Search results for: wavelet networks.

Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: M. Tarafdar Haque, A. Taheri

Abstract:

Application of neural networks in execution of programmed pulse width modulation (PPWM) of a voltage source inverter (VSI) is studied in this paper. Using the proposed method it is possible to cancel out the desired harmonics in output of VSI in addition to control the magnitude of fundamental harmonic, contineously. By checking the non-trained values and a performance index, the most appropriate neural network is proposed. It is shown that neural networks may solve the custom difficulties of practical utilization of PPWM such as large size of memory, complex digital circuits and controlling the magnitude of output voltage in a discrete manner.

Keywords: Neural Network, Inverter, PPWM.

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Authors: Dimitra Alexiou

Abstract:

In an urban area the location allocation of emergency services mobile units, such as ambulances, police patrol cars must be designed so as to achieve a prompt response to demand locations. In this paper the partition of a given urban network into distinct sub-networks is performed such that the vertices in each component are close and simultaneously the sums of the corresponding population in the sub-networks are almost uniform. The objective here is to position appropriately in each sub-network a mobile emergency unit in order to reduce the response time to the demands. A mathematical model in framework of graph theory is developed. In order to clarify the corresponding method a relevant numerical example is presented on a small network.

Keywords: Distances, Emergency Service, Graph Partition, location.

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Authors: Siddhartha Chauhan, Nitin Kumar Kotania

Abstract:

Traditional Wireless Sensor Networks (WSNs) generally use static sinks to collect data from the sensor nodes via multiple forwarding. Therefore, network suffers with some problems like long message relay time, bottle neck problem which reduces the performance of the network.

Many approaches have been proposed to prevent this problem with the help of mobile sink to collect the data from the sensor nodes, but these approaches still suffer from the buffer overflow problem due to limited memory size of sensor nodes. This paper proposes an energy efficient scheme for data gathering which overcomes the buffer overflow problem. The proposed scheme creates virtual grid structure of heterogeneous nodes. Scheme has been designed for sensor nodes having variable sensing rate. Every node finds out its buffer overflow time and on the basis of this cluster heads are elected. A controlled traversing approach is used by the proposed scheme in order to transmit data to sink. The effectiveness of the proposed scheme is verified by simulation.

Keywords: Buffer overflow problem, Mobile sink, Virtual grid, Wireless sensor networks.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.

Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.

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Authors: Madhuri Khambete, Madhuri Joshi

Abstract:

Quality evaluation of an image is an important task in image processing applications. In case of image compression, quality of decompressed image is also the criterion for evaluation of given coding scheme. In the process of compression -decompression various artifacts such as blocking artifacts, blur artifact, ringing or edge artifact are observed. However quantification of these artifacts is a difficult task. We propose here novel method to quantify blur and ringing artifact in an image.

Keywords: Blur, Compression, Objective Quality assessment, Ringing artifact.

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Authors: Bingquan Shen

Abstract:

Convolutional Neural Networks (CNN) have demonstrated their effectiveness in synthesizing 3D views of object instances at various viewpoints. Given the problem where one have limited viewpoints of a particular object for classification, we present a pose normalization architecture to transform the object to existing viewpoints in the training dataset before classification to yield better classification performance. We have demonstrated that this Pose Normalization Network (PNN) can capture the style of the target object and is able to re-render it to a desired viewpoint. Moreover, we have shown that the PNN improves the classification result for the 3D chairs dataset and ShapeNet airplanes dataset when given only images at limited viewpoint, as compared to a CNN baseline.

Keywords: Convolutional neural networks, object classification, pose normalization, viewpoint invariant.

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Authors: Jiann-Ming Wu, Hsiao-Chang Chen, Chun-Chang Wu, Pei-Hsun Hsu

Abstract:

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

Keywords: Blind image deconvolution, linear shift-invariant(LSI), linear image degradation model, radial basis functions (rbf), recursive function, annealed Hopfield neural networks.

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Authors: V. Agrawal, A. Sharma

Abstract:

High Strength Concrete (HSC) is defined as concrete that meets special combination of performance and uniformity requirements that cannot be achieved routinely using conventional constituents and normal mixing, placing, and curing procedures. It is a highly complex material, which makes modeling its behavior a very difficult task. This paper aimed to show possible applicability of Neural Networks (NN) to predict the slump in High Strength Concrete (HSC). Neural Network models is constructed, trained and tested using the available test data of 349 different concrete mix designs of High Strength Concrete (HSC) gathered from a particular Ready Mix Concrete (RMC) batching plant. The most versatile Neural Network model is selected to predict the slump in concrete. The data used in the Neural Network models are arranged in a format of eight input parameters that cover the Cement, Fly Ash, Sand, Coarse Aggregate (10 mm), Coarse Aggregate (20 mm), Water, Super-Plasticizer and Water/Binder ratio. Furthermore, to test the accuracy for predicting slump in concrete, the final selected model is further used to test the data of 40 different concrete mix designs of High Strength Concrete (HSC) taken from the other batching plant. The results are compared on the basis of error function (or performance function).

