Search results for: Distributed learning

Authors: N. Paparisteidi, D. Rodamitou

Abstract:

This article focuses on the skills development and path planning of students studying computer science at EPITECH: French private institute of higher education. We examine students’ points of view and experience in a blended learning model based on a skills development curriculum. The study is based on the collection of four main categories of data: semi-participant observation, distribution of questionnaires, interviews, and analysis of internal school databases. The findings seem to indicate that a skills-based program on active learning enables students to develop their learning strategies as well as their personal skills and to actively engage in the creation of their career path and contribute to providing additional information to curricula planners and decision-makers about learning design in higher education.

Keywords: Active learning, blended learning, higher education, skills development.

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Authors: Mafawez Alharbi, Mahdi Jemmali

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E-learning is a developing area especially in education. E-learning can provide several benefits to learners. An intelligent system to collect all components satisfying user preferences is so important. This research presents an approach that it capable to personalize e-information and give the user their needs following their preferences. This proposal can make some knowledge after more evaluations made by the user. In addition, it can learn from the habit from the user. Finally, we show a walk-through to prove how intelligent process work.

Keywords: Artificial intelligence, architecture, e-learning, software engineering, processing.

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Authors: Komon Paisal

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The aim of this research was to create collaborative learning activities in the course of Principles of Mathematics for graduate level by investigating the students’ ability in proving the mathematics principles as well as their attitudes towards the activities. The samples composed of 2 main group; lecturers and students. The lecturers consisted of 3 teachers who taught the course of Principles of Mathematics at Rajabhat Suan Sunandha Unicersity in the academic year 2012. The students consisted of 32 students joining the cooperative learning activities in the subject of Principles of Mathematics in the academic year 2012. The research tools included activity plan for cooperative learning, testing on mathematics with the reliability of 0.8067 and the attitude questionnaires reported by the students. The results showed that: 1) the efficiency of the developed cooperative learning activities was 69.76/ 68.57 which was lower than the set criteria at 70/70. 2) The students joining the cooperative learning activities were able to prove the principles of mathematics at the average of 70%. 3) The students joining the cooperative learning activities reported moderate attitude towards the activities.

Keywords: Instructional Design, Pedagogical, Teaching/ Learning Strategies.

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Authors: Kanika Sood, Sijie Shang

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A fundamental goal of education includes preparing students to become a part of the global workforce by making beneficial contributions to society. In this paper, we analyze student performance for multiple courses that involve different teaching pedagogies: a cooperative learning technique and an inquiry-based learning strategy. Student performance includes student engagement, grades, and attendance records. We perform this study in the Computer Science department for online and in-person courses for 450 students. We will perform correlation analysis to study the relationship between student scores and other parameters such as gender, mode of learning. We use natural language processing and machine learning to analyze student feedback data and performance data. We assess the learning outcomes of two teaching pedagogies for undergraduate and graduate courses to showcase the impact of pedagogical adoption and learning outcome as determinants of academic achievement. Early findings suggest that when using the specified pedagogies, students become experts on their topics and illustrate enhanced engagement with peers.

Keywords: Bag-of-words, cooperative learning, education, inquiry-based learning, in-person learning, Natural Language Processing, online learning, sentiment analysis, teaching pedagogy.

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Authors: Afaf Alharbi, Qianni Zhang

Abstract:

The identification of malignant tissue in histopathological slides holds significant importance in both clinical settings and pathology research. This paper presents a methodology aimed at automatically categorizing cancerous tissue through the utilization of a multiple instance learning framework. This framework is specifically developed to acquire knowledge of the Bernoulli distribution of the bag label probability by employing neural networks. Furthermore, we put forward a neural network-based permutation-invariant aggregation operator, equivalent to attention mechanisms, which is applied to the multi-instance learning network. Through empirical evaluation on an openly available colon cancer histopathology dataset, we provide evidence that our approach surpasses various conventional deep learning methods.

