Search results for: computing clusters

Authors: Raksha Sharma, Vishnu Kant Soni, Manoj Kumar Mishra, Prachet Bhuyan

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Grid computing is a form of distributed computing that involves coordinating and sharing computational power, data storage and network resources across dynamic and geographically dispersed organizations. Scheduling onto the Grid is NP-complete, so there is no best scheduling algorithm for all grid computing systems. An alternative is to select an appropriate scheduling algorithm to use in a given grid environment because of the characteristics of the tasks, machines and network connectivity. Job and resource scheduling is one of the key research area in grid computing. The goal of scheduling is to achieve highest possible system throughput and to match the application need with the available computing resources. Motivation of the survey is to encourage the amateur researcher in the field of grid computing, so that they can understand easily the concept of scheduling and can contribute in developing more efficient scheduling algorithm. This will benefit interested researchers to carry out further work in this thrust area of research.

Keywords: Grid Computing, Job Scheduling, ResourceScheduling.

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Authors: L. Sellami, D. Idoughi, P. F. Tiako

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Cloud computing provides infrastructure to the enterprise through the Internet allowing access to cloud services at anytime and anywhere. This pervasive aspect of the services, the distributed nature of data and the wide use of information make cloud computing vulnerable to intrusions that violate the security of the cloud. This requires the use of security mechanisms to detect malicious behavior in network communications and hosts such as intrusion detection systems (IDS). In this article, we focus on the detection of intrusion into the cloud sing IDSs. We base ourselves on client authentication in the computing cloud. This technique allows to detect the abnormal use of ubiquitous service and prevents the intrusion of cloud computing. This is an approach based on client authentication data. Our IDS provides intrusion detection inside and outside cloud computing network. It is a double protection approach: The security user node and the global security cloud computing.

Keywords: Cloud computing, intrusion detection system, privacy, trust.

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Authors: Ei Phyo Wai, Nay Min Tun

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Computation of facility location problem for every location in the country is not easy simultaneously. Solving the problem is described by using cluster computing. A technique is to design parallel algorithm by using local search with single swap method in order to solve that problem on clusters. Parallel implementation is done by the use of portable parallel programming, Message Passing Interface (MPI), on Microsoft Windows Compute Cluster. In this paper, it presents the algorithm that used local search with single swap method and implementation of the system of a facility to be opened by using MPI on cluster. If large datasets are considered, the process of calculating a reasonable cost for a facility becomes time consuming. The result shows parallel computation of facility location problem on cluster speedups and scales well as problem size increases.

Keywords: cluster, cost, demand, facility location

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Authors: Sandesh Achar

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Artificial intelligence (AI) is being increasingly incorporated into many applications across various sectors such as health, education, security, and agriculture. Recently, there has been rapid development in cloud computing technology, resulting in AI’s implementation into cloud computing to enhance and optimize the technology service rendered. The deployment of AI in cloud-based applications has brought about autonomous computing, whereby systems achieve stated results without human intervention. Despite the amount of research into autonomous computing, work incorporating AI/ML into cloud computing to enhance its performance and resource allocation remains a fundamental challenge. This paper highlights different manifestations, roles, trends, and challenges related to AI-based cloud computing models. This work reviews and highlights investigations and progress in the domain. Future directions are suggested for leveraging AI/ML in next-generation computing for emerging computing paradigms such as cloud environments. Adopting AI-based algorithms and techniques to increase operational efficiency, cost savings, automation, reducing energy consumption and solving complex cloud computing issues are the major findings outlined in this paper.

Keywords: Artificial intelligence, AI, cloud computing, deep learning, machine learning, ML, internet of things, IoT.

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Authors: Sauravjyoti Sarmah, Rosy Das, Dhruba Kr. Bhattacharyya

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Clustering algorithms help to understand the hidden information present in datasets. A dataset may contain intrinsic and nested clusters, the detection of which is of utmost importance. This paper presents a Distributed Grid-based Density Clustering algorithm capable of identifying arbitrary shaped embedded clusters as well as multi-density clusters over large spatial datasets. For handling massive datasets, we implemented our method using a 'sharednothing' architecture where multiple computers are interconnected over a network. Experimental results are reported to establish the superiority of the technique in terms of scale-up, speedup as well as cluster quality.

