Search results for: algorithm analysis

Authors: Israa Sh. Tawfic, Sema Koc Kayhan

Abstract:

In this paper, first, we propose least support orthogonal matching pursuit (LS-OMP) algorithm to improve the performance, of the OMP (orthogonal matching pursuit) algorithm. LS-OMP algorithm adaptively chooses optimum L (least part of support), at each iteration. This modification helps to reduce the computational complexity significantly and performs better than OMP algorithm. Second, we give the procedure for the invisible image watermarking in the presence of compressive sampling. The image reconstruction based on a set of watermarked measurements is performed using LS-OMP.

Keywords: compressed sensing, orthogonal matching pursuit, restricted isometry property, signal reconstruction, least support orthogonal matching pursuit, watermark

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Authors: Linyu Wang, Jiahui Ma, Jianhong Xiang, Hanyu Jiang

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the traditional greedy compressed sensing algorithm needs to know the signal sparsity when recovering the signal, but the signal sparsity in the practical application can not be obtained as a priori information, and the recovery accuracy is low, which does not meet the needs of practical application. To solve this problem, this paper puts forward Piecewise adaptive backtracking orthogonal least squares algorithm. The algorithm is divided into two stages. In the first stage, the sparsity pre-estimation strategy is adopted, which can quickly approach the real sparsity and reduce time consumption. In the second stage iteration, the correction strategy and adaptive step size are used to accurately estimate the sparsity, and the backtracking idea is introduced to improve the accuracy of signal recovery. Through experimental simulation, the algorithm can accurately recover the estimated signal with fewer iterations when the sparsity is unknown.

Keywords: compressed sensing, greedy algorithm, least square method, adaptive reconstruction

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Authors: Ahmad M. Awwad, Jehad Al-Sadi

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The star network is one of the promising interconnection networks for future high speed parallel computers, it is expected to be one of the future-generation networks. The star network is both edge and vertex symmetry, it was shown to have many gorgeous topological proprieties also it is owns hierarchical structure framework. Although much of the research work has been done on this promising network in literature, it still suffers from having enough algorithms for load balancing problem. In this paper we try to work on this issue by investigating and proposing an efficient algorithm for load balancing problem for the star network. The proposed algorithm is called Star Clustered Dimension Exchange Method SCDEM to be implemented on the star network. The proposed algorithm is based on the Clustered Dimension Exchange Method (CDEM). The SCDEM algorithm is shown to be efficient in redistributing the load balancing as evenly as possible among all nodes of different factor networks.

Keywords: load balancing, star network, interconnection networks, algorithm

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Authors: M. Nageswara Rao, V. S. N. K. Chaitanya, K. Amarendranath

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This paper presents an optimal allocation and sizing of Distributed Generation (DG) in Radial Distribution Network (RDN) for total power loss minimization and enhances the voltage profile of the system. The two main important part of this study first is to find optimal allocation and second is optimum size of DG. The locations of DGs are identified by Analytical expressions and crow search algorithm has been employed to determine the optimum size of DG. In this study, the DG has been placed on single and multiple allocations.CSA is a meta-heuristic algorithm inspired by the intelligent behavior of the crows. Crows stores their excess food in different locations and memorizes those locations to retrieve it when it is needed. They follow each other to do thievery to obtain better food source. This analysis is tested on IEEE 33 bus and IEEE 69 bus under MATLAB environment and the results are compared with existing methods.

Keywords: analytical expression, distributed generation, crow search algorithm, power loss, voltage profile

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Authors: Te-Jen Chang, I-Hui Pan, Ping-Sheng Huang, Shan-Jen Cheng

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In this paper, a fast multiplication computing method utilizing the complement representation method and canonical recoding technique is proposed. By performing complements and canonical recoding technique, the number of partial products can be reduced. Based on these techniques, we propose an algorithm that provides an efficient multiplication method. On average, our proposed algorithm is to reduce the number of k-bit additions from (0.25k+logk/k+2.5) to (k/6 +logk/k+2.5), where k is the bit-length of the multiplicand A and multiplier B. We can therefore efficiently speed up the overall performance of the multiplication. Moreover, if we use the new proposes to compute common-multiplicand multiplication, the computational complexity can be reduced from (0.5 k+2 logk/k+5) to (k/3+2 logk/k+5) k-bit additions.