Keywords: Attention Multiple Instance Learning, Multiple Instance Learning, transfer learning, histopathological slides, cancer tissue classification.

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Authors: Amir Lotfi, Seyed Hamid Hosseini

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During the recent past, due to the increase of electrical energy demand and governmental resources constraints in creating additional capacity in the generation, transmission, and distribution, privatization, and restructuring in electrical industry have been considered. So, in most of the countries, different parts of electrical industry like generation, transmission, and distribution have been separated in order to create competition. Considering these changes, environmental issues, energy growth, investment of private equity in energy generation units and difficulties of transmission lines expansion, distributed generation (DG) units have been used in power systems. Moreover, reduction in the need for transmission and distribution, the increase of reliability, improvement of power quality, and reduction of power loss have caused DG to be placed in power systems. On the other hand, considering low liquidity need, private investors tend to spend their money for DGs. In this project, the main goal is to offer an algorithm for planning and placing DGs in order to reduce the need for transmission and distribution network.

Keywords: Planning, transmission, distributed generation, power security, power systems.

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Authors: E. Heikkilä

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The paper discusses European Lifelong Learning policy in the European enlargement to the Balkan. The European Lifelong Learning policy with Human Capital approach is researched in the country case of Macedonia. The paper argues that Human Capital approach focusing on instrumental and economic importance of learning for employability and economic growth needs to be complemented with Capability Approach for intrinsic and noneconomic needs of learning among the ethnic minorities. The paper identifies two dimensions of importance – minority languages and civic education – that the Capability Approach may develop to guarantee equal opportunities to all to benefit from European educational and lifelong learning development and to build an inclusive and socially just democracy in Macedonia.

Keywords: Capability approach, European lifelong learning, human capital theory.

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Authors: Peter A. Bibby

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Research has suggested that implicit learning tasks may rely on episodic processing to generate above chance performance on the standard classification tasks. The current research examines the invariant features task (McGeorge and Burton, 1990) and argues that such episodic processing is indeed important. The results of the experiment suggest that both rejection and similarity strategies are used by participants in this task to simultaneously reject unfamiliar items and to accept (falsely) familiar items. Primarily these decisions are based on the presence of low or high frequency goal based features of the stimuli presented in the incidental learning phase. It is proposed that a goal based analysis of the incidental learning task provides a simple step in understanding which features of the episodic processing are most important for explaining the match between incidental, implicit learning and test performance.

Keywords: Episodic processing, incidental learning, implicitlearning, invariant learning.

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Authors: Grace Adebisi Fayombo

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This study investigated the relationships between the active learning strategies (discussion, video clips, game show, role– play, five minute paper, clarification pauses, and small group) and academic achievement among a sample of 158 undergraduate psychology students in The University of the West Indies (UWI), Barbados. Results revealed statistically significant positive correlations between active learning strategies and students’ academic achievement; so also the active learning strategies contributed 22% (Rsq=0.222) to the variance being accounted for in academic achievement and this was found to be statistically significant (F(7,150) = 6.12, p < .05). Additionally, group work emerged as the best active learning strategy and had the highest correlation with the students’ academic achievement. These results were discussed in the light of the importance of the active learning strategies promoting academic achievement among the university students.

Keywords: Academic achievement, active learning strategies, psychology, undergraduates.

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Authors: Marcello Bettoni

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As a learning theory tries to borrow from science a framework to found its method, it shows paradoxes and paralysing contraddictions. This results, on one hand, from adopting a learning/teaching model as it were a mere “transfer of data" (mechanical learning approach), and on the other hand from borrowing the complexity theory (an indeterministic and non-linear model), that risks to vanish every educational effort. This work is aimed at describing existing criticism, unveiling the antinomic nature of such paradoxes, focussing on a view where neither the mechanical learning perspective nor the chaotic and nonlinear model can threaten and jeopardize the educational work. Author intends to go back over the steps that led to these paradoxes and to unveil their antinomic nature. Actually this could serve the purpose to explain some current misunderstandings about the real usefulness of Ict within the youth-s learning process and growth.

