Search results for: extended airfoil database

Authors: H. El Fadili, K. Zenkouar, H. Qjidaa

Abstract:

This paper proposes a neural network weights and topology optimization using genetic evolution and the backpropagation training algorithm. The proposed crossover and mutation operators aims to adapt the networks architectures and weights during the evolution process. Through a specific inheritance procedure, the weights are transmitted from the parents to their offsprings, which allows re-exploitation of the already trained networks and hence the acceleration of the global convergence of the algorithm. In the preprocessing phase, a new feature extraction method is proposed based on Legendre moments with the Maximum entropy principle MEP as a selection criterion. This allows a global search space reduction in the design of the networks. The proposed method has been applied and tested on the well known MNIST database of handwritten digits.

Keywords: Genetic algorithm, Legendre Moments, MEP, Neural Network.

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Authors: Amine Naït-Ali

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The aim of this paper is to present a new method which can be used for progressive transmission of electrocardiogram (ECG). The idea consists in transforming any ECG signal to an image, containing one beat in each row. In the first step, the beats are synchronized in order to reduce the high frequencies due to inter-beat transitions. The obtained image is then transformed using a discrete version of Radon Transform (DRT). Hence, transmitting the ECG, leads to transmit the most significant energy of the transformed image in Radon domain. For decoding purpose, the receptor needs to use the inverse Radon Transform as well as the two synchronization frames. The presented protocol can be adapted for lossy to lossless compression systems. In lossy mode we show that the compression ratio can be multiplied by an average factor of 2 for an acceptable quality of reconstructed signal. These results have been obtained on real signals from MIT database.

Keywords: Discrete Radon Transform, ECG compression, synchronization.

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Authors: Aji P. Wibawa, Andrew Nafalski, Neil Murray, Wayan F. Mahmudy

Abstract:

Since the one-to-one word translator does not have the facility to translate pragmatic aspects of Javanese, the parallel text alignment model described uses a phrase pair combination. The algorithm aligns the parallel text automatically from the beginning to the end of each sentence. Even though the results of the phrase pair combination outperform the previous algorithm, it is still inefficient. Recording all possible combinations consume more space in the database and time consuming. The original algorithm is modified by applying the edit distance coefficient to improve the data-storage efficiency. As a result, the data-storage consumption is 90% reduced as well as its learning period (42s).

Keywords: edit distance coefficient, Javanese, parallel text alignment, phrase pair combination

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Authors: Ahmed Mateen, Zhu Qingsheng, Ahmad Bilal

Abstract:

In the current age of technology, information is the most precious asset of a company. Today, companies have a large amount of data. As the data become larger, access to data for some particular information is becoming slower day by day. Faster data processing to shape it in the form of information is the biggest issue. The major problems in distributed databases are the efficiency of data distribution and response time of data distribution. The security of data distribution is also a big issue. For these problems, we proposed a strategy that can maximize the efficiency of data distribution and also increase its response time. This technique gives better results for secure data distribution from multiple heterogeneous sources. The newly proposed technique facilitates the companies for secure data sharing efficiently and quickly.

Keywords: ER-schema, electronic record, P2P framework, API, query formulation.

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Authors: N. Ullah, A. Haddad, F. Van Der Linde

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This paper investigates the effects of breaks in bonds, breaks in the earthing system and breaks in earth wire on the rise of the earth potential (EPR) in a substation and at the transmission tower bases using various models of an L6 tower. Different approaches were adopted to examine the integrity of the earthing system and the terminal towers. These effects were investigated to see the associated difference in the EPR magnitudes with respect to a healthy system at various locations. Comparisons of the computed EPR magnitudes were then made between the healthy and unhealthy system to detect any difference. The studies were conducted at power frequency for a uniform soil with different soil resistivities. It was found that full breaks in the double bond of the terminal towers increase the EPR significantly at the fault location, while they reduce EPR at the terminal tower bases. A fault on the isolated section of the grid can result in EPR values up to 8 times of those on a healthy system at higher soil resistivities, provided that the extended earthing system stays connected to the grid.

