Search results for: mixed method analysis

Authors: Fang Yao, Minglei Chen

Abstract:

City shrinkage is one of the thorny problems that many European cities have to face with nowadays. It is mainly expressed as the decrease of population in these cities. Eastern Germany is one of the pioneers of European shrinking cities with long shrinking history. The paper selects one representative shrinking city Halle (Saale) in eastern Germany as research objective, collecting and investigating nearly 20 years (1993-2010) municipal data after the reunification of Germany. These data based on five dimensions, which are demographic, economic, social, spatial and environmental and total 16 eligible variables. Factor Analysis is used to deal with these variables in order to assess the most important factors affecting shrinking Halle. The results show that there are three main factors determine the shrinkage of Halle, respectively named “demographical and economical factor”, “social stability factor”, and “city vitality factor”. The three factors act at different time period of Halle’s shrinkage: from 1993 to 1997 the demographical and economical factor played an important role; from 1997 to 2004 the social stability factor is significant to city shrinkage; since 2005 city vitality factor determines the shrinkage of Halle. In recent years, the shrinkage in Halle mitigates that shows the sign of growing population. Thus the city Halle should focus on attaching more importance on the city vitality factor to prevent the city from shrinkage. Meanwhile, the city should possess a positive perspective to shift the growth-oriented development to tap the potential of shrinking cities. This method is expected to apply to further research and other shrinking cities

Keywords: Demography, Factor analysis, Halle, Shrinking cities.

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Authors: A. S. Kipcak, P. Gurses, K. Kunt, E. Moroydor Derun, S. Piskin

Abstract:

There are many kinds of metal borates found not only in nature but also synthesized in the laboratory such as magnesium borates. Due to its excellent properties, as remarkable ceramic materials, they have also application areas in anti-wear and friction reducing additives as well as electro-conductive treating agents. The synthesis of magnesium borate powders can be fulfilled simply with two different methods, hydrothermal and thermal synthesis. Microwave assisted method, also another way of producing magnesium borate, can be classified into thermal synthesis because of using the principles of solid state synthesis. It also contributes producing particles with small size and high purity in nano-size material synthesize. In this study the production of magnesium borates, are aimed using MgCl2.6H2O and H3BO3. The identification of both starting materials and products were made by the equipments of, X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). After several synthesis steps magnesium borates were synthesized and characterized by XRD and FT-IR, as well.

Keywords: FT-IR, magnesium borates, microwave method, XRD.

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Authors: Peyman Shadman Heidari, Mohammad Khorasani

Abstract:

The principal purpose of this article is to present a new method based on Adaptive Neural Network Fuzzy Inference System (ANFIS) to generate additional artificial earthquake accelerograms from presented data, which are compatible with specified response spectra. The proposed method uses the learning abilities of ANFIS to develop the knowledge of the inverse mapping from response spectrum to earthquake records. In addition, wavelet packet transform is used to decompose specified earthquake records and then ANFISs are trained to relate the response spectrum of records to their wavelet packet coefficients. Finally, an interpretive example is presented which uses an ensemble of recorded accelerograms to demonstrate the effectiveness of the proposed method.

Keywords: Adaptive Neural Network Fuzzy Inference System, Wavelet Packet Transform, Response Spectrum.

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Authors: A. K. Al-Othman, K. M. EL-Nagger

Abstract:

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED). Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using one system. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED).

Keywords: Security Constrained Economic Dispatch, Direct Search method, optimization.

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Authors: T. Hacib, M. R. Mekideche, N. Ferkha

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This paper presents an approach which is based on the use of supervised feed forward neural network, namely multilayer perceptron (MLP) neural network and finite element method (FEM) to solve the inverse problem of parameters identification. The approach is used to identify unknown parameters of ferromagnetic materials. The methodology used in this study consists in the simulation of a large number of parameters in a material under test, using the finite element method (FEM). Both variations in relative magnetic permeability and electrical conductivity of the material under test are considered. Then, the obtained results are used to generate a set of vectors for the training of MLP neural network. Finally, the obtained neural network is used to evaluate a group of new materials, simulated by the FEM, but not belonging to the original dataset. Noisy data, added to the probe measurements is used to enhance the robustness of the method. The reached results demonstrate the efficiency of the proposed approach, and encourage future works on this subject.

Keywords: Inverse problem, MLP neural network, parametersidentification, FEM.