Keywords: Clustering, Density-based, Grid-based, Adaptive Grid.

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Authors: Alaa Alwani, Hassan Artail, Haidar Safa, Ayman Abi Abdallah, Bashir Basha, Tarek Abdel Khalek

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The noticeable advance in the area of computer technology has paved the way for the invention of powerful mobile devices. However, limited storage, short battery life, and relatively low computational power define the major problems of such devices. Due to the ever increasing computational requirements, such devices may fail to process needed tasks under certain constraints. One of the proposed solutions to this drawback is the introduction of Collaborative Computing, a new concept dealing with the distribution of computational tasks amongst several handhelds. This paper introduces the basics of Collaborative Computing, and proposes a new protocol that aims at managing and optimizing computing tasks in Ad-Hoc Collaborative Computing Environments.

Keywords: Handheld devices, Collaborative Computing, mainprocess, Collaboration Table.

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Authors: Chin-Hung Li, Te-Ming Chen, Ying-Chuan Chen, Shuen-Tai Wang

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This paper proposes a new approach to offer a private cloud service in HPC clusters. In particular, our approach relies on automatically scheduling users- customized environment request as a normal job in batch system. After finishing virtualization request jobs, those guest operating systems will dismiss so that compute nodes will be released again for computing. We present initial work on the innovative integration of HPC batch system and virtualization tools that aims at coexistence such that they suffice for meeting the minimizing interference required by a traditional HPC cluster. Given the design of initial infrastructure, the proposed effort has the potential to positively impact on synergy model. The results from the experiment concluded that goal for provisioning customized cluster environment indeed can be fulfilled by using virtual machines, and efficiency can be improved with proper setup and arrangements.

Keywords: Cloud Computing, HPC Cluster, Private Cloud, Virtualization

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Authors: H. Afer, N. Rouag, R. Penelle

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In the Fe-3%Si sheets, grade Hi-B, with AlN and MnS as inhibitors, the Goss grains which abnormally grow do not have a size greater than the average size of the primary matrix. In this heterogeneous microstructure, the size factor is not a required condition for the secondary recrystallization. The onset of the small Goss grain abnormal growth appears to be related to a particular behavior of their grain boundaries, to the local texture and to the distribution of the inhibitors. The presence and the evolution of oriented clusters ensure to the small Goss grains a favorable neighborhood to grow. The modified Monte-Carlo approach, which is applied, considers the local environment of each grain. The grain growth is dependent of its real spatial position; the matrix heterogeneity is then taken into account. The grain growth conditions are considered in the global matrix and in different matrixes corresponding to A component clusters. The grain growth behaviour is considered with introduction of energy only, energy and mobility, energy and mobility and precipitates.

Keywords: Abnormal grain growth, grain boundary energy andmobility, neighbourhood, oriented clusters.

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Authors: A.M. Fahim, A. M. Salem, F. A. Torkey, M. A. Ramadan

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Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, a density based clustering algorithm (DCBRD) is presented, relying on a knowledge acquired from the data by dividing the data space into overlapped regions. The proposed algorithm discovers arbitrary shaped clusters, requires no input parameters and uses the same definitions of DBSCAN algorithm. We performed an experimental evaluation of the effectiveness and efficiency of it, and compared this results with that of DBSCAN. The results of our experiments demonstrate that the proposed algorithm is significantly efficient in discovering clusters of arbitrary shape and size.

Keywords: Clustering Algorithms, Arbitrary Shape of clusters, cluster Analysis.

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Authors: E. N. Sathishkumar, K. Thangavel, T. Chandrasekhar

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Feature selection is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that all genes are not important in gene expression data. Some of the genes may be redundant, and others may be irrelevant and noisy. Here a novel approach is proposed Hybrid K-Mean-Quick Reduct (KMQR) algorithm for gene selection from gene expression data. In this study, the entire dataset is divided into clusters by applying K-Means algorithm. Each cluster contains similar genes. The high class discriminated genes has been selected based on their degree of dependence by applying Quick Reduct algorithm to all the clusters. Average Correlation Value (ACV) is calculated for the high class discriminated genes. The clusters which have the ACV value as 1 is determined as significant clusters, whose classification accuracy will be equal or high when comparing to the accuracy of the entire dataset. The proposed algorithm is evaluated using WEKA classifiers and compared. The proposed work shows that the high classification accuracy.

