for the ANN and SVM models, respectively. The obtained results illustrated the comparison of the predictive power of different methods for rainfall estimation.

Keywords: Machine learning, decision tree, artificial neural network, support vector machine, root mean square error.

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744 New Product-Type Estimators for the Population Mean Using Quartiles of the Auxiliary Variable

Authors: Amer Ibrahim Falah Al-Omari

Abstract:

In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.

Keywords: Product estimator, auxiliary variable, simple random sampling, extreme ranked set sampling

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743 Affine Projection Adaptive Filter with Variable Regularization

Authors: Young-Seok Choi

Abstract:

We propose two affine projection algorithms (APA) with variable regularization parameter. The proposed algorithms dynamically update the regularization parameter that is fixed in the conventional regularized APA (R-APA) using a gradient descent based approach. By introducing the normalized gradient, the proposed algorithms give birth to an efficient and a robust update scheme for the regularization parameter. Through experiments we demonstrate that the proposed algorithms outperform conventional R-APA in terms of the convergence rate and the misadjustment error.

Keywords: Affine projection, regularization, gradient descent, system identification.

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742 A Robust Audio Fingerprinting Algorithm in MP3 Compressed Domain

Authors: Ruili Zhou, Yuesheng Zhu

Abstract:

In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.

Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM

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741 The Enhancement of Target Localization Using Ship-Borne Electro-Optical Stabilized Platform

Authors: Jaehoon Ha, Byungmo Kang, Kilho Hong, Jungsoo Park

Abstract:

Electro-optical (EO) stabilized platforms have been widely used for surveillance and reconnaissance on various types of vehicles, from surface ships to unmanned air vehicles (UAVs). EO stabilized platforms usually consist of an assembly of structure, bearings, and motors called gimbals in which a gyroscope is installed. EO elements such as a CCD camera and IR camera, are mounted to a gimbal, which has a range of motion in elevation and azimuth and can designate and track a target. In addition, a laser range finder (LRF) can be added to the gimbal in order to acquire the precise slant range from the platform to the target. Recently, a versatile functionality of target localization is needed in order to cooperate with the weapon systems that are mounted on the same platform. The target information, such as its location or velocity, needed to be more accurate. The accuracy of the target information depends on diverse component errors and alignment errors of each component. Specially, the type of moving platform can affect the accuracy of the target information. In the case of flying platforms, or UAVs, the target location error can be increased with altitude so it is important to measure altitude as precisely as possible. In the case of surface ships, target location error can be increased with obliqueness of the elevation angle of the gimbal since the altitude of the EO stabilized platform is supposed to be relatively low. The farther the slant ranges from the surface ship to the target, the more extreme the obliqueness of the elevation angle. This can hamper the precise acquisition of the target information. So far, there have been many studies on EO stabilized platforms of flying vehicles. However, few researchers have focused on ship-borne EO stabilized platforms of the surface ship. In this paper, we deal with a target localization method when an EO stabilized platform is located on the mast of a surface ship. Especially, we need to overcome the limitation caused by the obliqueness of the elevation angle of the gimbal. We introduce a well-known approach for target localization using Unscented Kalman Filter (UKF) and present the problem definition showing the above-mentioned limitation. Finally, we want to show the effectiveness of the approach that will be demonstrated through computer simulations.

Keywords: Target localization, ship-borne electro-optical stabilized platform, unscented Kalman filter.

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740 The Relative Efficiency Based on the MSE in Generalized Ridge Estimate

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A relative efficiency is defined as Ridge Estimate in the general linear model. The relative efficiency is based on the Mean square error. In this paper, we put forward a parameter of Ridge Estimate and discussions are made on the relative efficiency between the ridge estimation and the General Ridge Estimate. Eventually, this paper proves that the estimation is better than the general ridge estimate, which is based on the MSE.

Keywords: Ridge estimate, generalized ridge estimate, MSE, relative efficiency.

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739 The use of a Bespoke Computer Game For Teaching Analogue Electronics

Authors: Olaf Hallan Graven, Dag Andreas Hals Samuelsen

Abstract:

An implementation of a design for a game based virtual learning environment is described. The game is developed for a course in analogue electronics, and the topic is the design of a power supply. This task can be solved in a number of different ways, with certain constraints, giving the students a certain amount of freedom, although the game is designed not to facilitate trial-and error approach. The use of storytelling and a virtual gaming environment provides the student with the learning material in a MMORPG environment. The game is tested on a group of second year electrical engineering students with good results.