Keywords: Bonding, earthing, EPR, integrity, system.

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Authors: Emrah Bulut, Okan Duru, Shigeru Yoshida

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In this study, a fuzzy integrated logical forecasting method (FILF) is extended for multi-variate systems by using a vector autoregressive model. Fuzzy time series forecasting (FTSF) method was recently introduced by Song and Chissom [1]-[2] after that Chen improved the FTSF method. Rather than the existing literature, the proposed model is not only compared with the previous FTS models, but also with the conventional time series methods such as the classical vector autoregressive model. The cluster optimization is based on the C-means clustering method. An empirical study is performed for the prediction of the chartering rates of a group of dry bulk cargo ships. The root mean squared error (RMSE) metric is used for the comparing of results of methods and the proposed method has superiority than both traditional FTS methods and also the classical time series methods.

Keywords: C-means clustering, Fuzzy time series, Multi-variate design

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Authors: C. Schneider, M. M. Seizmeir, T. Suchanek, M. Hutter-Mironovová, M. Bdiwi, M. Putz

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In this paper, a suitable measurement setup is presented to conduct force and pressure measurements for transient contact cases at the example of lathe machine tending. Empirical measurements were executed on a selected collaborative robot’s behavior regarding allowable operating speeds under consideration of sensor- and workpiece-specific factors. Comparisons between the theoretic calculations proposed in ISO/TS 15066 and the practical measurement results reveal a basis for future research. With the created database, preliminary risk assessment and economic assessment procedures of collaborative machine tending cells can be facilitated.

Keywords: biomechanical thresholds, collaborative robots, force and pressure measurements, machine tending, transient contact

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Authors: G. Parmar, R. Prasad, S. Mukherjee

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The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

Keywords: Genetic algorithm, Integral square error, Orderreduction, Stability equation method.

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Authors: Jito Vanualailai, Bibhya Sharma

Abstract:

Swarm principles are increasingly being used to design controllers for the coordination of multi-robot systems or, in general, multi-agent systems. This paper proposes a two-dimensional Lagrangian swarm model that enables the planar agents, modeled as point masses, to swarm whilst effectively avoiding each other and obstacles in the environment. A novel method, based on an extended Lyapunov approach, is used to construct the model. Importantly, the Lyapunov method ensures a form of practical stability that guarantees an emergent behavior, namely, a cohesive and wellspaced swarm with a constant arrangement of individuals about the swarm centroid. Computer simulations illustrate this basic feature of collective behavior. As an application, we show how multiple planar mobile unicycle-like robots swarm to eventually form patterns in which their velocities and orientations stabilize.

Keywords: Attractive-repulsive swarm model, individual-based swarm model, Lagrangian swarm model, Lyapunov stability, Lyapunov-like function, practical stability, unicycle.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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Authors: M. A. Adeboyejo, O. O. Adeosun

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Pioneer networked systems assume that connections are reliable, and a faulty operation will be considered in case of losing a connection. Transient connections are typical of mobile devices. Areas of application of data sharing system such as these, lead to the conclusion that network connections may not always be reliable, and that the conventional approaches can be improved. Nigerian commercial banking industry is a critical system whose operation is increasingly becoming dependent on information technology (IT) driven information system. The proposed solution to this problem makes use of a hierarchically clustered network structure which we selected to reflect (as much as possible) the typical organizational structure of the Nigerian commercial banks. Representative transactions such as data updates and replication of the results of such updates were used to simulate the proposed model to show its applicability.

Keywords: Dependability, reliability, data redundancy.

