http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aans/2011/374816/Multilayer perceptron (MLP) with back-propagation learning rule is adopted to predict the winning rates of two teams according to their official statistical data of 2006 World Cup Football Game at the previous stages. There are training samples from three classes: win, draw, and loss. At the new stage, new training samples are selected from the previous stages and are added to the training samples, then we retrain the neural network. It is a type of on-line learning. The 8 features are selected with ad hoc choice. We use the theorem of Mirchandani and Cao to determine the number of hidden nodes. And after the testing in the learning convergence, the MLP is determined as 8-2-3 model. The learning rate and momentum coefficient are determined in the cross-learning. The prediction accuracy achieves 75% if the draw games are excluded.Kou-Yuan Huang and Kai-Ju ChenCopyright © 2011 Kou-Yuan Huang and Kai-Ju Chen. All rights reserved.http://www.hindawi.com/journals/aans/2011/523094/The use of hybrid intelligent systems (HISs) is necessary to bring the behavior of intelligent autonomous vehicles (IAVs) near the human one in recognition, learning, adaptation, generalization, decision making, and action. First, the necessity of HIS and some navigation approaches based on fuzzy ArtMap neural networks (FAMNNs) are discussed. Indeed, such approaches can provide IAV with more autonomy, intelligence, and real-time processing capabilities. Second, an FAMNN-based navigation approach is suggested. Indeed, this approach must provide vehicles with capability, after supervised fast stable learning: simplified fuzzy ArtMap (SFAM), to recognize both target-location and obstacle-avoidance situations using FAMNN1 and FAMNN2, respectively. Afterwards, the decision making and action consist of two association stages, carried out by reinforcement trial and error learning, and their coordination using NN3. Then, NN3 allows to decide among the five (05) actions to move towards 30∘, 60∘, 90∘, 120∘, and 150∘. Third, simulation results display the ability of the FAMNN-based approach to provide IAV with intelligent behaviors allowing to intelligently navigate in partially structured environments. Finally, a discussion, dealing with the suggested approach and how its robustness would be if implemented on real vehicle, is given.Amine Chohra and Ouahiba AzouaouiCopyright © 2011 Amine Chohra and Ouahiba Azouaoui. All rights reserved.http://www.hindawi.com/journals/aans/2011/941426/For the first time the global dissipativity of a class of cellular neural networks with multipantograph delays is studied. On the one hand, some delay-dependent sufficient conditions are obtained by directly constructing suitable Lyapunov functionals; on the other hand, firstly the transformation transforms the cellular neural networks with multipantograph delays into the cellular neural networks with constant delays and variable coefficients, and then constructing Lyapunov functionals, some delay-independent sufficient conditions are given. These new sufficient conditions can ensure global dissipativity together with their sets of attraction and can be applied to design global dissipative cellular neural networks with multipantograph delays and easily checked in practice by simple algebraic methods. An example is given to illustrate the correctness of the results.Liqun ZhouCopyright © 2011 Liqun Zhou. All rights reserved.http://www.hindawi.com/journals/aans/2011/751908/We used five years of global solar radiation data to estimate the monthly average of daily global solar irradiation on a horizontal surface based on a single parameter, sunshine hours, using the artificial neural network method. The station under the study is located in Kampala, Uganda at a latitude of 0.19°N, a longitude of 32.34°E, and an altitude of 1200 m above sea level. The five-year data was split into two parts in 2003–2006 and 2007-2008; the first part was used for training, and the latter was used for testing the neural network. Amongst the models tested, the feed-forward back-propagation network with one hidden layer (65 neurons) and with the tangent sigmoid as the transfer function emerged as the more appropriate model. Results obtained using the proposed model showed good agreement between the estimated and actual values of global solar irradiation. A correlation coefficient of 0.963 was obtained with a mean bias error of 0.055 MJ/m2 and a root mean square error of 0.521 MJ/m2. The single-parameter ANN model shows promise for estimating global solar irradiation at places where monitoring stations are not established and stations where we have one common parameter (sunshine hours).Karoro Angela, Ssenyonga Taddeo, and Mubiru JamesCopyright © 2011 Karoro Angela et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/673016/This paper introduces some novel models for all steps of a face recognition system. In the step of face detection, we propose a hybrid model combining AdaBoost and Artificial Neural Network (ABANN) to solve the process efficiently. In the next step, labeled faces detected by ABANN will be aligned by Active Shape Model and Multi Layer Perceptron. In