Keywords: analogue electronics, e-learning, computer games for learning, virtual reality

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738 Study of Adaptive Filtering Algorithms and the Equalization of Radio Mobile Channel

Authors: Said Elkassimi, Said Safi, B. Manaut

Abstract:

This paper presented a study of three algorithms, the equalization algorithm to equalize the transmission channel with ZF and MMSE criteria, application of channel Bran A, and adaptive filtering algorithms LMS and RLS to estimate the parameters of the equalizer filter, i.e. move to the channel estimation and therefore reflect the temporal variations of the channel, and reduce the error in the transmitted signal. So far the performance of the algorithm equalizer with ZF and MMSE criteria both in the case without noise, a comparison of performance of the LMS and RLS algorithm.

Keywords: Adaptive filtering second equalizer, LMS, RLS Bran A, Proakis (B) MMSE, ZF.

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737 The Impact of Revenue Gap on Economic Growth: A Case Study of Pakistan

Authors: M. Ilyas, M. W. Siddiqi

Abstract:

This study employs auto-regressive distributed lag (ARDL) bounds approach to cointegration for long run and errorcorrection modeling (ECM) for short run analysis to examine the relationship between revenue gap and economic growth for Pakistan using annual time series data over the period 1980 to 2008. The short and long run results indicate that revenue gap is statistical significant and negatively effect economic growth. The significant and negative coefficient of error correction term in ECM indicates that after a shock, the long rum equilibrium will again converge towards equilibrium about 10.406 percent within a year.

Keywords: ARDL cointegration, Economic Growth, RevenueGap, Pakistan.

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736 pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

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735 A Study on Inference from Distance Variables in Hedonic Regression

Authors: Yan Wang, Yasushi Asami, Yukio Sadahiro

Abstract:

In urban area, several landmarks may affect housing price and rents, and hedonic analysis should employ distance variables corresponding to each landmarks. Unfortunately, the effects of distances to landmarks on housing prices are generally not consistent with the true price. These distance variables may cause magnitude error in regression, pointing a problem of spatial multicollinearity. In this paper, we provided some approaches for getting the samples with less bias and method on locating the specific sampling area to avoid the multicollinerity problem in two specific landmarks case.

Keywords: Landmarks, hedonic regression, distance variables, collinearity, multicollinerity.

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734 The Application of Hybrid Orthonomal Bernstein and Block-Pulse Functions in Finding Numerical Solution of Fredholm Fuzzy Integral Equations

Authors: Mahmoud Zarrini, Sanaz Torkaman

Abstract:

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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733 A Cooperative Space-Time Transmission Scheme Based On Symbol Combinations

Authors: Keunhong Chae, Seokho Yoon

Abstract:

This paper proposes a cooperative Alamouti space time transmission scheme with low relay complexity for the cooperative communication systems. In the proposed scheme, the source node combines the data symbols to construct the Alamouti-coded form at the destination node, while the conventional scheme performs the corresponding operations at the relay nodes. In simulation results, it is shown that the proposed scheme achieves the second order cooperative diversity while maintaining the same bit error rate (BER) performance as that of the conventional scheme.

Keywords: Space-time transmission, cooperative communication system, MIMO.

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732 On Constructing Approximate Convex Hull

Authors: M. Zahid Hossain, M. Ashraful Amin

Abstract:

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.

Keywords: Convex hull, Approximation algorithm, Computational geometry, Linear time.

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731 Joint Transmitter-Receiver Optimization for Bonded Wireline Communications

Authors: Mohammed H. Nafie, Ahmed F. Shalash

Abstract:

With the advent of DSL services, high data rates are now available over phone lines, yet higher rates are in demand. In this paper, we optimize the transmit filters that can be used over wireline channels. Results showing the bit error rates when optimized filters are used, and with a decision feedback equalizer (DFE) employed in the receiver, are given. We then show that significantly higher throughput can be achieved by modeling the channel as a multiple input multiple output (MIMO) channel. A receiver that employs a MIMO-DFE that deals jointly with several users is proposed and shown to provide significant improvement over the conventional DFE.

Keywords: DFE, MIMO Channels, Receiver Architectures, Transmit Filters.

