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Estimation of Inputs for a Desired Output of a Cooperative and Supportive Neural Network
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In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick sort. In our first study in this paper, we reconfirm this through computer experiments for inputs from Cauchy distribution for which expectation theoretically does not exist. Additionally, the algorithm is found to be sensitive to parameters of the input probability distribution demanding further investigation on parameterized complexity. The results on this algorithm for Binomial inputs in our second study are very encouraging in that direction.
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In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick sort. In our first study in this paper, we reconfirm this through computer experiments for inputs from Cauchy distribution for which expectation theoretically does not exist. Additionally, the algorithm is found to be sensitive to parameters of the input probability distribution demanding further investigation on parameterized complexity. The results on this algorithm for Binomial inputs in our second study are very encouraging in that direction.
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Schizophrenia is one of mental disorder that affects the mind, feeling, and behavior. Its treatment is usually permanent and quite complicated; therefore, early detection is important. Kernel KC-means and support vector machines are the methods known as a good classifier. This research, therefore, aims to compare kernel KC-means and support vector machines, using data obtained from Northwestern University, which consists of 171 schizophrenia and 221 non-schizophrenia samples. The performance accuracy, F1-score, and running time were examined using the 10-fold cross-validation method. From the experiments, kernel KC-means with the sixth-order polynomial kernel gives 87.18 percent accuracy and 93.15 percent F1-score at the faster running time than support vector machines. However, with the same kernel, it was further deduced from the results that support vector machines provides better performance with an accuracy of 88.78 percent and F1-score of 94.05 percent.
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Neural network is an important tool for reliability analysis, including estimation of reliability or utility function which are too complicated to be analytical expressed for large or complex system. It has been demonstrated the neural network has significant improvement in the parameter estimation accuracy over the traditional chi-square test. There are many parameters of a neural network that should be determined while training the dataset, since different setups of algorithm parameters affect the estimation performance in either accuracy or computation efficiency. In this paper, neural network training is used to estimate the utility function for the parallel-series redundancy allocation problem, and weighted principal component based multi-response optimization method is applied to find the optimal setting of neural network parameters so that the simultaneous minimizations of training error and computing time are achieved.
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Uncertainty is a pervasive in real world environment due to vagueness, is associated with the difficulty of making sharp distinctions and ambiguity, is associated with situations in which the choices among several precise alternatives cannot be perfectly resolved. Analysis of large collections of uncertain data is a primary task in the real world applications, because data is incomplete, inaccurate and inefficient. Representation of uncertain data in various forms such as Data Stream models, Linkage models, Graphical models and so on, which is the most simple, natural way to process and produce the optimized results through Query processing. In this paper, we propose the Uncertain Data model can be represented as Possibilistic data model and vice versa for the process of uncertain data using various data models such as possibilistic linkage model, Data streams, Possibilistic Graphs. This paper presents representation and process of Possiblistic Linkage model through Possible Worlds with the use of product-based operator.
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The clustering is a without monitoring process and one of the most common data mining techniques. The purpose of clustering is grouping similar data together in a group, so were most similar to each other in a cluster and the difference with most other instances in the cluster are. In this paper we focus on clustering partition k-means, due to ease of implementation and high-speed performance of large data sets, After 30 year it is still very popular among the developed clustering algorithm and then for improvement problem of placing of k-means algorithm in local optimal, we pose extended PSO algorithm, that its name is ECPSO. Our new algorithm is able to be cause of exit from local optimal and with high percent produce the problem’s optimal answer. The probe of results show that mooted algorithm have better performance regards as other clustering algorithms specially in two index, the carefulness of clustering and the quality of clustering.
