Search results for: retrieval algorithms

Authors: S. Ramana Babu, V. Ramachandra Raju, K. Ramji

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This paper presents the effect of actuation schemes on the performance of parallel manipulators and also how the singularity loci have been changed in the reachable workspace of the manipulator with the choice of actuation scheme to drive the manipulator. The performance of the eight possible actuation schemes of 3RRR planar parallel manipulator is compared with each other. The optimal design problem is formulated to find the manipulator geometry that maximizes the singularity free conditioned workspace for all the eight actuation cases, the optimization problem is solved by using genetic algorithms.

Keywords: Actuation schemes, GCI, genetic algorithms.

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Authors: Chang-le Lu, Yong Chen

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The shortest path question is in a graph theory model question, and it is applied in many fields. The most short-path question may divide into two kinds: Single sources most short-path, all apexes to most short-path. This article mainly introduces the problem of all apexes to most short-path, and gives a new parallel algorithm of all apexes to most short-path according to the Dijkstra algorithm. At last this paper realizes the parallel algorithms in the technology of C # multithreading.

Keywords: Dijkstra algorithm, parallel algorithms, multi-thread technology, most short-path, ratio.

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Authors: Muhammad Rehan Usman, Muhammad Arslan Usman, Soo Young Shin

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The new era of digital communication has brought up many challenges that network operators need to overcome. The high demand of mobile data rates require improved networks, which is a challenge for the operators in terms of maintaining the quality of experience (QoE) for their consumers. In live video transmission, there is a sheer need for live surveillance of the videos in order to maintain the quality of the network. For this purpose objective algorithms are employed to monitor the quality of the videos that are transmitted over a network. In order to test these objective algorithms, subjective quality assessment of the streamed videos is required, as the human eye is the best source of perceptual assessment. In this paper we have conducted subjective evaluation of videos with varying spatial and temporal impairments. These videos were impaired with frame freezing distortions so that the impact of frame freezing on the quality of experience could be studied. We present subjective Mean Opinion Score (MOS) for these videos that can be used for fine tuning the objective algorithms for video quality assessment.

Keywords: Frame freezing, mean opinion score, objective assessment, subjective evaluation.

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Authors: V. Sudha, D. Sriram Kumar

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Orthogonal Frequency Division Multiplexing (OFDM) has been used in many advanced wireless communication systems due to its high spectral efficiency and robustness to frequency selective fading channels. However, the major concern with OFDM system is the high peak-to-average power ratio (PAPR) of the transmitted signal. Some of the popular techniques used for PAPR reduction in OFDM system are conventional partial transmit sequences (CPTS) and clipping. In this paper, a parallel combination/hybrid scheme of PAPR reduction using clipping and CPTS algorithms is proposed. The proposed method intelligently applies both the algorithms in order to reduce both PAPR as well as computational complexity. The proposed scheme slightly degrades bit error rate (BER) performance due to clipping operation and it can be reduced by selecting an appropriate value of the clipping ratio (CR). The simulation results show that the proposed algorithm achieves significant PAPR reduction with much reduced computational complexity.

Keywords: CCDF, OFDM, PAPR, PTS.

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Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag

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This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.

Keywords: Density Estimation, SVM, Learning Algorithms, Parameters Estimation.

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Authors: Safeer Hussain Khan

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In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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Authors: Hanan Ahmed-Hosni Mahmoud, Nadia Al-Ghreimil

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In-place sorting algorithms play an important role in many fields such as very large database systems, data warehouses, data mining, etc. Such algorithms maximize the size of data that can be processed in main memory without input/output operations. In this paper, a novel in-place sorting algorithm is presented. The algorithm comprises two phases; rearranging the input unsorted array in place, resulting segments that are ordered relative to each other but whose elements are yet to be sorted. The first phase requires linear time, while, in the second phase, elements of each segment are sorted inplace in the order of z log (z), where z is the size of the segment, and O(1) auxiliary storage. The algorithm performs, in the worst case, for an array of size n, an O(n log z) element comparisons and O(n log z) element moves. Further, no auxiliary arithmetic operations with indices are required. Besides these theoretical achievements of this algorithm, it is of practical interest, because of its simplicity. Experimental results also show that it outperforms other in-place sorting algorithms. Finally, the analysis of time and space complexity, and required number of moves are presented, along with the auxiliary storage requirements of the proposed algorithm.