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730 Bitrate Reduction Using FMO for Video Streaming over Packet Networks

Authors: Le Thanh Ha, Hye-Soo Kim, Chun-Su Park, Seung-Won Jung, Sung-Jea Ko

Abstract:

Flexible macroblock ordering (FMO), adopted in the H.264 standard, allows to partition all macroblocks (MBs) in a frame into separate groups of MBs called Slice Groups (SGs). FMO can not only support error-resilience, but also control the size of video packets for different network types. However, it is well-known that the number of bits required for encoding the frame is increased by adopting FMO. In this paper, we propose a novel algorithm that can reduce the bitrate overhead caused by utilizing FMO. In the proposed algorithm, all MBs are grouped in SGs based on the similarity of the transform coefficients. Experimental results show that our algorithm can reduce the bitrate as compared with conventional FMO.

Keywords: Data Partition, Entropy Coding, Greedy Algorithm, H.264/AVC, Slice Group.

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729 A New Correlation for Overall Sherwood Number in Packed Liquid-Liquid Extraction Column

Authors: S. GhaffariTooran, H. Abolghasemi, H. Bahmanyar, M. Esmaeili, A. Safari

Abstract:

Using plug flow model in conjunction with experimental solute concentration profiles, overall volumetric mass transfer coefficient based on continuous phase (Koca), in a packed liquid-liquid extraction column has been optimized. Number of 12 experiments has been done using standard system of water/acid acetic/toluene in a 6 cm diameter, 120 cm height column. Thorough consideration of influencing parameters we intended to correlate dimensionless parameters in term of overall Sherwood number which has an acceptable average error of about 15.8%.

Keywords: Packed column, mass transfer coefficient, solvent extraction, Sherwood number.

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728 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay

Abstract:

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.

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727 A Compact Pi Network for Reducing Bit Error Rate in Dispersive FIR Channel Noise Model

Authors: Kavita Burse, R.N. Yadav, S.C. Shrivastava, Vishnu Pratap Singh Kirar

Abstract:

During signal transmission, the combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel which distort and add noise to the signal. This causes the well defined signal constellation to spread causing errors in bit detection. A compact pi neural network with minimum number of nodes is proposed. The replacement of summation at each node by multiplication results in more powerful mapping. The resultant pi network is tested on six different channels.

Keywords: Additive white Gaussian noise, digitalcommunication system, multiplicative neuron, Pi neural network.

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726 Algebraic Quantum Error Correction Codes

Authors: Ming-Chung Tsai, Kuan-Peng Chen, Zheng-Yao

Abstract:

A systematic and exhaustive method based on the group structure of a unitary Lie algebra is proposed to generate an enormous number of quantum codes. With respect to the algebraic structure, the orthogonality condition, which is the central rule of generating quantum codes, is proved to be fully equivalent to the distinguishability of the elements in this structure. In addition, four types of quantum codes are classified according to the relation of the codeword operators and some initial quantum state. By linking the unitary Lie algebra with the additive group, the classical correspondences of some of these quantum codes can be rendered.

Keywords: Quotient-Algebra Partition, Codeword Spinors, Basis Codewords, Syndrome Spinors

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725 More on Gaussian Quadratures for Fuzzy Functions

Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

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724 Algorithm for Determining the Parameters of a Two-Layer Soil Model

Authors: Adekitan I. Aderibigbe, Fakolujo A. Olaosebikan

Abstract:

The parameters of a two-layer soil can be determined by processing resistivity data obtained from resistivity measurements carried out on the soil of interest. The processing usually entails applying the resistivity data as inputs to an optimisation function. This paper proposes an algorithm which utilises the square error as an optimisation function. Resistivity data from previous works were applied to test the accuracy of the new algorithm developed and the result obtained conforms significantly to results from previous works.

 

Keywords: Algorithm, earthing, resistivity, two-layer soil-model.

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723 Integral Methods in the Determination of Temperature Fields of Cooled Blades of Gas Turbines

Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

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722 Numerical Modeling of Temperature Fields in Aviation Gas Turbine Elements

Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

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721 A Kernel Classifier using Linearised Bregman Iteration

Authors: K. A. D. N. K Wimalawarne

Abstract:

In this paper we introduce a novel kernel classifier based on a iterative shrinkage algorithm developed for compressive sensing. We have adopted Bregman iteration with soft and hard shrinkage functions and generalized hinge loss for solving l1 norm minimization problem for classification. Our experimental results with face recognition and digit classification using SVM as the benchmark have shown that our method has a close error rate compared to SVM but do not perform better than SVM. We have found that the soft shrinkage method give more accuracy and in some situations more sparseness than hard shrinkage methods.

