Search results for: machine-learning algorithms
784 Iterative Clustering Algorithm for Analyzing Temporal Patterns of Gene Expression
Authors: Seo Young Kim, Jae Won Lee, Jong Sung Bae
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Microarray experiments are information rich; however, extensive data mining is required to identify the patterns that characterize the underlying mechanisms of action. For biologists, a key aim when analyzing microarray data is to group genes based on the temporal patterns of their expression levels. In this paper, we used an iterative clustering method to find temporal patterns of gene expression. We evaluated the performance of this method by applying it to real sporulation data and simulated data. The patterns obtained using the iterative clustering were found to be superior to those obtained using existing clustering algorithms.Keywords: Clustering, microarray experiment, temporal pattern of gene expression data.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1354783 Energy Efficient Resource Allocation in Distributed Computing Systems
Authors: Samee Ullah Khan, C. Ardil
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The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1789782 A High Bitrate Information Hiding Algorithm for Video in Video
Authors: Wang Shou-Dao, Xiao Chuang-Bai, Lin Yu
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In high bitrate information hiding techniques, 1 bit is embedded within each 4 x 4 Discrete Cosine Transform (DCT) coefficient block by means of vector quantization, then the hidden bit can be effectively extracted in terminal end. In this paper high bitrate information hiding algorithms are summarized, and the scheme of video in video is implemented. Experimental result shows that the host video which is embedded numerous auxiliary information have little visually quality decline. Peak Signal to Noise Ratio (PSNR)Y of host video only degrades 0.22dB in average, while the hidden information has a high percentage of survives and keeps a high robustness in H.264/AVC compression, the average Bit Error Rate(BER) of hiding information is 0.015%.Keywords: Information Hiding, Embed, Quantification, Extract
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1897781 Visual Search Based Indoor Localization in Low Light via RGB-D Camera
Authors: Yali Zheng, Peipei Luo, Shinan Chen, Jiasheng Hao, Hong Cheng
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Most of traditional visual indoor navigation algorithms and methods only consider the localization in ordinary daytime, while we focus on the indoor re-localization in low light in the paper. As RGB images are degraded in low light, less discriminative infrared and depth image pairs are taken, as the input, by RGB-D cameras, the most similar candidates, as the output, are searched from databases which is built in the bag-of-word framework. Epipolar constraints can be used to relocalize the query infrared and depth image sequence. We evaluate our method in two datasets captured by Kinect2. The results demonstrate very promising re-localization results for indoor navigation system in low light environments.Keywords: Indoor navigation, low light, RGB-D camera, vision based.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1674780 Solving Machine Loading Problem in Flexible Manufacturing Systems Using Particle Swarm Optimization
Authors: S. G. Ponnambalam, Low Seng Kiat
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In this paper, a particle swarm optimization (PSO) algorithm is proposed to solve machine loading problem in flexible manufacturing system (FMS), with bicriterion objectives of minimizing system unbalance and maximizing system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools. The performance of the PSO is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The results support that the proposed PSO is comparable with the algorithms reported in the literature.Keywords: Machine loading problem, FMS, Particle Swarm Optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2119779 Elimination of Redundant Links in Web Pages– Mathematical Approach
Authors: G. Poonkuzhali, K.Thiagarajan, K.Sarukesi
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With the enormous growth on the web, users get easily lost in the rich hyper structure. Thus developing user friendly and automated tools for providing relevant information without any redundant links to the users to cater to their needs is the primary task for the website owners. Most of the existing web mining algorithms have concentrated on finding frequent patterns while neglecting the less frequent one that are likely to contain the outlying data such as noise, irrelevant and redundant data. This paper proposes new algorithm for mining the web content by detecting the redundant links from the web documents using set theoretical(classical mathematics) such as subset, union, intersection etc,. Then the redundant links is removed from the original web content to get the required information by the user..Keywords: Web documents, Web content mining, redundantlink, outliers, set theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2013778 Delay-Independent Closed-Loop Stabilization of Neutral System with Infinite Delays
Authors: I. Davies, O. L. C. Haas
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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2760777 An Optimal Algorithm for HTML Page Building Process
Authors: Maryam Jasim Abdullah, Bassim. H. Graimed, Jalal. S. Hameed
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Demand over web services is in growing with increases number of Web users. Web service is applied by Web application. Web application size is affected by its user-s requirements and interests. Differential in requirements and interests lead to growing of Web application size. The efficient way to save store spaces for more data and information is achieved by implementing algorithms to compress the contents of Web application documents. This paper introduces an algorithm to reduce Web application size based on reduction of the contents of HTML files. It removes unimportant contents regardless of the HTML file size. The removing is not ignored any character that is predicted in the HTML building process.