Keywords: Auxiliary storage sorting, in-place sorting, sorting.

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

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As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling. The research proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling. The paper concludes the challenges and improvement directions for Deep Reinforcement Learning-based resource scheduling algorithms.

Keywords: Resource scheduling, deep reinforcement learning, distributed system, artificial intelligence.

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Authors: Shilpy Sharma

Abstract:

As the web continues to grow exponentially, the idea of crawling the entire web on a regular basis becomes less and less feasible, so the need to include information on specific domain, domain-specific search engines was proposed. As more information becomes available on the World Wide Web, it becomes more difficult to provide effective search tools for information access. Today, people access web information through two main kinds of search interfaces: Browsers (clicking and following hyperlinks) and Query Engines (queries in the form of a set of keywords showing the topic of interest) [2]. Better support is needed for expressing one's information need and returning high quality search results by web search tools. There appears to be a need for systems that do reasoning under uncertainty and are flexible enough to recover from the contradictions, inconsistencies, and irregularities that such reasoning involves. In a multi-view problem, the features of the domain can be partitioned into disjoint subsets (views) that are sufficient to learn the target concept. Semi-supervised, multi-view algorithms, which reduce the amount of labeled data required for learning, rely on the assumptions that the views are compatible and uncorrelated. This paper describes the use of semi-structured machine learning approach with Active learning for the “Domain Specific Search Engines". A domain-specific search engine is “An information access system that allows access to all the information on the web that is relevant to a particular domain. The proposed work shows that with the help of this approach relevant data can be extracted with the minimum queries fired by the user. It requires small number of labeled data and pool of unlabelled data on which the learning algorithm is applied to extract the required data.

Keywords: Search engines; machine learning, Informationretrieval, Active logic.

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Authors: Mohsen Ebrahimi, Milad M. Rabieh

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In this paper, two very different optimization algorithms, Genetic and DIRECT algorithms, are used to history match a bottomhole pressure response for a reservoir with wellbore storage and skin with the best possible analytical model. No initial guesses are available for reservoir parameters. The results show that the matching process is much faster and more accurate for DIRECT method in comparison with Genetic algorithm. It is furthermore concluded that the DIRECT algorithm does not need any initial guesses, whereas Genetic algorithm needs to be tuned according to initial guesses.

Keywords: DIRECT algorithm, Genetic algorithm, Analytical modeling, History match

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Authors: S. I. Abu Alasal, M. M. Esbeih, E. R. Fayyad, R. S. Gharaibeh, M. Z. Ali, A. A. Freewan, M. M. Jamhawi

Abstract:

This research proposes a novel reconstruction protocol for restoring missing surfaces and low-quality edges and shapes in photos of artifacts at historical sites. The protocol starts with the extraction of a cloud of points. This extraction process is based on four subordinate algorithms, which differ in the robustness and amount of resultant. Moreover, they use different -but complementary- accuracy to some related features and to the way they build a quality mesh. The performance of our proposed protocol is compared with other state-of-the-art algorithms and toolkits. The statistical analysis shows that our algorithm significantly outperforms its rivals in the resultant quality of its object files used to reconstruct the desired model.

Keywords: Meshes, Point Clouds, Surface Reconstruction Protocols, 3D Reconstruction.

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Authors: Mohd Fikri Azli bin Abdullah, Ali Fahmi Perwira Negara, Md. Shohel Sayeed, Deok-Jai Choi, Kalaiarasi Sonai Muthu

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Rapid advancement in computing technology brings computers and humans to be seamlessly integrated in future. The emergence of smartphone has driven computing era towards ubiquitous and pervasive computing. Recognizing human activity has garnered a lot of interest and has raised significant researches- concerns in identifying contextual information useful to human activity recognition. Not only unobtrusive to users in daily life, smartphone has embedded built-in sensors that capable to sense contextual information of its users supported with wide range capability of network connections. In this paper, we will discuss the classification algorithms used in smartphone-based human activity. Existing technologies pertaining to smartphone-based researches in human activity recognition will be highlighted and discussed. Our paper will also present our findings and opinions to formulate improvement ideas in current researches- trends. Understanding research trends will enable researchers to have clearer research direction and common vision on latest smartphone-based human activity recognition area.

