Search results for: Memetic algorithms
849 New Design Constraints of FIR Filter on Magnitude and Phase of Error Function
Authors: Raghvendra Kumar, Lillie Dewan
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Exchange algorithm with constraints on magnitude and phase error separately in new way is presented in this paper. An important feature of the algorithms presented in this paper is that they allow for design constraints which often arise in practical filter design problems. Meeting required minimum stopband attenuation or a maximum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by the methods proposed here. This new algorithm may have important advantages over existing technique, with respect to the speed and stability of convergence, memory requirement and low ripples.
Keywords: Least square estimation, Constraints, Exchange algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1656848 Higher Order Statistics for Identification of Minimum Phase Channels
Authors: Mohammed Zidane, Said Safi, Mohamed Sabri, Ahmed Boumezzough
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This paper describes a blind algorithm, which is compared with two another algorithms proposed in the literature, for estimating of the minimum phase channel parameters. In order to identify blindly the impulse response of these channels, we have used Higher Order Statistics (HOS) to build our algorithm. The simulation results in noisy environment, demonstrate that the proposed method could estimate the phase and magnitude with high accuracy of these channels blindly and without any information about the input, except that the input excitation is identically and independent distribute (i.i.d) and non-Gaussian.
Keywords: System Identification, Higher Order Statistics, Communication Channels.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1675847 The Synthetic T2 Quality Control Chart and its Multi-Objective Optimization
Authors: Francisco Aparisi, Marco A. de Luna
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In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1561846 Extended Least Squares LS–SVM
Authors: József Valyon, Gábor Horváth
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Among neural models the Support Vector Machine (SVM) solutions are attracting increasing attention, mostly because they eliminate certain crucial questions involved by neural network construction. The main drawback of standard SVM is its high computational complexity, therefore recently a new technique, the Least Squares SVM (LS–SVM) has been introduced. In this paper we present an extended view of the Least Squares Support Vector Regression (LS–SVR), which enables us to develop new formulations and algorithms to this regression technique. Based on manipulating the linear equation set -which embodies all information about the regression in the learning process- some new methods are introduced to simplify the formulations, speed up the calculations and/or provide better results.Keywords: Function estimation, Least–Squares Support VectorMachines, Regression, System Modeling
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2014845 Architecture Based on Dynamic Graphs for the Dynamic Reconfiguration of Farms of Computers
Authors: Carmen Navarrete, Eloy Anguiano
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In the last years, the computers have increased their capacity of calculus and networks, for the interconnection of these machines. The networks have been improved until obtaining the actual high rates of data transferring. The programs that nowadays try to take advantage of these new technologies cannot be written using the traditional techniques of programming, since most of the algorithms were designed for being executed in an only processor,in a nonconcurrent form instead of being executed concurrently ina set of processors working and communicating through a network.This paper aims to present the ongoing development of a new system for the reconfiguration of grouping of computers, taking into account these new technologies.