Keywords: HTML code, HTML tag, WEB applications, Document compression, DOM tree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2037776 Morphological Description of Cervical Cell Images for the Pathological Recognition
Authors: N. Lassouaoui, L. Hamami, N. Nouali
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The tracking allows to detect the tumor affections of cervical cancer, it is particularly complex and consuming time, because it consists in seeking some abnormal cells among a cluster of normal cells. In this paper, we present our proposed computer system for helping the doctors in tracking the cervical cancer. Knowing that the diagnosis of the malignancy is based in the set of atypical morphological details of all cells, herein, we present an unsupervised genetic algorithm for the separation of cell components since the diagnosis is doing by analysis of the core and the cytoplasm. We give also the various algorithms used for computing the morphological characteristics of cells (Ratio core/cytoplasm, cellular deformity, ...) necessary for the recognition of illness.
Keywords: Cervical cell, morphological analysis, recognition, segmentation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1938775 Data Placement in Heterogeneous Storage of Short Videos
Authors: W. Jaipahkdee, C. Srinilta
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The overall service performance of I/O intensive system depends mainly on workload on its storage system. In heterogeneous storage environment where storage elements from different vendors with different capacity and performance are put together, workload should be distributed according to storage capability. This paper addresses data placement issue in short video sharing website. Workload contributed by a video is estimated by the number of views and life time span of existing videos in same category. Experiment was conducted on 42,000 video titles in six weeks. Result showed that the proposed algorithm distributed workload and maintained balance better than round robin and random algorithms.Keywords: data placement, heterogeneous storage system, YouTube, short videos
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1487774 Impulsive Noise-Resilient Subband Adaptive Filter
Authors: Young-Seok Choi
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We present a new subband adaptive filter (R-SAF) which is robust against impulsive noise in system identification. To address the vulnerability of adaptive filters based on the L2-norm optimization criterion against impulsive noise, the R-SAF comes from the L1-norm optimization criterion with a constraint on the energy of the weight update. Minimizing L1-norm of the a posteriori error in each subband with a constraint on minimum disturbance gives rise to the robustness against the impulsive noise and the capable convergence performance. Experimental results clearly demonstrate that the proposed R-SAF outperforms the classical adaptive filtering algorithms when impulsive noise as well as background noise exist.Keywords: Subband adaptive filter, L1-norm, system identification, robustness, impulsive interference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1469773 Multiobjective Optimal Power Flow Using Hybrid Evolutionary Algorithm
Authors: Alawode Kehinde O., Jubril Abimbola M. Komolafe Olusola A.
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This paper solves the environmental/ economic dispatch power system problem using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and its hybrid with a Convergence Accelerator Operator (CAO), called the NSGA-II/CAO. These multiobjective evolutionary algorithms were applied to the standard IEEE 30-bus six-generator test system. Several optimization runs were carried out on different cases of problem complexity. Different quality measure which compare the performance of the two solution techniques were considered. The results demonstrated that the inclusion of the CAO in the original NSGA-II improves its convergence while preserving the diversity properties of the solution set.Keywords: optimal power flow, multiobjective power dispatch, evolutionary algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2265772 Impact of Fair Share and its Configurations on Parallel Job Scheduling Algorithms
Authors: Sangsuree Vasupongayya
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To provide a better understanding of fair share policies supported by current production schedulers and their impact on scheduling performance, A relative fair share policy supported in four well-known production job schedulers is evaluated in this study. The experimental results show that fair share indeed reduces heavy-demand users from dominating the system resources. However, the detailed per-user performance analysis show that some types of users may suffer unfairness under fair share, possibly due to priority mechanisms used by the current production schedulers. These users typically are not heavy-demands users but they have mixture of jobs that do not spread out.
Keywords: Fair share, Parallel job scheduler, Backfill, Measures
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2088771 Harmony Search-based K-Coverage Enhancement in Wireless Sensor Networks
Authors: Shaimaa M. Mohamed, Haitham S. Hamza, Imane A. Saroit
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Many wireless sensor network applications require K-coverage of the monitored area. In this paper, we propose a scalable harmony search based algorithm in terms of execution time, K-Coverage Enhancement Algorithm (KCEA), it attempts to enhance initial coverage, and achieve the required K-coverage degree for a specific application efficiently. Simulation results show that the proposed algorithm achieves coverage improvement of 5.34% compared to K-Coverage Rate Deployment (K-CRD), which achieves 1.31% when deploying one additional sensor. Moreover, the proposed algorithm is more time efficient.