Keywords: Clustering, Gene Selection, K-Mean-Quick Reduct, Rough Sets.

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Authors: Shuen-Tai Wang, Ying-Chuan Chen, Hsi-Ya Chang

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The rapid improvement of the microprocessor and network has made it possible for the PC cluster to compete with conventional supercomputers. Lots of high throughput type of applications can be satisfied by using the current desktop PCs, especially for those in PC classrooms, and leave the supercomputers for the demands from large scale high performance parallel computations. This paper presents our development on enabling an automated deployment mechanism for cluster computing to utilize the computing power of PCs such as reside in PC classroom. After well deployment, these PCs can be transformed into a pre-configured cluster computing resource immediately without touching the existing education/training environment installed on these PCs. Thus, the training activities will not be affected by this additional activity to harvest idle computing cycles. The time and manpower required to build and manage a computing platform in geographically distributed PC classrooms also can be reduced by this development.

Keywords: PC cluster, automated deployment, cluster computing, PC classroom.

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Authors: Abbas Al-Refaie

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The research examines the factors that affect customer churn (CC) in the Jordanian telecom industry. A total of 700 surveys were distributed. Cluster analysis revealed three main clusters. Results showed that CC and customer satisfaction (CS) were the key determinants in forming the three clusters. In two clusters, the center values of CC were high, indicating that the customers were loyal and SC was expensive and time- and energy-consuming. Still, the mobile service provider (MSP) should enhance its communication (COM), and value added services (VASs), as well as customer complaint management systems (CCMS). Finally, for the third cluster the center of the CC indicates a poor level of loyalty, which facilitates customers churn to another MSP. The results of this study provide valuable feedback for MSP decision makers regarding approaches to improving their performance and reducing CC.

Keywords: Cluster analysis, telecom industry, switching cost, customer churn.

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Authors: Aabiah Nayeem, Fariha Shafiq, Mustabshra Aftab, Rabia Saman Pirzada, Samia Ghazala

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In this modern era of technology, the concept of Internet of Things is very popular in every domain. It is a widely distributed system of things in which the data collected from sensory devices is transmitted, analyzed locally/collectively then broadcasted to network where action can be taken remotely via mobile/web apps. Today’s mobile computing is also gaining importance as the services are provided during mobility. Through mobile computing, data are transmitted via computer without physically connected to a fixed point. The challenge is to provide services with high speed and security. Also, the data gathered from the mobiles must be processed in a secured way. Mobile computing is strongly influenced by internet of things. In this paper, we have discussed security issues and challenges of internet of things and mobile computing and we have compared both of them on the basis of similarities and dissimilarities.

Keywords: Embedded computing, internet of things, mobile computing, and wireless technologies.

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Authors: A. M. Fahim, G. Saake, A. M. Salem, F. A. Torkey, M. A. Ramadan

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Data clustering is an important data exploration technique with many applications in data mining. The k-means algorithm is well known for its efficiency in clustering large data sets. However, this algorithm is suitable for spherical shaped clusters of similar sizes and densities. The quality of the resulting clusters decreases when the data set contains spherical shaped with large variance in sizes. In this paper, we introduce a competent procedure to overcome this problem. The proposed method is based on shifting the center of the large cluster toward the small cluster, and recomputing the membership of small cluster points, the experimental results reveal that the proposed algorithm produces satisfactory results.

Keywords: K-Means, Data Clustering, Cluster Analysis.

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Authors: A. M. Fahim, G. Saake, A. M. Salem, F. A. Torkey, M. A. Ramadan

Abstract:

Data clustering is an important data exploration technique with many applications in data mining. We present an enhanced version of the well known single link clustering algorithm. We will refer to this algorithm as DCBOR. The proposed algorithm alleviates the chain effect by removing the outliers from the given dataset. So this algorithm provides outlier detection and data clustering simultaneously. This algorithm does not need to update the distance matrix, since the algorithm depends on merging the most k-nearest objects in one step and the cluster continues grow as long as possible under specified condition. So the algorithm consists of two phases; at the first phase, it removes the outliers from the input dataset. At the second phase, it performs the clustering process. This algorithm discovers clusters of different shapes, sizes, densities and requires only one input parameter; this parameter represents a threshold for outlier points. The value of the input parameter is ranging from 0 to 1. The algorithm supports the user in determining an appropriate value for it. We have tested this algorithm on different datasets contain outlier and connecting clusters by chain of density points, and the algorithm discovers the correct clusters. The results of our experiments demonstrate the effectiveness and the efficiency of DCBOR.