Keywords: Dynamic network topology, resource and task allocation, parallel computing, heterogeneous computing, dynamic reconfiguration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1367844 An Adaptive Model for Blind Image Restoration using Bayesian Approach
Authors: S.K. Satpathy, S.K. Nayak, K. K. Nagwanshi, S. Panda, C. Ardil
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Image restoration involves elimination of noise. Filtering techniques were adopted so far to restore images since last five decades. In this paper, we consider the problem of image restoration degraded by a blur function and corrupted by random noise. A method for reducing additive noise in images by explicit analysis of local image statistics is introduced and compared to other noise reduction methods. The proposed method, which makes use of an a priori noise model, has been evaluated on various types of images. Bayesian based algorithms and technique of image processing have been described and substantiated with experimentation using MATLAB.Keywords: Image Restoration, Probability DensityFunction (PDF), Neural Networks, Bayesian Classifier.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2250843 Improving Digital Image Edge Detection by Fuzzy Systems
Authors: Begol, Moslem, Maghooli, Keivan
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Image Edge Detection is one of the most important parts of image processing. In this paper, by fuzzy technique, a new method is used to improve digital image edge detection. In this method, a 3x3 mask is employed to process each pixel by means of vicinity. Each pixel is considered a fuzzy input and by examining fuzzy rules in its vicinity, the edge pixel is specified and by utilizing calculation algorithms in image processing, edges are displayed more clearly. This method shows significant improvement compared to different edge detection methods (e.g. Sobel, Canny).Keywords: Fuzzy Systems, Edge Detection, Fuzzy edgedetection
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2093842 A New Self-stabilizing Algorithm for Maximal 2-packing
Authors: Zhengnan Shi
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In the self-stabilizing algorithmic paradigm, each node has a local view of the system, in a finite amount of time the system converges to a global state with desired property. In a graph G = (V, E), a subset S C V is a 2-packing if Vi c V: IN[i] n SI <1. In this paper, an ID-based, constant space, self-stabilizing algorithm that stabilizes to a maximal 2-packing in an arbitrary graph is proposed. It is shown that the algorithm stabilizes in 0(n3) moves under any scheduler (daemon). Specifically, it is shown that the algorithm stabilizes in linear time-steps under a synchronous daemon where every privileged node moves at each time-step.Keywords: self-stabilization, 2-packing, distributed computing, fault tolerance, graph algorithms
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1673841 Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay
Authors: M.J. Park, K.H. Kim, O.M. Kwon
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This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.
Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1751840 Association Rule and Decision Tree based Methodsfor Fuzzy Rule Base Generation
Authors: Ferenc Peter Pach, Janos Abonyi
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This paper focuses on the data-driven generation of fuzzy IF...THEN rules. The resulted fuzzy rule base can be applied to build a classifier, a model used for prediction, or it can be applied to form a decision support system. Among the wide range of possible approaches, the decision tree and the association rule based algorithms are overviewed, and two new approaches are presented based on the a priori fuzzy clustering based partitioning of the continuous input variables. An application study is also presented, where the developed methods are tested on the well known Wisconsin Breast Cancer classification problem. Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2310839 Fuzzy Controller Design for Ball and Beam System with an Improved Ant Colony Optimization
Authors: Yeong-Hwa Chang, Chia-Wen Chang, Hung-Wei Lin, C.W. Tao
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In this paper, an improved ant colony optimization (ACO) algorithm is proposed to enhance the performance of global optimum search. The strategy of the proposed algorithm has the capability of fuzzy pheromone updating, adaptive parameter tuning, and mechanism resetting. The proposed method is utilized to tune the parameters of the fuzzy controller for a real beam and ball system. Simulation and experimental results indicate that better performance can be achieved compared to the conventional ACO algorithms in the aspect of convergence speed and accuracy.Keywords: Ant colony algorithm, Fuzzy control, ball and beamsystem
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2200838 Extended Minimal Controller Synthesis for Voltage-Fed Induction Motor Based on the Hyperstability Theory
Authors: A. Ramdane, F.Naceri, S. Ramdane
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in this work, we present a new strategy of direct adaptive control denoted: Extended minimal controller synthesis (EMCS). This algorithm is designed for an induction motor, which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The main motivation of the EMCS control is to enhance the robustness of the MRAC algorithms, i.e. the rejection of bounded effects of rapidly varying external disturbances.
Keywords: Adaptive Control, Simple model reference adaptive control (SMRAC), Extended Minimal Controller synthesis (EMCS), Induction Motor (IM)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1643837 Upgrading Performance of DSR Routing Protocol in Mobile Ad Hoc Networks
Authors: Mehdi Alilou, Mehdi Dehghan
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Routing in mobile ad hoc networks is a challenging task because nodes are free to move randomly. In DSR like all On- Demand routing algorithms, route discovery mechanism is associated with great delay. More Clearly in DSR routing protocol to send route reply packet, when current route breaks, destination seeks a new route. In this paper we try to change route selection mechanism proactively. We also define a link stability parameter in which a stability value is assigned to each link. Given this feature, destination node can estimate stability of routes and can select the best and more stable route. Therefore we can reduce the delay and jitter of sending data packets.
