Search results for: generating

Authors: Bahare Fatemi, Seyed Mehran Kazemi, Nazanin Mehrasa

Abstract:

Sudoku is a logic-based combinatorial puzzle game which people in different ages enjoy playing it. The challenging and addictive nature of this game has made it a ubiquitous game. Most magazines, newspapers, puzzle books, etc. publish lots of Sudoku puzzles every day. These puzzles often come in different levels of difficulty so that all people, from beginner to expert, can play the game and enjoy it. Generating puzzles with different levels of difficulty is a major concern of Sudoku designers. There are several works in the literature which propose ways of generating puzzles having a desirable level of difficulty. In this paper, we propose a method based on constraint satisfaction problems to evaluate the difficulty of the Sudoku puzzles. Then we propose a hill climbing method to generate puzzles with different levels of difficulty. Whereas other methods are usually capable of generating puzzles with only few number of difficulty levels, our method can be used to generate puzzles with arbitrary number of different difficulty levels. We test our method by generating puzzles with different levels of difficulty and having a group of 15 people solve all the puzzles and recording the time they spend for each puzzle.

Keywords: Constraint satisfaction problem, generating Sudoku puzzles, hill climbing.

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Authors: Mariam Vardiashvili

Abstract:

The economic value of the asset impairment process is quite large. Impairment reflects the reduction of future economic benefits or service potentials itemized in the asset. The assets owned by public sector entities bring economic benefits or are used for delivery of the free-of-charge services. Consequently, they are classified as cash-generating and non-cash-generating assets. IPSAS 21 - Impairment of non-cash-generating assets, and IPSAS 26 - Impairment of cash-generating assets, have been designed considering this specificity.  When measuring impairment of assets, it is important to select the relevant methods. For measurement of the impaired Non-Cash-Generating Assets, IPSAS 21 recommends three methods: Depreciated Replacement Cost Approach, Restoration Cost Approach, and  Service Units Approach. Impairment of Value in Use of Cash-Generating Assets (according to IPSAS 26) is measured by discounted value of the money sources to be received in future. Value in use of the cash-generating asserts (as per IPSAS 26) is measured by the discounted value of the money sources to be received in the future. The article provides classification of the assets in the public sector  as non-cash-generating assets and cash-generating assets and, deals also with the factors which should be considered when evaluating  impairment of assets. An essence of impairment of the non-financial assets and the methods of measurement thereof evaluation are formulated according to IPSAS 21 and IPSAS 26. The main emphasis is put on different methods of measurement of the value in use of the impaired Cash-Generating Assets and Non-Cash-Generation Assets and the methods of their selection. The traditional and the expected cash flow approaches for calculation of the discounted value are reviewed. The article also discusses the issues of recognition of impairment loss and its reflection in the financial reporting. The article concludes that despite a functional purpose of the impaired asset, whichever method is used for measuring the asset, presentation of realistic information regarding the value of the assets should be ensured in the financial reporting. In the theoretical development of the issue, the methods of scientific abstraction, analysis and synthesis were used. The research was carried out with a systemic approach. The research process uses international standards of accounting, theoretical researches and publications of Georgian and foreign scientists.

Keywords: Non-cash-generating assets, cash-generating assets, recoverable value, recoverable service amount, value in use.

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Authors: M. H. Yee, J. Md Yunos, W. Othman, R. Hassan, T. K. Tee, M. M. Mohamad

Abstract:

The generation of an idea that goes through several  phases is affected by individual factors, interests, preferences and  motivation. The purpose of this research was to analyze the  difference in difficulties of generating ideas according to individual  learning styles. A total of 375 technical students from four technical  universities in Malaysia were randomly selected as samples. The  Kolb Learning Styles Inventory and a set of developed questionnaires  were used in this research. The results showed that the most dominant  learning style among technical students is Doer. A total of 319  (85.1%) technical students faced difficulties in solving individual  assignments. Most of the problem faced by technical students is the  difficulty of generating ideas for solving individual assignments.  There was no significant difference in difficulties of generating ideas  according to students’ learning styles. Therefore, students need to  learn higher order thinking skills enabling students to generate ideas  and consequently complete assignments.

 

Keywords: Difference, difficulties, generating idea, learning styles.

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

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The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.

Keywords: Appell’s functions, Gauss hypergeometric functions, Heat polynomials, Kampe’ de Fe’riet function, Laguerre polynomials, Lauricella’s function, Saran’s functions.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

Smart Dust particles, are small smart materials used for generating weather maps. We investigate question of the optimal number of Smart Dust particles necessary for generating precise, computationally feasible and cost effective 3–D weather maps. We also give an optimal matching algorithm for the generalized scenario, when there are N Smart Dust particles and M ground receivers.

