Search results for: Genetic algorithm

Authors: Dong-Hyung Kim, Ji Yeong Lee, Chang-Soo Han

Abstract:

This paper presents a sensor-based motion planning algorithm for 3-DOF car-like robots with a nonholonomic constraint. Similar to the classic Bug family algorithms, the proposed algorithm enables the car-like robot to navigate in a completely unknown environment using only the range sensor information. The car-like robot uses the local range sensor view to determine the local path so that it moves towards the goal. To guarantee that the robot can approach the goal, the two modes of motion are repeated, termed motion-to-goal and wall-following. The motion-to-goal behavior lets the robot directly move toward the goal, and the wall-following behavior makes the robot circumnavigate the obstacle boundary until it meets the leaving condition. For each behavior, the nonholonomic motion for the car-like robot is planned in terms of the instantaneous turning radius. The proposed algorithm is implemented to the real robot and the experimental results show the performance of proposed algorithm.

Keywords: Motion planning, car-like robot, bug algorithm, autonomous motion planning, nonholonomic constraint.

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Authors: Aji P. Wibawa, Andrew Nafalski, Neil Murray, Wayan F. Mahmudy

Abstract:

Since the one-to-one word translator does not have the facility to translate pragmatic aspects of Javanese, the parallel text alignment model described uses a phrase pair combination. The algorithm aligns the parallel text automatically from the beginning to the end of each sentence. Even though the results of the phrase pair combination outperform the previous algorithm, it is still inefficient. Recording all possible combinations consume more space in the database and time consuming. The original algorithm is modified by applying the edit distance coefficient to improve the data-storage efficiency. As a result, the data-storage consumption is 90% reduced as well as its learning period (42s).

Keywords: edit distance coefficient, Javanese, parallel text alignment, phrase pair combination

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Authors: I. A. Farhat

Abstract:

The problem of optimal planning of multiple sources of distributed generation (DG) in distribution networks is treated in this paper using an improved Ant Colony Optimization algorithm (ACO). This objective of this problem is to determine the DG optimal size and location that in order to minimize the network real power losses. Considering the multiple sources of DG, both size and location are simultaneously optimized in a single run of the proposed ACO algorithm. The various practical constraints of the problem are taken into consideration by the problem formulation and the algorithm implementation. A radial power flow algorithm for distribution networks is adopted and applied to satisfy these constraints. To validate the proposed technique and demonstrate its effectiveness, the well-know 69-bus feeder standard test system is employed.cm.

Keywords: About Ant Colony Optimization (ACO), Distributed Generation (DG).

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Keywords: matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Reza Sirjani, Nobosse Tafem Bolan

Abstract:

Many optimization techniques available in the literature have been developed in order to solve the problem of voltage stability enhancement in power systems. However, there are a number of drawbacks in the use of previous techniques aimed at determining the optimal location and size of reactive compensators in a network. In this paper, an Improved Cuckoo Search algorithm is applied as an appropriate optimization algorithm to determine the optimum location and size of a Static Var Compensator (SVC) in a transmission network. The main objectives are voltage stability improvement and total cost minimization. The results of the presented technique are then compared with other available optimization techniques.

Keywords: Cuckoo search algorithm, optimization, power system, var compensators, voltage stability.

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Authors: N. Mpofu, M. Sears

Abstract:

In this paper, we propose a novel algorithm for delineating the endocardial wall from a human heart ultrasound scan. We assume that the gray levels in the ultrasound images are independent and identically distributed random variables with different Rician Inverse Gaussian (RiIG) distributions. Both synthetic and real clinical data will be used for testing the algorithm. Algorithm performance will be evaluated using the expert radiologist evaluation of a soft copy of an ultrasound scan during the scanning process and secondly, doctor’s conclusion after going through a printed copy of the same scan. Successful implementation of this algorithm should make it possible to differentiate normal from abnormal soft tissue and help disease identification, what stage the disease is in and how best to treat the patient. We hope that an automated system that uses this algorithm will be useful in public hospitals especially in Third World countries where problems such as shortage of skilled radiologists and shortage of ultrasound machines are common. These public hospitals are usually the first and last stop for most patients in these countries.

Keywords: Endorcardial Wall, Rician Inverse Distributions, Segmentation, Ultrasound Images.

