Search results for: back propagation rule

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

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

Keywords: tides, prediction, support vector machines, genetic algorithm, back-propagation neural network, risk, hazards

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Authors: Ritesh Kumar, Gitanjali Chhetri, Mandira Bhatia, Mohit Mishra, Abhijith Bailur, Abhinav

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The prevalence of the internet and technology in our day to day lives is creating more security issues than ever. The need for protecting and providing a secure access to private and business data has led to the development of many security systems. One of the potential solutions is to employ the bio-metric authentication technique. In this paper we present an innovative biometric authentication method that utilizes a person’s EEG signal, which is acquired in response to an auditory stimulus,and transferred wirelessly to a computer that has the necessary ANN algorithm-Multi layer perceptrol neural network because of is its ability to differentiate between information which is not linearly separable.In order to determine the weights of the hidden layer we use Gaussian random weight initialization. MLP utilizes a supervised learning technique called Back propagation for training the network. The complex algorithm used for EEG classification reduces the chances of intrusion into the protected public or private data.

Keywords: EEG signal, auditory evoked potential, biometrics, multilayer perceptron neural network, back propagation rule, Gaussian random weight initialization

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Authors: Bin Mu, Site Li, Shijin Yuan

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Under the circumstance of environment deterioration, people are increasingly concerned about the quality of the environment, especially air quality. As a result, it is of great value to give accurate and timely forecast of AQI (air quality index). In order to simplify influencing factors of air quality in a city, and forecast the city’s AQI tomorrow, this study used MATLAB software and adopted the method of constructing a mathematic model of PCA-GABP to provide a solution. To be specific, this study firstly made principal component analysis (PCA) of influencing factors of AQI tomorrow including aspects of weather, industry waste gas and IAQI data today. Then, we used the back propagation neural network model (BP), which is optimized by genetic algorithm (GA), to give forecast of AQI tomorrow. In order to verify validity and accuracy of PCA-GABP model’s forecast capability. The study uses two statistical indices to evaluate AQI forecast results (normalized mean square error and fractional bias). Eventually, this study reduces mean square error by optimizing individual gene structure in genetic algorithm and adjusting the parameters of back propagation model. To conclude, the performance of the model to forecast AQI is comparatively convincing and the model is expected to take positive effect in AQI forecast in the future.

Keywords: AQI forecast, principal component analysis, genetic algorithm, back propagation neural network model

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Authors: Ajoy Kumar Das, Prasenjit Dey

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Heat transfer due to forced convection of copper water based nanofluid has been predicted by Artificial Neural network (ANN). The present nanofluid is formed by mixing copper nano particles in water and the volume fractions are considered here are 0% to 15% and the Reynolds number are kept constant at 100. The back propagation algorithm is used to train the network. The present ANN is trained by the input and output data which has been obtained from the numerical simulation, performed in finite volume based Computational Fluid Dynamics (CFD) commercial software Ansys Fluent. The numerical simulation based results are compared with the back propagation based ANN results. It is found that the forced convection heat transfer of water based nanofluid can be predicted correctly by ANN. It is also observed that the back propagation ANN can predict the heat transfer characteristics of nanofluid very quickly compared to standard CFD method.

Keywords: forced convection, square cylinder, nanofluid, neural network

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Authors: R. Loukil, M. Chtourou, T. Damak

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This paper investigates the training of multilayer neural network using the classic approach. Then, for estimation purposes, we suggest the use of a specific neural observer that we study its training algorithm which is the back-propagation one in the case of the disponibility of the state and in the case of an unmeasurable state. A MATLAB simulation example will be studied to highlight the usefulness of this kind of observer.