Keywords: DSR, MANET, proactive, routing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2364836 Matrix Completion with Heterogeneous Observation Cost Using Sparsity-Number of Column-Space
Authors: Ilqar Ramazanli
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The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.
Keywords: Matrix completion, adaptive learning, heterogeneous cost, Matroid optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 501835 Combined Simulated Annealing and Genetic Algorithm to Solve Optimization Problems
Authors: Younis R. Elhaddad
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Combinatorial optimization problems arise in many scientific and practical applications. Therefore many researchers try to find or improve different methods to solve these problems with high quality results and in less time. Genetic Algorithm (GA) and Simulated Annealing (SA) have been used to solve optimization problems. Both GA and SA search a solution space throughout a sequence of iterative states. However, there are also significant differences between them. The GA mechanism is parallel on a set of solutions and exchanges information using the crossover operation. SA works on a single solution at a time. In this work SA and GA are combined using new technique in order to overcome the disadvantages' of both algorithms.
Keywords: Genetic Algorithm, Optimization problems, Simulated Annealing, Traveling Salesman Problem
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3448834 Comparative Study of Universities’ Web Structure Mining
Authors: Z. Abdullah, A. R. Hamdan
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This paper is meant to analyze the ranking of University of Malaysia Terengganu, UMT’s website in the World Wide Web. There are only few researches have been done on comparing the ranking of universities’ websites so this research will be able to determine whether the existing UMT’s website is serving its purpose which is to introduce UMT to the world. The ranking is based on hub and authority values which are accordance to the structure of the website. These values are computed using two websearching algorithms, HITS and SALSA. Three other universities’ websites are used as the benchmarks which are UM, Harvard and Stanford. The result is clearly showing that more work has to be done on the existing UMT’s website where important pages according to the benchmarks, do not exist in UMT’s pages. The ranking of UMT’s website will act as a guideline for the web-developer to develop a more efficient website.Keywords: Algorithm, ranking, website, web structure mining.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1670833 Modeling and Optimization of Aggregate Production Planning - A Genetic Algorithm Approach
Authors: B. Fahimnia, L.H.S. Luong, R. M. Marian
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The Aggregate Production Plan (APP) is a schedule of the organization-s overall operations over a planning horizon to satisfy demand while minimizing costs. It is the baseline for any further planning and formulating the master production scheduling, resources, capacity and raw material planning. This paper presents a methodology to model the Aggregate Production Planning problem, which is combinatorial in nature, when optimized with Genetic Algorithms. This is done considering a multitude of constraints of contradictory nature and the optimization criterion – overall cost, made up of costs with production, work force, inventory, and subcontracting. A case study of substantial size, used to develop the model, is presented, along with the genetic operators.Keywords: Aggregate Production Planning, Costs, and Optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2588832 Two Individual Genetic Algorithm
Authors: Younis R. Elhaddad, Aiman S.Gannous
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The particular interests of this paper is to explore if the simple Genetic Algorithms (GA) starts with population of only two individuals and applying different crossover technique over these parents to produced 104 children, each one has different attributes inherited from their parents; is better than starting with population of 100 individuals; and using only one type crossover (order crossover OX). For this reason we implement GA with 52 different crossover techniques; each one produce two children; which means 104 different children will be produced and this may discover more search space, also we implement classic GA with order crossover and many experiments were done over 3 Travel Salesman Problem (TSP) to find out which method is better, and according to the results we can say that GA with Multi-crossovers is much better.
Keywords: Artificial intelligence, genetic algorithm, order crossover, travel salesman problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1418831 A Mean–Variance–Skewness Portfolio Optimization Model
Authors: Kostas Metaxiotis
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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.
Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1421830 A Rapid Code Acquisition Scheme in OOC-Based CDMA Systems
Authors: Keunhong Chae, Seokho Yoon
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We propose a code acquisition scheme called improved multiple-shift (IMS) for optical code division multiple access systems, where the optical orthogonal code is used instead of the pseudo noise code. Although the IMS algorithm has a similar process to that of the conventional MS algorithm, it has a better code acquisition performance than the conventional MS algorithm. We analyze the code acquisition performance of the IMS algorithm and compare the code acquisition performances of the MS and the IMS algorithms in single-user and multi-user environments.
Keywords: Code acquisition, optical CDMA, optical orthogonal code, serial algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2163829 Approximation Incremental Training Algorithm Based on a Changeable Training Set
Authors: Yi-Fan Zhu, Wei Zhang, Xuan Zhou, Qun Li, Yong-Lin Lei
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The quick training algorithms and accurate solution procedure for incremental learning aim at improving the efficiency of training of SVR, whereas there are some disadvantages for them, i.e. the nonconvergence of the formers for changeable training set and the inefficiency of the latter for a massive dataset. In order to handle the problems, a new training algorithm for a changeable training set, named Approximation Incremental Training Algorithm (AITA), was proposed. This paper explored the reason of nonconvergence theoretically and discussed the realization of AITA, and finally demonstrated the benefits of AITA both on precision and efficiency.Keywords: support vector regression, incremental learning, changeable training set, quick training algorithm, accurate solutionprocedure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1487828 Analysis of Histogram Asymmetry for Waste Recognition
Authors: Janusz Bobulski, Kamila Pasternak
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Despite many years of effort and research, the problem of waste management is still current. There is a lack of fast and effective algorithms for classifying individual waste fractions. Many programs and projects improve statistics on the percentage of waste recycled every year. In these efforts, it is worth using modern Computer Vision techniques supported by artificial intelligence. In the article, we present a method of identifying plastic waste based on the asymmetry analysis of the histogram of the image containing the waste. The method is simple but effective (94%), which allows it to be implemented on devices with low computing power, in particular on microcomputers. Such de-vices will be used both at home and in waste sorting plants.
Keywords: Computer vision, environmental protection, image processing, waste management.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 325827 Ranking - Convex Risk Minimization
Authors: Wojciech Rejchel
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The problem of ranking (rank regression) has become popular in the machine learning community. This theory relates to problems, in which one has to predict (guess) the order between objects on the basis of vectors describing their observed features. In many ranking algorithms a convex loss function is used instead of the 0-1 loss. It makes these procedures computationally efficient. Hence, convex risk minimizers and their statistical properties are investigated in this paper. Fast rates of convergence are obtained under conditions, that look similarly to the ones from the classification theory. Methods used in this paper come from the theory of U-processes as well as empirical processes.
Keywords: Convex loss function, empirical risk minimization, empirical process, U-process, boosting, euclidean family.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1417826 Quantitative Analysis of PCA, ICA, LDA and SVM in Face Recognition
Authors: Liton Jude Rozario, Mohammad Reduanul Haque, Md. Ziarul Islam, Mohammad Shorif Uddin
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Face recognition is a technique to automatically identify or verify individuals. It receives great attention in identification, authentication, security and many more applications. Diverse methods had been proposed for this purpose and also a lot of comparative studies were performed. However, researchers could not reach unified conclusion. In this paper, we are reporting an extensive quantitative accuracy analysis of four most widely used face recognition algorithms: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) using AT&T, Sheffield and Bangladeshi people face databases under diverse situations such as illumination, alignment and pose variations.
Keywords: PCA, ICA, LDA, SVM, face recognition, noise.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2433825 Cultivating Docile Bodies in The Matrix Trilogy
Authors: Julian Iliev
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Currently, philosophical interpretations of The Matrix trilogy have seen a decline. This study examines the human pods and growing fields in The Matrix trilogy. Their functionality is juxtaposed to Michel Foucault’s concept of docile bodies, linking fictional and contemporary worlds. The comparison illustrates the effects of body manipulation. This paradigm is scrutinized through the power of invisibility. The invisibility of the human pods and fields parallels the hidden algorithms employed by contemporary tech giants. The utilization and secondary manipulation of user’s data are further veiled in secrecy.