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

Abstract:

This paper is aimed at proposing a rhombus shaped wearable fractal antenna for wireless communication systems. The geometrical descriptors of the antenna have been obtained using bacterial foraging optimization (BFO) for wide band operation. The method of moment based IE3D software has been used to simulate the antenna and observed that miniaturization of 13.08% has been achieved without degrading the resonating properties of the proposed antenna. An analysis with different substrates has also been done in order to evaluate the effectiveness of electrical permittivity on the presented structure. The proposed antenna has low profile, light weight and has successfully demonstrated wideband and multiband characteristics for wearable electronic applications.

Keywords: BFO, bandwidth, electrical permittivity, fractals, wearable antenna.

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Authors: A. Zerarka, A. Soukeur, N. Khelil

Abstract:

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.

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Authors: Tudor Barbu

Abstract:

We provide a supervised speech-independent voice recognition technique in this paper. In the feature extraction stage we propose a mel-cepstral based approach. Our feature vector classification method uses a special nonlinear metric, derived from the Hausdorff distance for sets, and a minimum mean distance classifier.

Keywords: Text-independent speaker recognition, mel cepstral analysis, speech feature vector, Hausdorff-based metric, supervised classification.

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Authors: H. B. Darbandi, M. R. Ito, J. Little

Abstract:

This paper describes a probabilistic method for three-dimensional object recognition using a shared pool of surface signatures. This technique uses flatness, orientation, and convexity signatures that encode the surface of a free-form object into three discriminative vectors, and then creates a shared pool of data by clustering the signatures using a distance function. This method applies the Bayes-s rule for recognition process, and it is extensible to a large collection of three-dimensional objects.

Keywords: Object recognition, modeling, classification, computer vision.

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Authors: S. A. Naeini, A. Khalili

Abstract:

Nowadays, tunnels with different applications are developed, and most of them are related to subway tunnels. The excavation of shallow tunnels that pass under municipal utilities is very important, and the surface settlement control is an important factor in the design. The study sought to analyze the settlement and also to find an appropriate model in order to predict the behavior of the tunnel in Tehran subway line-3. The displacement in these sections is also determined by using numerical analyses and numerical modeling. In addition, the Adaptive Neuro-Fuzzy Inference System (ANFIS) method is utilized by Hybrid training algorithm. The database pertinent to the optimum network was obtained from 46 subway tunnels in Iran and Turkey which have been constructed by the new Austrian tunneling method (NATM) with similar parameters based on type of their soil. The surface settlement was measured, and the acquired results were compared to the predicted values. The results disclosed that computing intelligence is a good substitute for numerical modeling.

Keywords: Settlement, subway line, FLAC3D, ANFIS method.

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Authors: Shishen Xie, Yingda L. Xie

Abstract:

Tuberculosis (TB) is a potentially serious infectious disease that remains a health concern. The Interferon Gamma Release Assay (IGRA) is a blood test to find out if an individual is tuberculous positive or negative. This study applies statistical analysis to the clinical data of interferon-gamma levels of seventy-three subjects who diagnosed pulmonary TB in an anti-tuberculous treatment. Data analysis is performed to determine if there is a significant decline in interferon-gamma levels for the subjects during a period of six months, and to infer if the anti-tuberculous treatment is effective.

Keywords: Data analysis, interferon gamma release assay, statistical methods, tuberculosis infection.

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Authors: Lucas A. Silva, Carla R. Aguiar

Abstract:

This work presents a proposal to perform contextual sentiment analysis using a supervised learning algorithm and disregarding the extensive training of annotators. To achieve this goal, a web platform was developed to perform the entire procedure outlined in this paper. The main contribution of the pipeline described in this article is to simplify and automate the annotation process through a system of analysis of congruence between the notes. This ensured satisfactory results even without using specialized annotators in the context of the research, avoiding the generation of biased training data for the classifiers. For this, a case study was conducted in a blog of entrepreneurship. The experimental results were consistent with the literature related annotation using formalized process with experts.

Keywords: Contextualized classifier, naïve Bayes, sentiment analysis, untrained annotators.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: Zone-Ching Lin, Meng-Hua Lin, Ying-Chih Hsu

Abstract:

This paper uses quasi-steady molecular statics model and diamond tool to carry out simulation temperature rise of nanoscale orthogonal cutting single-crystal silicon. It further qualitatively analyzes temperature field of silicon workpiece without considering heat transfer and considering heat transfer. This paper supposes that the temperature rise of workpiece is mainly caused by two heat sources: plastic deformation heat and friction heat. Then, this paper develops a theoretical model about production of the plastic deformation heat and friction heat during nanoscale orthogonal cutting. After the increased temperature produced by these two heat sources are added up, the acquired total temperature rise at each atom of the workpiece is substituted in heat transfer finite difference equation to carry out heat transfer and calculates the temperature field in each step and makes related analysis.

