Search results for: cluster validity
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 743

Search results for: cluster validity

503 Controlled Synchronization of an Array of Nonlinear System with Time Delays

Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

Abstract:

In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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502 A Simplified Distribution for Nonlinear Seas

Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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501 Selection Initial modes for Belief K-modes Method

Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

Abstract:

The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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500 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method

Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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499 A New Algorithm for Solving Isothermal Carbonization of Wood Particle

Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

Abstract:

A new algorithm based on the lattice Boltzmann method (LBM) is proposed as a potential solver for one-dimensional heat and mass transfer for isothermal carbonization of wood particles. To check the validity of this algorithm, the LBM results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and particle size on the evolution of the local temperature and mass loss inside the wood particle.

Keywords: Lattice Boltzmann Method, pyrolysis, conduction, carbonization.

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498 Triple-input Single-output Voltage-mode Multifunction Filter Using Only Two Current Conveyors

Authors: Mehmet Sagbas, Kemal Fidanboylu, M. Can Bayram

Abstract:

A new voltage-mode triple-input single-output multifunction filter using only two current conveyors is presented. The proposed filter which possesses three inputs and single-output can generate all biquadratic filtering functions at the output terminal by selecting different input signal combinations. The validity of the proposed filter is verified through PSPICE simulations.

Keywords: Active Filters, Voltage mode, Current conveyor

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497 Modelling Peer Group Dieting Behaviour

Authors: M. J. Cunha

Abstract:

The aim of this paper is to understand how peers can influence adolescent girls- dieting behaviour and their body image. Departing from imitation and social learning theories, we study whether adolescent girls tend to model their peer group dieting behaviours, thus influencing their body image construction. Our study was conducted through an enquiry applied to a cluster sample of 466 adolescent high school girls in Lisbon city public schools. Our main findings point to an association between girls- and peers- dieting behaviours, thus reinforcing the modelling hypothesis.

Keywords: Modelling, Diet, Body image, Adolescent girls, Peer group.

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496 The Estimation Method of Stress Distribution for Beam Structures Using the Terrestrial Laser Scanning

Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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495 The Relevance of Intellectual Capital: An Analysis of Spanish Universities

Authors: Yolanda Ramírez, Ángel Tejada, Agustín Baidez

Abstract:

In recent years, the intellectual capital reporting in higher education institutions has been acquiring progressive importance worldwide. Intellectual capital approaches becomes critical at universities, mainly due to the fact that knowledge is the main output as well as input in these institutions. Universities produce knowledge, either through scientific and technical research (the results of investigation, publications, etc.) or through teaching (students trained and productive relationships with their stakeholders). The purpose of the present paper is to identify the intangible elements about which university stakeholders demand most information. The results of a study done at Spanish universities are used to see which groups of universities have stakeholders who are more proactive to the disclosure of intellectual capital.

Keywords: Intellectual capital, universities, Spain, cluster analysis.

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494 Efficient Web Usage Mining Based on K-Medoids Clustering Technique

Authors: P. Sengottuvelan, T. Gopalakrishnan

Abstract:

Web Usage Mining is the application of data mining techniques to find usage patterns from web log data, so as to grasp required patterns and serve the requirements of Web-based applications. User’s expertise on the internet may be improved by minimizing user’s web access latency. This may be done by predicting the future search page earlier and the same may be prefetched and cached. Therefore, to enhance the standard of web services, it is needed topic to research the user web navigation behavior. Analysis of user’s web navigation behavior is achieved through modeling web navigation history. We propose this technique which cluster’s the user sessions, based on the K-medoids technique.

Keywords: Clustering, K-medoids, Recommendation, User Session, Web Usage Mining.

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493 New PTH Moment Stable Criteria of Stochastic Neural Networks

Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.