this alignment step, we propose a new 2D local texture model based on Multi Layer Perceptron. The classifier of the model significantly improves the accuracy and the robustness of local searching on faces with expression variation and ambiguous contours. In the feature extraction step, we describe a methodology for improving the efficiency by the association of two methods: geometric feature based method and Independent Component Analysis method. In the face matching step, we apply a model combining many Neural Networks for matching geometric features of human face. The model links many Neural Networks together, so we call it Multi Artificial Neural Network. MIT + CMU database is used for evaluating our proposed methods for face detection and alignment. Finally, the experimental results of all steps on CallTech database show the feasibility of our proposed model.Thai Hoang LeCopyright © 2011 Thai Hoang Le. All rights reserved.http://www.hindawi.com/journals/aans/2011/786535/A damage assessment procedure has been developed using artificial neural network (ANN) for prestressed concrete beams. The methodology had been formulated using the results obtained from an experimental study conducted in the laboratory. Prestressed concrete (PSC) rectangular beams were cast, and pitting corrosion was introduced in the prestressing wires and was allowed to be snapped using accelerated corrosion process. Both static and dynamic tests were conducted to study the behaviour of perfect and damaged beams. The measured output from both static and dynamic tests was taken as input to train the neural network. Back propagation network was chosen for this purpose, which was written using the programming package MATLAB. The trained network was tested using separate test data obtained from the tests. A damage assessment procedure was developed using the trained network, it was validated using the data available in literature, and the outcome is presented in this paper.K. Sumangala and C. Antony JeyaseharCopyright © 2011 K. Sumangala and C. Antony Jeyasehar. All rights reserved.http://www.hindawi.com/journals/aans/2011/617427/The Self-Organizing Map (SOM) algorithm is widely used for building topographic maps of data represented in a vectorial space, but it does not operate with dissimilarity data. Soft Topographic Map (STM) algorithm is an extension of SOM to arbitrary distance measures, and it creates a map using a set of units, organized in a rectangular lattice, defining data neighbourhood relationships. In the last years, a new standard for identifying bacteria using genotypic information began to be developed. In this new approach, phylogenetic relationships of bacteria could be determined by comparing a stable part of the bacteria genetic code, the so-called “housekeeping genes.” The goal of this work is to build a topographic representation of bacteria clusters, by means of self-organizing maps, starting from genotypic features regarding housekeeping genes.Massimo La Rosa, Riccardo Rizzo, and Alfonso UrsoCopyright © 2011 Massimo La Rosa et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/142054/This paper explores the possibility of developing a prediction model using artificial neural networks (ANNs), which could be used to estimate monthly average daily direct solar radiation for locations in Uganda. Direct solar radiation is a component of the global solar radiation and is quite significant in the performance assessment of various solar energy applications. Results from the paper have shown good agreement between the estimated and measured values of direct solar irradiation. A correlation coefficient of 0.998 was obtained with mean bias error of 0.005 MJ/m2 and root mean square error of 0.197 MJ/m2. The comparison between the ANN and empirical model emphasized the superiority of the proposed ANN prediction model. The application of the proposed ANN model can be extended to other locations with similar climate and terrain.James MubiruCopyright © 2011 James Mubiru. All rights reserved.http://www.hindawi.com/journals/aans/2011/453169/The increased complexity of plants and the development of sophisticated control systems have encouraged the parallel development of efficient rapid fault detection and isolation (FDI) systems. FDI in industrial system has lately become of great significance. This paper proposes a new technique for short time fault detection and diagnosis in nonlinear dynamic systems with multi inputs and multi outputs. The main contribution of this paper is to develop a FDI schema according to reference models of fault-free and faulty behaviors designed with neural networks. Fault detection is obtained according to residuals that result from the comparison of measured signals with the outputs of the fault free reference model. Then, Euclidean distance from the outputs of models of faults to the measurements leads to fault isolation. The advantage of this method is to provide not only early detection but also early diagnosis thanks to the parallel computation of the models of faults and to the proposed decision algorithm. The effectiveness of this approach is illustrated with simulations on DAMADICS benchmark.Yahia Kourd, Dimitri Lefebvre, and Noureddine