Keywords: training, estimation purposes, neural observer, back-propagation, unmeasurable state

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Authors: Royan Dawud Aldian, Endah Purwanti, Soegianto Soelistiono

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In this research we have been developed an automatic investigation to classify normal children voice or autistic by using modern computation technology that is computation based on artificial neural network. The superiority of this computation technology is its capability on processing and saving data. In this research, digital voice features are gotten from the coefficient of linear-predictive coding with auto-correlation method and have been transformed in frequency domain using fast fourier transform, which used as input of artificial neural network in back-propagation method so that will make the difference between normal children and autistic automatically. The result of back-propagation method shows that successful classification capability for normal children voice experiment data is 100% whereas, for autistic children voice experiment data is 100%. The success rate using back-propagation classification system for the entire test data is 100%.

Keywords: autism, artificial neural network, backpropagation, linier predictive coding, fast fourier transform

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Authors: Grace Titilayo, Kolawole-Amao

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Influence and authority of law within society should be respected by all and sundry regardless of individual status. Rule of law implies that every citizen is subject to the law. In a society governed by the rule of law, government and its officials and agents are also held subject to and accountable under the law. Law should not be employed to suit individual tenets. Where the rule of law operates, the government is the government of law and not of men. Corruption is a factor that kills the growth of the rule of law. Where corruption flourishes, the rule of law fails, simply put, corruption is a threat to the rule of law. It bastardized and undermines the rule of law and good governance principles - where men rule at their discretion rather than the use of the rule of law which makes governance processes ineffective. Corruption is prevalent all over the world, and has extremely far reaching effects. Many of the world’s greatest challenges have been amplified by corruption, for example poverty, unequal distribution of wealth and resources, and world hunger and it weakens the application and the entrenchment of the rule of law. It saps citizens' trust in their governments and undercuts government credibility. This paper will discuss the rule of law in the present democratic system in Nigeria, the impact of corruption on the rule of law in Nigeria and how corruption undermines and subverts the entrenchment of the rule of law in the present day Nigeria.

Keywords: rule of law, corruption, Nigeria, influence, authority

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Authors: Sahin Emrah Amrahov, Fatih Aybar, Serhat Dogan

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In this paper we consider the rule reduct generation problem. Rule Reduct Generation (RG) and Modified Rule Generation (MRG) algorithms, that are used to solve this problem, are well-known. Alternative to these algorithms, we develop Pruning Rule Generation (PRG) algorithm. We compare the PRG algorithm with RG and MRG.

Keywords: rough sets, decision rules, rule induction, classification

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Authors: Chia-Hao Chang, Geng-Gui Wang, Jee-Cheng Wu

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The prediction of a landslide is a difficult task because it requires a detailed study of past activities using a complete range of investigative methods to determine the changing condition. In this research, first step, LiDAR 1-meter by 1-meter resolution of digital elevation model (DEM) was used to generate six environmental factors of landslide. Then, back-propagation neural networks (BPNN) was adopted to identify scarp, landslide areas and non-landslide areas. The BPNN uses 6 environmental factors in input layer and 1 output layer. Moreover, 6 landslide areas are used as training areas and 4 landslide areas as test areas in the BPNN. The hidden layer is set to be 1 and 2; the hidden layer neurons are set to be 4, 5, 6, 7 and 8; the learning rates are set to be 0.01, 0.1 and 0.5. When using 1 hidden layer with 7 neurons and the learning rate sets to be 0.5, the result of Network training root mean square error is 0.001388. Finally, evaluation of BPNN classification accuracy by the confusion matrix shows that the overall accuracy can reach 94.4%, and the Kappa value is 0.7464.

Keywords: digital elevation model, DEM, environmental factors, back-propagation neural network, BPNN, LiDAR

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Authors: Amit R. Bhende, G. K. Awari

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Remaining useful life (RUL) prediction is one of key technologies to realize prognostics and health management that is being widely applied in many industrial systems to ensure high system availability over their life cycles. The present work proposes a data-driven method of RUL prediction based on multiple health state assessment for rolling element bearings. Bearing degradation data at three different conditions from run to failure is used. A RUL prediction model is separately built in each condition. Feed forward back propagation neural network models are developed for prediction modeling.