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492 Designing of Full Adder Using Low Power Techniques

Authors: Shashank Gautam

Abstract:

This paper proposes techniques like MT CMOS, POWER GATING, DUAL STACK, GALEOR and LECTOR to reduce the leakage power. A Full Adder has been designed using these techniques and power dissipation is calculated and is compared with general CMOS logic of Full Adder. Simulation results show the validity of the proposed techniques is effective to save power dissipation and to increase the speed of operation of the circuits to a large extent.

Keywords: Low Power, MT CMOS, Galeor, Lector, Power Gating, Dual Stack, Full Adder.

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491 Index t-SNE: Tracking Dynamics of High-Dimensional Datasets with Coherent Embeddings

Authors: G. Candel, D. Naccache

Abstract:

t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic, and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n2) to O(n2/k), and the memory requirement from n2 to 2(n/k)2 which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: Concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning.

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490 Morphological Description of Cervical Cell Images for the Pathological Recognition

Authors: N. Lassouaoui, L. Hamami, N. Nouali

Abstract:

The tracking allows to detect the tumor affections of cervical cancer, it is particularly complex and consuming time, because it consists in seeking some abnormal cells among a cluster of normal cells. In this paper, we present our proposed computer system for helping the doctors in tracking the cervical cancer. Knowing that the diagnosis of the malignancy is based in the set of atypical morphological details of all cells, herein, we present an unsupervised genetic algorithm for the separation of cell components since the diagnosis is doing by analysis of the core and the cytoplasm. We give also the various algorithms used for computing the morphological characteristics of cells (Ratio core/cytoplasm, cellular deformity, ...) necessary for the recognition of illness.

Keywords: Cervical cell, morphological analysis, recognition, segmentation.

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489 Neutron Flux Characterization for Radioisotope Production at ETRR-2

Authors: A. M. Hassanain, Nader M. A. Mohamed, M. Naguib Aly, Alya A. Badawi, M. A. Gaheen

Abstract:

The thermal, epithermal and fast fluxes were calculated for three irradiation channels at Egypt Second Research Reactor (ETRR-2) using CITVAP code. The validity of the calculations was verified by experimental measurements. There are some deviations between measurements and calculations. This is due to approximations in the calculation models used, homogenization of regions, condensation of energy groups and uncertainty in nuclear data used. Neutron flux data for the three irradiation channels are now available. This would enable predicting the irradiation conditions needed for future radioisotope production.

Keywords: ETRR-2, Neutron flux, Radioisotope production, CITVAP

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488 Statistical Analysis of First Order Plus Dead-time System using Operational Matrix

Authors: Pham Luu Trung Duong, Moonyong Lee

Abstract:

To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.

Keywords: First order plus dead-time, Operational matrix, Statistical analysis, Walsh function.

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487 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method

Authors: Nemat Abazari, Reza Abazari

Abstract:

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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486 Quality of Service Evaluation using a Combination of Fuzzy C-Means and Regression Model

Authors: Aboagela Dogman, Reza Saatchi, Samir Al-Khayatt

Abstract:

In this study, a network quality of service (QoS) evaluation system was proposed. The system used a combination of fuzzy C-means (FCM) and regression model to analyse and assess the QoS in a simulated network. Network QoS parameters of multimedia applications were intelligently analysed by FCM clustering algorithm. The QoS parameters for each FCM cluster centre were then inputted to a regression model in order to quantify the overall QoS. The proposed QoS evaluation system provided valuable information about the network-s QoS patterns and based on this information, the overall network-s QoS was effectively quantified.

Keywords: Fuzzy C-means; regression model, network quality of service

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485 pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

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484 Benchmarking: Performance on ALPS and Formosa Clusters

Authors: Chih-Wei Hsieh, Chau-Yi Chou, Sheng-HsiuKuo, Tsung-Che Tsai, I-Chen Wu

Abstract:

This paper presents the benchmarking results and performance evaluation of differentclustersbuilt atthe National Center for High-Performance Computingin Taiwan. Performance of processor, memory subsystem andinterconnect is a critical factor in the overall performance of high performance computing platforms. The evaluation compares different system architecture and software platforms. Most supercomputer used HPL to benchmark their system performance, in accordance with the requirement of the TOP500 List. In this paper we consider system memory access factors that affect benchmark performance, such as processor and memory performance.We hope these works will provide useful information for future development and construct cluster system.