Keywords: Classification algorithms, Human Activity Recognition (HAR), Smartphones

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Authors: Umar Albalawi, Sang C. Suh, Jinoh Kim

Abstract:

As internet continues to expand its usage with an  enormous number of applications, cyber-threats have significantly  increased accordingly. Thus, accurate detection of malicious traffic in  a timely manner is a critical concern in today’s Internet for security.  One approach for intrusion detection is to use Machine Learning (ML)  techniques. Several methods based on ML algorithms have been  introduced over the past years, but they are largely limited in terms of  detection accuracy and/or time and space complexity to run. In this  work, we present a novel method for intrusion detection that  incorporates a set of supervised learning algorithms. The proposed  technique provides high accuracy and outperforms existing techniques  that simply utilizes a single learning method. In addition, our  technique relies on partial flow information (rather than full  information) for detection, and thus, it is light-weight and desirable for  online operations with the property of early identification. With the  mid-Atlantic CCDC intrusion dataset publicly available, we show that  our proposed technique yields a high degree of detection rate over 99%  with a very low false alarm rate (0.4%). 

 

Keywords: Intrusion Detection, Supervised Learning, Traffic Classification.

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Authors: Mafarja Majdi, Salwani Abdullah, Najmeh S. Jaddi

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One of the global combinatorial optimization problems in machine learning is feature selection. It concerned with removing the irrelevant, noisy, and redundant data, along with keeping the original meaning of the original data. Attribute reduction in rough set theory is an important feature selection method. Since attribute reduction is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, we proposed two feature selection mechanisms based on memetic algorithms (MAs) which combine the genetic algorithm with a fuzzy record to record travel algorithm and a fuzzy controlled great deluge algorithm, to identify a good balance between local search and genetic search. In order to verify the proposed approaches, numerical experiments are carried out on thirteen datasets. The results show that the MAs approaches are efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.

Keywords: Rough Set Theory, Attribute Reduction, Fuzzy Logic, Memetic Algorithms, Record to Record Algorithm, Great Deluge Algorithm.

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Authors: Bing-Fei Wu, Yen-Lin Chen, Chung-Cheng Chiu

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In this study, a new criterion for determining the number of classes an image should be segmented is proposed. This criterion is based on discriminant analysis for measuring the separability among the segmented classes of pixels. Based on the new discriminant criterion, two algorithms for recursively segmenting the image into determined number of classes are proposed. The proposed methods can automatically and correctly segment objects with various illuminations into separated images for further processing. Experiments on the extraction of text strings from complex document images demonstrate the effectiveness of the proposed methods.1

Keywords: image segmentation, multilevel thresholding, clustering, discriminant analysis

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Authors: Weng Ian Ho, Seng Fat Wong

Abstract:

In recent years, Radio Frequency Identification (RFID) is followed with interest by many researches, especially for the purpose of indoor positioning as the innate properties of RFID are profitable for achieving it. A lot of algorithms or schemes are proposed to be used in the RFID-based positioning system, but most of them are lack of environmental consideration and it induces inaccuracy of application. In this research, a lot of algorithms and schemes of RFID indoor positioning are discussed to see whether effective or not on application, and some rules are summarized for achieving accurate positioning. On the other hand, a new term “Noise Factor" is involved to describe the signal loss between the target and the obstacle. As a result, experimental data can be obtained but not only simulation; and the performance of the positioning system can be expressed substantially.

Keywords: Indoor positioning, LANDMARC, noise factors, RFID.

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Authors: Mehmet Hacibeyoglu, Ahmet Arslan, Sirzat Kahramanli

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This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive Bayes, C4.5 and CN2 data mining classification algorithms. As the result the classification accuracies of the six datasets are improved averagely by 1.71% to 12.31%.

Keywords: Data mining classification algorithms, entropy-baseddiscretization method

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Authors: Johann Barbier, Eric Filiol, Kichenakoumar Mayoura

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We present in this paper a new approach for specific JPEG steganalysis and propose studying statistics of the compressed DCT coefficients. Traditionally, steganographic algorithms try to preserve statistics of the DCT and of the spatial domain, but they cannot preserve both and also control the alteration of the compressed data. We have noticed a deviation of the entropy of the compressed data after a first embedding. This deviation is greater when the image is a cover medium than when the image is a stego image. To observe this deviation, we pointed out new statistic features and combined them with the Multiple Embedding Method. This approach is motivated by the Avalanche Criterion of the JPEG lossless compression step. This criterion makes possible the design of detectors whose detection rates are independent of the payload. Finally, we designed a Fisher discriminant based classifier for well known steganographic algorithms, Outguess, F5 and Hide and Seek. The experiemental results we obtained show the efficiency of our classifier for these algorithms. Moreover, it is also designed to work with low embedding rates (< 10-5) and according to the avalanche criterion of RLE and Huffman compression step, its efficiency is independent of the quantity of hidden information.