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IEEE PROJECTS 2015 1 crore projects is a leading Guide for ieee Projects and real time projects Works Provider. It has been provided Lot of Guidance for Thousands of Students & made them more beneficial in all Technology Training. Dot Net DOTNET Project Domain list 2015 1. IEEE based on datamining and knowledge engineering 2. IEEE based on mobile computing 3. IEEE based on networking 4. IEEE based on Image processing 5. IEEE based on Multimedia 6. IEEE based on Network security 7. IEEE based on parallel and distributed systems Java Project Domain list 2015 1. IEEE based on datamining and knowledge engineering 2. IEEE based on mobile computing 3. IEEE based on networking 4. IEEE based on Image processing 5. IEEE based on Multimedia 6. IEEE based on Network security 7. IEEE based on parallel and distributed systems ECE IEEE Projects 2015 1. Matlab project 2. Ns2 project 3. Embedded project 4. Robotics project Eligibility Final Year students of 1. BSc (C.S) 2. BCA/B.E(C.S) 3. B.Tech IT 4. BE (C.S) 5. MSc (C.S) 6. MSc (IT) 7. MCA 8. MS (IT) 9. ME(ALL) 10. BE(ECE)(EEE)(E&I) TECHNOLOGY USED AND FOR TRAINING IN 1. DOT NET 2. C sharp 3. ASP 4. VB 5. SQL SERVER 6. JAVA 7. J2EE 8. STRINGS 9. ORACLE 10. VB dotNET 11. EMBEDDED 12. MAT LAB 13. LAB VIEW 14. Multi Sim CONTACT US 1 CRORE PROJECTS Door No: 214/215,2nd Floor, No. 172, Raahat Plaza, (Shopping Mall) ,Arcot Road, Vadapalani, Chennai, Tamin Nadu, INDIA - 600 026 Email id: 1croreprojects@gmail.com website:1croreprojects.com Phone : +91 97518 00789 / +91 72999 51536
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In this paper, the exponential synchronization of secure communication system is introduced and a novel secure communication design combined with linear receiver is constructed to ensure the global exponential stability of the resulting error signals. Besides, the guaranteed exponential convergence rate of the proposed secure communication system can be correctly calculated. Finally, some numerical simulations are offered to demonstrate the correctness and feasibility of the obtained results. Yeong-Jeu Sun "New Design Architecture of Chaotic Secure Communication System Combined with Linear Receiver" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38214.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38214/new-design-architecture-of-chaotic-secure-communication-system-combined-with-linear-receiver/yeongjeu-sun
New Design Architecture of Chaotic Secure Communication System Combined with ...
New Design Architecture of Chaotic Secure Communication System Combined with ...
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The core of the vision IRJES is to disseminate new knowledge and technology for the benefit of all, ranging from academic research and professional communities to industry professionals in a range of topics in computer science and engineering. It also provides a place for high-caliber researchers, practitioners and PhD students to present ongoing research and development in these areas.
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In this work, we propose a Hybrid particle swarm optimization-Simulated annealing algorithm and present a comparison with i) Simulated annealing algorithm and ii) Back propagation algorithm for training neural networks. These neural networks were then tested on a classification task. In particle swarm optimization behaviour of a particle is influenced by the experiential knowledge of the particle as well as socially exchanged information. Particle swarm optimization follows a parallel search strategy. In simulated annealing uphill moves are made in the search space in a stochastic fashion in addition to the downhill moves. Simulated annealing therefore has better scope of escaping local minima and reach a global minimum in the search space. Thus simulated annealing gives a selective randomness to the search. Back propagation algorithm uses gradient descent approach search for minimizing the error. Our goal of global minima in the task being done here is to come to lowest energy state, where energy state is being modelled as the sum of the squares of the error between the target and observed output values for all the training samples. We compared the performance of the neural networks of identical architectures trained by the i) Hybrid particle swarm optimization-simulated annealing, ii) Simulated annealing and iii) Back propagation algorithms respectively on a classification task and noted the results obtained. Neural network trained by Hybrid particle swarm optimization-simulated annealing has given better results compared to the neural networks trained by the Simulated annealing and Back propagation algorithms in the tests conducted by us.
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Hybrid PSO-SA algorithm for training a Neural Network for Classification
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Survey on classification algorithms for data mining (comparison and evaluation)
Survey on classification algorithms for data mining (comparison and evaluation)
Alexander Decker
Probabilistic Methods of Signal and System Analysis, 3/e stresses the engineering applications of probability theory, presenting the material at a level and in a manner ideally suited to engineering students at the junior or senior level. It is also useful as a review for graduate students and practicing engineers. Thoroughly revised and updated, this third edition incorporates increased use of the computer in both text examples and selected problems. It utilizes MATLAB as a computational tool and includes new sections relating to Bernoulli trials, correlation of data sets, smoothing of data, computer computation of correlation functions and spectral densities, and computer simulation of systems. All computer examples can be run using the Student Version of MATLAB. Almost all of the examples and many of the problems have been modified or changed entirely, and a number of new problems have been added. A separate appendix discusses and illustrates the application of computers to signal and system analysis
Probabilistic Methods Of Signal And System Analysis, 3rd Edition
Probabilistic Methods Of Signal And System Analysis, 3rd Edition
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https://www.irjet.net/archives/V6/i4/IRJET-V6I4844.pdf
IRJET- Semantics based Document Clustering
IRJET- Semantics based Document Clustering
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The clustering is a without monitoring process and one of the most common data mining techniques. The purpose of clustering is grouping similar data together in a group, so were most similar to each other in a cluster and the difference with most other instances in the cluster are. In this paper we focus on clustering partition k-means, due to ease of implementation and high-speed performance of large data sets, After 30 year it is still very popular among the developed clustering algorithm and then for improvement problem of placing of k-means algorithm in local optimal, we pose extended PSO algorithm, that its name is ECPSO. Our new algorithm is able to be cause of exit from local optimal and with high percent produce the problem’s optimal answer. The probe of results show that mooted algorithm have better performance regards as other clustering algorithms specially in two index, the carefulness of clustering and the quality of clustering.