Keywords: Data Clustering, Clustering Algorithms, Handling Noise, Arbitrary Shape of Clusters.

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Authors: Vishnu Kant Soni, Raksha Sharma, Manoj Kumar Mishra

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Grid computing is a high performance computing environment to solve larger scale computational applications. Grid computing contains resource management, job scheduling, security problems, information management and so on. Job scheduling is a fundamental and important issue in achieving high performance in grid computing systems. However, it is a big challenge to design an efficient scheduler and its implementation. In Grid Computing, there is a need of further improvement in Job Scheduling algorithm to schedule the light-weight or small jobs into a coarse-grained or group of jobs, which will reduce the communication time, processing time and enhance resource utilization. This Grouping strategy considers the processing power, memory-size and bandwidth requirements of each job to realize the real grid system. The experimental results demonstrate that the proposed scheduling algorithm efficiently reduces the processing time of jobs in comparison to others.

Keywords: Grid computing, Job grouping and Jobscheduling.

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Authors: Pornpimol Bungkomkhun, Surapong Auwatanamongkol

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This paper presents a supervised clustering algorithm, namely Grid-Based Supervised Clustering (GBSC), which is able to identify clusters of any shapes and sizes without presuming any canonical form for data distribution. The GBSC needs no prespecified number of clusters, is insensitive to the order of the input data objects, and is capable of handling outliers. Built on the combination of grid-based clustering and density-based clustering, under the assistance of the downward closure property of density used in bottom-up subspace clustering, the GBSC can notably reduce its search space to avoid the memory confinement situation during its execution. On two-dimension synthetic datasets, the GBSC can identify clusters with different shapes and sizes correctly. The GBSC also outperforms other five supervised clustering algorithms when the experiments are performed on some UCI datasets.

Keywords: supervised clustering, grid-based clustering, subspace clustering

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Authors: Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid

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Deoxyribonucleic Acid or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science and mathematics. Thus, in this paper, the possibility of DNA-based computing to solve an absolute 1-center problem by molecular manipulations is presented. This is truly the first attempt to solve such a problem by DNA-based computing approach. Since, part of the procedures involve with shortest path computation, research works on DNA computing for shortest path Traveling Salesman Problem, in short, TSP are reviewed. These approaches are studied and only the appropriate one is adapted in designing the computation procedures. This DNA-based computation is designed in such a way that every path is encoded by oligonucleotides and the path-s length is directly proportional to the length of oligonucleotides. Using these properties, gel electrophoresis is performed in order to separate the respective DNA molecules according to their length. One expectation arise from this paper is that it is possible to verify the instance absolute 1-center problem using DNA computing by laboratory experiments.

Keywords: DNA computing, operation research, 1-center problem.

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Authors: Shuen-Tai Wang, Ying-Chuan Chen, Yu-Ching Lin

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There has been renewal of interest in the relation between Green IT and cloud computing in recent years. Cloud computing has to be a highly elastic environment which provides stable services to users. The growing use of cloud computing facilities has caused marked energy consumption, putting negative pressure on electricity cost of computing center or data center. Each year more and more network devices, storages and computers are purchased and put to use, but it is not just the number of computers that is driving energy consumption upward. We could foresee that the power consumption of cloud computing facilities will double, triple, or even more in the next decade. This paper aims at resource allocation and scheduling technologies that are short of or have not well developed yet to reduce energy utilization in cloud computing platform. In particular, our approach relies on recalling services dynamically onto appropriate amount of the machines according to user’s requirement and temporarily shutting down the machines after finish in order to conserve energy. We present initial work on integration of resource and power management system that focuses on reducing power consumption such that they suffice for meeting the minimizing quality of service required by the cloud computing platform.

Keywords: Cloud computing, energy utilization, power consumption, resource allocation.

