Search results for: space vector SVPWM

Authors: Pavel Y. Tabakov, Kevin Duffy

Abstract:

The present study presents a new approach to automatic data clustering and classification problems in large and complex databases and, at the same time, derives specific types of explicit rules describing each cluster. The method works well in both sparse and dense multidimensional data spaces. The members of the data space can be of the same nature or represent different classes. A number of N-dimensional ellipsoids are used for enclosing the data clouds. Due to the geometry of an ellipsoid and its free rotation in space the detection of clusters becomes very efficient. The method is based on genetic algorithms that are used for the optimization of location, orientation and geometric characteristics of the hyper-ellipsoids. The proposed approach can serve as a basis for the development of general knowledge systems for discovering hidden knowledge and unexpected patterns and rules in various large databases.

Keywords: Classification, clustering, data minig, genetic algorithms.

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Authors: Valentina Koliskina

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Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.

Keywords: Eddy currents, magnetic permeability, Besselfunctions

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Authors: M. Mika, L. Pina, M. Landova, L. Sveda, R. Havlikova, V. Marsikova, R. Hudec, A. Inneman

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Future astronomical projects on large space x-ray imaging telescopes require novel substrates and technologies for the construction of their reflecting mirrors. The mirrors must be lightweight and precisely shaped to achieve large collecting area with high angular resolution. The new materials and technologies must be cost-effective. Currently, the most promising materials are glass or silicon foils. We focused on precise shaping these foils by thermal forming process. We studied free and forced slumping in the temperature region of hot plastic deformation and compared the shapes obtained by the different slumping processes. We measured the shapes and the surface quality of the foils. In the experiments, we varied both heat-treatment temperature and time following our experiment design. The obtained data and relations we can use for modeling and optimizing the thermal forming procedure.

Keywords: Glass, silicon, thermal forming, x-ray

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Authors: Viet-Hung Truong, Seung-Eock Kim

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This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: Advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame.

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

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Authors: Fernanda M. Assef, Maria Teresinha A. Steiner

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The aim of this paper is to compare and discuss better classifier algorithm options for credit risk assessment by applying different Machine Learning techniques. Using records from a Brazilian financial institution, this study uses a database of 5,432 companies that are clients of the bank, where 2,600 clients are classified as non-defaulters, 1,551 are classified as defaulters and 1,281 are temporarily defaulters, meaning that the clients are overdue on their payments for up 180 days. For each case, a total of 15 attributes was considered for a one-against-all assessment using four different techniques: Artificial Neural Networks Multilayer Perceptron (ANN-MLP), Artificial Neural Networks Radial Basis Functions (ANN-RBF), Logistic Regression (LR) and finally Support Vector Machines (SVM). For each method, different parameters were analyzed in order to obtain different results when the best of each technique was compared. Initially the data were coded in thermometer code (numerical attributes) or dummy coding (for nominal attributes). The methods were then evaluated for each parameter and the best result of each technique was compared in terms of accuracy, false positives, false negatives, true positives and true negatives. This comparison showed that the best method, in terms of accuracy, was ANN-RBF (79.20% for non-defaulter classification, 97.74% for defaulters and 75.37% for the temporarily defaulter classification). However, the best accuracy does not always represent the best technique. For instance, on the classification of temporarily defaulters, this technique, in terms of false positives, was surpassed by SVM, which had the lowest rate (0.07%) of false positive classifications. All these intrinsic details are discussed considering the results found, and an overview of what was presented is shown in the conclusion of this study.

Keywords: Artificial Neural Networks, ANNs, classifier algorithms, credit risk assessment, logistic regression, machine learning, support vector machines.

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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For optimal unbiased filter as mean-square and in the case of functioning anomalous noises in the observation memory channel, we have proved insensitivity of filter to inaccurate knowledge of the anomalous noise intensity matrix and its equivalence to truncated filter plotted only by non anomalous components of an observation vector.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

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Authors: Prasad Senadheera, Younousse Saidi, Frans JM Maathuis