Extended pso algorithm for improvement problems k means clustering algorithm
Extended pso algorithm for improvement problems k means clustering algorithm
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IEEE PROJECTS 2015 1 crore projects is a leading Guide for ieee Projects and real time projects Works Provider. It has been provided Lot of Guidance for Thousands of Students & made them more beneficial in all Technology Training. Dot Net DOTNET Project Domain list 2015 1. IEEE based on datamining and knowledge engineering 2. IEEE based on mobile computing 3. IEEE based on networking 4. IEEE based on Image processing 5. IEEE based on Multimedia 6. IEEE based on Network security 7. IEEE based on parallel and distributed systems Java Project Domain list 2015 1. IEEE based on datamining and knowledge engineering 2. IEEE based on mobile computing 3. IEEE based on networking 4. IEEE based on Image processing 5. IEEE based on Multimedia 6. IEEE based on Network security 7. IEEE based on parallel and distributed systems ECE IEEE Projects 2015 1. Matlab project 2. Ns2 project 3. Embedded project 4. Robotics project Eligibility Final Year students of 1. BSc (C.S) 2. BCA/B.E(C.S) 3. B.Tech IT 4. BE (C.S) 5. MSc (C.S) 6. MSc (IT) 7. MCA 8. MS (IT) 9. ME(ALL) 10. BE(ECE)(EEE)(E&I) TECHNOLOGY USED AND FOR TRAINING IN 1. DOT NET 2. C sharp 3. ASP 4. VB 5. SQL SERVER 6. JAVA 7. J2EE 8. STRINGS 9. ORACLE 10. VB dotNET 11. EMBEDDED 12. MAT LAB 13. LAB VIEW 14. Multi Sim CONTACT US 1 CRORE PROJECTS Door No: 214/215,2nd Floor, No. 172, Raahat Plaza, (Shopping Mall) ,Arcot Road, Vadapalani, Chennai, Tamin Nadu, INDIA - 600 026 Email id: 1croreprojects@gmail.com website:1croreprojects.com Phone : +91 97518 00789 / +91 72999 51536
Scalable Constrained Spectral Clustering
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The role of materialized views is becoming vital in today’s distributed Data warehouses. Materialization is where parts of the data cube are pre-computed. Some of the real time distributed architectures are maintaining materialization transparencies in the sense the users are not known with the materialization at a node. Usually what all followed by them is a cache maintenance mechanism where the query results are cached. When a query requesting materialization arrives at a distributed node it checks in its cache and if the materialization is available answers the query. What if materialization is not available- the node communicates the query in the network until a node answering the requested materialization is available. This type of network communication increases the number of query forwarding’s between nodes. The aim of this paper is to reduce the multiple redirects. In this paper we propose a new CB-pattern tree indexing to identify the exact distributed node where the needed materialization is available.
Cb pattern trees identifying
Cb pattern trees identifying
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Model reduction-of-linear-systems-by conventional-and-evolutionary-techniques
Cemal Ardil
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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In the past few years, Grid computing came up as next generation computing platform which is a combination of heterogeneous computing resources combined by a network across dynamic and geographically separated organizations. So, it provides the perfect computing environment to solve large-scale computational demands. As the Grid computing demands are still increasing from day to day due to rise in large number of complex jobs worldwide. So, the jobs may take much longer time to complete due to poor distribution of batches or groups of jobs to inappropriate CPU’s. Therefore there is need to develop an efficient dynamic job scheduling algorithm that would assign jobs to appropriate CPU’s dynamically. The main problem which dealt in the paper is, how to distribute the jobs when the payload, importance, urgency, flow time etc. dynamically keeps on changing as the grid expands or is flooded with number of job requests from different machines within the grid. In this paper, we present a scheduling strategy which takes the advantage of decision tree algorithm to take dynamic decision based on the current scenarios and which automatically incorporates factor analysis for considering the distribution of jobs.
Bragged Regression Tree Algorithm for Dynamic Distribution and Scheduling of ...