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Authors: Emma K. Sales

Abstract:

Durian is the flagship fruit of Mindanao and there is an abundance of several cultivars with many confusing identities/ names. The project was conducted to develop procedure for reliable and rapid detection and sorting of durian planting materials. Moreover, it is also aimed to establish specific genetic or DNA markers for routine testing and authentication of durian cultivars in question. The project developed molecular procedures for routine testing. SSR primers were also screened and identified for their utility in discriminating durian cultivars collected. Results of the study showed the following accomplishments: 1. Twenty (29) SSR primers were selected and identified based on their ability to discriminate durian cultivars, 2. Optimized and established standard procedure for identification and authentication of Durian cultivars 3. Genetic profile of durian is now available at Biotech Unit Our results demonstrate the relevance of using molecular techniques in evaluating and identifying durian clones. The most polymorphic primers tested in this study could be useful tools for detecting variation even at the early stage of the plant especially for commercial purposes. The process developed combines the efficiency of the microsatellites development process with the optimization of non-radioactive detection process resulting in a user-friendly protocol that can be performed in two (2) weeks and easily incorporated into laboratories about to start microsatellite development projects. This can be of great importance to extend microsatellite analyses to other crop species where minimal genetic information is currently available. With this, the University can now be a service laboratory for routine testing and authentication of durian clones.

Keywords: DNA, SSR Analysis, genotype, genetic diversity, cultivars.

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Authors: S. M. Kamruzzaman, Md. Monirul Islam

Abstract:

Although backpropagation ANNs generally predict better than decision trees do for pattern classification problems, they are often regarded as black boxes, i.e., their predictions cannot be explained as those of decision trees. In many applications, it is desirable to extract knowledge from trained ANNs for the users to gain a better understanding of how the networks solve the problems. A new rule extraction algorithm, called rule extraction from artificial neural networks (REANN) is proposed and implemented to extract symbolic rules from ANNs. A standard three-layer feedforward ANN is the basis of the algorithm. A four-phase training algorithm is proposed for backpropagation learning. Explicitness of the extracted rules is supported by comparing them to the symbolic rules generated by other methods. Extracted rules are comparable with other methods in terms of number of rules, average number of conditions for a rule, and predictive accuracy. Extensive experimental studies on several benchmarks classification problems, such as breast cancer, iris, diabetes, and season classification problems, demonstrate the effectiveness of the proposed approach with good generalization ability.

Keywords: Backpropagation, clustering algorithm, constructivealgorithm, continuous activation function, pruning algorithm, ruleextraction algorithm, symbolic rules.

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Authors: Fabio Fabris, Alex A. Freitas

Abstract:

Hierarchical classification is a special type of classification task where the class labels are organised into a hierarchy, with more generic class labels being ancestors of more specific ones. Meta-learning for classification-algorithm recommendation consists of recommending to the user a classification algorithm, from a pool of candidate algorithms, for a dataset, based on the past performance of the candidate algorithms in other datasets. Meta-learning is normally used in conventional, non-hierarchical classification. By contrast, this paper proposes a meta-learning approach for more challenging task of hierarchical classification, and evaluates it in a large number of bioinformatics datasets. Hierarchical classification is especially relevant for bioinformatics problems, as protein and gene functions tend to be organised into a hierarchy of class labels. This work proposes meta-learning approach for recommending the best hierarchical classification algorithm to a hierarchical classification dataset. This work’s contributions are: 1) proposing an algorithm for splitting hierarchical datasets into new datasets to increase the number of meta-instances, 2) proposing meta-features for hierarchical classification, and 3) interpreting decision-tree meta-models for hierarchical classification algorithm recommendation.

Keywords: Algorithm recommendation, meta-learning, bioinformatics, hierarchical classification.

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Authors: Hao He, Shaoqian Li

Abstract:

In this paper, we study the cooperative communications where multiple cognitive radio (CR) transmit-receive pairs competitive maximize their own throughputs. In CR networks, the influences of primary users and the spectrum availability are usually different among CR users. Due to the existence of multiple relay nodes and the different spectrum availability, each CR transmit-receive pair should not only select the relay node but also choose the appropriate channel. For this distributed problem, we propose a game theoretic framework to formulate this problem and we apply a regret-matching learning algorithm which is leading to correlated equilibrium. We further formulate a modified regret-matching learning algorithm which is fully distributed and only use the local information of each CR transmit-receive pair. This modified algorithm is more practical and suitable for the cooperative communications in CR network. Simulation results show the algorithm convergence and the modified learning algorithm can achieve comparable performance to the original regretmatching learning algorithm.

Keywords: cognitive radio, cooperative communication, relay selection, channel choice, regret-matching learning, correlated equilibrium.