GuersiCopyright © 2011 Yahia Kourd et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/249136/A novel and effective approach to synchronization analysis of neural networks is investigated by using the nonlinear operator named the generalized Dahlquist constant and the general intermittent control. The proposed approach offers a design procedure for synchronization of a large class of neural networks. The numerical simulations whose theoretical results are applied to typical neural networks with and without delayed item demonstrate the effectiveness and feasibility of the proposed technique.Zhang QunliCopyright © 2011 Zhang Qunli. All rights reserved.http://www.hindawi.com/journals/aans/2011/189368/The associative Hopfield memory is a form of recurrent Artificial Neural Network (ANN) that can be used in applications such as pattern recognition, noise removal, information retrieval, and combinatorial optimization problems. This paper presents the implementation of the Hopfield Neural Network (HNN) parallel architecture on a SRAM-based FPGA. The main advantage of the proposed implementation is its high performance and cost effectiveness: it requires O(1) multiplications and O(log⁡ N) additions, whereas most others require O(N) multiplications and O(N) additions.W. Mansour, R. Ayoubi, H. Ziade, R. Velazco, and W. EL FalouCopyright © 2011 W. Mansour et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/431357/This paper presents the prediction of pollution severity of the polymeric insulators used in power transmission lines using adaptive neurofuzzy inference system (ANFIS) model. In this work, laboratory-based pollution performance tests were carried out on 11 kV silicone rubber polymeric insulator under AC voltage at different pollution levels with sodium chloride as a contaminant. Leakage current was measured during the laboratory tests. Time domain and frequency domain characteristics of leakage current, such as mean value, maximum value, standard deviation, and total harmonics distortion (THD), have been extracted, which jointly describe the pollution severity of the polymeric insulator surface. Leakage current characteristics are used as the inputs of ANFIS model. The pollution severity index “equivalent salt deposit density” (ESDD) is used as the output of the proposed model. Results of the research can give sufficient prewarning time before pollution flashover and help in the condition based maintenance (CBM) chart preparation.C. Muniraj and S. ChandrasekarCopyright © 2011 C. Muniraj and S. Chandrasekar. All rights reserved.http://www.hindawi.com/journals/aans/2011/532785/With the emerging trend of restructuring in the electric power industry, many transmission lines have been forced to operate at almost their full capacities worldwide. Due to this, more incidents of voltage instability and collapse are being observed throughout the world leading to major system breakdowns. To avoid these undesirable incidents, a fast and accurate estimation of voltage stability margin is required. In this paper, genetic algorithm based back propagation neural network (GABPNN) has been proposed for voltage stability margin estimation which is an indication of the power system's proximity to voltage collapse. The proposed approach utilizes a hybrid algorithm that integrates genetic algorithm and the back propagation neural network. The proposed algorithm aims to combine the capacity of GAs in avoiding local minima and at the same time fast execution of the BP algorithm. Input features for GABPNN are selected on the basis of angular distance-based clustering technique. The performance of the proposed GABPNN approach has been compared with the most commonly used gradient based BP neural network by estimating the voltage stability margin at different loading conditions in 6-bus and IEEE 30-bus system. GA based neural network learns faster, at the same time it provides more accurate voltage stability margin estimation as compared to that based on BP algorithm. It is found to be suitable for online applications in energy management systems.Garima Singh and Laxmi SrivastavaCopyright © 2011 Garima Singh and Laxmi Srivastava. All rights reserved.http://www.hindawi.com/journals/aans/2011/302572/This paper considers the applications of resampling methods to support vector machines (SVMs). We take into account the leaving-one-out cross-validation (CV) when determining the optimum tuning parameters and bootstrapping the deviance in order to summarize the measure of goodness-of-fit in SVMs. The leaving-one-out CV is also adapted in order to provide estimates of the bias of the excess error in a prediction rule constructed with training samples. We analyze the data from a mackerel-egg survey and a liver-disease study.Masaaki Tsujitani and Yusuke TanakaCopyright © 2011 Masaaki Tsujitani and Yusuke Tanaka. All rights reserved.http://www.hindawi.com/journals/aans/2011/107498/A hybrid learning scheme (ePSO-BP) to train Chebyshev Functional Link Neural Network (CFLNN) for classification is presented. The proposed method is referred as hybrid CFLNN (HCFLNN). The HCFLNN is a type of feed-forward neural networks which have the ability to transform the nonlinear input space into higher