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Automated Essay Grading using Features Selection
Automated Essay Grading using Features Selection
IRJET Journal
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Classification of text data using feature clustering algorithm
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eSAT Publishing House
Large-scale analysis of genome sequences is in progress around the world, the major application of which is to establish the evolutionary relationship among the species using phylogenetic trees. Hierarchical agglomerative algorithms can be used to generate such phylogenetic trees given the distance matrix representing the dissimilarity among the species. ClustalW and Muscle are two general purpose programs that generates distance matrix from the input DNA or protein sequences. The limitation of these programs is that they are based on Smith-Waterman algorithm which uses dynamic programming for doing the pair-wise alignment. This is an extremely time consuming process and the existing systems may even fail to work for larger input data set. To overcome this limitation, we have used the frequency of codons usage as an approximation to find dissimilarity among species. The proposed technique further reduces the complexity by extracting only the significant features of the species from the mtDNA sequences using the techniques like frequent codons, codons with maximum range value or PCA technique. We have observed that the proposed system produces nearly accurate results in a significantly reduced running time.
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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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Artificial neural networks can achieve high computation rates by employing a massive number of simple processing elements with a high degree of connectivity between the elements. Neural networks with feedback connections provide a computing model capable of exploiting fine- grained parallelism to solve a rich class of complex problems. In this paper we discuss a complex series-parallel system subjected to finite common cause and finite human error failures and its reliability using neural network method.
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Recurrent Neural Networks are a type of Artificial Neural Networks which are adept at dealing with problems which have a temporal aspect to them. These networks exhibit dynamic properties due to their recurrent connections. Most of the advances in deep learning employ some form of Recurrent Neural Networks for their model architecture. RNN's have proven to be an effective technique in applications like computer vision and natural language processing. In this paper, we demonstrate the effectiveness of RNNs for the task of English to Hindi Machine Translation. We perform experiments using different neural network architectures - employing Gated Recurrent Units, Long Short Term Memory Units and Attention Mechanism and report the results for each architecture. Our results show a substantial increase in translation quality over Rule-Based and Statistical Machine Translation approaches.
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This paper presents an approach based on applying an aggregated predictor formed by multiple versions of a multilayer neural network with a back-propagation optimization algorithm for helping the engineer to get a list of the most appropriate well-test interpretation models for a given set of pressure/ production data. The proposed method consists of three stages: (1) data decorrelation through principal component analysis to reduce the covariance between the variables and the dimension of the input layer in the artificial neural network, (2) bootstrap replicates of the learning set where the data is repeatedly sampled with a random split of the data into train sets and using these as new learning sets, and (3) automatic reservoir model identification through aggregated predictor formed by a plurality vote when predicting a new class. This method is described in detail to ensure successful replication of results. The required training and test dataset were generated by using analytical solution models. In our case, there were used 600 samples: 300 for training, 100 for cross-validation, and 200 for testing. Different network structures were tested during this study to arrive at optimum network design. We notice that the single net methodology always brings about confusion in selecting the correct model even though the training results for the constructed networks are close to 1. We notice also that the principal component analysis is an effective strategy in reducing the number of input features, simplifying the network structure, and lowering the training time of the ANN. The results obtained show that the proposed model provides better performance when predicting new data with a coefficient of correlation approximately equal to 95% Compared to a previous approach 80%, the combination of the PCA and ANN is more stable and determine the more accurate results with lesser computational complexity than was feasible previously. Clearly, the aggregated predictor is more stable and shows less bad classes compared to the previous approach.
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This research tackles disaster prevention problems in dense urban areas, concentrating on the urban fire challenge in Historic Cairo district, Egypt, through disaster risk management approach. The study area suffers from the strike of several urban fire outbreaks, that resulted in disfiguring historic monuments and destroying unregulated traditional markets. Therefore, the study investigates the significance of hazard management and how can urban strategies improve the city resilient through reducing the impact of natural and man-made threats. The main findings of the research are the determination of the vulnerability factors in Historic Cairo district, either regarding management deficiency or issues related to the existing urban form. It is found that the absence of the mitigation and preparedness phases is the main problem in the risk management cycle in the case study. Additionally, the coping initiatives adopted by local authorities to address risks are random and insufficient. The study concludes with recommendations which invoke incorporating hazard management stages (pre disaster, during disaster and post disaster) into the process of evolving development planning. Finally, solutions are offered to mitigate, prepare, respond and recover from fire disasters in the case study. The solutions include urban policies, land-use planning, urban design outlines, safety regulation and public awareness and training.