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Authors: Tom Snir, Eitan Rubin

Abstract:

Mendelian Disease Genes represent a collection of single points of failure for the various systems they constitute. Such genes have been shown, on average, to encode longer proteins than 'non-disease' proteins. Existing models suggest that this results from the increased likeli-hood of longer genes undergoing mutations. Here, we show that in saturated mutagenesis experiments performed on model organisms, where the likelihood of each gene mutating is one, a similar relationship between length and the probability of a gene being lethal was observed. We thus suggest an extended model demonstrating that the likelihood of a mutated gene to produce a severe phenotype is length-dependent. Using the occurrence of conserved domains, we bring evidence that this dependency results from a correlation between protein length and the number of functions it performs. We propose that protein length thus serves as a proxy for protein cardinality in different networks required for the organism's survival and well-being. We use this example to argue that the collection of Mendelian Disease Genes can, and should, be used to study the rules governing systems vulnerability in living organisms.

Keywords: Systems Biology, Protein Length

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Authors: S. S. Mahlangu, R. K. K. Mbaya, D. D. Delport, H. Van. Zyl

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The degrading effect due to bacterial growth on the structural integrity of concrete floor surfaces is predictable; this consequently cause development of surface micro cracks in which organisms penetrate through resulting in surface spalling. Hence, the need to develop mix design meeting the requirement of floor surfaces exposed to aggressive agent to improve certain material properties with good workability, extended lifespan and low cost is essential. In this work, tests were performed to examine the microbial activity on kitchen floor surfaces and the effect of adding admixtures. The biochemical test shows the existence of microorganisms (E.coli, Streptococcus) on newly casted structure. Of up to 6% porosity was reduced and improvement on structural integrity was observed upon adding mineral admixtures from the concrete mortar. The SEM result after 84 days of curing specimens, shows that chemical admixtures have significant role to enable retard bacterial penetration and good quality structure is achieved.

Keywords: Admixture, organisms, porosity and strength.

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Authors: Frederick Wedzerai Nyakudya

Abstract:

In this paper, we examine the relationship between human capital, personal wealth and social capital to explain the differences in start-up rates between female and male entrepreneurs. Since our dependent variable is dichotomous, we examine the determinants of these using a maximum likelihood logit estimator. We used the Global Entrepreneurship Monitor database covering the period 2006 to 2009 with 421 usable cases drawn from the Lower Layer Super Output Areas in East Midlands in the United Kingdom. We found evidence indicating that a female positively moderates the positive relationships between indicators of human capital and personal wealth with start-up activity. The findings have implications for programs, policies, and practices to encourage more females to engage in start-up activity.

Keywords: Entrepreneurship, Global Entrepreneurship Monitor, gender gap, women's entrepreneurship.

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Authors: Masato Nishi, Tetsushi Kaburagi, Masashi Kurose, Tei Hirashima, Tetsusei Kurasiki

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The process of thermoforming a carbon fiber reinforced thermoplastic (CFRTP) has increased its presence in the automotive industry for its wide applicability to the mass production car. A non-isothermal forming for CFRTP can shorten its cycle time to less than 1 minute. In this paper, the textile reinforcement FE model which the authors proposed in a previous work is extended to the CFRTP model for non-isothermal forming simulation. The effect of thermoplastic is given by adding shell elements which consider thermal effect to the textile reinforcement model. By applying Reuss model to the stress calculation of thermoplastic, the proposed model can accurately predict in-plane shear behavior, which is the key deformation mode during forming, in the range of the process temperature. Using the proposed model, thermoforming simulation was conducted and the results are in good agreement with the experimental results.

Keywords: Carbon fiber reinforced thermoplastic (CFRTP), Finite element analysis (FEA), Pre-impregnated textile composite, Non-isothermal forming.

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Authors: V. Komarova

Abstract:

The main purpose of this research is the calculation of implicit prices of the environmental level of air quality in the city of Moscow on the basis of housing property prices. The database used contains records of approximately 20 thousand apartments and has been provided by a leading real estate agency operating in Russia. The explanatory variables include physical characteristics of the houses, environmental (industry emissions), neighbourhood sociodemographic and geographic data: GPS coordinates of each house. The hedonic regression results for ecological variables show «negative» prices while increasing the level of air contamination from such substances as carbon monoxide, nitrogen dioxide, sulphur dioxide, and particles (CO, NO2, SO2, TSP). The marginal willingness to pay for higher environmental quality is presented for linear and log-log models.