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Authors: Irina Astrova, Arne Koschel, Björn Siekmann, Mark Starrach, Christopher Tebbe, StefanWolf, Marc Schaaf

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This paper deals with the combination of OSGi and cloud computing. Both technologies are mainly placed in the field of distributed computing. Therefore, it is discussed how different approaches from different institutions work. In addition, the approaches are compared to each other.

Keywords: Cloud computing, OSGi, distributed environments.

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Authors: Jasraj Meena, Malay Kumar, Manu Vardhan

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Cloud computing is a new technology in industry and academia. The technology has grown and matured in last half decade and proven their significant role in changing environment of IT infrastructure where cloud services and resources are offered over the network. Cloud technology enables users to use services and resources without being concerned about the technical implications of technology. There are substantial research work has been performed for the usage of cloud computing in educational institutes and majority of them provides cloud services over high-end blade servers or other high-end CPUs. However, this paper proposes a new stack called “CiCKAStack” which provide cloud services over unutilized computing resources, named as commodity computers. “CiCKAStack” provides IaaS and PaaS using underlying commodity computers. This will not only increasing the utilization of existing computing resources but also provide organize file system, on demand computing resource and design and development environment.

Keywords: Commodity Computers, Cloud Computing, KVM, Cloudstack, Appscale.

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Authors: Karanjeet Singh Kahlon, Gurvinder Singh, Arjan Singh

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In the past few years there is a change in the view of high performance applications and parallel computing. Initially such applications were targeted towards dedicated parallel machines. Recently trend is changing towards building meta-applications composed of several modules that exploit heterogeneous platforms and employ hybrid forms of parallelism. The aim of this paper is to propose a model of virtual parallel computing. Virtual parallel computing system provides a flexible object oriented software framework that makes it easy for programmers to write various parallel applications.

Keywords: Applet, Efficiency, Java, LAN

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Authors: Roohi Shabrin S., Devi Prasad B., Prabu D., Pallavi R. S., Revathi P.

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Due to memory leaks, often-valuable system memory gets wasted and denied for other processes thereby affecting the computational performance. If an application-s memory usage exceeds virtual memory size, it can leads to system crash. Current memory leak detection techniques for clusters are reactive and display the memory leak information after the execution of the process (they detect memory leak only after it occur). This paper presents a Dynamic Memory Monitoring Agent (DMMA) technique. DMMA framework is a dynamic memory leak detection, that detects the memory leak while application is in execution phase, when memory leak in any process in the cluster is identified by DMMA it gives information to the end users to enable them to take corrective actions and also DMMA submit the affected process to healthy node in the system. Thus provides reliable service to the user. DMMA maintains information about memory consumption of executing processes and based on this information and critical states, DMMA can improve reliability and efficaciousness of cluster computing.

Keywords: Dynamic Memory Monitoring Agent (DMMA), Cluster Computing, Memory Leak, Fault Tolerant Framework, Dynamic Memory Leak Detection (DMLD).

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Authors: Laureano Rodríguez, Gladys Casas, Ricardo Grau, Yailen Martínez

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The classical temporal scan statistic is often used to identify disease clusters. In recent years, this method has become as a very popular technique and its field of application has been notably increased. Many bioinformatic problems have been solved with this technique. In this paper a new scan fuzzy method is proposed. The behaviors of classic and fuzzy scan techniques are studied with simulated data. ROC curves are calculated, being demonstrated the superiority of the fuzzy scan technique.

Keywords: Scan statistic, fuzzy scan, simulating study

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Authors: Md. Anwar Hossain Masud, Xiaodi Huang

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The massive proliferation of affordable computers, Internet broadband connectivity and rich education content has created a global phenomenon in which information and communication technology (ICT) is being used to transform education. Therefore, there is a need to redesign the educational system to meet the needs better. The advent of computers with sophisticated software has made it possible to solve many complex problems very fast and at a lower cost. This paper introduces the characteristics of the current E-Learning and then analyses the concept of cloud computing and describes the architecture of cloud computing platform by combining the features of E-Learning. The authors have tried to introduce cloud computing to e-learning, build an e-learning cloud, and make an active research and exploration for it from the following aspects: architecture, construction method and external interface with the model.