Keywords: Quasi-steady molecular statics, Nanoscale orthogonal cutting, Finite difference, Temperature.

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Authors: Rebecca Angeles

Abstract:

This case study features the Kuehne + Nagel PharmaChain solution for ‘cold chain’ pharmaceutical and biologic product shipments with IOT-enabled features for shipment temperature and location tracking. Using the case study method and content analysis, this research project investigates the application of the structurational model of technology theory introduced by Orlikowski in order to interpret the firm’s entry and participation in the IOT-impelled marketplace.

Keywords: Internet of things, IoT, radio frequency identification, supply chain management, business intelligence.

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Authors: Anasheh Maridiroosi, Ali Reza Mahjoub, Hanieh Fakhri

Abstract:

Heteropoly acid nanoparticles anchored on graphene oxide based on UiO-66 were synthesized via in-situ growth hydrothermal method and tested for photodegradation of a tetracycline as critical pollutant. Results showed that presence of graphene oxide and UiO-66 with high specific surface area, great electron mobility and various functional groups make an excellent support for heteropoly acid and improve photocatalytic efficiency up to 95% for tetracycline. Furthermore, total organic carbon (TOC) analysis verified 79% mineralization of this pollutant under optimum condition.

Keywords: Heteropoly acid, graphene oxide, MOF, tetracycline.

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Authors: M. Stoklasa, H. Starzyczna, L. Zotykova

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This article deals with consumer ethnocentrism in the Moravian-Silesian region in the Czech Republic. Research was focused on finding out how strong consumer ethnocentrism is in the region and how it depends on demographic factors. The used method is CETSCALE and the data were obtained by questionnaire survey, analyzed by IBM SPSS. From the thousands of respondents the representative sample of 414 for MS region was created based on demographic factors of gender, age, education and income. The research analysis disclosed that consumer ethnocentrism in MS region depends on education and income and is independent on gender and age.

Keywords: Consumer ethnocentrism, demographic factors, foreign products, local products.

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Authors: Sungwon Jo

Abstract:

Ceramics comprise the largest proportion of Korea-s cultural heritage currently preserved (Cited from “The Beauty of Old Ceramics of Korea" written by Yoon Yong-iee). Thus, this researcher conducted this investigation in an attempt to gain insight into Korea-s past culture and the lost period of the colonial period and the Korean War by looking into the ceramics. Korea, China and Japan are part of the similar cultural bloc within the East Asian region. Their porcelains manifest distinctive characteristics by each nation along with similarities. Thus, this research seeks to find the distinctive characteristics of the Korean porcelain by conducting comparative analysis of the similarities and distinctive characteristics. These distinctive characteristics are manifested effectively in the colors of the porcelains following the materials that can be obtained in Korea, China and Japan and production method. Likewise, this research seeks to identify the characteristics of the Korean porcelains- colors based on the comparative analysis of the porcelain colors. The reasons that porcelains were selected were because they are the most well preserved cultural remains in Korea and since they have both similarities and distinctive characteristics due to the cultural interchanges among Korea, China and Japan, which facilitates comparative study. The research targets include Korea, China and Japan-s porcelains. By comparing the colors of the porcelains from Korea, China and Japan that have their distinctive characteristics, this research seeks to identify Korea-specific porcelain colors. These colors derive from the materials that can be obtained only in Korea, and they are affected by the ideologies that governed at the time. This research is meaningful in the sense that this identifies the colors that embraces the Korean culture and provides important data by leveraging the study of the characteristics of the Korea-specific porcelains.

Keywords: The colors of Korean pottery, The colors of China pottery, The colors of Japan pottery, The unique identity of Korea, Pottery History.

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Authors: M. Ramachandra, G. Dilip Maruthi, R. Rashmi

Abstract:

This paper aims to study the corrosion property of aluminum matrix nanocomposite of an aluminum alloy (Al-6061) reinforced with zirconium dioxide (ZrO₂) particles. The zirconium dioxide particles are synthesized by solution combustion method. The nanocomposite materials are prepared by mechanical stir casting method, varying the percentage of n-ZrO₂ (2.5%, 5% and 7.5% by weight). The corrosion behavior of base metal (Al-6061) and Al/ZrO₂ nanocomposite in seawater (3.5% NaCl solution) is measured using the potential control method. The corrosion rate is evaluated by Tafel extrapolation technique. The corrosion potential increases with the increase in wt.% of n-ZrO₂ in the nanocomposite which means the decrease in corrosion rate. It is found that on addition of n-ZrO2 particles to the aluminum matrix, the corrosion rate has decreased compared to the base metal.