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Rice seed expression (cDNA) library in the Lambda Zap 11® phage constructed from the developing grain 10-20 days after flowering was transformed into yeast for functional complementation assays in three salt sensitive yeast mutants S. cerevisiae strain CY162, G19 and Axt3K. Transformed cells of G19 and Axt3K with pYES vector with cDNA inserts showed enhance tolerance than those with empty pYes vector. Sequencing of the cDNA inserts revealed that they encode for the putative proteins with the sequence homologous to rice putative protein PROLM24 (Os06g31070), a prolamin precursor. Expression of this cDNA did not affect yeast growth in absence of salt. Axt3k and G19 strains expressing the PROLM24 were able to grow upto 400 mM and 600 mM of NaCl respectively. Similarly, Axt3k mutant with PROLM24 expression showed comparatively higher growth rate in the medium with excess LiCl (50 mM). The observation that expression of PROLM24 rescued the salt sensitive phenotypes of G19 and Axt3k indicates the existence of a regulatory system that ameliorates the effect of salt stress in the transformed yeast mutants. However, the exact function of the cDNA sequence, which shows partial sequence homology to yeast UTR1 is not clear. Although UTR1 involved in ferrous uptake and iron homeostasis in yeast cells, there is no evidence to prove its role in Na+ homeostasis in yeast cells. Absence of transmembrane regions in Os06g31070 protein indicates that salt tolerance is achieved not through the direct functional complementation of the mutant genes but through an alternative mechanism.

Keywords: Rice seed expression, salt stress, prolamin, salinitytolerance, Oryza sativa

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Authors: Khine Phyu, Aung Myint Aye

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This paper presents results of measurements campaign carried out at a carrier frequency of 24GHz with the help of TPLINK router in indoor line-of-sight (LOS) scenarios. Firstly, the radio wave propagation strategies are analyzed in some rooms with router of point to point Ad hoc network. Then floor attenuation is defined for 3 floors in experimental region. The free space model and dual slope models are modified by considering the influence of corridor conditions on each floor. Using these models, indoor signal attenuation can be estimated in modeling of indoor radio wave propagation. These results and modified models can also be used in planning the networks of future personal communications services.

Keywords: radio wave signal analyzing, LOS radio wavepropagation, indoor radio wave propagation, free space model, tworay model and indoor attenuation.

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Authors: N.Vahdatifar, Ss.Mortazavi, R.Kianinezhad

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In this paper, a Neural Network based predictive DTC algorithm is proposed .This approach is used as an alternative to classical approaches .An appropriate riate Feed - forward network is chosen and based on its value of derivative electromagnetic torque ; optimal stator voltage vector is determined to be applied to the induction motor (by inverter). Moreover, an appropriate torque and flux observer is proposed.

Keywords: Neural Networks, Predictive DTC

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Authors: Roman Graf, Sergiu Gordea, Heather M. Ryan

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This paper presents an approach for easy creation and classification of institutional risk profiles supporting endangerment analysis of file formats. The main contribution of this work is the employment of data mining techniques to support set up of the most important risk factors. Subsequently, risk profiles employ risk factors classifier and associated configurations to support digital preservation experts with a semi-automatic estimation of endangerment group for file format risk profiles. Our goal is to make use of an expert knowledge base, accuired through a digital preservation survey in order to detect preservation risks for a particular institution. Another contribution is support for visualisation of risk factors for a requried dimension for analysis. Using the naive Bayes method, the decision support system recommends to an expert the matching risk profile group for the previously selected institutional risk profile. The proposed methods improve the visibility of risk factor values and the quality of a digital preservation process. The presented approach is designed to facilitate decision making for the preservation of digital content in libraries and archives using domain expert knowledge and values of file format risk profiles. To facilitate decision-making, the aggregated information about the risk factors is presented as a multidimensional vector. The goal is to visualise particular dimensions of this vector for analysis by an expert and to define its profile group. The sample risk profile calculation and the visualisation of some risk factor dimensions is presented in the evaluation section.

Keywords: linked open data, information integration, digital libraries, data mining.

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Authors: Gláucya C. Boechat, Jeneffer C. Ferreira, Edson C. B. Carvalho

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This paper presents a boarding on biometric authentication through the Keystrokes Dynamics that it intends to identify a person from its habitual rhythm to type in conventional keyboard. Seven done experiments: verifying amount of prototypes, threshold, features and the variation of the choice of the times of the features vector. The results show that the use of the Keystroke Dynamics is simple and efficient for personal authentication, getting optimum resulted using 90% of the features with 4.44% FRR and 0% FAR.

Keywords: Biometrics techniques, Keystroke Dynamics, patternrecognition.