Keywords: Remote sensing, smart dust, matching, optimization.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Richard Joseph, Nerey Mvungi

Abstract:

An electric power system includes a generating, a transmission, a distribution, and consumers subsystems. An electrical power network in Tanzania keeps growing larger by the day and become more complex so that, most utilities have long wished for real-time monitoring and remote control of electrical power system elements such as substations, intelligent devices, power lines, capacitor banks, feeder switches, fault analyzers and other physical facilities. In this paper, the concept of automation of management of power systems from generation level to end user levels was determined by using Power System Simulator for Engineering (PSS/E) version 30.3.2.

Keywords: Automation, Distribution subsystem, Generating subsystem, PSS/E, TANESCO, Transmission subsystem.

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Authors: Lu Zou, Dianfu MA, Ying Wang, Xianqi Zhao

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Avionic software architecture has transit from a federated avionics architecture to an integrated modular avionics (IMA) .ARINC 653 (Avionics Application Standard Software Interface) is a software specification for space and time partitioning in Safety-critical avionics Real-time operating systems. Methods to transform the abstract avionics application logic function to the executable model have been brought up, however with less consideration about the code generating input and output model specific for ARINC 653 platform and inner-task synchronous dynamic interaction order sequence. In this paper, we proposed an AADL-based model-driven design methodology to fulfill the purpose to automatically generating Cµ executable model on ARINC 653 platform from the ARINC653 architecture which defined as AADL653 in order to facilitate the development of the avionics software constructed on ARINC653 OS. This paper presents the mapping rules between the AADL653 elements and the elements in Cµ language, and define the code generating rules , designs an automatic C µ code generator .Then, we use a case to illustrate our approach. Finally, we give the related work and future research directions.

Keywords: IMA, ARINC653, AADL653, code generation.

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Authors: Dae-Hee Son, Soon-Ryul Nam

Abstract:

The power system frequency falls when disturbance such as rapid increase of system load or loss of a generating unit occurs in power systems. Especially, increase in the number of renewable generating units has a bad influence on the power system because of loss of generating unit depending on the circumstance. Conventional technologies use frequency droop control battery output for the frequency regulation and balance between supply and demand. If power is supplied using the fast output characteristic of the battery, power system stability can be further more improved. To improve the power system stability, we propose battery output control using ROCOF (Rate of Change of Frequency) in this paper. The bigger the power difference between the supply and the demand, the bigger the ROCOF drops. Battery output is controlled proportionally to the magnitude of the ROCOF, allowing for faster response to power imbalances. To simulate the control method of battery output system, we develop the user defined model using PSS/E and confirm that power system stability is improved by comparing with frequency droop control.

Keywords: PSS/E user defined model, power deviation, frequency droop control, ROCOF, rate of change of frequency.

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Authors: Chalakorn Chitsaart, Suchada Rianmora, Mann Rattana-Areeyagon, Wutichai Namjaiprasert

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G-code is the main factor in computer numerical control (CNC) machine for controlling the toolpaths and generating the profile of the object’s features. For obtaining high surface accuracy of the surface finish, non-stop operation is required for CNC machine. Recently, to design a new product, the strategy that concerns about a change that has low impact on business and does not consume lot of resources has been introduced. Cost and time for designing minor changes can be reduced since the traditional geometric details of the existing models are applied. In order to support this strategy as the alternative channel for machining operation, this research proposes the automatic generating codes for CNC milling operation. Using this technique can assist the manufacturer to easily change the size and the geometric shape of the product during the operation where the time spent for setting up or processing the machine are reduced. The algorithm implemented on MATLAB platform is developed by analyzing and evaluating the geometric information of the part. Codes are created rapidly to control the operations of the machine. Comparing to the codes obtained from CAM, this developed algorithm can shortly generate and simulate the cutting profile of the part.

Keywords: Geometric shapes, Milling operation, Minor changes, CNC Machine, G-code, and Cutting parameters.

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Authors: Mahmoud Gilany, Wael Al-Hasawi

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Preliminary studies on Kuwait high voltage transmission system show significant increase in the short circuit level at some of the grid substations and some generating stations. This increase results from the growth in the power transmission systems in size and complexity. New generating stations are expected to be added to the system within the next few years. This paper describes the study analysis performed to evaluate the available and potential solutions to control SC levels in Kuwait power system. It also presents a modified planning of the transmission network in order to fulfill this task.

Keywords: Short circuit current, network splitting, fault current limiter, power transmission planning.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: Shan Gao

Abstract:

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.