Keywords: Al6061 alloy, corrosion, solution combustion, stir casting, Potentiostat, Zirconium Dioxide.

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Authors: A. Perolini

Abstract:

Feature and model selection are in the center of attention of many researches because of their impact on classifiers- performance. Both selections are usually performed separately but recent developments suggest using a combined GA-SVM approach to perform them simultaneously. This approach improves the performance of the classifier identifying the best subset of variables and the optimal parameters- values. Although GA-SVM is an effective method it is computationally expensive, thus a rough method can be considered. The paper investigates a joined approach of Genetic Algorithm and kernel matrix criteria to perform simultaneously feature and model selection for SVM classification problem. The purpose of this research is to improve the classification performance of SVM through an efficient approach, the Kernel Matrix Genetic Algorithm method (KMGA).

Keywords: Feature and model selection, Genetic Algorithms, Support Vector Machines, kernel matrix.

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Authors: Tanwarat Kajsongkram, Saowalux Rotamporn, Sirinat Limbunruang, Sirinan Thubthimthed

Abstract:

High Performance Liquid Chromatography (HPLC) method was developed and validated for simultaneous estimation of 6-Gingerol(6G) and 6-Shogaol(6S) in joint pain relief gel containing ginger extract. The chromatographic separation was achieved by using C18 column, 150 x 4.6mm i.d., 5μ Luna, mobile phase containing acetonitrile and water (gradient elution). The flow rate was 1.0 ml/min and the absorbance was monitored at 282 nm. The proposed method was validated in terms of the analytical parameters such as specificity, accuracy, precision, linearity, range, limit of detection (LOD), limit of quantification (LOQ), and determined based on the International Conference on Harmonization (ICH) guidelines. The linearity ranges of 6G and 6S were obtained over 20- 60 and 6-18 μg/ml respectively. Good linearity was observed over the above-mentioned range with linear regression equation Y= 11016x- 23778 for 6G and Y = 19276x-19604 for 6S (x is concentration of analytes in μg/ml and Y is peak area). The value of correlation coefficient was found to be 0.9994 for both markers. The limit of detection (LOD) and limit of quantification (LOQ) for 6G were 0.8567 and 2.8555 μg/ml and for 6S were 0.3672 and 1.2238 μg/ml respectively. The recovery range for 6G and 6S were found to be 91.57 to 102.36 % and 84.73 to 92.85 % for all three spiked levels. The RSD values from repeated extractions for 6G and 6S were 3.43 and 3.09% respectively. The validation of developed method on precision, accuracy, specificity, linearity, and range were also performed with well-accepted results.

Keywords: Ginger, 6-gingerol, HPLC, 6-shogaol.

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Authors: Mu-Yen Chen, Min-Hsuan Fan, Chia-Chen Chen, Siang-Yu Jhong

Abstract:

In recent years, real estate prediction or valuation has been a topic of discussion in many developed countries. Improper hype created by investors leads to fluctuating prices of real estate, affecting many consumers to purchase their own homes. Therefore, scholars from various countries have conducted research in real estate valuation and prediction. With the back-propagation neural network that has been popular in recent years and the orthogonal array in the Taguchi method, this study aimed to find the optimal parameter combination at different levels of orthogonal array after the system presented different parameter combinations, so that the artificial neural network obtained the most accurate results. The experimental results also demonstrated that the method presented in the study had a better result than traditional machine learning. Finally, it also showed that the model proposed in this study had the optimal predictive effect, and could significantly reduce the cost of time in simulation operation. The best predictive results could be found with a fewer number of experiments more efficiently. Thus users could predict a real estate transaction price that is not far from the current actual prices.

Keywords: Artificial Neural Network, Taguchi Method, Real Estate Valuation Model.