Keywords: Performance Evaluation, Benchmarking and High-Performance Computing

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483 Adaptive Routing Protocol for Dynamic Wireless Sensor Networks

Authors: Fayez Mostafa Alhamoui, Adnan Hadi Mahdi Al- Helali

Abstract:

The main issue in designing a wireless sensor network (WSN) is the finding of a proper routing protocol that complies with the several requirements of high reliability, short latency, scalability, low power consumption, and many others. This paper proposes a novel routing algorithm that complies with these design requirements. The new routing protocol divides the WSN into several subnetworks and each sub-network is divided into several clusters. This division is designed to reduce the number of radio transmission and hence decreases the power consumption. The network division may be changed dynamically to adapt with the network changes and allows the realization of the design requirements.

Keywords: Wireless sensor networks, routing protocols, ad hoc topology, cluster, sub-network, WSN design requirements.

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482 Development of Blower for Air Management System of Fuel Cell Modules

Authors: Joo-Han Kim, Jung-Moo Seo, Ha Gyeong Sung, Se Hyun Rhyu

Abstract:

This study presents a blower for air management system of fuel cell modules. A blower is composed of BLDC motor and impeller. Magnetic equivalent circuit model and finite element analysis are used to design the motor, and an improved structure is considered to reduce a mechanical loss induced from bearing units. Finally, air blower system combined with the motor and an impeller is manufactured and output properties, such as an air pressure and an amount of flowing air, are measured. Through the experimental results, a validity of the simulated one is confirmed.

Keywords: Fuel cell modules, BLDC motor, Impeller, Air management

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481 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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480 Development and Validation of an Instrument Measuring the Coping Strategies in Situations of Stress

Authors: Lucie Côté, Martin Lauzier, Guy Beauchamp, France Guertin

Abstract:

Stress causes deleterious effects to the physical, psychological and organizational levels, which highlight the need to use effective coping strategies to deal with it. Several coping models exist, but they don’t integrate the different strategies in a coherent way nor do they take into account the new research on the emotional coping and acceptance of the stressful situation. To fill these gaps, an integrative model incorporating the main coping strategies was developed. This model arises from the review of the scientific literature on coping and from a qualitative study carried out among workers with low or high levels of stress, as well as from an analysis of clinical cases. The model allows one to understand under what circumstances the strategies are effective or ineffective and to learn how one might use them more wisely. It includes Specific Strategies in controllable situations (the Modification of the Situation and the Resignation-Disempowerment), Specific Strategies in non-controllable situations (Acceptance and Stubborn Relentlessness) as well as so-called General Strategies (Wellbeing and Avoidance). This study is intended to undertake and present the process of development and validation of an instrument to measure coping strategies based on this model. An initial pool of items has been generated from the conceptual definitions and three expert judges have validated the content. Of these, 18 items have been selected for a short form questionnaire. A sample of 300 students and employees from a Quebec university was used for the validation of the questionnaire. Concerning the reliability of the instrument, the indices observed following the inter-rater agreement (Krippendorff’s alpha) and the calculation of the coefficients for internal consistency (Cronbach's alpha) are satisfactory. To evaluate the construct validity, a confirmatory factor analysis using MPlus supports the existence of a model with six factors. The results of this analysis suggest also that this configuration is superior to other alternative models. The correlations show that the factors are only loosely related to each other. Overall, the analyses carried out suggest that the instrument has good psychometric qualities and demonstrates the relevance of further work to establish predictive validity and reconfirm its structure. This instrument will help researchers and clinicians better understand and assess coping strategies to cope with stress and thus prevent mental health issues.