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Authors: Jun-Kwon Jung, Sung-Min Jung, Tae-Kyung Kim, Tai-Myoung Chung

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CloudSim is a useful tool to simulate the cloud environment. It shows the service availability, the power consumption, and the network traffic of services on the cloud environment. Moreover, it supports to calculate a network communication delay through a network topology data easily. CloudSim allows inputting a file of topology data, but it does not provide any generating process. Thus, it needs the file of topology data generated from some other tools. The BRITE is typical network topology generator. Also, it supports various type of topology generating algorithms. If CloudSim can include the BRITE, network simulation for clouds is easier than existing version. This paper shows the potential of connection between BRITE and CloudSim. Also, it proposes the direction to link between them.

Keywords: Cloud, simulation, topology, BRITE, network.

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Authors: Hashem Dehghanniri

Abstract:

Crime scripting is a simple and effective crime modeling technique that aims to improve understanding of security analysts about security and crime incidents. Low-quality scripts provide a wrong, incomplete, or sophisticated understanding of the crime commission process, which oppose the purpose of their application, e.g., identifying effective and cost-efficient situational crime prevention (SCP) measures. One important and overlooked factor in generating quality scripts is the crime scripting method. This study investigates the problems within the existing crime scripting practices and proposes a crime scripting approach that contributes to generating quality crime scripts. It was validated by experienced crime scripters. This framework helps analysts develop better crime scripts and contributes to their effective application, e.g., SCP measures identification or policy-making.

Keywords: Attack modeling, crime commission process, crime script, situational crime prevention.

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Authors: Jin Myoung Kim, Tae Ho Cho

Abstract:

Wireless Sensor networks have a wide spectrum of civil and military applications that call for secure communication such as the terrorist tracking, target surveillance in hostile environments. For the secure communication in these application areas, we propose a method for generating a hierarchical key structure for the efficient group key management. In this paper, we apply A* algorithm in generating a hierarchical key structure by considering the history data of the ratio of addition and eviction of sensor nodes in a location where sensor nodes are deployed. Thus generated key tree structure provides an efficient way of managing the group key in terms of energy consumption when addition and eviction event occurs. A* algorithm tries to minimize the number of messages needed for group key management by the history data. The experimentation with the tree shows efficiency of the proposed method.

Keywords: Heuristic search, key management, security, sensor network.

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Authors: Maros Barabas, Michal Drozd, Petr Hanacek

Abstract:

A novel behavioral detection framework is proposed to detect zero day buffer overflow vulnerabilities (based on network behavioral signatures) using zero-day exploits, instead of the signature-based or anomaly-based detection solutions currently available for IDPS techniques. At first we present the detection model that uses shadow honeypot. Our system is used for the online processing of network attacks and generating a behavior detection profile. The detection profile represents the dataset of 112 types of metrics describing the exact behavior of malware in the network. In this paper we present the examples of generating behavioral signatures for two attacks – a buffer overflow exploit on FTP server and well known Conficker worm. We demonstrated the visualization of important aspects by showing the differences between valid behavior and the attacks. Based on these metrics we can detect attacks with a very high probability of success, the process of detection is however very expensive.

Keywords: behavioral signatures, metrics, network, security design

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Authors: Lars Laußat, Manfred Helmus, Kamil Szczesny, Markus König

Abstract:

As one result of the project “Reactive Construction Project Scheduling using Real Time Construction Logistic Data and Simulation”, a procedure for using data about uncertain resource availability assumptions in reactive scheduling processes has been developed. Prediction data about resource availability is generated in a formalized way using real-time monitoring data e.g. from auto-ID systems on the construction site and in the supply chains. The paper focusses on the formalization of the procedure for monitoring construction logistic processes, for the detection of disturbance and for generating of new and uncertain scheduling assumptions for the reactive resource constrained simulation procedure that is and will be further described in other papers.

Keywords: Auto-ID, Construction Logistic, Fuzzy, Monitoring, RFID, Scheduling.

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Authors: Katsunori Miura, Kiyoshi Akama, Hiroshi Mabuchi

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In the Equivalent Transformation (ET) computation model, a program is constructed by the successive accumulation of ET rules. A method by meta-computation by which a correct ET rule is generated has been proposed. Although the method covers a broad range in the generation of ET rules, all important ET rules are not necessarily generated. Generation of more ET rules can be achieved by supplementing generation methods which are specialized for important ET rules. A Specialization-by-Equation (Speq) rule is one of those important rules. A Speq rule describes a procedure in which two variables included in an atom conjunction are equalized due to predicate constraints. In this paper, we propose an algorithm that systematically and recursively generate Speq rules and discuss its effectiveness in the synthesis of ET programs. A Speq rule is generated based on proof of a logical formula consisting of given atom set and dis-equality. The proof is carried out by utilizing some ET rules and the ultimately obtained rules in generating Speq rules.