Keywords: Compressed frequency domain, Fisher discriminant, specific JPEG steganalysis.

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Authors: Safa Adi

Abstract:

This paper will consider the problem of sequential mining patterns embedded in a database by handling the time constraints as defined in the GSP algorithm (level wise algorithms). We will compare two previous approaches GTC and PSP, that resumes the general principles of GSP. Furthermore this paper will discuss PG-hybrid algorithm, that using PSP and GTC. The results show that PSP and GTC are more efficient than GSP. On the other hand, the GTC algorithm performs better than PSP. The PG-hybrid algorithm use PSP algorithm for the two first passes on the database, and GTC approach for the following scans. Experiments show that the hybrid approach is very efficient for short, frequent sequences.

Keywords: Database, GTC algorithm, PSP algorithm, sequential patterns, time constraints.

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Authors: Daniel F. Garcia, Julio Molleda, Francisco Gonzalez, Ruben Usamentiaga

Abstract:

The development of many measurement and inspection systems of products based on real-time image processing can not be carried out totally in a laboratory due to the size or the temperature of the manufactured products. Those systems must be developed in successive phases. Firstly, the system is installed in the production line with only an operational service to acquire images of the products and other complementary signals. Next, a recording service of the image and signals must be developed and integrated in the system. Only after a large set of images of products is available, the development of the real-time image processing algorithms for measurement or inspection of the products can be accomplished under realistic conditions. Finally, the recording service is turned off or eliminated and the system operates only with the real-time services for the acquisition and processing of the images. This article presents a systematic performance evaluation of the image compression algorithms currently available to implement a real-time recording service. The results allow establishing a trade off between the reduction or compression of the image size and the CPU time required to get that compression level.

Keywords: Lossless image compression, codec performanceevaluation, grayscale codec comparison, real-time image recording.

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Authors: Nidal F. Shilbayeh, Remah W. Al-Khatib, Sameer A. Nooh

Abstract:

Arabic offline handwriting recognition systems are considered as one of the most challenging topics. Arabic Handwritten Numeral Strings are used to automate systems that deal with numbers such as postal code, banking account numbers and numbers on car plates. Segmentation of connected numerals is the main bottleneck in the handwritten numeral recognition system.  This is in turn can increase the speed and efficiency of the recognition system. In this paper, we proposed algorithms for automatic segmentation and feature extraction of Arabic handwritten numeral strings based on Watershed approach. The algorithms have been designed and implemented to achieve the main goal of segmenting and extracting the string of numeral digits written by hand especially in a courtesy amount of bank checks. The segmentation algorithm partitions the string into multiple regions that can be associated with the properties of one or more criteria. The numeral extraction algorithm extracts the numeral string digits into separated individual digit. Both algorithms for segmentation and feature extraction have been tested successfully and efficiently for all types of numerals.

Keywords: Handwritten numerals, segmentation, courtesy amount, feature extraction, numeral recognition.

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Authors: Mohamed Boulouird, Moha M'Rabet Hassani

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In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.

Keywords: Cumulants, Identification, MA models, Parameter estimation

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Authors: A. Ghaffari, A. S. Mostafavi

Abstract:

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, mitosis and cell division. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks that control the activities of cyclin-dependent kinases (CDK). The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. In this paper, an innovative approach has been proposed that uses genetic algorithms to mine a set of behavior data output by a biological system in order to determine the kinetic parameters of the system. In our approach, the machine learning method is integrated with the framework of existent biological information in a wiring diagram so that its findings are expressed in a form of system dynamic behavior. By numerical simulations it has been illustrated that the model is consistent with experiments and successfully shown that such application of genetic algorithms will highly improve the performance of mathematical model of the cell division cycle to simulate such a complicated bio-system.