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This paper presents a new methodology for designing a neuro-fuzzy control for complex physical systems. By developing a Neural -Fuzzy system learning with linguistic teaching signals. The advantage of this technique is that, produce a simple and well-performing system because it selects the fuzzy sets and the numerical numbers and process both numerical and linguistic information. This approach is able to process and learn numerical information as well as linguistic information. The proposed control scheme is applied to a multi-area power system with hydraulic and thermal turbines.
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This work develops a new modular architecture that emulates a recentlydiscovered biological paradigm. It originates from the human brain where the information flows along two different pathways and is processed along two time scales: one is a fast neural network (NN) and the other is a slow network called the glial network (GN). It was found that the neural network is powered and controlled by the glial network. Based on our biological knowledge of glial cells and the powerful concept of modularity, a novel approach called artificial neuroglial Network (ANGN) was designed and an algorithm based on different concepts of modularity was also developed. The implementation is based on the notion of multi-time scale systems. Validation is performed through an asynchronous machine (ASM) modeled in the standard singularly perturbed form. We apply the geometrical approach, based on Gerschgorin’s circle theorem (GCT), to separate the fast and slow variables, as well as the singular perturbation method (SPM) to determine the reduced models. This new architecture makes it possible to obtain smaller networks with less complexity and better performance.
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Turbidity is a measure of water quality. Excessive turbidity poses a threat to health and causes pollution. Most of the available mathematical models of water treatment plants do not capture turbidity. A reliable model is essential for effective removal of turbidity in the water treatment plant. This paper presents a comparison of Hammerstein Wiener and neural network technique for estimating of turbidity in water treatment plant. The models were validated using an experimental data from Tamburawa water treatment plant in Kano, Nigeria. Simulation results demonstrated that the neural network model outperformed the Hammerstein-Wiener model in estimating the turbidity. The neural network model may serve as a valuable tool for predicting the turbidity in the plant.
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Algorithms developed for scheduling applications on heterogeneous multiprocessor system focus on a single objective such as execution time, cost or total data transmission time. However, if more than one objective (e.g. execution cost and time, which may be in conflict) are considered, then the problem becomes more challenging. This project is proposed to develop a multiobjective scheduling algorithm using Evolutionary techniques for scheduling a set of dependent tasks on available resources in a multiprocessor environment which will minimize the makespan and reliability cost. A Non-dominated sorting Genetic Algorithm-II procedure has been developed to get the pareto- optimal solutions. NSGA-II is a Elitist Evolutionary algorithm, and it takes the initial parental solution without any changes, in all iteration to eliminate the problem of loss of some pareto-optimal solutions.NSGA-II uses crowding distance concept to create a diversity of the solutions.
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This paper discusses the design of active controllers for achieving generalized projective synchronization (GPS) of identical hyperchaotic Lü systems (Chen, Lu, Lü and Yu, 2006), identical hyperchaotic Cai systems (Wang and Cai, 2009) and non-identical hyperchaotic Lü and hyperchaotic Cai systems. The synchronization results (GPS) for the hyperchaotic systems have been derived using active control method and established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is very effective and convenient for achieving the GPS of the hyperchaotic systems addressed in this paper. Numerical simulations are provided to illustrate the effectiveness of the GPS synchronization results derived in this paper.
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In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the function projective method. Using this technique allows for a scaling function instead of a constant thereby giving a better method in applications in secure communication. Numerical simulations are presented to demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal system.
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PHP and MySQL project on Hall Booking System is a web based project and it has been developed in PHP and MySQL and we can manage Payment, Booking, Inventory, Booking Dates, Customers and Hall from this project. The main objective to develop Hall Booking System PHP, MySQL, JAVA SCRIPT and BOOTSRAP Project is to overcome the manual errors and make a computerized system. In this project, there are various type of modules available to manage Customers, Booking, Payment. We can also generate reports for Booking, Payment, Booking Dates, Hall. Here the Payment module manage all the operations of Payment, Booking module can manage Booking, Inventory module is normally developed for managing Inventory, Booking Dates module manages Booking Dates operations, Customers module has been implemented to manage Customers. In this project all the modules like Payment, Booking Dates, Booking are tightly coupled and we can track the information easily. Ifyou are looking for Free Hall Booking System Project in PHP and MySQL then you can visit our free projects section. We can easily get the list of wedding halls & lawns in Nagpur. Also we have detailed contact information for some particular hall. But we cannot get the availability about hall. So background behind this web portal is that it gives the area wise listing of wedding halls & lawns with the detailed information of individual and also display for particular date the hall is available or not. Just dial is the system in which we can only find the name of Hall and Lawns in city. In just dial we cannot find Halls in specific area. This system cannot show all information about any Hall. This system is not able to book the Halls online. The A Web Based Hall Booking Management System is designed to overcome the disadvantage of previous system.We can easily get the list of Wedding Halls. But we cannot get the availability about Hall. So background behind this web portal is that it gives the area wise listing of Wedding Halls with the detailed information of individual and also display for particular date the Hall is available or not. This is a special type of web portal to easily get the information of all Wedding Halls in Nagpur which display separate calendar for separate Hall. For particular date the Hall. We can availability of Hall as well as Lawns detailed information about individuals Hall in our web portal . It provides all facilities to clients with lowest cost and lowest maintenance problems.