Keywords: Docile bodies, film trilogies, Matrix movies, Michel Foucault, visibility, invisibility.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 183824 Unrelated Parallel Machines Scheduling Problem Using an Ant Colony Optimization Approach
Authors: Y. K. Lin, H. T. Hsieh, F. Y. Hsieh
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Total weighted tardiness is a measure of customer satisfaction. Minimizing it represents satisfying the general requirement of on-time delivery. In this research, we consider an ant colony optimization (ACO) algorithm to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense. Computational results show that the proposed ACO algorithm is giving promising results compared to other existing algorithms.Keywords: ant colony optimization, total weighted tardiness, unrelated parallel machines.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1895823 A Multi Steps Algorithm for Sperm Segmentation in Microscopic Image
Authors: Fereidoon Nowshiravan Rahatabad, Mohammad Hassan Moradi, Vahid Reza Nafisi
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Nothing that an effective cure for infertility happens when we can find a unique solution, a great deal of study has been done in this field and this is a hot research subject for to days study. So we could analyze the men-s seaman and find out about fertility and infertility and from this find a true cure for this, since this will be a non invasive and low risk procedure, it will be greatly welcomed. In this research, the procedure has been based on few Algorithms enhancement and segmentation of images which has been done on the images taken from microscope in different fertility institution and have obtained a suitable result from the computer images which in turn help us to distinguish these sperms from fluids and its surroundings.Keywords: Computer-Assisted Sperm Analysis (CASA), Spermidentification, Segmentation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1642822 Bounds on Reliability of Parallel Computer Interconnection Systems
Authors: Ranjan Kumar Dash, Chita Ranjan Tripathy
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The evaluation of residual reliability of large sized parallel computer interconnection systems is not practicable with the existing methods. Under such conditions, one must go for approximation techniques which provide the upper bound and lower bound on this reliability. In this context, a new approximation method for providing bounds on residual reliability is proposed here. The proposed method is well supported by two algorithms for simulation purpose. The bounds on residual reliability of three different categories of interconnection topologies are efficiently found by using the proposed methodKeywords: Parallel computer network, reliability, probabilisticgraph, interconnection networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1346821 Proposal of Data Collection from Probes
Authors: M. Kebisek, L. Spendla, M. Kopcek, T. Skulavik
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In our paper we describe the security capabilities of data collection. Data are collected with probes located in the near and distant surroundings of the company. Considering the numerous obstacles e.g. forests, hills, urban areas, the data collection is realized in several ways. The collection of data uses connection via wireless communication, LAN network, GSM network and in certain areas data are collected by using vehicles. In order to ensure the connection to the server most of the probes have ability to communicate in several ways. Collected data are archived and subsequently used in supervisory applications. To ensure the collection of the required data, it is necessary to propose algorithms that will allow the probes to select suitable communication channel.
Keywords: Communication, computer network, data collection, probe.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1787820 Using Probe Person Data for Travel Mode Detection
Authors: Muhammad Awais Shafique, Eiji Hato, Hideki Yaginuma
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Recently GPS data is used in a lot of studies to automatically reconstruct travel patterns for trip survey. The aim is to minimize the use of questionnaire surveys and travel diaries so as to reduce their negative effects. In this paper data acquired from GPS and accelerometer embedded in smart phones is utilized to predict the mode of transportation used by the phone carrier. For prediction, Support Vector Machine (SVM) and Adaptive boosting (AdaBoost) are employed. Moreover a unique method to improve the prediction results from these algorithms is also proposed. Results suggest that the prediction accuracy of AdaBoost after improvement is relatively better than the rest.
Keywords: Accelerometer, AdaBoost, GPS, Mode Prediction, Support vector Machine.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2455