Keywords: algorithm design, complexity analysis, canonical recoding, public key cryptography, common-multiplicand multiplication

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Authors: Jeugert Kujtila, Kristi Hoxhalli, Ramazan Dalipi, Erjon Cota, Ardit Murati, Erind Bedalli

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Clustering is a versatile instrument in the analysis of collections of data providing insights of the underlying structures of the dataset and enhancing the modeling capabilities. The fuzzy approach to the clustering problem increases the flexibility involving the concept of partial memberships (some value in the continuous interval [0, 1]) of the instances in the clusters. Several fuzzy clustering algorithms have been devised like FCM, Gustafson-Kessel, Gath-Geva, kernel-based FCM, PCM etc. Each of these algorithms has its own advantages and drawbacks, so none of these algorithms would be able to perform superiorly in all datasets. In this paper we will experimentally compare FCM, GK, GG algorithm and a hybrid two-stage fuzzy clustering model combining the FCM and Gath-Geva algorithms. Firstly we will theoretically dis-cuss the advantages and drawbacks for each of these algorithms and we will describe the hybrid clustering model exploiting the advantages and diminishing the drawbacks of each algorithm. Secondly we will experimentally compare the accuracy of the hybrid model by applying it on several benchmark and synthetic datasets.

Keywords: fuzzy clustering, fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm, hybrid clustering model

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli

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Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach.

Keywords: firefly algorithm, metaheuristic algorithm, multilevel inverter, SHEPWM

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Authors: Daniel Kostrzewa, Henryk Josiński

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The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals’ selection. The goal of the project was to evaluate the exIWO by testing its usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows comparing the experimental results with optimal values.

Keywords: expanded invasive weed optimization algorithm (exIWO), traveling salesman problem (TSP), heuristic approach, inversion operator

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Authors: Daljinder Singh, J.S.Dhillon, Balraj Singh

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According to no free lunch theorem, a single search technique cannot perform best in all conditions. Optimization method can be attractive choice to solve optimization problem that may have exclusive advantages like robust and reliable performance, global search capability, little information requirement, ease of implementation, parallelism, no requirement of differentiable and continuous objective function. In order to synergize between exploration and exploitation and to further enhance the performance of Bat algorithm, the paper proposed a modified bat algorithm that adds additional search procedure based on bat’s previous experience. The proposed algorithm is used for solving the economic load dispatch (ELD) problem. The practical constraint such valve-point loading along with power balance constraints and generator limit are undertaken. To take care of power demand constraint variable elimination method is exploited. The proposed algorithm is tested on various ELD problems. The results obtained show that the proposed algorithm is capable of performing better in majority of ELD problems considered and is at par with existing algorithms for some of problems.

Keywords: bat algorithm, economic load dispatch, penalty method, variable elimination method

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Authors: Pongchanun Luangpaiboon, Wanwisa Sarasang

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In this paper, a performance of shuffled frog leaping algorithm was investigated on the stealth laser dicing process. Effect of problem on the performance of the algorithm was based on the tolerance of meandering data. From the customer specification it could be less than five microns with the target of zero microns. Currently, the meandering levels are unsatisfactory when compared to the customer specification. Firstly, the two-level factorial design was applied to preliminary study the statistically significant effects of five process variables. In this study one influential process variable is integer. From the experimental results, the new operating condition from the algorithm was superior when compared to the current manufacturing condition.