dimensional-space where linear separability is possible. Moreover, the proposed HCFLNN combines the best attribute of particle swarm optimization (PSO), back propagation learning (BP learning), and functional link neural networks (FLNNs). The proposed method eliminates the need of hidden layer by expanding the input patterns using Chebyshev orthogonal polynomials. We have shown its effectiveness of classifying the unknown pattern using the publicly available datasets obtained from UCI repository. The computational results are then compared with functional link neural network (FLNN) with a generic basis functions, PSO-based FLNN, and EFLN. From the comparative study, we observed that the performance of the HCFLNN outperforms FLNN, PSO-based FLNN, and EFLN in terms of classification accuracy.Satchidananda DehuriCopyright © 2011 Satchidananda Dehuri. All rights reserved.http://www.hindawi.com/journals/aans/2011/407497/Adaptive natural gradient learning avoids singularities in the parameter space of multilayer perceptrons. However, it requires a larger number of additional parameters than ordinary backpropagation in the form of the Fisher information matrix. This paper describes a new approach to natural gradient learning that uses a smaller Fisher information matrix. It also uses a prior distribution on the neural network parameters and an annealed learning rate. While this new approach is computationally simpler, its performance is comparable to that of adaptive natural gradient learning.Michael R. Bastian, Jacob H. Gunther, and Todd K. MoonCopyright © 2011 Michael R. Bastian et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/607374/The objective of this paper is to delineate a method for determining the yield strength of a material in a virtually nondestructive manner. Conventional test methods for predicting the yield strength require the removal of large material samples from the in-service component, which is impractical. In this paper, the power of neural networks in predicting the yield strength from the data obtained by conducting tension test on newly developed dumb-bell-shaped miniature specimen is demonstrated using the self-organizing capabilities of the ANN. The input to the neural network is the breakaway load obtained from the miniature test, and the output obtained from the model is yield strength value. The value of the yield strength estimated by neural network is found to be in good agreement (<5% error) with that of the actual value from the standard test. The neural network models are convenient and powerful tools for practical applications in solving various problems in engineering.G. Partheepan, D. K. Sehgal, and R. K. PandeyCopyright © 2011 G. Partheepan et al. All rights reserved.http://www.hindawi.com/journals/aans/2011/814769/We present a spatiotemporal model, namely, procedural neural networks for stock price prediction. Compared with some successful traditional models on simulating stock market, such as BNN (backpropagation neural networks, HMM (hidden Markov model) and SVM (support vector machine)), the procedural neural network model processes both spacial and temporal information synchronously without slide time window, which is typically used in the well-known recurrent neural networks. Two different structures of procedural neural networks are constructed for modeling multidimensional time series problems. Learning algorithms for training the models and sustained improvement of learning are presented and discussed. Experiments on Yahoo stock market of the past decade years are implemented, and simulation results are compared by PNN, BNN, HMM, and SVM.Jiuzhen Liang, Wei Song, and Mei WangCopyright © 2011 Jiuzhen Liang et al. All rights reserved.http://www.hindawi.com/journals/aans/2010/142540/A novel training algorithm is proposed for the formation of Self-Organizing Maps (SOM). In the proposed model, the weights are updated incrementally by using a higher-order difference equation, which implements a low-pass digital filter. It is possible to improve selected features of the self-organization process with respect to the basic SOM by suitably designing the filter. Moreover, from this model, new visualization tools can be derived for cluster visualization and for monitoring the quality of the map.Mauro Tucci and Marco RaugiCopyright © 2010 Mauro Tucci and Marco Raugi. All rights reserved.http://www.hindawi.com/journals/aans/2010/814702/Feedback error-learning (FEL) controller that consists of a proportional-integral-derivative (PID) controller and an artificial neural network (ANN) had applicability to functional electrical stimulation (FES). Because of the integral (reset) windup, however, delay or overshoot sometimes occurred in feedback FES control, which was considered to cause inappropriate ANN learning and to limit the feasibility of the FEL controller for FES to controlling 1-DOF movements stimulating 2 muscles. In this paper, an FEL-FES controller was developed applying antireset windup (ARW) scheme that worked based on total controller output. The FEL-FES controller with the ARW was examined in controlling 2-DOF movements of the wrist joint stimulating 4 muscles through computer simulation. The developed FEL-FES