Keywords: bearing degradation data, remaining useful life (RUL), back propagation, prognosis

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Authors: B. Chandra

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In Association Rule Mining, much attention has been paid for developing algorithms for large (frequent/closed/maximal) itemsets but very little attention has been paid to improve the performance of rule generation algorithms. Rule generation is an important part of Association Rule Mining. In this paper, a novel approach named NARG (Association Rule using Antecedent Support) has been proposed for rule generation that uses memory resident data structure named FCET (Frequent Closed Enumeration Tree) to find frequent/closed itemsets. In addition, the computational speed of NARG is enhanced by giving importance to the rules that have lower antecedent support. Comparative performance evaluation of NARG with fast association rule mining algorithm for rule generation has been done on synthetic datasets and real life datasets (taken from UCI Machine Learning Repository). Performance analysis shows that NARG is computationally faster in comparison to the existing algorithms for rule generation.

Keywords: knowledge discovery, association rule mining, antecedent support, rule generation

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Authors: A. Clementking, C. Jothi Venkateswaran

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Mathematical and computational functionalities such as descriptive mining, optimization, and predictions are espoused to resolve natural resource planning. The water quality prediction and its attributes influence determinations are adopted optimization techniques. The water properties are tainted while merging water resource one with another. This work aimed to predict influencing water resource distribution connectivity in accordance to water quality and sediment using an innovative proposed master-slave neural network back-propagation model. The experiment results are arrived through collecting water quality attributes, computation of water quality index, design and development of neural network model to determine water quality and sediment, master–slave back propagation neural network back-propagation model to determine variations on water quality and sediment attributes between the water resources and the recommendation for connectivity. The homogeneous and parallel biochemical reactions are influences water quality and sediment while distributing water from one location to another. Therefore, an innovative master-slave neural network model [M (9:9:2)::S(9:9:2)] designed and developed to predict the attribute variations. The result of training dataset given as an input to master model and its maximum weights are assigned as an input to the slave model to predict the water quality. The developed master-slave model is predicted physicochemical attributes weight variations for 85 % to 90% of water quality as a target values.The sediment level variations also predicated from 0.01 to 0.05% of each water quality percentage. The model produced the significant variations on physiochemical attribute weights. According to the predicated experimental weight variation on training data set, effective recommendations are made to connect different resources.

Keywords: master-slave back propagation neural network model(MSBPNNM), water quality analysis, multivariate analysis, environmental mining

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Authors: Angga S. Fajar, A. Aminullah, J. Kiyono, R. A. Safitri

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This paper discusses about the application of ANN for optimizing of bridge structure design. ANN has been applied in various field of science concerning prediction and optimization. The structural optimization has several benefit including accelerate structural design process, saving the structural material, and minimize self-weight and mass of structure. In this paper, there are three types of bridge structure that being optimized including PSC I-girder superstructure, composite steel-concrete girder superstructure, and RC bridge pier. The different optimization strategy on each bridge structure implement back propagation method of ANN is conducted in this research. The optimal weight and easier design process of bridge structure with satisfied error are achieved.

Keywords: bridge structures, ANN, optimization, back propagation

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Authors: Thi Thao Nguyen, Andrew McLennan, Shino Takayama

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We study the probabilistic allocation of finitely many indivisible objects to finitely many agents. Well known allocation rules for this problem include random priority, the market mechanism proposed by Hylland and Zeckhauser [1979], and the probabilistic serial rule of Bogomolnaia and Moulin [2001]. We propose a new allocation rule, which we call the lexico-graphic (serial) rule, that is tailored for situations in which each agent's primary concern is to maximize the probability of receiving her favourite object. Three axioms, lex efficiency, lex envy freeness and fairness, are proposed and fully characterize the lexicographic serial rule. We also discuss how our axioms and the lexicographic rule are related to other allocation rules, particularly the probabilistic serial rule.