Keywords: Artificial Neural Networks, Concrete, prediction ofslump, slump in concrete

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Authors: Alaa Al Hawari, Mohammad Khader, Tarek Zayed, Osama Moselhi

Abstract:

Ground Penetrating Radar (GPR) is one of the most effective electromagnetic techniques for non-destructive non-invasive subsurface features investigation. Water leak from pipelines is the most common undesirable reason of potable water losses. Rapid detection of such losses is going to enhance the use of the Water Distribution Networks (WDN) and decrease threatens associated with water mains leaks. In this study, GPR approach was developed to detect leaks by implementing an appropriate imaging analyzing strategy based on image refinement, reflection polarity and reflection amplitude that would ease the process of interpreting the collected raw radargram image.

Keywords: Water Networks, Leakage, Water pipelines, Ground Penetrating Radar.

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Authors: Fayez Mostafa Alhamoui, Adnan Hadi Mahdi Al- Helali

Abstract:

The main issue in designing a wireless sensor network (WSN) is the finding of a proper routing protocol that complies with the several requirements of high reliability, short latency, scalability, low power consumption, and many others. This paper proposes a novel routing algorithm that complies with these design requirements. The new routing protocol divides the WSN into several subnetworks and each sub-network is divided into several clusters. This division is designed to reduce the number of radio transmission and hence decreases the power consumption. The network division may be changed dynamically to adapt with the network changes and allows the realization of the design requirements.

Keywords: Wireless sensor networks, routing protocols, ad hoc topology, cluster, sub-network, WSN design requirements.

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Authors: Xingyuan Qu, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: Delay-dependent stability, time-varying delays, Lyapunov functional, linear matrix inequality (LMI).

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Authors: Daiming Wang

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.

Keywords: Periodic solutions, global exponential stability, coincidence degree, M-matrix.

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Authors: Laurent Enel, Franck Guillem

Abstract:

This paper considers the benefits gained by using an efficient quality of service management such as DiffServ technique to improve the performance of military communications. Low delay and no blockage must be achieved especially for real time tactical data. All traffic flows generated by different applications do not need same bandwidth, same latency, same error ratio and this scalable technique of packet management based on priority levels is analysed. End to end architectures supporting various traffic flows and including lowbandwidth and high-delay HF or SHF military links as well as unprotected Internet sub domains are studied. A tuning of Diffserv parameters is proposed in accordance with different loads of various traffic and different operational situations.

Keywords: Military data networks, Quality of service, Tacticalsystems.

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Authors: Nima Farkhondeh Jahromi, George Papaefthymiou, Lou van der Sluis

Abstract:

The incorporation of renewable energy sources for the sustainable electricity production is undertaking a more prominent role in electric power systems. Thus, it will be an indispensable incident that the characteristics of future power networks, their prospective stability for instance, get influenced by the imposed features of sustainable energy sources. One of the distinctive attributes of the sustainable energy sources is exhibiting the stochastic behavior. This paper investigates the impacts of this stochastic behavior on the small disturbance rotor angle stability in the upcoming electric power networks. Considering the various types of renewable energy sources and the vast variety of system configurations, the sensitivity analysis can be an efficient breakthrough towards generalizing the effects of new energy sources on the concept of stability. In this paper, the definition of small disturbance angle stability for future power systems and the iterative-stochastic way of its analysis are presented. Also, the effects of system parameters on this type of stability are described by performing a sensitivity analysis for an electric power test system.

Keywords: Power systems stability, Renewable energy sources, Stochastic behavior, Small disturbance rotor angle stability.

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Authors: Yan Yu, Wang Yu, Chen Xintong, Liu Yi, Zhang Yanzhong, Wang Yanji, Chen Xingyu, Zhang Miaocheng, Tong Yi

Abstract:

Neuromorphic computing based on spiking neural networks (SNNs) has emerged as a promising avenue for building the next generation of intelligent computing systems. Owing to their high-density integration, low power, and outstanding nonlinearity, memristors have attracted emerging attention on achieving SNNs. However, fabricating a low-power and robust memristor-based spiking neuron without extra electrical components is still a challenge for brain-inspired systems. In this work, we demonstrate a TiO2-based threshold switching (TS) memristor to emulate a leaky integrate-and-fire (LIF) neuron without auxiliary circuits, used to realize single layer fully connected (FC) SNNs. Moreover, our TiO2-based resistive switching (RS) memristors realize spiking-time-dependent-plasticity (STDP), originating from the Ag diffusion-based filamentary mechanism. This work demonstrates that TiO2-based memristors may provide an efficient method to construct hardware neuromorphic computing systems.