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Authors: Asmaa M. Hussein, Amr Wassal, Ahmed Farouk Al-Sadek, A. F. Abd El-Rahman

Abstract:

In this study, a multivariate analysis of potato spectroscopic data was presented to detect the presence of brown rot disease or not. Near-Infrared (NIR) spectroscopy (1,350-2,500 nm) combined with multivariate analysis was used as a rapid, non-destructive technique for the detection of brown rot disease in potatoes. Spectral measurements were performed in 565 samples, which were chosen randomly at the infection place in the potato slice. In this study, 254 infected and 311 uninfected (brown rot-free) samples were analyzed using different advanced statistical analysis techniques. The discrimination performance of different multivariate analysis techniques, including classification, pre-processing, and dimension reduction, were compared. Applying a random forest algorithm classifier with different pre-processing techniques to raw spectra had the best performance as the total classification accuracy of 98.7% was achieved in discriminating infected potatoes from control.

Keywords: Brown rot disease, NIR spectroscopy, potato, random forest.

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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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Authors: A. Ghafouri, N. Pourmahmoud, I. Mirzaee

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In this numerical study, effects of using Al2O3-water nanofluid on the rate of heat transfer have been investigated. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the nanoparticle diameter 30, 60 and 90 nm and the solid volume fraction 0 to 0.04. Results are presented by average Nusselt number and normalized Nusselt number in different range of φ and D for mixed convection dominated regime. It is found that different heat transfer rate is predicted when the effect of nanoparticle diameter is taken into account.

Keywords: Nano-fluid, nanoparticle diameter, heat transfer enhancement, square enclosure, Nusselt number.

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Authors: Mohammed A. Hajeeh

Abstract:

This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: Repairable models, imperfect, availability, exponential distribution.

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Authors: Hussain A. Alkharusi, Said S. Aldhafri, Hilal Z. Alnabhani, Muna Alkalbani

Abstract:

Analyzing classroom assessments is one of the responsibilities of the teacher. It aims improving teacher’s instruction and assessment as well as student learning. The present study investigated factors that might explain variation in teachers’ practices regarding analysis of classroom assessments. The factors considered in the investigation included gender, in-service assessment training, teaching load, teaching experience, knowledge in assessment, attitude towards quantitative aspects of assessment, and self-perceived competence in analyzing assessments. Participants were 246 in-service teachers in Oman. Results of a stepwise multiple linear regression analysis revealed that self-perceived competence was the only significant factor explaining the variance in teachers’ analysis of assessments. Implications for research and practice are discussed.

 

Keywords: Analysis of assessment, Classroom assessment, In-service teachers, Self-competence.

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Authors: S. Umarani, D. Sharmila

Abstract:

A Distributed Denial of Service (DDoS) attack is a major threat to cyber security. It originates from the network layer or the application layer of compromised/attacker systems which are connected to the network. The impact of this attack ranges from the simple inconvenience to use a particular service to causing major failures at the targeted server. When there is heavy traffic flow to a target server, it is necessary to classify the legitimate access and attacks. In this paper, a novel method is proposed to detect DDoS attacks from the traces of traffic flow. An access matrix is created from the traces. As the access matrix is multi dimensional, Principle Component Analysis (PCA) is used to reduce the attributes used for detection. Two classifiers Naive Bayes and K-Nearest neighborhood are used to classify the traffic as normal or abnormal. The performance of the classifier with PCA selected attributes and actual attributes of access matrix is compared by the detection rate and False Positive Rate (FPR).

Keywords: Distributed Denial of Service (DDoS) attack, Application layer DDoS, DDoS Detection, K- Nearest neighborhood classifier, Naive Bayes Classifier, Principle Component Analysis.

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Authors: A. Falsafain, S. M. Taheri, M. Mashinchi

Abstract:

Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameters of two Normal distributions, as well as the parameters of the Exponential and Poisson distributions.

Keywords: Confidence interval. Fuzzy number. Fuzzy estimation.

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Authors: Hossein Mirzaee, Farhad Besharati

Abstract:

A combination of image fusion and quad tree decomposition method is used for detecting the sunspot trajectories in each month and computation of the latitudes of these trajectories in each solar hemisphere. Daily solar images taken with SOHO satellite are fused for each month and the result of fused image is decomposed with Quad Tree decomposition method in order to classifying the sunspot trajectories and then to achieve the precise information about latitudes of sunspot trajectories. Also with fusion we deduce some physical remarkable conclusions about sun magnetic fields behavior. Using quad tree decomposition we give information about the region on sun surface and the space angle that tremendous flares and hot plasma gases permeate interplanetary space and attack to satellites and human technical systems. Here sunspot images in June, July and August 2001 are used for studying and give a method to compute the latitude of sunspot trajectories in each month with sunspot images.

Keywords: Quad Tree Decomposition, Sunspot.

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