controller was found to realize appropriately inverse dynamics model and to have a possibility of being used as an open-loop controller. The developed controller would be effective in multiple DOF movement control stimulating several muscles.Takashi Watanabe and Keisuke FukushimaCopyright © 2010 Takashi Watanabe and Keisuke Fukushima. All rights reserved.http://www.hindawi.com/journals/aans/2010/309841/The aim of this study was to compare multilayer perceptron neural networks (NNs) with standard logistic regression (LR) to identify key covariates impacting on mortality from cancer causes, disease-free survival (DFS), and disease recurrence using Area Under Receiver-Operating Characteristics (AUROC) in breast cancer patients. From 1996 to 2004, 2,535 patients diagnosed with primary breast cancer entered into the study at a single French centre, where they received standard treatment. For specific mortality as well as DFS analysis, the ROC curves were greater with the NN models compared to LR model with better sensitivity and specificity. Four predictive factors were retained by both approaches for mortality: clinical size stage, Scarff Bloom Richardson grade, number of invaded nodes, and progesterone receptor. The results enhanced the relevance of the use of NN models in predictive analysis in oncology, which appeared to be more accurate in prediction in this French breast cancer cohort.Valérie Bourdès, Stéphane Bonnevay, Paolo Lisboa, Rémy Defrance, David Pérol, Sylvie Chabaud, Thomas Bachelot, Thérèse Gargi, and Sylvie NégrierCopyright © 2010 Valérie Bourdès et al. All rights reserved.http://www.hindawi.com/journals/aans/2010/984381/A new approach for determining the coefficients of a complex-valued autoregressive (CAR) and complex-valued autoregressive moving average (CARMA) model coefficients using complex-valued neural network (CVNN) technique is discussed in this paper. The CAR and complex-valued moving average (CMA) coefficients which constitute a CARMA model are computed simultaneously from the adaptive weights and coefficients of the linear activation functions in a two-layered CVNN. The performance of the proposed technique has been evaluated using simulated complex-valued data (CVD) with three different types of activation functions. The results show that the proposed method can accurately determine the model coefficients provided that the network is properly trained. Furthermore, application of the developed CVNN-based technique for MRI K-space reconstruction results in images with improve resolution.A. M. Aibinu, M. J. E. Salami, and A. A. ShafieCopyright © 2010 A. M. Aibinu et al. All rights reserved.http://www.hindawi.com/journals/aans/2010/597373/This paper presents a methodology named Optimally Pruned K-Nearest Neighbors (OP-KNNs) which has the advantage of competing with state-of-the-art methods while remaining fast. It builds a one hidden-layer feedforward neural network using K-Nearest Neighbors as kernels to perform regression. Multiresponse Sparse Regression (MRSR) is used in order to rank each kth nearest neighbor and finally Leave-One-Out estimation is used to select the optimal number of neighbors and to estimate the generalization performances. Since computational time of this method is small, this paper presents a strategy using OP-KNN to perform Variable Selection which is tested successfully on eight real-life data sets from different application fields. In summary, the most significant characteristic of this method is that it provides good performance and a comparatively simple model at extremely high-learning speed.Qi Yu, Yoan Miche, Antti Sorjamaa, Alberto Guillen, Amaury Lendasse, and Eric SéverinCopyright © 2010 Qi Yu et al. All rights reserved.http://www.hindawi.com/journals/aans/2009/193139/Two artificial neural networks (ANN), back-propagation neural network (BPNN) and the radial basis function neural network (RBFNN), are proposed to predict the carbonation depth of prestressed concrete. In order to generate the training and testing data for the ANNs, an accelerated carbonation experiment was carried out, and the influence of stress level of concrete on carbonation process was taken into account especially. Then, based on the experimental results, the BPNN and RBFNN models which all take the stress level of concrete, water-cement ratio, cement-fine aggregate, cement-coarse aggregate ratio and testing age as input parameters were built and all the training and testing work was performed in MATLAB. It can be found that the two ANN models seem to have a high prediction and generalization capability in evaluation of carbonation depth, and the largest absolute percentage errors of BPNN and RBFNN are 10.88% and 8.46%, respectively. The RBFNN model shows a better prediction precision in comparison to BPNN model.Chunhua Lu and Ronggui LiuCopyright © 2009 Chunhua Lu and Ronggui Liu. All rights reserved.http://www.hindawi.com/journals/aans/2009/308239/Artificial neural networks (ANNs) are a form of artificial intelligence that has proved to provide a high level of competency in solving many complex engineering problems that are beyond the computational capability of classical mathematics and traditional procedures. In particular, ANNs