Keywords: Air pollution, environment, hedonic prices, real estate, willingness to pay.

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Authors: Daniel Siahaan, Aditya Prapanca

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The emerging Semantic Web has been attracted many researchers and developers. New applications have been developed on top of Semantic Web and many supporting tools introduced to improve its software development process. Metadata modeling is one of development process where supporting tools exists. The existing tools are lack of readability and easiness for a domain knowledge expert to graphically models a problem in semantic model. In this paper, a metadata modeling tool called RDFGraph is proposed. This tool is meant to solve those problems. RDFGraph is also designed to work with modern database management systems that support RDF and to improve the performance of the query execution process. The testing result shows that the rules used in RDFGraph follows the W3C standard and the graphical model produced in this tool is properly translated and correct.

Keywords: CASE tool, data modeling, semantic web

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

High temperature deformation behavior of cast Fe-20Cr-5Al alloy has been investigated in this study by performing tensile and compression tests at temperatures from 1100 to 1200oC. Rectangular ingots of which the dimensions were 300×300×100 in millimeter were cast using vacuum induction melting. Phase equilibrium was calculated using the FactSage®, thermodynamic software and database. Tensile strength of cast Fe-20Cr-5Al alloy was 4 MPa at 1200oC. With temperature decreased, tensile strength increased rapidly and reached up to 13 MPa at 1100oC. Elongation also increased from 18 to 80% with temperature decreased from 1200oC to 1100oC. Microstructure observation revealed that M23C6 carbide was precipitated along the grain boundary and within the matrix.

Keywords: Fe-20Cr-5Al alloy, high temperature deformation, aging treatment, microstructure, mechanical properties.

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Authors: Padmanabhan Balasubramanian, R. Chinnadurai

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This paper deals with a power-conscious ANDEXOR- Inverter type logic implementation for a complex class of Boolean functions, namely Achilles- heel functions. Different variants of the above function class have been considered viz. positive, negative and pure horn for analysis and simulation purposes. The proposed realization is compared with the decomposed implementation corresponding to an existing standard AND-EXOR logic minimizer; both result in Boolean networks with good testability attribute. It could be noted that an AND-OR-EXOR type logic network does not exist for the positive phase of this unique class of logic function. Experimental results report significant savings in all the power consumption components for designs based on standard cells pertaining to a 130nm UMC CMOS process The simulations have been extended to validate the savings across all three library corners (typical, best and worst case specifications).

Keywords: Achilles' heel functions, AND-EXOR-Inverter logic, CMOS technology, low power design.

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Authors: Ritsuko Kawasaki (Aiba), Takeshi Hiromatsu

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Management is required to understand all information security risks within an organization, and to make decisions on which information security risks should be treated in what level by allocating how much amount of cost. However, such decision-making is not usually easy, because various measures for risk treatment must be selected with the suitable application levels. In addition, some measures may have objectives conflicting with each other. It also makes the selection difficult. Moreover, risks generally have trends and it also should be considered in risk treatment. Therefore, this paper provides the extension of the model proposed in the previous study. The original model supports the selection of measures by applying a combination of weighted average method and goal programming method for multi-objective analysis to find an optimal solution. The extended model includes the notion of weights to the risks, and the larger weight means the priority of the risk.

Keywords: Information security risk treatment, Selection of risk measures, Risk acceptanceand Multi-objective optimization.