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Ijetcas14 536
1.
International Association of
Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS) www.iasir.net IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 99 ISSN (Print): 2279-0047 ISSN (Online): 2279-0055 Estimation of Inputs for a Desired Output of a Cooperative and Supportive Neural Network 1P. Raja Sekhara Rao, 2K. Venkata Ratnam, 3P.Lalitha 1Department of Mathematics, Government Polytechnic, Addanki - 523 201, Prakasam, A.P., INDIA. 2Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad campus, Jawahar Nagar, Hyderabad-500078, INDIA. 3Department of Mathematics, St. Francis College for Women, Begumpet, Hyderabad, INDIA. __________________________________________________________________________________________ Abstract: In this paper a cooperative and supportive neural network involving time delays is considered. External inputs to the network are allowed to vary with respect to time. Asymptotic behavior of solutions of network system with variable inputs is studied with respect to its counterpart of constant inputs. With suitable restrictions on the inputs, it is noticed that solution of the network may be made to approach a pre-specified output. Keywords: Co-operative and Supportive Neural Network, Variable Inputs, Desired Output, Convergence. __________________________________________________________________________________________ I. Introduction This paper deals with the study of influence of time varying exogenous inputs on a cooperative and supportive neural network. A model of a cooperative and supportive network (CSNN, for short) is introduced by Sree Hari Rao and Raja Sekhara Rao [9]. It takes into account the collective capabilities of neurons involved with tasks divided and distributed to sub networks of neurons. Applications to such networks are many, for example, in industrial information management (hierarchical systems) which involve distribution and monitoring of various tasks. They are also useful in classification and clustering problems, data mining and financial engineering [6,7,8]. They are also utilized for parameter estimation of auto regressive signals and to decompose complex classification tasks into simpler subtasks and solve then. In a recent paper [11], the authors considered time delays in transmission of information from sub-networks to main one as well as in processing of information in sub-network itself (before transmission of information to main network). Qualitative properties of solutions of the system are studied. Sufficient conditions for global asymptotic stability of equilibrium pattern of the system are established even in the presence of time delays. In the present paper, we wish to consider the CSNN model of [11] with time delays to study the influence of time varying inputs on the system. The motivation for this study stems from the observations of [10] that the applicability a neural network may be increased by the choice of inputs and inputs play a key role in attaining desired outputs. Proper choice of could be an alternative for modifying the neural network for each application and existing neural network may be utilized for different tasks, thus. Besides this, the presence of time varying inputs make the system non autonomous and the study enriches the literature. Mathematical studies of neural networks have been concentrated on stability of equilibrium patterns. Equilibria are stationary solutions of the system and correspond to memory states of the network. Stability of an equilibrium implies a recall of memory state. Thus, such stability analysis of neural networks is confined to recall of memories only and we may not reach the desired output for which the network is intended. In the present study, we deviate from this recall of memories but look for ways of reaching a desired solution. An attempt is made in [9] to explain briefly the influence of variable inputs on asymptotic nature of solutions of CSNN model. The present study extends this work. We concentrate on the interplay between the inputs and outputs of the network. For this, several results are established for estimation or restriction of inputs for getting a desired or pre-specified output and understand the behavior of solutions in the presence of variable inputs. The work also extends the study of [10] carried out for BAM networks. As remarked in [10], convergence to a desired output for a given output explained here should not be confused with convergence of output function of the network. Results are available in literature which consider time varying inputs in various directions [1- 3,5,12] but our emphasis here is on utilization of these inputs to make solutions of system approach an a priori value of output. We reiterate that this is not yet another usual study on qualitative behavior of solutions of the system under the influence of variable inputs. The paper is organized as follows. In Section 2, the model under consideration is explained. Asymptotic behavior of solutions and their relation with the solutions of corresponding system with constant inputs are discussed. Section 3 deals with the input-output trade-off. Estimates on inputs are provided for approaching a desired, preset output for the network. A discussion follows in Section 4.