Keywords: Compressive sensing, Bregman iteration, Generalisedhinge loss, sparse, kernels, shrinkage functions

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720 Classification of Germinatable Mung Bean by Near Infrared Hyperspectral Imaging

Authors: Kaewkarn Phuangsombat, Arthit Phuangsombat, Anupun Terdwongworakul

Abstract:

Hard seeds will not grow and can cause mold in sprouting process. Thus, the hard seeds need to be separated from the normal seeds. Near infrared hyperspectral imaging in a range of 900 to 1700 nm was implemented to develop a model by partial least squares discriminant analysis to discriminate the hard seeds from the normal seeds. The orientation of the seeds was also studied to compare the performance of the models. The model based on hilum-up orientation achieved the best result giving the coefficient of determination of 0.98, and root mean square error of prediction of 0.07 with classification accuracy was equal to 100%.

Keywords: Mung bean, near infrared, germinatability, hard seed.

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719 Electron Density Discrepancy Analysis of Energy Metabolism Coenzymes

Authors: Alan Luo, Hunter N. B. Moseley

Abstract:

Many macromolecular structure entries in the Protein Data Bank (PDB) have a range of regional (localized) quality issues, be it derived from X-ray crystallography, Nuclear Magnetic Resonance (NMR) spectroscopy, or other experimental approaches. However, most PDB entries are judged by global quality metrics like R-factor, R-free, and resolution for X-ray crystallography or backbone phi-psi distribution statistics and average restraint violations for NMR. Regional quality is often ignored when PDB entries are re-used for a variety of structurally based analyses. The binding of ligands, especially ligands involved in energy metabolism, is of particular interest in many structurally focused protein studies. Using a regional quality metric that provides chemically interpretable information from electron density maps, a significant number of outliers in regional structural quality was detected across X-ray crystallographic PDB entries for proteins bound to biochemically critical ligands. In this study, a series of analyses was performed to evaluate both specific and general potential factors that could promote these outliers. In particular, these potential factors were the minimum distance to a metal ion, the minimum distance to a crystal contact, and the isotropic atomic b-factor. To evaluate these potential factors, Fisher’s exact tests were performed, using regional quality criteria of outlier (top 1%, 2.5%, 5%, or 10%) versus non-outlier compared to a potential factor metric above versus below a certain outlier cutoff. The results revealed a consistent general effect from region-specific normalized b-factors but no specific effect from metal ion contact distances and only a very weak effect from crystal contact distance as compared to the b-factor results. These findings indicate that no single specific potential factor explains a majority of the outlier ligand-bound regions, implying that human error is likely as important as these other factors. Thus, all factors, including human error, should be considered when regions of low structural quality are detected. Also, the downstream re-use of protein structures for studying ligand-bound conformations should screen the regional quality of the binding sites. Doing so prevents misinterpretation due to the presence of structural uncertainty or flaws in regions of interest.

Keywords: Biomacromolecular structure, coenzyme, electron density discrepancy analysis, X-ray crystallography.

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718 Determination of Measurement Uncertainty in Extracting of Forming Limit Diagrams

Authors: M. Mahboubkhah, H. Fayazfar

Abstract:

In this research, Forming Limit Diagrams for supertension sheet metals which are using in automobile industry have been obtained. The exerted strains to sheet metals have been measured with four different methods and the errors of each method have also been represented. These methods have been compared with together and the most efficient and economic way of extracting of the exerted strains to sheet metals has been introduced. In this paper total error and uncertainty of FLD extraction procedures have been derived. Determination of the measurement uncertainty in extracting of FLD has a great importance in design and analysis of the sheet metal forming process.

Keywords: Forming Limit Diagram, Major and Minor Strain, Measurement Uncertainty.

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717 Approximating Fixed Points by a Two-Step Iterative Algorithm

Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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716 Antenna Array Beamforming Using Neural Network

Authors: Maja Sarevska, Abdel-Badeeh M. Salem

Abstract:

This paper considers the problem of Null-Steering beamforming using Neural Network (NN) approach for antenna array system. Two cases are presented. First, unlike the other authors, the estimated Direction Of Arrivals (DOAs) are used for antenna array weights NN-based determination and the imprecise DOAs estimations are taken into account. Second, the blind null-steering beamforming is presented. In this case the antenna array outputs are presented at the input of the NN without DOAs estimation. The results of computer simulations will show much better relative mean error performances of the first NN approach compared to the NNbased blind beamforming.

Keywords: Beamforming, DOAs, neural network.

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