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Authors: M. Kalamani, S. Valarmathy, M. Krishnamoorthi

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In this paper, Least Mean Square (LMS) adaptive noise reduction algorithm is proposed to enhance the speech signal from the noisy speech. In this, the speech signal is enhanced by varying the step size as the function of the input signal. Objective and subjective measures are made under various noises for the proposed and existing algorithms. From the experimental results, it is seen that the proposed LMS adaptive noise reduction algorithm reduces Mean square Error (MSE) and Log Spectral Distance (LSD) as compared to that of the earlier methods under various noise conditions with different input SNR levels. In addition, the proposed algorithm increases the Peak Signal to Noise Ratio (PSNR) and Segmental SNR improvement (ΔSNRseg) values; improves the Mean Opinion Score (MOS) as compared to that of the various existing LMS adaptive noise reduction algorithms. From these experimental results, it is observed that the proposed LMS adaptive noise reduction algorithm reduces the speech distortion and residual noise as compared to that of the existing methods.

Keywords: LMS, speech enhancement, speech quality, residual noise.

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Authors: Emanuele Stomeo, Tatiana Kalganova, Cyrille Lambert

Abstract:

Evolvable hardware (EHW) is a developing field that applies evolutionary algorithm (EA) to automatically design circuits, antennas, robot controllers etc. A lot of research has been done in this area and several different EAs have been introduced to tackle numerous problems, as scalability, evolvability etc. However every time a specific EA is chosen for solving a particular task, all its components, such as population size, initialization, selection mechanism, mutation rate, and genetic operators, should be selected in order to achieve the best results. In the last three decade the selection of the right parameters for the EA-s components for solving different “test-problems" has been investigated. In this paper the behaviour of mutation rate for designing logic circuits, which has not been done before, has been deeply analyzed. The mutation rate for an EHW system modifies the number of inputs of each logic gates, the functionality (for example from AND to NOR) and the connectivity between logic gates. The behaviour of the mutation has been analyzed based on the number of generations, genotype redundancy and number of logic gates for the evolved circuits. The experimental results found provide the behaviour of the mutation rate during evolution for the design and optimization of simple logic circuits. The experimental results propose the best mutation rate to be used for designing combinational logic circuits. The research presented is particular important for those who would like to implement a dynamic mutation rate inside the evolutionary algorithm for evolving digital circuits. The researches on the mutation rate during the last 40 years are also summarized.

Keywords: Design of logic circuit, evolutionary computation, evolvable hardware, mutation rate.

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Authors: Sang-Youl Lee

Abstract:

This study deals with an advanced numerical techniques to detect tensile forces in cable-stayed structures. The proposed method allows us not only to avoid the trap of minimum at initial searching stage but also to find their final solutions in better numerical efficiency. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the cable model modeled using the finite element method. The results indicate that the proposed method is computationally efficient in characterizing the tensile force variation for cable-stayed structures.

Keywords: Tensile force detection, cable-stayed structures, hybrid system identification (h-SI), dynamic response.

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Authors: Fuzhang Zhao

Abstract:

Particle swarm optimization (PSO) is becoming one of the most important swarm intelligent paradigms for solving global optimization problems. Although some progress has been made to improve PSO algorithms over the last two decades, additional work is still needed to balance parameters to achieve better numerical properties of accuracy, efficiency, and stability. In the optimal PSO algorithm, the optimal weightings of (√ 5 − 1)/2 and (3 − √5)/2 are used for the cognitive factor and the social factor, respectively. By the same token, the same optimal weightings have been applied for intensification searches and diversification searches, respectively. Perturbation and constriction effects are optimally balanced. Simulations of the de Jong, the Rosenbrock, and the Griewank functions show that the optimal PSO algorithm indeed achieves better numerical properties and outperforms the canonical PSO algorithm.

Keywords: Diversification search, intensification search, optimal weighting, particle swarm optimization.

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Authors: A. S. Poornima, R. Aparna, B. B. Amberker, Prashant Koulgi

Abstract:

In this paper, we propose use of convolutional codes for file dispersal. The proposed method is comparable in complexity to the information Dispersal Algorithm proposed by M.Rabin and for particular choices of (non-binary) convolutional codes, is almost as efficient as that algorithm in terms of controlling expansion in the total storage. Further, our proposed dispersal method allows string search.

Keywords: Convolutional codes, File dispersal, Filereconstruction, Information Dispersal Algorithm, String search.

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Authors: Feifei Lee, Qiu Chen, Koji Kotani, Tadahiro Ohmi

Abstract:

In this paper, we propose an improved fast search algorithm using combined histogram features and temporal division method for short MPEG video clips from large video database. There are two types of histogram features used to generate more robust features. The first one is based on the adjacent pixel intensity difference quantization (APIDQ) algorithm, which had been reliably applied to human face recognition previously. An APIDQ histogram is utilized as the feature vector of the frame image. Another one is ordinal feature which is robust to color distortion. Combined with active search [4], a temporal pruning algorithm, fast and robust video search can be realized. The proposed search algorithm has been evaluated by 6 hours of video to search for given 200 MPEG video clips which each length is 30 seconds. Experimental results show the proposed algorithm can detect the similar video clip in merely 120ms, and Equal Error Rate (ERR) of 1% is achieved, which is more accurately and robust than conventional fast video search algorithm.