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Authors: Iqbalur Rahman, Miftahur Rahman, Abul L Haque, Mostafizur Rahman,

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In this paper, RSA encryption algorithm and its hardware implementation in Xilinx-s Virtex Field Programmable Gate Arrays (FPGA) is analyzed. The issues of scalability, flexible performance, and silicon efficiency for the hardware acceleration of public key crypto systems are being explored in the present work. Using techniques based on the interleaved math for exponentiation, the proposed RSA calculation architecture is compared to existing FPGA-based solutions for speed, FPGA utilization, and scalability. The paper covers the RSA encryption algorithm, interleaved multiplication, Miller Rabin algorithm for primality test, extended Euclidean math, basic FPGA technology, and the implementation details of the proposed RSA calculation architecture. Performance of several alternative hardware architectures is discussed and compared. Finally, conclusion is drawn, highlighting the advantages of a fully flexible & parameterized design.

Keywords: Crypto Accelerator, FPGA, Public Key Cryptography, RSA.

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Authors: Kitty Kioskli, Nineta Polemi

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Evaluating the levels of cyber-security risks within an enterprise is most important in protecting its information system, services and all its digital assets against security incidents (e.g. accidents, malicious acts, massive cyber-attacks). The existing risk assessment methodologies (e.g. eBIOS, OCTAVE, CRAMM, NIST-800) adopt a technical approach considering as attack factors only the capability, intention and target of the attacker, and not paying attention to the attacker’s psychological profile and personality traits. In this paper, a socio-technical approach is proposed in cyber risk assessment, in order to achieve more realistic risk estimates by considering the personality traits of the attackers. In particular, based upon principles from investigative psychology and behavioural science, a multi-dimensional, extended, quantifiable model for an attacker’s profile is developed, which becomes an additional factor in the cyber risk level calculation.

Keywords: Attacker, behavioural models, cyber risk assessment, cyber-security, human factors, investigative psychology, ISO27001, ISO27005.

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Authors: S. Liepina, A. Jemeljanovs

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Tasks of the work were study the possible E.coli contamination in red deer meat, identify pathogenic strains from isolated E.coli, determine their incidence in red deer meat and determine the presence of VT1, VT2 and eaeA genes for the pathogenic E.coli. 8 (10%) samples were randomly selected from 80 analysed isolates of E.coli and PCR reaction was performed on them. PCR was done both on initial materials – samples of red deer meat - and for already isolated liqueurs. Two of analysed venison samples contain verotoxin-producing strains of E. coli. It means that this meat is not safe to consumer. It was proven by the sequestration reaction of E. coli and by comparison of the obtained results with the database of microorganism genome available on the internet that the isolated culture corresponds to region 16S rDNS of E. coli thus presenting correctness of the microbiological methods.

Keywords: Deer meat, pathogenic Escherichia coli

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Authors: Semeh Ben Salem, Sami Naouali, Moetez Sallami

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The increasing amount of collected data has limited the performance of the current analyzing algorithms. Thus, developing new cost-effective algorithms in terms of complexity, scalability, and accuracy raised significant interests. In this paper, a modified effective k-means based algorithm is developed and experimented. The new algorithm aims to reduce the computational load without significantly affecting the quality of the clusterings. The algorithm uses the City Block distance and a new stop criterion to guarantee the convergence. Conducted experiments on a real data set show its high performance when compared with the original k-means version.

Keywords: Pattern recognition, partitional clustering, K-means clustering, Manhattan distance, terrorism data analysis.

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Authors: M. Abdou, M. K. Khalil

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The heat pipe is a thermal device which allows efficient transport of thermal energy. The experimental work of this research was split into two phases; phase 1 is the development of the facilities, material and test rig preparation. Phase 2 is the actual experiments and measurements of the thermal control mockup inside the modified vacuum chamber (MVC). Due to limited funds, the development on the thermal control subsystem was delayed and the experimental facilities such as suitable thermal vacuum chamber with space standard specifications were not available from the beginning of the research and had to be procured over a period of time. In all, these delays extended the project by one and a half year. Thermal control subsystem needs a special facility and equipment to be tested. The available vacuum chamber is not suitable for the thermal tests. Consequently, the modification of the chamber was a must. A vacuum chamber has been modified to be used as a Thermal Vaccum Chamber (TVC). A MVC is a vacuum chamber modified by using a stainless mirror box with perfect reflectability and the infrared lamp connected with the voltage regulator to vary the lamp intensity as it will be illustrated through the paper.