Keywords: stealth laser dicing process, meandering, meta-heuristics, shuffled frog leaping algorithm

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Authors: Mouataz Zreika, Maria Estela Varua

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Stock investment decisions are often made based on current events of the global economy and the analysis of historical data. Conversely, visual representation could assist investors’ gain deeper understanding and better insight on stock market trends more efficiently. The trend analysis is based on long-term data collection. The study adopts a hybrid method that combines the Clustering algorithm and Force-directed algorithm to overcome the scalability problem when visualizing large data. This method exemplifies the potential relationships between each stock, as well as determining the degree of strength and connectivity, which will provide investors another understanding of the stock relationship for reference. Information derived from visualization will also help them make an informed decision. The results of the experiments show that the proposed method is able to produced visualized data aesthetically by providing clearer views for connectivity and edge weights.

Keywords: clustering, force-directed, graph drawing, stock investment analysis

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Authors: Wafa Slaibi Alsharafat

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Genetic algorithms (GA) are random algorithms as random numbers that are generated during the operation of the algorithm determine what happens. This means that if GA is applied twice to optimize exactly the same problem it might produces two different answers. In this project, we propose an evolutionary algorithm and Genetic Algorithm (GA) to be implemented in symmetric encryption and decryption. Here, user's message and user secret information (key) which represent plain text to be transferred into cipher text.

Keywords: GA, encryption, decryption, crossover

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Authors: Xingxing Peng

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With the development of society, there are more and more online communication scenarios such as teleconference and online education. In the process of conference communication, the quality of voice communication is a very important part, and noise may cause the communication effect of participants to be greatly reduced. Therefore, voice noise reduction has an important impact on scenarios such as voice calls. This research focuses on the key technologies of the sound transmission process. The purpose is to maintain the audio quality to the maximum so that the listener can hear clearer and smoother sound. Firstly, to solve the problem that the traditional speech enhancement algorithm is not ideal when dealing with non-stationary noise, an adaptive speech noise reduction algorithm is studied in this paper. Traditional noise estimation methods are mainly used to deal with stationary noise. In this chapter, we study the spectral characteristics of different noise types, especially the characteristics of non-stationary Burst noise, and design a noise estimator module to deal with non-stationary noise. Noise features are extracted from non-speech segments, and the noise estimation module is adjusted in real time according to different noise characteristics. This adaptive algorithm can enhance speech according to different noise characteristics, improve the performance of traditional algorithms to deal with non-stationary noise, so as to achieve better enhancement effect. The experimental results show that the algorithm proposed in this chapter is effective and can better adapt to different types of noise, so as to obtain better speech enhancement effect.

Keywords: speech noise reduction, speech enhancement, self-adaptation, Wiener filter algorithm

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Authors: Doyin Afolabi, Phillip Adewole, Oladipupo Sennaike

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Most well-known classifiers, including the decision tree algorithm, can make predictions on balanced datasets efficiently. However, the decision tree algorithm tends to be biased towards imbalanced datasets because of the skewness of the distribution of such datasets. To overcome this problem, this study proposes a weighted decision tree algorithm that aims to remove the bias toward the majority class and prevents the reduction of majority observations in imbalance datasets classification. The proposed weighted decision tree algorithm was tested on three imbalanced datasets- cancer dataset, german credit dataset, and banknote dataset. The specificity, sensitivity, and accuracy metrics were used to evaluate the performance of the proposed decision tree algorithm on the datasets. The evaluation results show that for some of the weights of our proposed decision tree, the specificity, sensitivity, and accuracy metrics gave better results compared to that of the ID3 decision tree and decision tree induced with minority entropy for all three datasets.

Keywords: data mining, decision tree, classification, imbalance dataset

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Authors: Orhun Vural, Oguz Bayat, Rustu Akay, Osman N. Ucan

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This study presents a new parallel approach clustering of GPS data. Evaluation has been made by comparing execution time of various clustering algorithms on GPS data. This paper aims to propose a parallel based on neighborhood K-means algorithm to make it faster. The proposed parallelization approach assumes that each GPS data represents a vehicle and to communicate between vehicles close to each other after vehicles are clustered. This parallelization approach has been examined on different sized continuously changing GPS data and compared with serial K-means algorithm and other serial clustering algorithms. The results demonstrated that proposed parallel K-means algorithm has been shown to work much faster than other clustering algorithms.