Keywords: Leaky integrate-and-fire, memristor, spiking neural networks, spiking-time-dependent-plasticity.

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Authors: C. Iraklis, G. Evmiridis, A. Iraklis

Abstract:

Renewable energy sources and distributed power generation units already have an important role in electrical power generation. A mixture of different technologies penetrating the electrical grid, adds complexity in the management of distribution networks. High penetration of distributed power generation units creates node over-voltages, huge power losses, unreliable power management, reverse power flow and congestion. This paper presents an optimization algorithm capable of reducing congestion and power losses, both described as a function of weighted sum. Two factors that describe congestion are being proposed. An upgraded selective particle swarm optimization algorithm (SPSO) is used as a solution tool focusing on the technique of network reconfiguration. The upgraded SPSO algorithm is achieved with the addition of a heuristic algorithm specializing in reduction of power losses, with several scenarios being tested. Results show significant improvement in minimization of losses and congestion while achieving very small calculation times.

Keywords: Congestion, distribution networks, loss reduction, particle swarm optimization, smart grid.

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Authors: A. Abid, F. M. Abbou, H. T. Ewe

Abstract:

Optical Bursts Switching (OBS) is a relatively new optical switching paradigm. Contention and burst loss in OBS networks are major concerns. To resolve contentions, an interesting alternative to discarding the entire data burst is to partially drop the burst. Partial burst dropping is based on burst segmentation concept that its implementation is constrained by some technical challenges, besides the complexity added to the algorithms and protocols on both edge and core nodes. In this paper, the burst segmentation concept is investigated, and an implementation scheme is proposed and evaluated. An appropriate dropping policy that effectively manages the size of the segmented data bursts is presented. The dropping policy is further supported by a new control packet format that provides constant transmission overhead.

Keywords: Burst length, Burst Segmentation, Optical BurstSwitching.

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Authors: Ritu Vijay, Rekha Govil

Abstract:

The design of a complete expansion that allows for compact representation of certain relevant classes of signals is a central problem in signal processing applications. Achieving such a representation means knowing the signal features for the purpose of denoising, classification, interpolation and forecasting. Multilayer Neural Networks are relatively a new class of techniques that are mathematically proven to approximate any continuous function arbitrarily well. Radial Basis Function Networks, which make use of Gaussian activation function, are also shown to be a universal approximator. In this age of ever-increasing digitization in the storage, processing, analysis and communication of information, there are numerous examples of applications where one needs to construct a continuously defined function or numerical algorithm to approximate, represent and reconstruct the given discrete data of a signal. Many a times one wishes to manipulate the data in a way that requires information not included explicitly in the data, which is done through interpolation and/or extrapolation. Tidal data are a very perfect example of time series and many statistical techniques have been applied for tidal data analysis and representation. ANN is recent addition to such techniques. In the present paper we describe the time series representation capabilities of a special type of ANN- Radial Basis Function networks and present the results of tidal data representation using RBF. Tidal data analysis & representation is one of the important requirements in marine science for forecasting.

Keywords: ANN, RBF, Tidal Data.

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Authors: A. Greco, N. Mammone, F.C. Morabito, M.Versaci

Abstract:

This paper is mainly concerned with the application of a novel technique of data interpretation to the characterization and classification of measurements of plasma columns in Tokamak reactors for nuclear fusion applications. The proposed method exploits several concepts derived from soft computing theory. In particular, Artifical Neural Networks have been exploited to classify magnetic variables useful to determine shape and position of the plasma with a reduced computational complexity. The proposed technique is used to analyze simulated databases of plasma equilibria based on ITER geometry configuration. As well as demonstrating the successful recovery of scalar equilibrium parameters, we show that the technique can yield practical advantages compares with earlier methods.

Keywords: Tokamak, sensors, artificial neural network.