Keywords: Efficiency, Envy free, Lexicographic, Probabilistic Serial Rule

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Authors: Slimane Ouhmad, Abdellah Halimi

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In this work, we have applied neural networks method MLP type to a database from an array of six sensors for the detection of three toxic gases. As the choice of the number of hidden layers and the weight values has a great influence on the convergence of the learning algorithm, we proposed, in this article, a mathematical formulation to determine the optimal number of hidden layers and good weight values based on the method of back propagation of errors. The results of this modeling have improved discrimination of these gases on the one hand, and optimize the computation time on the other hand, the comparison to other results achieved in this case.

Keywords: MLP Neural Network, back-propagation, number of neurons in the hidden layer, identification, computing time

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Authors: Osung Im, Neha Yadav, Eui Hoon Lee, Joong Hoon Kim

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Artificial Neural Network (ANN) approach is commonly used in lots of fields for forecasting. In water resources engineering, forecast of water level or inflow of reservoir is useful for various kind of purposes. Due to advantages of ANN, many papers were written for inflow prediction in river networks, but in this study, ANN is used in urban sewer networks. The growth of severe rain storm in Korea has increased flood damage severely, and the precipitation distribution is getting more erratic. Therefore, effective pump operation in pump station is an essential task for the reduction in urban area. If real time inflow of pump station reservoir can be predicted, it is possible to operate pump effectively for reducing the flood damage. This study used ANN model for pump station reservoir inflow prediction using upstream sewer depth data. For this study, rainfall events, sewer depth, and inflow into Banpo pump station reservoir between years of 2013-2014 were considered. Feed – Forward Back Propagation (FFBF), Cascade – Forward Back Propagation (CFBP), Elman Back Propagation (EBP) and Nonlinear Autoregressive Exogenous (NARX) were used as ANN model for prediction. A comparison of results with ANN model suggests that ANN is a powerful tool for inflow prediction using the sewer depth data.

Keywords: artificial neural network, forecasting, reservoir inflow, sewer depth

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Authors: Suzan Wedyan

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Data mining is one of the main phases in the Knowledge Discovery Database (KDD) which is responsible of finding hidden and useful knowledge from databases. There are many different tasks for data mining including regression, pattern recognition, clustering, classification, and association rule. In recent years a promising data mining approach called associative classification (AC) has been proposed, AC integrates classification and association rule discovery to build classification models (classifiers). This paper surveys and critically compares several AC algorithms with reference of the different procedures are used in each algorithm, such as rule learning, rule sorting, rule pruning, classifier building, and class allocation for test cases.

Keywords: associative classification, classification, data mining, learning, rule ranking, rule pruning, prediction

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Authors: Vijay Kr. Yadav, Nilam Rathi

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Accurate prediction of glucose level for diabetes mellitus is required to avoid affecting the functioning of major organs of human body. This study describes the fundamental assumptions and two different methodologies of the Blood glucose prediction. First is based on the back-propagation algorithm of Artificial Neural Network (ANN), and second is based on the Neuro-Fuzzy technique, called Fuzzy Inference System (FIS). Errors between proposed methods further discussed through various statistical methods such as mean square error (MSE), normalised mean absolute error (NMAE). The main objective of present study is to develop mathematical model for blood glucose prediction before 12 hours advanced using data set of three patients for 60 days. The comparative studies of the accuracy with other existing models are also made with same data set.

Keywords: back-propagation, diabetes mellitus, fuzzy inference system, neuro-fuzzy

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Authors: Pocholo Rodriguez, Anne Bernadine Ocampo, Ian Benedict Chan, Janric Micah Gray

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The state of an electric power system may be classified as either stable or unstable. The borderline of stability is at any condition for which a slight change in an unfavourable direction of any pertinent quantity will cause instability. Voltage instability in power distribution systems could lead to voltage collapse and thus power blackouts. The researchers will present an intelligent system using back propagation algorithm that can detect voltage instability and output voltage of a power distribution and classify it as stable or unstable. The researchers’ work is the use of parameters involved in voltage instability as input parameters to the neural network for training and testing purposes that can provide faster detection and monitoring of the power distribution system.