Keywords: parallel k-means algorithm, parallel clustering, clustering algorithms, clustering on flowing data

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Authors: Seyedmahdi Mousavihashemi

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One of the most important subjects of interest in researches is 'improving' which result in various algorithms. In so many geometrical problems we are faced with target functions which should be optimized. In group practices, all the functions’ cooperation lead to convergence. In the study, the optimization algorithm of dense particles is used. Usage of the algorithm improves the given performance norms. The results reveal that usage of swarm algorithm for reinforced particles in designing state feedback improves the given performance norm and in optimized designing of multi-target state feedback controlling, the network will maintain its bearing structure. The results also show that PSO is usable for optimization of state feedback controllers.

Keywords: multi-objective, enhanced, feedback, optimization, algorithm, particle, design

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Authors: Marina Franulovic, Robert Basan, Bozidar Krizan

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Constitutive modelling of material behaviour is becoming increasingly important in prediction of possible failures in highly loaded engineering components, and consequently, optimization of their design. In order to account for large number of phenomena that occur in the material during operation, such as kinematic hardening effect in low cycle fatigue behaviour of steels, complex nonlinear material models are used ever more frequently, despite of the complexity of determination of their parameters. As a method for the determination of these parameters, genetic algorithm is good choice because of its capability to provide very good approximation of the solution in systems with large number of unknown variables. For the application of genetic algorithm to parameter identification, inverse analysis must be primarily defined. It is used as a tool to fine-tune calculated stress-strain values with experimental ones. In order to choose proper objective function for inverse analysis among already existent and newly developed functions, the research is performed to investigate its influence on material behaviour modelling.

Keywords: genetic algorithm, kinematic hardening, material model, objective function

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Authors: Fariborz Ahmadi, Hamid Salehi, Khosrow Karimi

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A sensor network is set of sensor nodes that cooperate together to perform a predefined tasks. The important problem in this network is power consumption. So, in this paper one algorithm based on the eurygaster life is introduced to minimize power consumption by the nodes of these networks. In this method the search space of problem is divided into several partitions and each partition is investigated separately. The evaluation results show that our approach is more efficient in comparison to other evolutionary algorithm like genetic algorithm.

Keywords: evolutionary computation, genetic algorithm, particle swarm optimization, sensor network optimization

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Authors: Adeniran K. Ademuwagun, Alastair Allen

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The relationship dependence between RSS and distance in an enclosed environment is an important consideration because it is a factor that can influence the reliability of any localization algorithm founded on RSS. Several algorithms effectively reduce the variance of RSS to improve localization or accuracy performance. Our proposed algorithm essentially avoids this pitfall and consequently, its high adaptability in the face of erratic radio signal. Using 3 anchors in close proximity of each other, we are able to establish that RSS can be used as reliable indicator for localization with an acceptable degree of accuracy. Inherent in this concept, is the ability for each prospective anchor to validate (guarantee) the position or the proximity of the other 2 anchors involved in the localization and vice versa. This procedure ensures that the uncertainties of radio signals due to multipath effects in enclosed environments are minimized. A major driver of this idea is the implicit topological relationship among sensors due to raw radio signal strength. The algorithm is an area based algorithm; however, it does not trade accuracy for precision (i.e the size of the returned area).

Keywords: anchor nodes, centroid algorithm, communication graph, radio signal strength

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Authors: Said Baadel, Fadi Thabtah, Joan Lu

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Clustering involves the partitioning of n objects into k clusters. Many clustering algorithms use hard-partitioning techniques where each object is assigned to one cluster. In this paper, we propose an overlapping algorithm MCOKE which allows objects to belong to one or more clusters. The algorithm is different from fuzzy clustering techniques because objects that overlap are assigned a membership value of 1 (one) as opposed to a fuzzy membership degree. The algorithm is also different from other overlapping algorithms that require a similarity threshold to be defined as a priority which can be difficult to determine by novice users.