Keywords: Equivalent transformation, ET rule, Equation of two variables, Rule generation, Specialization-by-Equation rule

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Authors: A. Vani, M. N. Mamatha

Abstract:

Visual signal processing in human beings occurs in the occipital lobe of the brain. The signals that are generated in the brain are universal for all the human beings and they are called Visual Evoked Potential (VEP). Generally, the visually impaired people lose sight because of severe damage to only the eyes natural photo sensors, but the occipital lobe will still be functioning. In this paper, a technique of artificially generating VEP is proposed to enhance the visual ability of the subject. The system uses the electrical photoreceptors to capture image, process the image, to detect and recognize the subject or object. This voltage is further processed and can transmit wirelessly to a BIOMEMS implanted into occipital lobe of the patient’s brain. The proposed BIOMEMS consists of array of electrodes that generate the neuron potential which is similar to VEP of normal people. Thus, the neurons get the visual data from the BioMEMS which helps in generating partial vision or sight for the visually challenged patient. 

Keywords: Visual evoked potential, OpenViBe, BioMEMS, Neuro prosthesis.

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Authors: Ahmed S. Al-Abdulwahab

Abstract:

Generation system reliability assessment is an important task which can be performed using deterministic or probabilistic techniques. The probabilistic approaches have significant advantages over the deterministic methods. However, more complicated modeling is required by the probabilistic approaches. Power generation model is a basic requirement for this assessment. One form of the generation models is the well known capacity outage probability table (COPT). Different analytical techniques have been used to construct the COPT. These approaches require considerable mathematical modeling of the generating units. The unit-s models are combined to build the COPT which will add more burdens on the process of creating the COPT. Decimal to Binary Conversion (DBC) technique is widely and commonly applied in electronic systems and computing This paper proposes a novel utilization of the DBC to create the COPT without engaging in analytical modeling or time consuming simulations. The simple binary representation , “0 " and “1 " is used to model the states o f generating units. The proposed technique is proven to be an effective approach to build the generation model.

Keywords: Decimal to Binary, generation, reliability.

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Authors: Mohammed I. Abouheaf, Sofie Haesaert, Wei-Jen Lee, Frank L. Lewis

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Economic Dispatch is one of the most important power system management tools. It is used to allocate an amount of power generation to the generating units to meet the load demand. The Economic Dispatch problem is a large scale nonlinear constrained optimization problem. In general, heuristic optimization techniques are used to solve non-convex Economic Dispatch problem. In this paper, ideas from Reinforcement Learning are proposed to solve the non-convex Economic Dispatch problem. Q-Learning is a reinforcement learning techniques where each generating unit learn the optimal schedule of the generated power that minimizes the generation cost function. The eligibility traces are used to speed up the Q-Learning process. Q-Learning with eligibility traces is used to solve Economic Dispatch problems with valve point loading effect, multiple fuel options, and power transmission losses.

Keywords: Economic Dispatch, Non-Convex Cost Functions, Valve Point Loading Effect, Q-Learning, Eligibility Traces.

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Authors: S. R. Nikhashemi, L. Haj Paim, Ali Khatibi

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Structural Equation Modeling (SEM) was used to test a hypothesized model explaining Malaysian hypermarket customers’ perceptions of brand trust (BT), customer perceived value (CPV) and perceived service quality (PSQ) on building their brand loyalty (CBL) and generating positive word-of-mouth communication (WOM). Self-administered questionnaires were used to collect data from 374 Malaysian hypermarket customers from Mydin, Tesco, Aeon Big and Giant in Kuala Lumpur, a metropolitan city of Malaysia. The data strongly supported the model exhibiting that BT, CPV and PSQ are prerequisite factors in building customer brand loyalty, while PSQ has the strongest effect on prediction of customer brand loyalty compared to other factors. Besides, the present study suggests the effect of the aforementioned factors via customer brand loyalty strongly contributes to generate positive word of mouth communication.

Keywords: Brand trust, perceived value, perceived service quality, brand loyalty, positive word of mouth communication.