2.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 100 II. The Model and Asymptotic Behavior The following model is considered in [11], , In (2.1), , i=1,2,...,n denote a typical neuron in neural field X and denote a subgroup of neurons in another neuronal field Y and are attached to . may be considered to form the main group of neurons which are required to perform the task. constitute a subgroup of neurons attached to each to which assigns some of its task. support, coordinate and cooperate with in completing the task. and are positive constants known as passive decay rates of neurons and respectively. and are the synaptic connection weights and all these are assumed to be real or complex constants. denotes the rate of distribution of information between and . The weight connections connect the i th neuron in one neuronal field to the j th neuron in another neuronal field. The functions and are the neuronal output response functions and are more commonly known as the signal functions. The parameter signifies the time delay in transmission of information from sub network neuron to main network neuron . The delay in second equation represents the processing delays in the subsystems. and are exogenous inputs which are assumed to be constants in [11]. For more details of the terms and design of the CSNN, readers are referred to [9]. Introducing the time variables and (t), , in place of constant inputs and into the system (2.1), we get The following initial functions are assumed for the system (2.2). for , (2.3) where are continuous, bounded functions on and We assume that the response functions and satisfy conditions (2.4) (2.5) (2.6) where , , and are positive constants. Under the conditions (2.4)-(2.6) on the response functions and with and bounded, continuous functions on ) it is not difficult to see that the system (2.2) possesses unique solutions that are continuable in their maximal intervals of existence ([11]). Since (2.2) is non-autonomous it may not possess equilibrium patterns(constant solutions). A solution of (2.1) or (2.2) is denoted by where , throughout. Therefore, we study the asymptotic behavior of its solutions. We recall from [10] that two solutions and of the system (2.2) are asymptotically near if . In the following, we present results on asymptotic nearness of solutions of (2.2). Our first result is Theorem 2.1: For any pair of solutions and of (2.2), we have provided holds, where (2.7)
3.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 101 Proof: Consider the functional, Along the solutions of (2.2), the upper right derivative of V is given by using (2.4)-(2.6). . Integrating both sides with respect to t, Thus, V (t) is bounded on and for . But and are also bounded on . Hence, it follows that their derivatives are also bounded on
4.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 102 Therefore, and , are uniformly continuous on . Thus, we may conclude that and (e.g., [4]). This concludes the proof. The following result provides conditions under which all solutions of (2.2) are asymptotic to the solutions of (2.1), which shows that for a proper choice of input functions the stability of system (2.1) is not altered by the presence of time dependent inputs. Theorem 2.2: Assume that the parametric conditions (2.7) hold. Further, let inputs satisfy where . Then for any solutions (x, y) of (2.2) and Proof: To establish this, we employ the same functional as in Theorem 2.1, that is, Proceeding as in Theorem 2.1 we get after a simplification and rearrangement + Rest of the argument is same as that of Theorems 2.1, and hence, omitted. Thus, the conclusion follows. We now recall from [11] that the system (2.1) has a unique equilibrium pattern any set of input vectors provided the parameters satisfy, Then we have, Corollary 2.3: Assume that all the hypotheses of Theorem 2.2 are satisfied. Further if (2.1) possesses equilibrium pattern then all solutions (x, y) of (2.2) approach Proof: The result obviously follows form the observation that the equilibrium pattern is also a solution of (2.1) and the choice in Theorem 2.2. The following example illustrates the above results. Example 2.4: Consider the following system having two neurons in X each supported by two neurons in Y involving time delays as given by . Choose and . Then . Clearly conditions for both the existence of unique equilibrium and its stability are satisfied for any pair of constant inputs .
5.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 103 Now choose It is easy to see that since the condition holds, and we have (i). Conditions of Theorem 2.1 are satisfied and all solutions of the system are asymptotic to each other. (ii). Conditions of Corollary 2.3 are satisfied and all solutions of the system approach the equilibrium pattern of corresponding system with constant inputs. III. Estimations on Inputs for a Pre-specified Output In this section, we try to estimate our inputs, depending on the output given, that help the solutions to approach the given output. For an easy understanding of the concept, we avoid the complicated notation. We, therefore, rearrange our system (2.2) suitably. We use the following notation For , (2.2) may be represented as (3.1) in which We assume that is the desired output of the network. Further that both and are fixed with respect to t and are arbitrarily chosen. We now arrange (3.1) as (3.2) Conditions on response functions (2.2) to (2.6) may be modified as and for some || denoting appropriate norm. We have Theorem 3.1. Assume that the parameters of the system and the response functions satisfy the condition For an arbitrarily chosen output , the solutions of system (3.1) converge to provided the inputs satisfy either of the conditions or Proof . Then the upper right derivative of V along the solutions of (3.1), using (3.2), we have – – – This gives rise to Rest of the argument is similar to that of Theorem 2.1 and invoking the condition (i) on inputs. Again, it is easy to see from the last inequality above that for large t using conditions (ii) on and . Hence, in either of the cases, follows. The proof is complete. The following example illustrates the effectiveness of this result.