Keywords: data mining, k-means, MCOKE, overlapping

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Authors: Younis R. Elhaddad, Mohamed A. Alshaari

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Since 2700 B.C the problem of constructing magic squares attracts many researchers. Magic squares one of most difficult challenges for mathematicians. In this work, we describe how to construct and enumerate Pan- magic squares using genetic algorithm, using new chromosome encoding technique. The results were promising within reasonable time.

Keywords: genetic algorithm, magic square, pan-magic square, computational intelligence

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Authors: Shital Suresh Borse, Vijayalaxmi Kadroli

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E-commerce industries nowadays implement the latest AI, ML Techniques to improve their own performance and prediction accuracy. This helps to gain a huge profit from the online market. Ant Colony Optimization, Genetic algorithm, Particle Swarm Optimization, Neural Network & GWO help many e-commerce industries for up-gradation of their predictive performance. These algorithms are providing optimum results in various applications, such as stock price prediction, prediction of drug-target interaction & user ratings of similar products in e-commerce sites, etc. In this study, customer reviews will play an important role in prediction analysis. People showing much interest in buying a lot of services& products suggested by other customers. This ultimately increases net profit. In this work, a convolution neural network (CNN) is proposed which further is useful to optimize the prediction accuracy of an e-commerce website. This method shows that CNN is used to optimize hyperparameters of GWO algorithm using an appropriate coding scheme. Accurate model results are verified by comparing them to PSO results whose hyperparameters have been optimized by CNN in Amazon's customer review dataset. Here, experimental outcome proves that this proposed system using the GWO algorithm achieves superior execution in terms of accuracy, precision, recovery, etc. in prediction analysis compared to the existing systems.

Keywords: prediction analysis, e-commerce, machine learning, grey wolf optimization, particle swarm optimization, CNN

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Authors: Mohammad Tarek Al Muallim, Ozhan Duzenli, Ceyhun Ilguy

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Passive sonar is a method for detecting acoustic signals in the ocean. It detects the acoustic signals emanating from external sources. With passive sonar, we can determine the bearing of the target only, no information about the range of the target. Target Motion Analysis (TMA) is a process to estimate the position and speed of a target using passive sonar information. Since bearing is the only available information, the TMA technique called Bearing-only TMA. Many TMA techniques have been developed. However, until now, there is not a very effective method that could be used to always track an unknown target and extract its moving trace. In this work, a design of effective Bearing-only TMA Algorithm is done. The measured bearing angles are very noisy. Moreover, for multi-beam sonar, the measurements is quantized due to the sonar beam width. To deal with this, modified gain extended Kalman filter algorithm is used. The algorithm is fine-tuned, and many modules are added to improve the performance. A special validation gate module is used to insure stability of the algorithm. Many indicators of the performance and confidence level measurement are designed and tested. A new method to detect if the target is maneuvering is proposed. Moreover, a reactive optimal observer maneuver based on bearing measurements is proposed, which insure converging to the right solution all of the times. To test the performance of the proposed TMA algorithm a simulation is done with a MATLAB program. The simulator program tries to model a discrete scenario for an observer and a target. The simulator takes into consideration all the practical aspects of the problem such as a smooth transition in the speed, a circular turn of the ship, noisy measurements, and a quantized bearing measurement come for multi-beam sonar. The tests are done for a lot of given test scenarios. For all the tests, full tracking is achieved within 10 minutes with very little error. The range estimation error was less than 5%, speed error less than 5% and heading error less than 2 degree. For the online performance estimator, it is mostly aligned with the real performance. The range estimation confidence level gives a value equal to 90% when the range error less than 10%. The experiments show that the proposed TMA algorithm is very robust and has low estimation error. However, the converging time of the algorithm is needed to be improved.