Keywords: Antinomy, complexity, Leibniz, paradox

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Authors: Kyaw Myo Lin, Pyone Lai Swe, Khine Zin Oo

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In this paper, an approach combining analytical method for the distributed generator (DG) sizing and meta-heuristic search for the optimal location of DG has been presented. The optimal size of DG on each bus is estimated by the loss sensitivity factor method while the optimal sites are determined by Particle Swarm Optimization (PSO) based optimal reactive power dispatch for minimizing active power loss. To confirm the proposed approach, it has been tested on IEEE-30 bus test system. The adjustments of operating constraints and voltage profile improvements have also been observed. The obtained results show that the allocation of DGs results in a significant loss reduction with good voltage profiles and the combined approach is competent in keeping the system voltages within the acceptable limits.

Keywords: Analytical approach, distributed generations, optimal size, optimal location, optimal reactive power dispatch, particle swarm optimization algorithm.

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Authors: Kamil Aida-zade, C. Ardil

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We study the problem of synthesis of lumped sources control for the objects with distributed parameters on the basis of continuous observation of phase state at given points of object. In the proposed approach the phase state space (phase space) is beforehand somehow partitioned at observable points into given subsets (zones). The synthesizing control actions therewith are taken from the class of piecewise constant functions. The current values of control actions are determined by the subset of phase space that contains the aggregate of current states of object at the observable points (in these states control actions take constant values). In the paper such synthesized control actions are called zone control actions. A technique to obtain optimal values of zone control actions with the use of smooth optimization methods is given. With this aim, the formulas of objective functional gradient in the space of zone control actions are obtained.

Keywords: Feedback control, distributed systems, smooth optimization methods, lumped control synthesis.

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Authors: Leire Urcola, Amaia Altuzarra

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This communication is intended to provide some issues for thought on the importance of implementation of Blended Learning in traditional universities, particularly in the Spanish university system. In this respect, we believe that virtual environments are likely to meet some of the needs raised by the Bologna agreement, trying to maintain the quality of teaching and at the same time taking advantage of the functionalities that virtual learning platforms offer. We are aware that an approach of learning from an open and constructivist nature in universities is a complex process that faces significant technological, administrative and human barriers. Therefore, in order to put plans in our universities, it is necessary to analyze the state of the art of some indicators relating to the use of ICT, with special attention to virtual teaching and learning, so that we can identify the main obstacles and design adaptive strategies for their full integration in the education system. Finally, we present major initiatives launched in the European and state framework for the effective implementation of new virtual environments in the area of higher education.

Keywords: Blended learning, e-Learning, ICT, Virtual LearningEnvironments

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Authors: Narat Susilaworn, Nuttawuth Muenjohn

Abstract:

The study applied a combination of organisational learning models (Senge, 1994: Pedler, Burgoyne and Boydell, 1991) and later adopted fifteen organisational learning principles with one of the biggest energy providers in South East Asia. The purposes of the current study were to: a) investigate the company-s practices on fifteen organisational learning principles; b) explore the perceptions and expectations of its employees in relations to the principles; and c) compare the perceptions and expectations between management and non-management staff toward the fifteen factors. One hundred and ten employees responded on a designed questionnaire and the results indicated that the company was practicing activities that associated with organisational learning principles. Also, according to the T-test results, significant differences between management and non-management respondents were found. Research implications are also provided.

Keywords: Organisational learning, employee perception, organisational performance.

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Authors: Eleni Aggelogiannaki, Haralambos Sarimveis

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In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.

Keywords: Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.