Keywords: Fast search, Adjacent pixel intensity differencequantization (APIDQ), DC image, Histogram feature.

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Authors: Nuanwan Soonthornphisaj, Boonserm Kijsirikul

Abstract:

This paper presents a semi-supervised learning algorithm called Iterative-Cross Training (ICT) to solve the Web pages classification problems. We apply Inductive logic programming (ILP) as a strong learner in ICT. The objective of this research is to evaluate the potential of the strong learner in order to boost the performance of the weak learner of ICT. We compare the result with the supervised Naive Bayes, which is the well-known algorithm for the text classification problem. The performance of our learning algorithm is also compare with other semi-supervised learning algorithms which are Co-Training and EM. The experimental results show that ICT algorithm outperforms those algorithms and the performance of the weak learner can be enhanced by ILP system.

Keywords: Inductive Logic Programming, Semi-supervisedLearning, Web Page Categorization

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Authors: Chaiyut Sumpavakup, Thanatchai Kulworawanichpong

Abstract:

This paper presents the voltage regulation scheme of D-STATCOM under three-phase faults. It consists of the voltage detection and voltage regulation schemes in the 0dq reference. The proposed control strategy uses the proportional controller in which the proportional gain, kp, is appropriately adjusted by using genetic algorithms. To verify its use, a simplified 4-bus test system is situated by assuming a three-phase fault at bus 4. As a result, the DSTATCOM can resume the load voltage to the desired level within 1.8 ms. This confirms that the proposed voltage regulation scheme performs well under three-phase fault events.

Keywords: D-STATCOM, proportional controller, genetic algorithms.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: Chansiri Singhtaun

Abstract:

This paper proposes a mathematical model and examines the performance of an exact algorithm for a location– transportation problems in humanitarian relief. The model determines the number and location of distribution centers in a relief network, the amount of relief supplies to be stocked at each distribution center and the vehicles to take the supplies to meet the needs of disaster victims under capacity restriction, transportation and budgetary constraints. The computational experiments are conducted on the various sizes of problems that are generated. Branch and bound algorithm is applied for these problems. The results show that this algorithm can solve problem sizes of up to three candidate locations with five demand points and one candidate location with up to twenty demand points without premature termination.

Keywords: Disaster response, facility location, humanitarian relief, transportation.

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Authors: K. Metaxiotis, K. Liagkouras

Abstract:

This study presents an Expert System specially designed to be used with Multiobjective Evolutionary Algorithms (MOEAs) for the solution of the portfolio selection problem. The validation of the proposed hybrid System is done by using data sets from Hang Seng 31 in Hong Kong, DAX 100 in Germany and FTSE 100 in UK. The performance of the proposed system is assessed in comparison with the Non-dominated Sorting Genetic Algorithm II (NSGAII). The evaluation of the performance is based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it. The results show that the proposed hybrid system is efficient for the solution of this kind of problems.

Keywords: Expert Systems, Multiobjective optimization, Evolutionary Algorithms, Portfolio Selection.

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Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Keywords: Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

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Authors: Semeh Ben Salem, Sami Naouali, Moetez Sallami

Abstract:

The increasing amount of collected data has limited the performance of the current analyzing algorithms. Thus, developing new cost-effective algorithms in terms of complexity, scalability, and accuracy raised significant interests. In this paper, a modified effective k-means based algorithm is developed and experimented. The new algorithm aims to reduce the computational load without significantly affecting the quality of the clusterings. The algorithm uses the City Block distance and a new stop criterion to guarantee the convergence. Conducted experiments on a real data set show its high performance when compared with the original k-means version.

Keywords: Pattern recognition, partitional clustering, K-means clustering, Manhattan distance, terrorism data analysis.

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Authors: Hichem Sassi, Tawfik Najeh, Noureddine Liouane

Abstract:

The localization information is crucial for the operation of WSN. There are principally two types of localization algorithms. The Range-based localization algorithm has strict requirements on hardware, thus is expensive to be implemented in practice. The Range-free localization algorithm reduces the hardware cost. However, it can only achieve high accuracy in ideal scenarios. In this paper, we locate unknown nodes by incorporating the advantages of these two types of methods. The proposed algorithm makes the unknown nodes select the nearest anchor using the Received Signal Strength Indicator (RSSI) and choose two other anchors which are the most accurate to achieve the estimated location. Our algorithm improves the localization accuracy compared with previous algorithms, which has been demonstrated by the simulating results.