Keywords: Heat pipe, thermal control, thermal vacuum chamber, satellite.

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Authors: Thabet Slimani, Boutheina Ben Yaghlane, Khaled Mellouli

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In the last few years, the Semantic Web gained scientific acceptance as a means of relationships identification in knowledge base, widely known by semantic association. Query about complex relationships between entities is a strong requirement for many applications in analytical domains. In bioinformatics for example, it is critical to extract exchanges between proteins. Currently, the widely known result of such queries is to provide paths between connected entities from data graph. However, they do not always give good results while facing the user need by the best association or a set of limited best association, because they only consider all existing paths but ignore the path evaluation. In this paper, we present an approach for supporting association discovery queries. Our proposal includes (i) a query language PmSPRQL which provides a multiparadigm query expressions for association extraction and (ii) some quantification measures making easy the process of association ranking. The originality of our proposal is demonstrated by a performance evaluation of our approach on real world datasets.

Keywords: Association extraction, query Language, relationships, knowledge base, multi-paradigm query.

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Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

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The problem of N cracks interaction in an isotropic elastic solid is decomposed into a subproblem of a homogeneous solid without crack and N subproblems with each having a single crack subjected to unknown tractions on the two crack faces. The unknown tractions, namely pseudo tractions on each crack are expanded into polynomials with unknown coefficients, which have to be determined by the consistency condition, i.e. by the equivalence of the original multiple cracks interaction problem and the superposition of the N+1 subproblems. In this paper, Kachanov-s approach of average tractions is extended into the method of moments to approximately impose the consistence condition. Hence Kachanov-s method can be viewed as the zero-order method of moments. Numerical results of the stress intensity factors are presented for interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks. As the order of moment increases, the accuracy of the method of moments improves.

Keywords: Crack interaction, stress intensity factor, multiplecracks, method of moments.

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Authors: Dewi Nasien, Siti S. Yuhaniz, Habibollah Haron

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In a handwriting recognition problem, characters can be represented using chain codes. The main problem in representing characters using chain code is optimizing the length of the chain code. This paper proposes to use randomized algorithm to minimize the length of Freeman Chain Codes (FCC) generated from isolated handwritten characters. Feedforward neural network is used in the classification stage to recognize the image characters. Our test results show that by applying the proposed model, we reached a relatively high accuracy for the problem of isolated handwritten when tested on NIST database.

Keywords: Handwriting Recognition, Freeman Chain Code andFeedforward Backpropagation Neural Networks.

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Authors: Khalid Elasnaoui, Brahim Aksasse, Mohammed Ouanan

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In this paper, we are interested in the problem of finding similar images in a large database. For this purpose we propose a new algorithm based on a combination of the 2-D histogram intersection in the HSV space and statistical moments. The proposed histogram is based on a 3x3 window and not only on the intensity of the pixel. This approach overcome the drawback of the conventional 1-D histogram which is ignoring the spatial distribution of pixels in the image, while the statistical moments are used to escape the effects of the discretisation of the color space which is intrinsic to the use of histograms. We compare the performance of our new algorithm to various methods of the state of the art and we show that it has several advantages. It is fast, consumes little memory and requires no learning. To validate our results, we apply this algorithm to search for similar images in different image databases.

Keywords: 2-D histogram, Statistical moments, Indexing, Similarity distance, Histograms intersection.

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Authors: Basheer M. Al-Maqaleh, Kamal K. Bharadwaj

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Automated discovery of hierarchical structures in large data sets has been an active research area in the recent past. This paper focuses on the issue of mining generalized rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses flat rules as initial individuals of GP and discovers hierarchical structure. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Genetic Programming, Hierarchy, Knowledge Discovery in Database, Subsumption Matrix.

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