Keywords: target motion analysis, Kalman filter, passive sonar, bearing-only tracking

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Authors: Yuqing Chen, Ying Xu, Renfa Li

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The development of matrix completion theory provides new approaches for data gathering in Wireless Sensor Networks (WSN). The existing matrix completion algorithms for WSN mainly consider how to reduce the sampling number without considering the real-time performance when recovering the data matrix. In order to guarantee the recovery accuracy and reduce the recovery time consumed simultaneously, we propose a new ALM algorithm to recover the weather monitoring data. A lot of experiments have been carried out to investigate the performance of the proposed ALM algorithm by using different parameter settings, different sampling rates and sampling models. In addition, we compare the proposed ALM algorithm with some existing algorithms in the literature. Experimental results show that the ALM algorithm can obtain better overall recovery accuracy with less computing time, which demonstrate that the ALM algorithm is an effective and efficient approach for recovering the real world weather monitoring data in WSN.

Keywords: wireless sensor network, matrix completion, singular value thresholding, augmented Lagrange multiplier

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Authors: Sahin Emrah Amrahov, Fatih Aybar, Serhat Dogan

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In this paper we consider the rule reduct generation problem. Rule Reduct Generation (RG) and Modified Rule Generation (MRG) algorithms, that are used to solve this problem, are well-known. Alternative to these algorithms, we develop Pruning Rule Generation (PRG) algorithm. We compare the PRG algorithm with RG and MRG.

Keywords: rough sets, decision rules, rule induction, classification

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Authors: Nirmal Yadav, Tanuja Srivastava

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Shannon theory is an exact method to recover a band limited signals from its sampled values in discrete implementation, using sinc interpolators. But sinc based results are not much satisfactory for band-limited calculations so that convolution with window function, having compact support, has been introduced. Convolution Backprojection algorithm with window function is an approximation algorithm. In this paper, the error has been calculated, arises due to this approximation nature of reconstruction algorithm. This result will be defined for fan beam projection data which is more faster than parallel beam projection.

Keywords: computed tomography, convolution backprojection, radon transform, fan beam

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Authors: Shahram Jamali, Samira Hamed

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One of the open issues in Random Early Detection (RED) algorithm is how to set its parameters to reach high performance for the dynamic conditions of the network. Although original RED uses fixed values for its parameters, this paper follows a model-based approach to upgrade performance of the RED algorithm. It models the routers queue behavior by using the Markov model and uses this model to predict future conditions of the queue. This prediction helps the proposed algorithm to make some tunings over RED's parameters and provide efficiency and better performance. Widespread packet level simulations confirm that the proposed algorithm, called Markov-RED, outperforms RED and FARED in terms of queue stability, bottleneck utilization and dropped packets count.

Keywords: active queue management, RED, Markov model, random early detection algorithm

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Authors: Ahmed Z. Gabr, Ahmed A. Helal, Hussein E. Said

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With the incessant increase of power systems capacity and voltage grade, the safety of grounding grid becomes more and more prominent. In this paper, the designing substation grounding grid is presented by means of genetic algorithm (GA). This approach purposes to control the grounding cost of the power system with the aid of controlling grounding rod number and conductor lengths under the same safety limitations. The proposed technique is used for the design of the substation grounding grid in Khalda Petroleum Company “El-Qasr” power plant and the design was simulated by using CYMGRD software for results verification. The result of the design is highly complying with IEEE 80-2000 standard requirements.

Keywords: genetic algorithm, optimum grounding grid design, power system analysis, power system protection, single layer model, substation

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Authors: Juan Manuel Sanchez-Cartas, Gonzalo Leon

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A price competition algorithm for ABMs based on game theory principles is proposed to deal with the simulation of theoretical market models. The algorithm is applied to the classical Hotelling’s model and to a two-sided market model to show it leads to the optimal behavior predicted by theoretical models. However, when theoretical models fail to predict the equilibrium, the algorithm is capable of reaching a feasible outcome. Results highlight that the algorithm can be implemented in other simulation models to guarantee rational users and endogenous optimal behaviors. Also, it can be applied as a tool of verification given that is theoretically based.

Keywords: agent-based models, algorithmic game theory, multi-sided markets, price optimization

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