Keywords: Acceptance, coping strategies, measurement instrument, questionnaire, stress, validation process.

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479 Kohonen Self-Organizing Maps as a New Method for Determination of Salt Composition of Multi-Component Solutions

Authors: Sergey A. Burikov, Tatiana A. Dolenko, Kirill A. Gushchin, Sergey A. Dolenko

Abstract:

The paper presents the results of clusterization by Kohonen self-organizing maps (SOM) applied for analysis of array of Raman spectra of multi-component solutions of inorganic salts, for determination of types of salts present in the solution. It is demonstrated that use of SOM is a promising method for solution of clusterization and classification problems in spectroscopy of multicomponent objects, as attributing a pattern to some cluster may be used for recognition of component composition of the object.

Keywords: Kohonen self-organizing maps, clusterization, multicomponent solutions, Raman spectroscopy.

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478 Issue Reorganization Using the Measure of Relevance

Authors: William Wong Xiu Shun, Yoonjin Hyun, Mingyu Kim, Seongi Choi, Namgyu Kim

Abstract:

The need to extract R&D keywords from issues and use them to retrieve R&D information is increasing rapidly. However, it is difficult to identify related issues or distinguish them. Although the similarity between issues cannot be identified, with an R&D lexicon, issues that always share the same R&D keywords can be determined. In detail, the R&D keywords that are associated with a particular issue imply the key technology elements that are needed to solve a particular issue. Furthermore, the relationship among issues that share the same R&D keywords can be shown in a more systematic way by clustering them according to keywords. Thus, sharing R&D results and reusing R&D technology can be facilitated. Indirectly, redundant investment in R&D can be reduced as the relevant R&D information can be shared among corresponding issues and the reusability of related R&D can be improved. Therefore, a methodology to cluster issues from the perspective of common R&D keywords is proposed to satisfy these demands.

Keywords: Clustering, Social Network Analysis, Text Mining, Topic Analysis.

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477 Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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476 RAPD Analysis of Genetic Diversity of Castor Bean

Authors: M. Vivodík, Ž. Balážová, Z. Gálová

Abstract:

The aim of this work was to detect genetic variability among the set of 40 castor genotypes using 8 RAPD markers. Amplification of genomic DNA of 40 genotypes, using RAPD analysis, yielded in 66 fragments, with an average of 8.25 polymorphic fragments per primer. Number of amplified fragments ranged from 3 to 13, with the size of amplicons ranging from 100 to 1200 bp. Values of the polymorphic information content (PIC) value ranged from 0.556 to 0.895 with an average of 0.784 and diversity index (DI) value ranged from 0.621 to 0.896 with an average of 0.798. The dendrogram based on hierarchical cluster analysis using UPGMA algorithm was prepared and analyzed genotypes were grouped into two main clusters and only two genotypes could not be distinguished. Knowledge on the genetic diversity of castor can be used for future breeding programs for increased oil production for industrial uses.

Keywords: Dendrogram, polymorphism, RAPD technique, Ricinus communis L.

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475 A New Particle Filter Inspired by Biological Evolution: Genetic Filter

Authors: S. Park, J. Hwang, K. Rou, E. Kim

Abstract:

In this paper, we consider a new particle filter inspired by biological evolution. In the standard particle filter, a resampling scheme is used to decrease the degeneracy phenomenon and improve estimation performance. Unfortunately, however, it could cause the undesired the particle deprivation problem, as well. In order to overcome this problem of the particle filter, we propose a novel filtering method called the genetic filter. In the proposed filter, we embed the genetic algorithm into the particle filter and overcome the problems of the standard particle filter. The validity of the proposed method is demonstrated by computer simulation.

Keywords: Particle filter, genetic algorithm, evolutionary algorithm.

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474 Some Computational Results on MPI Parallel Implementation of Dense Simplex Method

Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

Abstract:

There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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