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Authors: P.S. Prakash, S. Selvan

Abstract:

Quality of Service (QoS) Routing aims to find path between source and destination satisfying the QoS requirements which efficiently using the network resources and underlying routing algorithm and to fmd low-cost paths that satisfy given QoS constraints. One of the key issues in providing end-to-end QoS guarantees in packet networks is determining feasible path that satisfies a number of QoS constraints. We present a Optimized Multi- Constrained Routing (OMCR) algorithm for the computation of constrained paths for QoS routing in computer networks. OMCR applies distance vector to construct a shortest path for each destination with reference to a given optimization metric, from which a set of feasible paths are derived at each node. OMCR is able to fmd feasible paths as well as optimize the utilization of network resources. OMCR operates with the hop-by-hop, connectionless routing model in IP Internet and does not create any loops while fmding the feasible paths. Nodes running OMCR not necessarily maintaining global view of network state such as topology, resource information and routing updates are sent only to neighboring nodes whereas its counterpart link-state routing method depend on complete network state for constrained path computation and that incurs excessive communication overhead.

Keywords: QoS Routing, Optimization, feasible path, multiple constraints.

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Authors: Hyoup-Sang Yoon

Abstract:

The quality of video transmitted by mobile ad hoc networks (MANETs) can be influenced by several factors, including protocol layers; parameter settings of each protocol. In this paper, we are concerned with understanding the functional relationship between these influential factors and objective video quality in MANETs. We illustrate a systematic statistical design of experiments (DOE) strategy can be used to analyze MANET parameters and performance. Using a 2^k factorial design, we quantify the main and interactive effects of 7 factors on a response metric (i.e., mean opinion score (MOS) calculated by PSNR with Evalvid package) we then develop a first-order linear regression model between the influential factors and the performance metric.

Keywords: Evalvid, full factorial design, mobile ad hoc networks, ns-2.

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Authors: Kriangkrai Maneerat, Chutima Prommak

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This paper presents an analysis of the localization accuracy of indoor positioning systems using Cramer-s rule via IEEE 802.15.4 wireless sensor networks. The objective is to study the impact of the methods used to convert the received signal strength into the distance that is used to compute the object location in the wireless indoor positioning system. Various methods were tested and the localization accuracy was analyzed. The experimental results show that the method based on the empirical data measured in the non line-of-sight (NLOS) environment yield the highest localization accuracy; with the minimum error distance less than 3 m.

Keywords: Indoor positioning systems, localization accuracy, wireless networks, Cramer's rule.

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Authors: Parvinder S. Sandhu, Roma Jaswal, Sandeep Khimta, Shailendra Singh

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As the majority of faults are found in a few of its modules so there is a need to investigate the modules that are affected severely as compared to other modules and proper maintenance need to be done in time especially for the critical applications. As, Neural networks, which have been already applied in software engineering applications to build reliability growth models predict the gross change or reusability metrics. Neural networks are non-linear sophisticated modeling techniques that are able to model complex functions. Neural network techniques are used when exact nature of input and outputs is not known. A key feature is that they learn the relationship between input and output through training. In this present work, various Neural Network Based techniques are explored and comparative analysis is performed for the prediction of level of need of maintenance by predicting level severity of faults present in NASA-s public domain defect dataset. The comparison of different algorithms is made on the basis of Mean Absolute Error, Root Mean Square Error and Accuracy Values. It is concluded that Generalized Regression Networks is the best algorithm for classification of the software components into different level of severity of impact of the faults. The algorithm can be used to develop model that can be used for identifying modules that are heavily affected by the faults.

Keywords: Neural Network, Software faults, Software Metric.

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Authors: Isao Taguchi, Yasuo Sugai

Abstract:

This paper proposes an efficient learning method for the layered neural networks based on the selection of training data and input characteristics of an output layer unit. Comparing to recent neural networks; pulse neural networks, quantum neuro computation, etc, the multilayer network is widely used due to its simple structure. When learning objects are complicated, the problems, such as unsuccessful learning or a significant time required in learning, remain unsolved. Focusing on the input data during the learning stage, we undertook an experiment to identify the data that makes large errors and interferes with the learning process. Our method devides the learning process into several stages. In general, input characteristics to an output layer unit show oscillation during learning process for complicated problems. The multi-stage learning method proposes by the authors for the function approximation problems of classifying learning data in a phased manner, focusing on their learnabilities prior to learning in the multi layered neural network, and demonstrates validity of the multi-stage learning method. Specifically, this paper verifies by computer experiments that both of learning accuracy and learning time are improved of the BP method as a learning rule of the multi-stage learning method. In learning, oscillatory phenomena of a learning curve serve an important role in learning performance. The authors also discuss the occurrence mechanisms of oscillatory phenomena in learning. Furthermore, the authors discuss the reasons that errors of some data remain large value even after learning, observing behaviors during learning.

Keywords: data selection, function approximation problem, multistage leaning, neural network, voluntary oscillation.