Keywords: Architecture, Cloud Computing, E-learning, Information Technology

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Authors: Weichang Du

Abstract:

This paper proposes a new of cloud computing for individual computer users to share applications in distributed communities, called community-based personal cloud computing (CPCC). The paper also presents a prototype design and implementation of CPCC. The users of CPCC are able to share their computing applications with other users of the community. Any member of the community is able to execute remote applications shared by other members. The remote applications behave in the same way as their local counterparts, allowing the user to enter input, receive output as well as providing the access to the local data of the user. CPCC provides a peer-to-peer (P2P) environment where each peer provides applications which can be used by the other peers that are connected CPCC.

Keywords: applications, cloud computing, services, software.

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Authors: Ajay Joshi, Surya Ismail

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This paper will present the initial findings of a research into distributed computer rendering. The goal of the research is to create a distributed computer system capable of rendering a 3D model into an MPEG-4 stream. This paper outlines the initial design, software architecture and hardware setup for the system. Distributed computing means designing and implementing programs that run on two or more interconnected computing systems. Distributed computing is often used to speed up the rendering of graphical imaging. Distributed computing systems are used to generate images for movies, games and simulations. A topic of interest is the application of distributed computing to the MPEG-4 standard. During the course of the research, a distributed system will be created that can render a 3D model into an MPEG-4 stream. It is expected that applying distributed computing principals will speed up rendering, thus improving the usefulness and efficiency of the MPEG-4 standard

Keywords: Cluster, parallel architecture, rendering, MPEG-4.

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Authors: Kamal K.Bharadwaj, Rekha Kandwal

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An important structuring mechanism for knowledge bases is building clusters based on the content of their knowledge objects. The objects are clustered based on the principle of maximizing the intraclass similarity and minimizing the interclass similarity. Clustering can also facilitate taxonomy formation, that is, the organization of observations into a hierarchy of classes that group similar events together. Hierarchical representation allows us to easily manage the complexity of knowledge, to view the knowledge at different levels of details, and to focus our attention on the interesting aspects only. One of such efficient and easy to understand systems is Hierarchical Production rule (HPRs) system. A HPR, a standard production rule augmented with generality and specificity information, is of the following form Decision If < condition> Generality Specificity . HPRs systems are capable of handling taxonomical structures inherent in the knowledge about the real world. In this paper, a set of related HPRs is called a cluster and is represented by a HPR-tree. This paper discusses an algorithm based on cumulative learning scenario for dynamic structuring of clusters. The proposed scheme incrementally incorporates new knowledge into the set of clusters from the previous episodes and also maintains summary of clusters as Synopsis to be used in the future episodes. Examples are given to demonstrate the behaviour of the proposed scheme. The suggested incremental structuring of clusters would be useful in mining data streams.

Keywords: Cumulative learning, clustering, data mining, hierarchical production rules.

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Authors: A.F.A. Abidin, N.S.M. Usop

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A computer cluster is a group of tightly coupled computers that work together closely so that in many respects they can be viewed as though they are a single computer. The components of a cluster are commonly, but not always, connected to each other through fast local area networks. Clusters are usually deployed to improve performance and/or availability over that provided by a single computer, while typically being much more cost-effective than single computers of comparable speed or availability. This paper proposed the way to implement the Beowulf Cluster in order to achieve high performance as well as high availability.

Keywords: Beowulf Cluster, grid computing, GridMPI, MPICH.

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Authors: Sameh H. Ghwanmeh

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In this study a clustering technique has been implemented which is K-Means like with hierarchical initial set (HKM). The goal of this study is to prove that clustering document sets do enhancement precision on information retrieval systems, since it was proved by Bellot & El-Beze on French language. A comparison is made between the traditional information retrieval system and the clustered one. Also the effect of increasing number of clusters on precision is studied. The indexing technique is Term Frequency * Inverse Document Frequency (TF * IDF). It has been found that the effect of Hierarchical K-Means Like clustering (HKM) with 3 clusters over 242 Arabic abstract documents from the Saudi Arabian National Computer Conference has significant results compared with traditional information retrieval system without clustering. Additionally it has been found that it is not necessary to increase the number of clusters to improve precision more.

Keywords: Hierarchical K-mean like clustering (HKM), Kmeans, cluster centroids, initial partition, and document distances

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