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Authors: Majlinda Fetaji, Alajdin Abazi, Zamir Dika, Bekim Fetaji

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The assessment of the efficacy of devised Mobile- Assisted Instructional Modes in Mobile Learning was the focus of this research. The study adopted pre-test, post-test, control group quasi-experimental design. Research instruments were developed, validated and used for collecting data. Findings revealed that the students exposed to Mobile Task Based Learning Mode (MTBLM) in using Mobile-Assisted Instruction (MAI) performed significantly better. The implication of these findings is that, the Audio tutorial and Practice Mode (ATPM) (Stimulus instruments) of MAI had been found better over the other modes used in the study.

Keywords: Mobile-Assisted instructions, Mobile learning, learning instructions, task based learning.

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Authors: Ekachai Phaisangittisagul, Rapeepol Chongprachawat

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Obtaining labeled data in supervised learning is often difficult and expensive, and thus the trained learning algorithm tends to be overfitting due to small number of training data. As a result, some researchers have focused on using unlabeled data which may not necessary to follow the same generative distribution as the labeled data to construct a high-level feature for improving performance on supervised learning tasks. In this paper, we investigate the impact of the relationship between unlabeled and labeled data for classification performance. Specifically, we will apply difference unlabeled data which have different degrees of relation to the labeled data for handwritten digit classification task based on MNIST dataset. Our experimental results show that the higher the degree of relation between unlabeled and labeled data, the better the classification performance. Although the unlabeled data that is completely from different generative distribution to the labeled data provides the lowest classification performance, we still achieve high classification performance. This leads to expanding the applicability of the supervised learning algorithms using unsupervised learning.

Keywords: Autoencoder, high-level feature, MNIST dataset, selftaught learning, supervised learning.

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Authors: Yingjun Ruan, Qingrong Liu, Weiguo Zhou, Toshiyuki Watanabe

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This paper has examined the energy consumption characteristics in six different buildings including apartments, offices, commercial buildings, hospitals, hotels and educational facilities. Then 5-hectare (50000m2) development site for respective building-s type has been assumed as case study to evaluate the introduction effect of Combined Heat and Power (CHP). All kinds of CHP systems with different distributed generation technologies including Gas Turbine (GT), Gas Engine (GE), Diesel Engine (DE), Solid Oxide Fuel Cell (SOFC) and Polymer Electrolyte Fuel Cell (PEFC), have been simulated by using HEATMAP, CHP system analysis software. And their primary energy utilization efficiency, energy saving ratio and CO2 reduction ratio have evaluated and compared respectively. The results can be summarized as follows: Various buildings have their special heat to power ratio characteristics. Matching the heat to power ratio demanded from an individual building with that supplied from a CHP system is very important. It is necessary to select a reasonable distributed generation technologies according to the load characteristics of various buildings. Distributed generation technologies with high energy generating efficiency and low heat to power ratio, like SOFC and PEFC is more reasonable selection for Building Combined Heat and Power (BCHP). CHP system is an attractive option for hotels, hospitals and apartments in Japan. The users can achieve high energy saving and environmental benefit by introducing a CHP systems. In others buildings, especially like commercial buildings and offices, the introduction of CHP system is unreasonable.

Keywords: Combined heat and power, distributed generation technologies, heat-tao-power ratio, energy saving ratio, CO2 reduction ratio

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Authors: Amit Gil, Helman Stern, Yael Edan

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A cognitive collaborative reinforcement learning algorithm (CCRL) that incorporates an advisor into the learning process is developed to improve supervised learning. An autonomous learner is enabled with a self awareness cognitive skill to decide when to solicit instructions from the advisor. The learner can also assess the value of advice, and accept or reject it. The method is evaluated for robotic motion planning using simulation. Tests are conducted for advisors with skill levels from expert to novice. The CCRL algorithm and a combined method integrating its logic with Clouse-s Introspection Approach, outperformed a base-line fully autonomous learner, and demonstrated robust performance when dealing with various advisor skill levels, learning to accept advice received from an expert, while rejecting that of less skilled collaborators. Although the CCRL algorithm is based on RL, it fits other machine learning methods, since advisor-s actions are only added to the outer layer.

Keywords: Robot learning, human-robot collaboration, motion planning, reinforcement learning.