Keywords: back-propagation algorithm, load instability, neural network, power distribution system

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Authors: Daniela Piana

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This work casts light on what lies underneath the rule of law. In order to do so it unfolds the arguments in three main steps. The first one is a pars destruens: the mainstreaming scholarship on judicial independence and judicial accountability is questioned under the large amount of data we have at our disposal (this step is accomplished in the first two paragraphs). The second step is the reframe of the concept of the rule of law and the consequent rise of a hidden dimension, which has been so far largely underexplored: responsiveness. The third step consists into offering the readers empirical support and drawing thereby consequences in terms of policy design and citizens engagement into the rule of law implementation (these two steps are accomplished in the third paragraph).

Keywords: rule of law, accountability, trust, citizens

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Authors: Seyed Jafar Hosseini, Rahim Vakilzadeh, Hassan Movassagi

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‘Negation of insinuation’ or ‘negation of dominance’ Rule is considered as one of the most important principles governing the policies and external relations of Islamic and religious countries. The stable and influential role which this rule puts on the behavior and policies of the Islamic religion and foreign policies of Islamic countries shows the importance of the presented topic. Among Islamic scholars, Imam Khomeini (RA) has been paid most attention to this rule on governing issues. In the present study, we are going to investigate the nature and dimensions of Negation of insinuation rule in Imam Khomeini's ideas with an analytical and descriptive method. The obtained results show that Negation of insinuation rule is an effective and main guidance in Imam's thoughts and behavior.

Keywords: negation of insinuation Rule, Imam Khomeini (RA), cultural domination, political domination, economic domination

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Authors: Kwan Hee Han, Jun Woo Lee, Sung Moon Bae, Twae Kyung Park

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ECA (Event-Condition-Action) languages are largely adopted for event processing since they are an intuitive and powerful paradigm for programming reactive systems. However, there are some limitations about ECA rules for processing of complex events such as coupling of event producer and consumer. The objective of this paper is to propose an ECA rule pattern to improve the current limitations of ECA rule, and to develop a prototype system. In this paper, conventional ECA rule is separated into 3 parts and each part is extended to meet the requirements of CEP. Finally, event processing logic is established by combining the relevant elements of 3 parts. The usability of proposed extended ECA rule is validated by a test scenario in this study.

Keywords: complex event processing, ECA rule, Event processing system, event-driven architecture, internet of things

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Authors: Wheyming Song, Hung-Hsiang Lin, Scott Lian

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In this research, we investigate the optimal dispatching rule for machines and manpower allocation in the solar ingot-wafer systems. The performance of the method is measured by the sales profit for each dollar paid to the operators in a one week at steady-state. The decision variables are identification-number of machines and operators when each job is required to be served in each process. We propose a rule which is a function of operator’s ability, corresponding salary, and standing location while in the factory. The rule is named ‘Multi-nominal distribution dispatch rule’. The proposed rule performs better than many traditional rules including generic algorithm and particle swarm optimization. Simulation results show that the proposed Multi-nominal distribution dispatch rule improvement on the sales profit dramatically.

Keywords: dispatching, solar ingot, simulation, flexsim

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant

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Authors: Seon Soon Choi

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It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to present the good probability distribution fit for the fatigue crack propagation life at a specified fatigue crack size in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed and the good probability distribution fit for the fatigue crack propagation life is presented. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: fatigue crack propagation life, load ratio, magnesium alloys, probability distribution

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Authors: Seon Soon Choi

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The principal purpose of this paper is to find the influence of maximum fatigue load on the probabilistic aspect of fatigue crack propagation life at a specified grown crack in magnesium alloys. The experiments of fatigue crack propagation are carried out in laboratory air under different conditions of the maximum fatigue loads to obtain the fatigue crack propagation data for the statistical analysis. In order to analyze the probabilistic aspect of fatigue crack propagation life, the goodness-of fit test for probability distribution of the fatigue crack propagation life at a specified grown crack is implemented through Anderson-Darling test. The good probability distribution of the fatigue crack propagation life is also verified under the conditions of the maximum fatigue loads.