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Authors: Veronika Antoniou, Rene Carraz, Yiorgos Hadjichristou

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The Green Urban Lab took the form of public installations that were placed at various locations in four cities in Cyprus. These installations - through which a series of events, activities, workshops and research took place - were the main tools in regenerating a series of urban public spaces in Cyprus. The purpose of this project was to identify issues and opportunities related to public space and to offer guidelines on how design and participatory democracy improvements could strengthen civil society, while raising the quality of the urban public scene. Giant inflatable structures were injected in important urban fragments in order to accommodate series of events. The design and playful installation generated a wide community engagement. The fluid presence of the installations acted as a catalyst for social interaction. They were accessed and viewed effortlessly and surprisingly, creating opportunities to rediscover public spaces.

Keywords: Bottom-up initiatives, creativity, public space, social innovation, urban environments.

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Authors: A. R. Aswatha, T. Basavaraju, N. Bhaskara Rao

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This paper presents a new technique for the optimum placement of processors to minimize the total effective communication load under multi-processor communication dominated environment. This is achieved by placing heavily loaded processors near each other and lightly loaded ones far away from one another in the physical grid locations. The results are mathematically proved for the Algorithms are described.

Keywords: Ascending Sort Index Vector, EffectiveCommunication Load, Effective Distance Matrix, OptimalPlacement, Sorting Order.

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Authors: Petru V. Notingher, Stefan Busoi, Laurentiu M. Dumitran, Cristina Stancu, Gabriel Tanasescu, Emanuel Balescu

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Degradation of polymeric insulation systems of electrical equipments increases the space charge density and the concentration of electrical dipoles. By consequence, the maximum values and the slopes of absorption/resorption (A/R) currents can change with insulation systems ageing. In this paper, an analysis of the nature of the A/R currents and the importance of their components, especially the polarization current and the current given by the space charge, is presented. The experimental study concerns the A/R currents measurements of plane samples (made from CALMICAGLAS tapes), virgin and thermally accelerated aged. The obtained results show that the ageing process produces an increase of the values and a decrease of shapes of the A/R currents. Finally, the possibility of estimating insulations ageing state and lifetime from A/R currents measurements is discussed.

Keywords: Insulation Systems, Absorption/Resorption Currents, Ageing, Lifetime.

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Authors: Hossein Mirzaee, Farhad Besharati

Abstract:

Solar sunspot rotation, latitudinal bands are studied based on intelligent computation methods. A combination of image fusion method with together tree decomposition is used to obtain quantitative values about the latitudes of trajectories on sun surface that sunspots rotate around them. Daily solar images taken with SOlar and Heliospheric (SOHO) satellite are fused for each month separately .The result of fused image is decomposed with Quad Tree decomposition method in order to achieve the precise information about latitudes of sunspot trajectories. Such analysis is useful for gathering information about the regions on sun surface and coordinates in space that is more expose to solar geomagnetic storms, tremendous flares and hot plasma gases permeate interplanetary space and help human to serve their technical systems. Here sunspot images in September, November and October in 2001 are used for studying the magnetic behavior of sun.

Keywords: Quad tree decomposition, sunspot image.

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Authors: Yanqun Li, Hong Geng

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The occurrence of Wenchuan earthquake in 2008 has led to severe damage to the rural areas of Chengdu city, such as the rupture of the social network, the stagnation of economic production and the rupture of living space. The post-disaster reconstruction has become a sustainable issue. As an important link to maintain the order of rural social development, social network should be an important content of post-disaster reconstruction. Therefore, this paper takes rural reconstruction communities in earthquake-stricken areas of Chengdu as the research object and adopts sociological research methods such as field survey, observation and interview to try to understand the transformation of rural social relations network under the influence of earthquake and its impact on rural space. It has found that rural societies under the earthquake generally experienced three phases: the break of stable social relations, the transition of temporary non-normal state, and the reorganization of social networks. The connotation of phased rural social relations also changed accordingly: turn to a new division of labor on the social orientation, turn to a capital flow and redistribution in new production mode on the capital orientation, and turn to relative decentralization after concentration on the spatial dimension. Along with such changes, rural areas have emerged some social issues such as the alienation of competition in the new industry division, the low social connection, the significant redistribution of capital, and the lack of public space. Based on a comprehensive review of these issues, this paper proposes the corresponding response mechanism. First of all, a reasonable division of labor should be established within the villages to realize diversified commodity supply. Secondly, the villages should adjust the industrial type to promote the equitable participation of capital allocation groups. Finally, external public spaces should be added to strengthen the field of social interaction within the communities.

Keywords: Social relations, social support networks, industrial division, capital allocation, public space.