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Authors: Anna Angelini, Enrica Gentile, Paola Plantamura, Vito Leonardo Plantamura

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A suitable e-learning system management needs to carry out a web-information system in order to allow integrated fruition of data and metadata concerning the activities typical of elearning environment. The definition of a “web information system" for e-learning takes advantage of the potentialities of Web technologies both as for the access to metadata present on the several platforms, and as for the implementation of courseware which make up the relative didactic environment. What information systems have in common is the technological environment on which they are generally implemented and the use of metadata in order to structure information at all cognitive and organization levels. In this work we are going to define a methodology for the implementation of a specific web information system for an e-learning environment.

Keywords: e-learning, information systems, coursemanagement, web-based system.

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Authors: S. Silverstone, J. Phadungtin

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Today-s Wi Fi generation utilize the latest technology in their daily lives. Instructors at National University, the second largest non profit private institution of higher learning in California, are incorporating these new tools to modify their Online class formats to better accommodate these new skills in their distance education delivery modes. The University provides accelerated learning in a one-course per month format both Onsite and Online. Since there has been such a significant increase in Online classes over the past three years, and it is expected to grow even more over the over the next five years, Instructors cannot afford to maintain the status quo and not take advantage of these new options. It is at the discretion of the instructors which accessory they use and how comfortable and familiar they are with the technology. This paper explores the effects and summarizes students- comments of some of these new technological options which have been recently provided in order to make students- online learning experience more exciting and meaningful.

Keywords: Asynchronous chats, synchronous learning, VoIP.

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Authors: M. Chaoui, M-T. Laskri

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The evolution of information and communication technology has made a very powerful support for the improvement of online learning platforms in creation of courses. This paper presents a study that attempts to explore new web architecture for creating an adaptive online learning system to profiles of learners, using the Web as a source for the automatic creation of courses for the online training platform. This architecture will reduce the time and decrease the effort performed by the drafters of the current e-learning platform, and direct adaptation of the Web content will greatly enrich the quality of online training courses.

Keywords: Web Content, e-Learning, Educational Content, LMS, Profiles of Learners

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Authors: Shashank N. Mathur, Anil K. Ahlawat, Virendra P. Vishwakarma

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In this paper, a comparative study of application of supervised and unsupervised learning algorithms on illumination invariant face recognition has been carried out. The supervised learning has been carried out with the help of using a bi-layered artificial neural network having one input, two hidden and one output layer. The gradient descent with momentum and adaptive learning rate back propagation learning algorithm has been used to implement the supervised learning in a way that both the inputs and corresponding outputs are provided at the time of training the network, thus here is an inherent clustering and optimized learning of weights which provide us with efficient results.. The unsupervised learning has been implemented with the help of a modified Counterpropagation network. The Counterpropagation network involves the process of clustering followed by application of Outstar rule to obtain the recognized face. The face recognition system has been developed for recognizing faces which have varying illumination intensities, where the database images vary in lighting with respect to angle of illumination with horizontal and vertical planes. The supervised and unsupervised learning algorithms have been implemented and have been tested exhaustively, with and without application of histogram equalization to get efficient results.

Keywords: Artificial Neural Networks, back propagation, Counterpropagation networks, face recognition, learning algorithms.

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Authors: Melvin A. Ballera

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Prior literature in the field of adaptive and personalized learning sequence in e-learning have proposed and implemented various mechanisms to improve the learning process such as individualization and personalization, but complex to implement due to expensive algorithmic programming and need of extensive and prior data. The main objective of personalizing learning sequence is to maximize learning by dynamically selecting the closest teaching operation in order to achieve the learning competency of learner. In this paper, a revolutionary technique has been proposed and tested to perform individualization and personalization using modified reversed roulette wheel selection algorithm that runs at O(n). The technique is simpler to implement and is algorithmically less expensive compared to other revolutionary algorithms since it collects the dynamic real time performance matrix such as examinations, reviews, and study to form the RWSA single numerical fitness value. Results show that the implemented system is capable of recommending new learning sequences that lessens time of study based on student's prior knowledge and real performance matrix.