Keywords: WSN, localization, DV-hop, RSSI.

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Authors: Lilac A. E. Al-Safadi

Abstract:

This paper proposes an auto-classification algorithm of Web pages using Data mining techniques. We consider the problem of discovering association rules between terms in a set of Web pages belonging to a category in a search engine database, and present an auto-classification algorithm for solving this problem that are fundamentally based on Apriori algorithm. The proposed technique has two phases. The first phase is a training phase where human experts determines the categories of different Web pages, and the supervised Data mining algorithm will combine these categories with appropriate weighted index terms according to the highest supported rules among the most frequent words. The second phase is the categorization phase where a web crawler will crawl through the World Wide Web to build a database categorized according to the result of the data mining approach. This database contains URLs and their categories.

Keywords: Information Processing on the Web, Data Mining, Document Classification.

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Authors: Davide Pierattoni, Ivan Macor, Pier Luca Montessoro

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In the recent years multimedia traffic and in particular VoIP services are growing dramatically. We present a new algorithm to control the resource utilization and to optimize the voice codec selection during SIP call setup on behalf of the traffic condition estimated on the network path. The most suitable methodologies and the tools that perform realtime evaluation of the available bandwidth on a network path have been integrated with our proposed algorithm: this selects the best codec for a VoIP call in function of the instantaneous available bandwidth on the path. The algorithm does not require any explicit feedback from the network, and this makes it easily deployable over the Internet. We have also performed intensive tests on real network scenarios with a software prototype, verifying the algorithm efficiency with different network topologies and traffic patterns between two SIP PBXs. The promising results obtained during the experimental validation of the algorithm are now the basis for the extension towards a larger set of multimedia services and the integration of our methodology with existing PBX appliances.

Keywords: Integrated voice-data communication, computernetwork performance, resource optimization.

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Authors: Jalil Z., Farooq M., Zafar H., Sabir M., Ashraf E.

Abstract:

Internet is largely composed of textual contents and a huge volume of digital contents gets floated over the Internet daily. The ease of information sharing and re-production has made it difficult to preserve author-s copyright. Digital watermarking came up as a solution for copyright protection of plain text problem after 1993. In this paper, we propose a zero text watermarking algorithm based on occurrence frequency of non-vowel ASCII characters and words for copyright protection of plain text. The embedding algorithm makes use of frequency non-vowel ASCII characters and words to generate a specialized author key. The extraction algorithm uses this key to extract watermark, hence identify the original copyright owner. Experimental results illustrate the effectiveness of the proposed algorithm on text encountering meaning preserving attacks performed by five independent attackers.

Keywords: Copyright protection, Digital watermarking, Document authentication, Information security, Watermark.

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Authors: Parvinder Singh Sandhu, Sumeet Kaur Sehra, Karmjit Kaur

Abstract:

Phylogenetic tree is a graphical representation of the evolutionary relationship among three or more genes or organisms. These trees show relatedness of data sets, species or genes divergence time and nature of their common ancestors. Quality of a phylogenetic tree requires parsimony criterion. Various approaches have been proposed for constructing most parsimonious trees. This paper is concerned about calculating and optimizing the changes of state that are needed called Small Parsimony Algorithms. This paper has proposed enhanced small parsimony algorithm to give better score based on number of evolutionary changes needed to produce the observed sequence changes tree and also give the ancestor of the given input.

Keywords: Phylogenetic Analysis, Small Parsimony, EnhancedFitch Algorithm, Enhanced Sakoff Algorithm.

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

Abstract:

For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: Differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization.

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Authors: Moung Young Lee, Chul Gyu Song

Abstract:

Photoacoustic imaging is the imaging technology that combines the optical imaging and ultrasound. This provides the high contrast and resolution due to optical imaging and ultrasound imaging, respectively. We developed the real-time photoacoustic tomography (PAT) system using linear-ultrasound transducer and digital acquisition (DAQ) board. There are two types of algorithm for reconstructing the photoacoustic signal. One is back-projection algorithm, the other is FFT algorithm. Especially, we used the non-uniform FFT algorithm. To evaluate the performance of our system and algorithms, we monitored two wires that stands at interval of 2.89 mm and 0.87 mm. Then, we compared the images reconstructed by algorithms. Finally, we monitored the two hairs crossed and compared between these algorithms.

Keywords: Back-projection, image comparison, non-uniform FFT, photoacoustic tomography.

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