have been applied successfully to almost all aspects of geotechnical engineering problems. Despite the increasing number and diversity of ANN applications in geotechnical engineering, the contents of reported applications indicate that the progress in ANN development and procedures is marginal and not moving forward since the mid-1990s. This paper presents a brief overview of ANN applications in geotechnical engineering, briefly provides an overview of the operation of ANN modeling, investigates the current research directions of ANNs in geotechnical engineering, and discusses some ANN modeling issues that need further attention in the future, including model robustness; transparency and knowledge extraction; extrapolation; uncertainty.Mohamed A. Shahin, Mark B. Jaksa, and Holger R. MaierCopyright © 2009 Mohamed A. Shahin et al. All rights reserved.http://www.hindawi.com/journals/aans/2009/942697/The bioelectric potentials associated with muscle activity constitute the electromyogram (EMG). These EMG signals are low-frequency and lower-magnitude signals. In this paper, it is presented that Jordan/Elman neural network can be effectively used for EMG signal noise removal, which is a typical nonlinear multivariable regression problem, as compared with other types of neural networks. Different neural network (NN) models with varying parameters were considered for the design of adaptive neural-network-based filter which is a typical SISO system. The performance parameters, that is, MSE, correlation coefficient, N/P, and t, are found to be in the expected range of values.V. R. Mankar and A. A. GhatolCopyright © 2009 V. R. Mankar and A. A. Ghatol. All rights reserved.http://www.hindawi.com/journals/aans/2009/724092/In order to simulate neuronal electrical activities, we must estimate the dynamics of channel conductances from physiological experimental data. However, this approach requires the formulation of differential equations that express the time course of channel conductance. On the other hand, if the dynamics are automatically estimated, neuronal activities can be easily simulated. By using a recurrent neural network (RNN), it is possible to estimate the dynamics of channel conductances without formulating the differential equations. In the present study, we estimated the dynamics of the Na+ and K+ conductances of a squid giant axon using two different fully connected RNNs and were able to reproduce various neuronal activities of the axon. The reproduced activities were an action potential, a threshold, a refractory phenomenon, a rebound action potential, and periodic action potentials with a constant stimulation. RNNs can be trained using channels other than the Na+ and K+ channels. Therefore, using our RNN estimation method, the dynamics of channel conductance can be automatically estimated and the neuronal activities can be simulated using the channel RNNs. An RNN can be a useful tool to estimate the dynamics of the channel conductance of a neuron, and by using the method presented here, it is possible to simulate neuronal activities more easily than by using the previous methods.Masaaki Takahashi and Kiyohisa NatsumeCopyright © 2009 Masaaki Takahashi and Kiyohisa Natsume. All rights reserved.http://www.hindawi.com/journals/aans/2009/467128/Reservoir computing (RC) is a new framework for neural computation. A reservoir is usually a recurrent neural network with fixed random connections. In this article, we propose an RC model in which the connections in the reservoir are modifiable. Specifically, we consider correlation-based learning (CBL), which modifies the connection weight between a given pair of neurons according to the correlation in their activities. We demonstrate that CBL enables the reservoir to reproduce almost the same spatiotemporal activity patterns in response to an identical input stimulus in the presence of noise. This result suggests that CBL enhances the robustness in the generation of the spatiotemporal activity pattern against noise in input signals. We apply our RC model to trace eyeblink conditioning. The reservoir bridged the gap of an interstimulus interval between the conditioned and unconditioned stimuli, and a readout neuron was able to learn and express the timed conditioned response.Tadashi Yamazaki and Shigeru TanakaCopyright © 2009 Tadashi Yamazaki and Shigeru Tanaka. All rights reserved.http://www.hindawi.com/journals/aans/2009/846040/The present paper proposes a recurrent neural network model and learning algorithm that can acquire the ability to generate desired multiple sequences. The network model is a dynamical system in which the transition function is a contraction mapping, and the learning algorithm is based on the gradient descent method. We show a numerical simulation in which a recurrent neural network obtains a multiple periodic attractor consisting of five Lissajous curves, or a Van der Pol oscillator with twelve different parameters. The present analysis clarifies that the model contains many stable regions as attractors, and multiple time series can be embedded into these regions by using the present learning method.Jun Namikawa and Jun TaniCopyright © 2009 Jun Namikawa and Jun Tani. All rights reserved.