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Authors: Chava Sunil Kumar, P.S. Subrahmanyan, J. Amarnath

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In this paper variation of spot price and total profits of the generating companies- through wholesale electricity trading are discussed with and without Central Generating Stations (CGS) share and seasonal variations are also considered. It demonstrates how proper analysis of generators- efficiencies and capabilities, types of generators owned, fuel costs, transmission losses and settling price variation using the solutions of Optimal Power Flow (OPF), can allow companies to maximize overall revenue. It illustrates how solutions of OPF can be used to maximize companies- revenue under different scenarios. And is also extended to computation of Available Transfer Capability (ATC) is very important to the transmission system security and market forecasting. From these results it is observed that how crucial it is for companies to plan their daily operations and is certainly useful in an online environment of deregulated power system. In this paper above tasks are demonstrated on 124 bus real-life Indian utility power system of Andhra Pradesh State Grid and results have been presented and analyzed.

Keywords: OPF, ATC, Electricity Market, Bid, Spot Price

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Authors: Takao Sakakura, Kazunori Fujimoto

Abstract:

This paper proposes an analytical method for the dynamics of generating firms- alliance networks along with business phases. Dynamics in network developments have previously been discussed in the research areas of organizational strategy rather than in the areas of regional cluster, where the static properties of the networks are often discussed. The analytical method introduces the concept of business phases into innovation processes and uses relationships called prior experiences; this idea was developed in organizational strategy to investigate the state of networks from the viewpoints of tradeoffs between link stabilization and node exploration. This paper also discusses the results of the analytical method using five cases of the network developments of firms. The idea of Embeddedness helps interpret the backgrounds of the analytical results. The analytical method is useful for policymakers of regional clusters to establish concrete evaluation targets and a viewpoint for comparisons of policy programs.

Keywords: Regional Clusters, Alliance Networks, Innovation Processes, Prior Experiences, Embeddedness.

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Authors: A. Belayadi, A. Mougari, L. Ait-Gougam, F. Mekideche-Chafa

Abstract:

The artificial neural network is one of the interesting techniques that have been advantageously used to deal with modeling problems. In this study, the computing with artificial neural network (CANN) is proposed. The model is applied to modulate the information processing of one-dimensional task. We aim to integrate a new method which is based on a new coding approach of generating the input-output mapping. The latter is based on increasing the neuron unit in the last layer. Accordingly, to show the efficiency of the approach under study, a comparison is made between the proposed method of generating the input-output set and the conventional method. The results illustrated that the increasing of the neuron units, in the last layer, allows to find the optimal network’s parameters that fit with the mapping data. Moreover, it permits to decrease the training time, during the computation process, which avoids the use of computers with high memory usage.

Keywords: Neural network computing, information processing, input-output mapping, training time, computers with high memory.

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Authors: Myriam Noureddine

Abstract:

During their activity, all systems must be operational without failures and in this context, the dependability concept is essential avoiding disruption of their function. As computer networks are systems with the same requirements of dependability, this article deals with an analysis of failures for a computer network. The proposed approach integrates specific tools of the plat-form KB3, usually applied in dependability studies of industrial systems. The methodology is supported by a multi-agent system formed by six agents grouped in three meta agents, dealing with two levels. The first level concerns a modeling step through a conceptual agent and a generating agent. The conceptual agent is dedicated to the building of the knowledge base from the system specifications written in the FIGARO language. The generating agent allows producing automatically both the structural model and a dependability model of the system. The second level, the simulation, shows the effects of the failures of the system through a simulation agent. The approach validation is obtained by its application on a specific computer network, giving an analysis of failures through their effects for the considered network.

Keywords: Computer network, dependability, KB3 plat-form, multi-agent system, failure.

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Authors: Chul H. Jo, Do Y. Kim, Bong K. Cho, Myeong J. Kim

Abstract:

The exhaustion of oil and the environmental pollution from the use of fossil fuel are increasing. Tidal current power (TCP) has been proposed as an alternative energy source because of its predictability and reliability. By applying a duct and single point mooring (SPM) system, a TCP device can amplify the generating power and keep its position properly. Because the generating power is proportional to cube of the current stream velocity, amplifying the current speed by applying a duct to a TCP system is an effective way to improve the efficiency of the power device. An SPM system can be applied at any water depth and is highly cost effective. Simple installation and maintenance procedures are also merits of an SPM system. In this study, we designed an SPM system for a duct-type TCP device for use in shallow water. Motions of the duct are investigated to obtain the response amplitude operator (RAO) as the magnitude of the transfer function. Parameters affecting the stability of the SPM system such as the fairlead departure angle, current velocity, and the number of clamp weights are analyzed and/or optimized. Wadam and OrcaFlex commercial software is used to design the mooring line.

Keywords: Mooring design, parametric analysis, response amplitude operator, single point mooring.

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Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

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A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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