Keywords: Cell cycle, Cyclin-dependent kinase, Fission yeast, Genetic algorithms, Mathematical modeling, Wiring diagram

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Authors: Mohamed E. Salem Abozaed

Abstract:

Detection and classification of power quality (PQ) disturbances is an important consideration to electrical utilities and many industrial customers so that diagnosis and mitigation of such disturbance can be implemented quickly. S-transform algorithm and continuous wavelet transforms (CWT) are time-frequency algorithms, and both of them are powerful in detection and classification of PQ disturbances. This paper presents detection and classification of PQ disturbances using S-transform and CWT algorithms. The results of detection and classification, provides that S-transform is more accurate in detection and classification for most PQ disturbance than CWT algorithm, where as CWT algorithm more powerful in detection in some disturbances like notching

Keywords: CWT, Disturbances classification, Disturbances detection, Power quality, S-transform.

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Authors: Ahmet Y. Arabul, Ibrahim Senol, Fatma Keskin Arabul, Mustafa G. Aydeniz, Yasemin Oner, Gokhan Kalkan

Abstract:

In the standards of IEC 60076-2 and IEC 60076-7, three different hot-spot temperature estimation methods are suggested. In this study, the algorithms which used in hot-spot temperature calculations are analyzed by comparing the algorithms with the results of an experimental set-up made by a Transformer Monitoring System (TMS) in use. In tested system, TMS uses only top oil temperature and load ratio for hot-spot temperature calculation. And also, it uses some constants from standards which are on agreed statements tables. During the tests, it came out that hot-spot temperature calculation method is just making a simple calculation and not uses significant all other variables that could affect the hot-spot temperature.

Keywords: Hot-spot temperature, monitoring system, power transformer, smart grid.

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Authors: Mir Hadi Seyedafsari, Iraj Hasanzadeh

Abstract:

Like other external sorting algorithms, the presented algorithm is a two step algorithm including internal and external steps. The first part of the algorithm is like the other similar algorithms but second part of that is including a new easy implementing method which has reduced the vast number of inputoutput operations saliently. As decreasing processor operating time does not have any effect on main algorithm speed, any improvement in it should be done through decreasing the number of input-output operations. This paper propose an easy algorithm for choose the correct record location of the final list. This decreases the time complexity and makes the algorithm faster.

Keywords: External sorting algorithm, internal sortingalgorithm, fast sorting, robust algorithm.

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Authors: Sharief F. Babiker, Abdelkareem Bedri, Rania Naeem

Abstract:

The implementation of single-electron tunneling (SET) simulators based on the master-equation (ME) formalism requires the efficient and accurate identification of an exhaustive list of active states and related tunnel events. Dynamic simulations also require the control of the emerging states and guarantee the safe elimination of decaying states. This paper describes algorithms for use in the stationary and dynamic control of the lists of active states and events. The paper presents results obtained using these algorithms with different SET structures.

Keywords: Active state, Coulomb blockade, Master Equation, Single electron devices

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

Abstract:

This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.

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Authors: Benjamin Gorry, Zezhi Chen, Kevin Hammond, Andy Wallace, Greg Michaelson

Abstract:

This paper describes new computer vision algorithms that have been developed to track moving objects as part of a long-term study into the design of (semi-)autonomous vehicles. We present the results of a study to exploit variable kernels for tracking in video sequences. The basis of our work is the mean shift object-tracking algorithm; for a moving target, it is usual to define a rectangular target window in an initial frame, and then process the data within that window to separate the tracked object from the background by the mean shift segmentation algorithm. Rather than use the standard, Epanechnikov kernel, we have used a kernel weighted by the Chamfer distance transform to improve the accuracy of target representation and localization, minimising the distance between the two distributions in RGB color space using the Bhattacharyya coefficient. Experimental results show the improved tracking capability and versatility of the algorithm in comparison with results using the standard kernel. These algorithms are incorporated as part of a robot test-bed architecture which has been used to demonstrate their effectiveness.

Keywords: Hume, functional programming, autonomous vehicle, pioneer robot, vision.

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Authors: Václav Sadílek, Miroslav Vořechovský

Abstract:

The paper deals with the classical fiber bundle model of equal load sharing, sometimes referred to as the Daniels’ bundle or the democratic bundle. Daniels formulated a multidimensional integral and also a recursive formula for evaluation of the strength cumulative distribution function. This paper describes three algorithms for evaluation of the recursive formula and also their implementations with source codes in the Python high-level programming language. A comparison of the algorithms are provided with respect to execution time. Analysis of orders of magnitudes of addends in the recursion is also provided.

Keywords: Daniels bundle model, equal load sharing, Python, mpmath.

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