Keywords: E-learning, fitness value, personalized learning sequence, reversed roulette wheel selection algorithms.

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Authors: M. Polanský

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This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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Authors: S. Rawashdi, D. Bshouty

Abstract:

This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: Awakeness, awareness, learning mathematics, pupils.

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Authors: Martina Holenko Dlab, Natasa Hoic-Bozic, Ivica Boticki

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This paper presents technologically innovative and scalable mobile learning solution within the SCOLLAm project (“Opening up education through Seamless and COLLAborative mobile learning on tablet computers”). The main research method applied during the development of the SCOLLAm mobile learning system is design-based research. It assumes iterative refinement of the system guided by collaboration between researches and practitioners. Following the identification of requirements, a multiplatform mobile learning system SCOLLAm [in]Form was developed. Several experiments were designed and conducted in the first and second grade of elementary school. SCOLLAm [in]Form system was used to design learning activities for math classes during which students practice calculation. System refinements were based on experience and interaction data gathered during class observations. In addition to implemented improvements, the data were used to outline possible improvements and deficiencies of the system that should be addressed in the next phase of the SCOLLAm [in]Form development.

Keywords: Adaptation, collaborative learning, educational technology, mobile learning, tablet computers.

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Authors: Mallikarjun B. Channappagoudar, Pallapa Venkataram

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As a node monitoring protocol, which is a part of network management, operates in distributed manner, conformance testing of such protocols is more tedious than testing a peer-to-peer protocol. Various works carried out to give the methodology to do conformance testing of distributed protocol. In this paper, we have presented a formal approach for conformance testing of a Node Monitoring Protocol, which uses both static and mobile agents, for MANETs. First, we use SDL to obtain MSCs, which represent the scenario descriptions by sequence diagrams, which in turn generate test sequences and test cases. Later, Testing and Test Control Notation Version-3 (TTCN-3) is used to execute test cases with respect to generated test sequences to know the conformance of protocol against the given specification. This approach shows, the effective conformance testing of the distributed protocols for the network with varying node density and complex behavior. Experimental results for the protocol scenario represent the effectiveness of the method used.

Keywords: Conformance Testing, FSM, Mobile agent, TTCN, Test sequence.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

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To minimize power losses, it is important to determine the location and size of local generators to be placed in unbalanced power distribution systems. On account of some inherent features of unbalanced distribution systems, such as radial structure, large number of nodes, a wide range of X/R ratios, the conventional techniques developed for the transmission systems generally fail on the determination of optimum size and location of distributed generators (DGs). This paper presents a simple method for investigating the problem of contemporaneously choosing best location and size of DG in three-phase unbalanced radial distribution system (URDS) for power loss minimization and to improve the voltage profile of the system. Best location of the DG is determined by using voltage index analysis and size of DG is computed by variational technique algorithm according to available standard size of DGs. This paper presents the results of simulations for 25-bus and IEEE 37- bus Unbalanced Radial Distribution system.

Keywords: Distributed generator, unbalanced radial distributionsystem, voltage index analysis, variational algorithm.

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Authors: Jamshaid ur Rehman, Shahida Wizarat

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The principal focus of this study is on the measurement and analysis of labor learnings in Pakistan. The study at the aggregate economy level focus on the labor productivity movements and at large-scale manufacturing level focus on the cost structure, with isolating the contribution of the learning curve. The analysis of S-shaped curve suggests that learnings are only below one half of aggregate learning curve and other half shows the retardation in learning, hence retardation in productivity movements. The study implies the existence of learning economies in term of cost reduction that is input cost per unit produced decreases by 0.51 percent every time the cumulative production output doubles.

Keywords: Cost, Inflection Point, Learning Curve, Minima, Maxima, and Productivity

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