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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Authors: T. Sopapirm, K-N. Areerak, K-L. Areerak, A. Srikaew

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The paper presents the applications of artificial intelligence technique called adaptive tabu search to design the controller of a buck converter. The averaging model derived from the DQ and generalized state-space averaging methods is applied to simulate the system during a searching process. The simulations using such averaging model require the faster computational time compared with that of the full topology model from the software packages. The reported model is suitable for the work in the paper in which the repeating calculation is needed for searching the best solution. The results will show that the proposed design technique can provide the better output waveforms compared with those designed from the classical method.

Keywords: Buck converter, adaptive tabu search, DQ method, generalized state-space averaging method, modeling and simulation

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Authors: M. Shanmugapriya, M. A. Maluk Mohamed, J. William

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A wireless sensor network (WSN) is a collection of sensor nodes organized into a cooperative network. These nodes communicate through a wireless antenna. Reduction in physical size and multiband operation is an important requirement of WSN antenna. Fractal antenna is used for miniaturization and multiband operation. The self-similar or self-affine and space filling property of fractal geometry increases the effective electrical length of the antenna, reduces the size and make them frequency independent. This paper elaborates on Dual band fractal antenna with Coplanar Waveguide (CPW) feed for WSN. The proposed antenna is designed on a FR4 substrate with the dimension of 27mm x 28.5mm x 1.6mm, resonates at 2.4GHz and 5.2GHz with a return loss less than -10dB. The design and simulation process is carried out using IE3D simulation software. The simulated and measured results are found in good agreement.

Keywords: CPW, Fractal, Iterations, Miniaturization, Space filling, Self Similar, WSN, WLAN.

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Authors: R.Sukesh Kumar, Abhisek Verma, Jasprit Singh

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In this work a novel approach for color image segmentation using higher order entropy as a textural feature for determination of thresholds over a two dimensional image histogram is discussed. A similar approach is applied to achieve multi-level thresholding in both grayscale and color images. The paper discusses two methods of color image segmentation using RGB space as the standard processing space. The threshold for segmentation is decided by the maximization of conditional entropy in the two dimensional histogram of the color image separated into three grayscale images of R, G and B. The features are first developed independently for the three ( R, G, B ) spaces, and combined to get different color component segmentation. By considering local maxima instead of the maximum of conditional entropy yields multiple thresholds for the same image which forms the basis for multilevel thresholding.

Keywords: conditional entropy, multi-level thresholding, segmentation, two dimensional image histogram

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Authors: C. Temaneh-Nyah, J. Makiche, J. Nujoma

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This paper considers the characterization of a complex electromagnetic environment due to multiple sources of electromagnetic radiation as a five-dimensional surface which can be described by a set of several surface sections including: instant EM field intensity distribution maps at a given frequency and altitude, instantaneous spectrum at a given location in space and the time evolution of the electromagnetic field spectrum at a given point in space. This characterization if done over time can enable the exposure levels of Radio Frequency Radiation at every point in the analysis area to be determined and results interpreted based on comparison of the determined RFR exposure level with the safe guidelines for general public exposure given by recognized body such as the International commission on non-ionizing radiation protection (ICNIRP), Institute of Electrical and Electronic Engineers (IEEE), the National Radiation Protection Authority (NRPA).

Keywords: Electromagnetic Environment, Electric Field Strength, Mathematical Models.

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Authors: Alessandra Battisti, Silvia Cimini

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This article stands in the context of rural communities in Brazil, where, like many others emerging countries, the overwhelming increasing markets and the overcrowded cities are leaving behind informal settlements based on obsolete agricultural economies and techniques. The pilot project for the community of Goiabeira reflects the attempt to imagine a development model that privileges the actual improvement of living conditions, the education and training, the social inclusion and participation of the dwellers of rural communities. Through the inclusion of operative public space, the aim is for them to become self-sustaining, encouraging the use of local resources for appropriate architectural, ecological and energy technologies and devices, that are efficient, affordable and foster community participation, in the respect of the surrounding environment.

Keywords: Economical development, environment conservation, local resources, participation and social inclusion.

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Authors: B. Su

Abstract:

Auckland has a temperate climate with comfortable warm, dry summers and mild, wet winters. An Auckland school normally does not need air conditioning for cooling during the summer and only need heating during the winter. The space hating energy is the major portion of winter school energy consumption and the winter energy consumption is major portion of annual school energy consumption. School building thermal design should focus on the winter thermal performance for reducing the space heating energy. A number of Auckland schools- design data and energy consumption data are used for this study. This pilot study investigates the relationships between their energy consumption data and school building design data to improve future school design for energy efficiency.