Keywords: Wireless Sensor Networks (WSN), Harmony Search Algorithms, K-Coverage, Mobile WSN.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2163770 Stabilization of a New Configurable Two- Wheeled Machine Using a PD-PID and a Hybrid FL Control Strategies: A Comparative Study
Authors: M. Almeshal, M. O. Tokhi, K. M. Goher
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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.
Keywords: double inverted pendulum, modelling, robust control, simulation,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1538769 Classification of Fuzzy Petri Nets, and Their Applications
Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha
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Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.
Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1631768 Universal Method for Timetable Construction based on Evolutionary Approach
Authors: Maciej Norberciak
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Timetabling problems are often hard and timeconsuming to solve. Most of the methods of solving them concern only one problem instance or class. This paper describes a universal method for solving large, highly constrained timetabling problems from different domains. The solution is based on evolutionary algorithm-s framework and operates on two levels – first-level evolutionary algorithm tries to find a solution basing on given set of operating parameters, second-level algorithm is used to establish those parameters. Tabu search is employed to speed up the solution finding process on first level. The method has been used to solve three different timetabling problems with promising results.Keywords: Evolutionary algorithms, tabu search, timetabling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1840767 RB-Matcher: String Matching Technique
Authors: Rajender Singh Chillar, Barjesh Kochar
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All Text processing systems allow their users to search a pattern of string from a given text. String matching is fundamental to database and text processing applications. Every text editor must contain a mechanism to search the current document for arbitrary strings. Spelling checkers scan an input text for words in the dictionary and reject any strings that do not match. We store our information in data bases so that later on we can retrieve the same and this retrieval can be done by using various string matching algorithms. This paper is describing a new string matching algorithm for various applications. A new algorithm has been designed with the help of Rabin Karp Matcher, to improve string matching process.Keywords: Algorithm, Complexity, Matching-patterns, Pattern, Rabin-Karp, String, text-processing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1765766 GPU-Based Volume Rendering for Medical Imagery
Authors: Hadjira Bentoumi, Pascal Gautron, Kadi Bouatouch
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We present a method for fast volume rendering using graphics hardware (GPU). To our knowledge, it is the first implementation on the GPU. Based on the Shear-Warp algorithm, our GPU-based method provides real-time frame rates and outperforms the CPU-based implementation. When the number of slices is not sufficient, we add in-between slices computed by interpolation. This improves then the quality of the rendered images. We have also implemented the ray marching algorithm on the GPU. The results generated by the three algorithms (CPU-based and GPU-based Shear- Warp, GPU-based Ray Marching) for two test models has proved that the ray marching algorithm outperforms the shear-warp methods in terms of speed up and image quality.Keywords: Volume rendering, graphics processors
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1853765 Delay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type
Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee
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This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.
Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1881764 Voltage Stability Proximity Index Determined by LES Algorithm
Authors: Benalia Nadia, Bensiali Nadia, Mekki Mounira
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In this paper, we propose an easily computable proximity index for predicting voltage collapse of a load bus using only measured values of the bus voltage and power; Using these measurements a polynomial of fourth order is obtained by using LES estimation algorithms. The sum of the absolute values of the polynomial coefficient gives an idea of the critical bus. We demonstrate the applicability of our proposed method on 6 bus test system. The results obtained verify its applicability, as well as its accuracy and the simplicity. From this indicator, it is allowed to predict the voltage instability or the proximity of a collapse. Results obtained by the PV curve are compared with corresponding values by QV curves and are observed to be in close agreement.
Keywords: least square method, Voltage Collapse, Voltage Stability, PV curve
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2283763 Adaptive Sampling Algorithm for ANN-based Performance Modeling of Nano-scale CMOS Inverter
Authors: Dipankar Dhabak, Soumya Pandit
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This paper presents an adaptive technique for generation of data required for construction of artificial neural network-based performance model of nano-scale CMOS inverter circuit. The training data are generated from the samples through SPICE simulation. The proposed algorithm has been compared to standard progressive sampling algorithms like arithmetic sampling and geometric sampling. The advantages of the present approach over the others have been demonstrated. The ANN predicted results have been compared with actual SPICE results. A very good accuracy has been obtained.Keywords: CMOS Inverter, Nano-scale, Adaptive Sampling, ArtificialNeural Network
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1608762 Comparison Analysis of the Wald-s and the Bayes Type Sequential Methods for Testing Hypotheses
Authors: K. J. Kachiashvili
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The Comparison analysis of the Wald-s and Bayestype sequential methods for testing hypotheses is offered. The merits of the new sequential test are: universality which consists in optimality (with given criteria) and uniformity of decision-making regions for any number of hypotheses; simplicity, convenience and uniformity of the algorithms of their realization; reliability of the obtained results and an opportunity of providing the errors probabilities of desirable values. There are given the Computation results of concrete examples which confirm the above-stated characteristics of the new method and characterize the considered methods in regard to each other.