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Authors: B. Golchin, N. Riahi

Abstract:

One of the most significant issues as attended a lot in recent years is that of recognizing the sentiments and emotions in social media texts. The analysis of sentiments and emotions is intended to recognize the conceptual information such as the opinions, feelings, attitudes and emotions of people towards the products, services, organizations, people, topics, events and features in the written text. These indicate the greatness of the problem space. In the real world, businesses and organizations are always looking for tools to gather ideas, emotions, and directions of people about their products, services, or events related to their own. This article uses the Twitter social network, one of the most popular social networks with about 420 million active users, to extract data. Using this social network, users can share their information and opinions about personal issues, policies, products, events, etc. It can be used with appropriate classification of emotional states due to the availability of its data. In this study, supervised learning and deep neural network algorithms are used to classify the emotional states of Twitter users. The use of deep learning methods to increase the learning capacity of the model is an advantage due to the large amount of available data. Tweets collected on various topics are classified into four classes using a combination of two Bidirectional Long Short Term Memory network and a Convolutional network. The results obtained from this study with an average accuracy of 93%, show good results extracted from the proposed framework and improved accuracy compared to previous work.

Keywords: emotion classification, sentiment analysis, social networks, deep neural networks

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Authors: Christian Endisch, Christoph Hackl, Dierk Schröder

Abstract:

This paper presents an exact pruning algorithm with adaptive pruning interval for general dynamic neural networks (GDNN). GDNNs are artificial neural networks with internal dynamics. All layers have feedback connections with time delays to the same and to all other layers. The structure of the plant is unknown, so the identification process is started with a larger network architecture than necessary. During parameter optimization with the Levenberg- Marquardt (LM) algorithm irrelevant weights of the dynamic neural network are deleted in order to find a model for the plant as simple as possible. The weights to be pruned are found by direct evaluation of the training data within a sliding time window. The influence of pruning on the identification system depends on the network architecture at pruning time and the selected weight to be deleted. As the architecture of the model is changed drastically during the identification and pruning process, it is suggested to adapt the pruning interval online. Two system identification examples show the architecture selection ability of the proposed pruning approach.

Keywords: System identification, dynamic neural network, recurrentneural network, GDNN, optimization, Levenberg Marquardt, realtime recurrent learning, network pruning, quasi-online learning.

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Authors: H. Khorashadi-Zadeh, M. R. Aghaebrahimi

Abstract:

A novel application of neural network approach to fault classification and fault location of Medium voltage cables is demonstrated in this paper. Different faults on a protected cable should be classified and located correctly. This paper presents the use of neural networks as a pattern classifier algorithm to perform these tasks. The proposed scheme is insensitive to variation of different parameters such as fault type, fault resistance, and fault inception angle. Studies show that the proposed technique is able to offer high accuracy in both of the fault classification and fault location tasks.

Keywords: Artificial neural networks, cable, fault location andfault classification.

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Authors: Kevin Fong-Rey Liu, Ken Yeh, Cheng-Wu Chen, Han-Hsi Liang

Abstract:

This paper proposes the use of Bayesian belief networks (BBN) as a higher level of health risk assessment for a dumping site of lead battery smelter factory. On the basis of the epidemiological studies, the actual hospital attendance records and expert experiences, the BBN is capable of capturing the probabilistic relationships between the hazardous substances and their adverse health effects, and accordingly inferring the morbidity of the adverse health effects. The provision of the morbidity rates of the related diseases is more informative and can alleviate the drawbacks of conventional methods.

Keywords: Bayesian belief networks, lead battery smelter factory, health risk assessment.

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Authors: Frank Emmert Streib, Matthias Dehmer, Jing Liu, Max Mühlhauser

Abstract:

In this paper we present a method for gene ranking from DNA microarray data. More precisely, we calculate the correlation networks, which are unweighted and undirected graphs, from microarray data of cervical cancer whereas each network represents a tissue of a certain tumor stage and each node in the network represents a gene. From these networks we extract one tree for each gene by a local decomposition of the correlation network. The interpretation of a tree is that it represents the n-nearest neighbor genes on the n-th level of a tree, measured by the Dijkstra distance, and, hence, gives the local embedding of a gene within the correlation network. For the obtained trees we measure the pairwise similarity between trees rooted by the same gene from normal to cancerous tissues. This evaluates the modification of the tree topology due to progression of the tumor. Finally, we rank the obtained similarity values from all tissue comparisons and select the top ranked genes. For these genes the local neighborhood in the correlation networks changes most between normal and cancerous tissues. As a result we find that the top ranked genes are candidates suspected to be involved in tumor growth and, hence, indicates that our method captures essential information from the underlying DNA microarray data of cervical cancer.

Keywords: Graph similarity, DNA microarray data, cancer.

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