Keywords: fatigue crack propagation life, magnesium alloys, maximum fatigue load, probability

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Authors: Wullapa Wongsinlatam

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Back propagation algorithm (BP) is a widely used technique in artificial neural network and has been used as a tool for solving the time series problems, such as decreasing training time, maximizing the ability to fall into local minima, and optimizing sensitivity of the initial weights and bias. This paper proposes an improvement of a BP technique which is called IM-COH algorithm (IM-COH). By combining IM-COH algorithm with cuckoo search algorithm (CS), the result is cuckoo search improved control output hidden layer algorithm (CS-IM-COH). This new algorithm has a better ability in optimizing sensitivity of the initial weights and bias than the original BP algorithm. In this research, the algorithm of CS-IM-COH is compared with the original BP, the IM-COH, and the original BP with CS (CS-BP). Furthermore, the selected benchmarks, four time series samples, are shown in this research for illustration. The research shows that the CS-IM-COH algorithm give the best forecasting results compared with the selected samples.

Keywords: artificial neural networks, back propagation algorithm, time series, local minima problem, metaheuristic optimization

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Authors: Mbuzeni Mathenjwa

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Upon their independence, most African countries adopted constitutions that proclaim respect for the rule of law. The decision to constitutionalise the rule of law is basically informed by the countries’ experience during the colonial era which was characterised by discrimination on various grounds including race, gender and religion. Despite the promise to be bound by and adhere to the rule of law, disrespect for the rule of law has become a norm in the African continent. This is evident from the reported incidence of abuse of power, failure to perform obligations imposed by law and flagrant disregard of the law by the Executive including the heads of states in the continent. In some African countries including South Africa, the courts of law have been approached to rule on the legality of the decisions of the executives, taken contrary to the prescripts of the law. South African Courts have laid down a number of decisions wherein they found that the conduct of the executive contravenes the rule of law. Consequently decisions of the executive have been declared invalid by courts. In this regard courts have become a safety net in preserving the rule of law in. Accordingly, this paper discusses the role of the courts in preserving the rule of law in Africa. This it does by explaining the notion of judicial independence and the doctrine of the rule of law. The explanation on the notion of judicial independence is relevant because only an independent judiciary can effectively review and set aside the decision of the executive including the president of a country. Furthermore, a comparative overview of the enforcement of the rule of law in African countries is done. The methods used for this research is literature review, and study of legislation and case law in selected African countries relating to the independence of the judiciary and the rule of law. Finally, a conclusion is drawn on the role of the independent judiciary to preserve the rule of law in Africa.

Keywords: Africa, constitutions, independence, judiciary

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Authors: A. Keshavarz

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A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: beam propagation, cos-Gaussian beam, numerical simulation, photorefractive crystal

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Authors: Avinash S. Jagtap, Sharad D. Gore, Rajendra G. Gurao

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Decision rules become more and more complex as the number of conditions increase. As a consequence, the complexity of the decision rule also influences the time complexity of computer implementation of such a rule. Consider, for example, a decision that depends on four conditions A, B, C and D. For simplicity, suppose each of these four conditions is binary. Even then the decision rule will consist of 16 lines, where each line will be of the form: If A and B and C and D, then action 1. If A and B and C but not D, then action 2 and so on. While executing this decision rule, each of the four conditions will be checked every time until all the four conditions in a line are satisfied. The minimum number of logical comparisons is 4 whereas the maximum number is 64. This paper proposes to present a complex decision rule in the form of a decision tree. A decision tree divides the cases into branches every time a condition is checked. In the form of a decision tree, every branching eliminates half of the cases that do not satisfy the related conditions. As a result, every branch of the decision tree involves only four logical comparisons and hence is significantly simpler than the corresponding complex decision rule. The conclusion of this paper is that every complex decision rule can be represented as a decision tree and the decision tree is mathematically equivalent but computationally much simpler than the original complex decision rule

Keywords: strategic, tactical, operational, adaptive, innovative

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