Keywords: Errors of types I and II, likelihood ratio, the Bayes Type Sequential test, the Wald's sequential test, averaged number of observations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1717761 Development of Heterogeneous Parallel Genetic Simulated Annealing Using Multi-Niche Crowding
Authors: Z. G. Wang, M. Rahman, Y. S. Wong, K. S. Neo
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In this paper, a new hybrid of genetic algorithm (GA) and simulated annealing (SA), referred to as GSA, is presented. In this algorithm, SA is incorporated into GA to escape from local optima. The concept of hierarchical parallel GA is employed to parallelize GSA for the optimization of multimodal functions. In addition, multi-niche crowding is used to maintain the diversity in the population of the parallel GSA (PGSA). The performance of the proposed algorithms is evaluated against a standard set of multimodal benchmark functions. The multi-niche crowding PGSA and normal PGSA show some remarkable improvement in comparison with the conventional parallel genetic algorithm and the breeder genetic algorithm (BGA).Keywords: Crowding, genetic algorithm, parallel geneticalgorithm, simulated annealing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1586760 Eclectic Rule-Extraction from Support Vector Machines
Authors: Nahla Barakat, Joachim Diederich
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Support vector machines (SVMs) have shown superior performance compared to other machine learning techniques, especially in classification problems. Yet one limitation of SVMs is the lack of an explanation capability which is crucial in some applications, e.g. in the medical and security domains. In this paper, a novel approach for eclectic rule-extraction from support vector machines is presented. This approach utilizes the knowledge acquired by the SVM and represented in its support vectors as well as the parameters associated with them. The approach includes three stages; training, propositional rule-extraction and rule quality evaluation. Results from four different experiments have demonstrated the value of the approach for extracting comprehensible rules of high accuracy and fidelity.Keywords: Data mining, hybrid rule-extraction algorithms, medical diagnosis, SVMs
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1707759 Steganalysis of Data Hiding via Halftoning and Coordinate Projection
Authors: Woong Hee Kim, Ilhwan Park
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Steganography is the art of hiding and transmitting data through apparently innocuous carriers in an effort to conceal the existence of the data. A lot of steganography algorithms have been proposed recently. Many of them use the digital image data as a carrier. In data hiding scheme of halftoning and coordinate projection, still image data is used as a carrier, and the data of carrier image are modified for data embedding. In this paper, we present three features for analysis of data hiding via halftoning and coordinate projection. Also, we present a classifier using the proposed three features.Keywords: Steganography, steganalysis, digital halftoning, data hiding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1599758 Finding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems
Authors: Pu Duan, Shi Cui, Choong Wah Chan
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Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this paper a new method is presented to find more non-supersingular elliptic curves for pairing-based cryptosystems with general embedding degree k and large values of cofactor h. In addition, some effective parameters of these non-supersingular elliptic curves are provided in this paper.Keywords: Family of group order, kth root of unity, non-supersingular elliptic curves polynomial field.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1733757 Cognitive SATP for Airborne Radar Based on Slow-Time Coding
Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu
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Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.Keywords: Space-time adaptive processing (STAP), signal-to-clutter ratio, slow-time coding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 849756 Kinematic Modelling and Maneuvering of A 5-Axes Articulated Robot Arm
Authors: T.C. Manjunath
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This paper features the kinematic modelling of a 5-axis stationary articulated robot arm which is used for doing successful robotic manipulation task in its workspace. To start with, a 5-axes articulated robot was designed entirely from scratch and from indigenous components and a brief kinematic modelling was performed and using this kinematic model, the pick and place task was performed successfully in the work space of the robot. A user friendly GUI was developed in C++ language which was used to perform the successful robotic manipulation task using the developed mathematical kinematic model. This developed kinematic model also incorporates the obstacle avoiding algorithms also during the pick and place operation.
Keywords: Robot, Sensors, Kinematics, Computer, Control, PNP, LCD, Software.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4464755 Ordinary Differential Equations with Inverted Functions
Authors: Thomas Kampke
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Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.
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