6.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 104 Example 3.2: Consider Now choose and Clearly, for given we have all the conditions of Theorem 3.1 are satisfied, and hence, for sufficiently large t. We shall now consider the time delay system corresponding to (2.2), (3.3) As has been done earlier for a given , we write (3.3) as (3.4) We have Theorem 3.3: Assume that the parameters of the system and the response functions satisfy the condition For an arbitrarily chosen output , solutions of system (3.3) converge to provided the inputs satisfy the condition Proof: Employing the functional using (3.4) and proceeding as in Theorem 2.1 and Theorem 3.1, the conclusion follows. Since the conditions on parameters and input functions in Theorem 3.1 and 3.3 are the same, it may imply that delays have no effect on convergence here Example 3.4: Consider Now choose and Clearly, for given we have all the conditions of Theorem 3.1 are satisfied, and hence, for sufficiently large t. Remark 3.5: Now consider the system (3.5) are constant inputs, given . It is easy to observe that is an equilibrium pattern of (3.5). Then from Corollary 2.4, we have, solutions of (3.3) approach whenever the variable inputs of (3.3) are well near those of (3.5) as specified in Corollary 2.4. Thus, by varying the external inputs of the system in the parameter space defined by as specified by Theorems 3.1 and 3.3, the solutions of the network approaches pre-specified output IV. Discussion In this article, we have extended the concept of approaching a desired output of a given network by suitable selection of inputs based on the given output for a cooperative and supportive neural network that was studied earlier for a BAM network ([10]). With the help of suitable Lyapunov functionals, results are established for asymptotic nearness and boundedness of solutions of the system also. It is noticed that inputs define a new space of equilibria for the network while they run through a space defined by output parameters. This way memory states of brain that are usually ignored by constant inputs may be recalled by varying the inputs to brain appropriately. Since the input-output relation is not direct but includes system parameters and functional responses, dynamics of entire system are involved in this process. It is hoped that this concept helps in utilizing the same network for different applications without altering its architecture. This shows how designed structures may be made emergent structures which are adaptive and flexible. Since the results hold good for all time delays (delay independent criteria) the results are applicable to delay-free case as well, i.e., models of [9].
7.
P. Raja Sekhara
Rao et al., International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014,pp. 99-105 IJETCAS 14-536; © 2014, IJETCAS All Rights Reserved Page 105 V. References [1] H. Bereketoglu and I. Gyori, Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay, Journal of Mathematical Analysis and Applications, 210(1997), 279-291. [2] Q.X. Dong, K. Matsui and X.K. Huang, Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear Analysis, 49(2002), 471-479. [3] M. Forti, P. Nistri and D. Papini, Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain, IEEE TNN 16(6): 1449-1463, 2005. [4] K. Gopalsamy and Xue-Zhong He, Delay-independent stability in bidirectional associative memory networks, IEEE TNN, 5(1994), 998-1002. [5] S. Hu and D. Liu, On global output convergence of a class of recurrent neural networks with time varying inputs, 18(2005), 171- 178. [6] B. Kosko, “Neural Networks and Fuzzy Systems - A Dynamical Systems Approach to Machine Intelligence", Prentice-Hall of India, New Delhi, 1994. [7] F.-L. Luo, R. Unbehauen, Applied Neural Networks for Signal Processing, Cambridge Univ. Press, Cambridge, UK, 1997. [8] B.B. Misra and S. Dehuri, Functional link artificial neural network for classification task in data mining, J. Computer Science, 3(12), 2007, 948-955. [9] V. Sree Hari Rao and P. Raja Sekhara Rao, Cooperative and Supportive Neural Networks, Physics Letters A 371 (2007) 101–110. [10] V. Sree Hari Rao and P. Raja Sekhara Rao, Time Varying Stimulations to Simple Neural Networks and Convergence to Desired Outputs, Communicated. [11] P. Raja Sekhara Rao, K.Venkata Ratnam and P. Lalitha, Delay Independent Stability of Co-operative and Supportive Neural Networks, Communicated. [12] Zhang Yi, J.C. Lv and L. Zhang, Output convergence analysis for a class of delayed recurrent neural networks with time varying inputs, IEEE TSMC, 36(1), 87-95, 2006.
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