Keywords: Building energy efficiency, building thermal performance, school building design, school energy consumption

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Authors: Meng-Hui Chen, Chiao-Wei Yu, Pei-Chann Chang

Abstract:

Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist. The main idea in this paper is using the peculiarity of ICA to explore the search space to solve the kinds of combinational problems. Otherwise, we also study to use the greed search to increase the local search ability. To verify the proposed algorithm in this paper, the experimental results of traveling salesman problem (TSP) is according to the traveling salesman problem library (TSPLIB). The results show that the proposed algorithm has higher performance than the other known methods.

Keywords: Traveling Salesman Problem, Artificial Chromosomes, Greedy Search, Imperial Competitive Algorithm.

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Authors: Ranajay Bhowmick

Abstract:

Elastoplastic analysis of a structural system involves defining failure/yield criterion, flow rules and hardening rules. The failure/yield criterion defines the limit beyond which the material flows plastically and hardens/softens or remains perfectly plastic before ultimate collapse. The failure/yield criterion is represented geometrically in three/two dimensional Haigh-Westergaard stress-space to facilitate a better understanding of the behavior of the material. In the present study geometric representations in three and two-dimensional stress-space of a few important failure/yield criterion are presented. The criteria presented are the modified forms obtained due to the conditional solutions of the equation of stress invariants. A comparison of the failure/yield surfaces is also presented here to obtain the effectiveness of each of them and it has been found that for identical conditions the Rankine’s criterion gives the largest values of limiting stresses.

Keywords: Deviatoric plane, failure criteria, geometric representation, hydrostatic axis, modified form.

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Authors: Siska Soesanti, Norihiro Nakai

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Bandung city center can be deemed as economic, social and cultural center. However the city center suffers from deterioration. The retail activities tend to shift outward the city center. Numerous idyllic residences changed into business premises in two villages situated in the north part of the city during 1990s, especially after a new highway and flyover opened. According to space syntax theory, the pattern of spatial integration in the urban grid is a prime determinant of movement patterns in the system. The syntactic analysis results show the flyover has insignificant influence on street network in the city center. However the flyover has been generating a major difference in the new commercial area since it has become relatively as strategic as the city center. Besides street network, local government policy, rapid private motorization and particular condition of each site also played important roles in encouraging the current commercial areas to flourish.

Keywords: City center, commercial area, space syntax, street network.

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Authors: Ayed Salman, Fawaz Al-Anzi, Aseel Al-Minayes

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Heuristics-based search methodologies normally work on searching a problem space of possible solutions toward finding a “satisfactory" solution based on “hints" estimated from the problem-specific knowledge. Research communities use different types of methodologies. Unfortunately, most of the times, these hints are immature and can lead toward hindering these methodologies by a premature convergence. This is due to a decrease of diversity in search space that leads to a total implosion and ultimately fitness stagnation of the population. In this paper, a novel Decision Maturity framework (DMF) is introduced as a solution to this problem. The framework simply improves the decision on the direction of the search by materializing hints enough before using them. Ideas from this framework are injected into the particle swarm optimization methodology. Results were obtained under both static and dynamic environment. The results show that decision maturity prevents premature converges to a high degree.

Keywords: Heuristic Search, hints, Particle Swarm Optimization, Decision Maturity Framework.

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Authors: Quoc-Nam Tran

Abstract:

The theory of Groebner Bases, which has recently been honored with the ACM Paris Kanellakis Theory and Practice Award, has become a crucial building block to computer algebra, and is widely used in science, engineering, and computer science. It is wellknown that Groebner bases computation is EXP-SPACE in a general polynomial ring setting. However, for many important applications in computer science such as satisfiability and automated verification of hardware and software, computations are performed in a Boolean ring. In this paper, we give an algorithm to show that Groebner bases computation is PSPACE in Boolean rings. We also show that with this discovery, the Groebner bases method can theoretically be as efficient as other methods for automated verification of hardware and software. Additionally, many useful and interesting properties of Groebner bases including the ability to efficiently convert the bases for different orders of variables making Groebner bases a promising method in automated verification.

Keywords: Algorithm, Complexity, Groebner basis, Applications of Computer Science.

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Authors: Hossein Mirzaee, Farhad Besharati

Abstract:

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

Keywords: Quad Tree Decomposition, Sunspot.

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