Let us introduce n ( 2) mappings f_i (i=1,2,,n) defined on complete linear metric spaces (X_i-1, ρ) (i=1,2,,n), respectively, and let f_i:X_i-1 X_i be completely continuous on bounded convex closed subsets X_i-1⁽⁰⁾ X_i-1, (i=1,2,,n 0), such that f_i(X_i-1⁽⁰⁾) X_i⁽⁰⁾. Moreover, let us introduce n set-valued mappings F_i : X_i-1 X_i (X_i)(the family of all non-empty closed compact subsets of X_i), (i=1,2,,n 0). Here, we have a fixed point theorem on the successively recurrent system of set-valued mapping equations: x_i F_i(x_i-1, f_i(x_i-1)), (i=1,2,,n 0). This theorem can be applied immediately to analysis of the availability of system of circular networks of channels undergone by uncertain fluctuations and to evaluation of the tolerability of behaviors of those systems. In this paper, mathematical situation and detailed proof are discussed, about this theorem.

There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. In this paper we attempt to evaluate the statistics of chaotic binary sequences of finite length. The large deviation theory for dynamical systems is useful for investigating this problem.

Recently binary or real-valued sequences generated by Chebyshev maps are proposed as spreading sequences in DS/CDMA systems. In this article, we consider sequences of real-valued functions of bounded variation, which include binary functions, of iterates generated by Chebyshev maps, and evaluate explicitly the upper bound of mixing rate of such sequences by defining the modified Perron-Frobenius operator associated with the Chebyshev maps.

We have experimentally observed the dynamics of laser outputs in a microchip laser with frequency-modulated feedback light. We have observed rich dynamics that can be interpreted as three types of dynamics at different frequencies: (1) periodic bursts at twice of the frequency of the modulation of the external mirror, (2) chaotic pulsations at the relaxation oscillation frequency, and (3) clusters at the instantaneous Doppler-shifted frequency. We have confirmed these rich dynamics by using numerical simulations.

A number of schemes have been proposed for communication using chaos over the past years. Regardless of the exact modulation method used, the transmitted signal must go through a physical channel which undesirably introduces distortion to the signal and adds noise to it. The problem is particularly serious when coherent-based demodulation is used because the necessary process of chaos synchronization is difficult to implement in practice. This paper addresses the channel distortion problem and proposes a technique for channel equalization in chaos-based communication systems. The proposed equalization is realized by a modified recurrent neural network (RNN) incorporating a specific training (equalizing) algorithm. Computer simulations are used to demonstrate the performance of the proposed equalizer in chaos-based communication systems. The Henon map and Chua's circuit are used to generate chaotic signals. It is shown that the proposed RNN-based equalizer outperforms conventional equalizers.

In this paper, we focus on an image encryption scheme based on a truncated Baker transformation. The truncated Baker transformation globally preserves the original dynamics of Baker transformation but incorporates a random local rotation operator between two neighbor elements in the mapping domain in order to keep a finite precision. It generates binary sequences (the dynamics of elements) which have statistically good features on ergodicity, mixing and chaotic properties. The image encryption scheme extended from the truncated Baker transformation efficiently shuffles the input gray level image satisfying fundamental conditions on confusion and diffusion required for image encryption schemes. However, this scheme uses many binary sequences and thus needs to keep a large volume of secret keys. In order to solve this problem we introduce Peano space-filling curve in this scheme, which remarkably reduce the key size and mapping iterations without deteriorating good shuffling properties attained by this scheme.

This paper investigates the behavior of one-dimensional discrete-time binary cellular neural networks with both the A- and B-templates and gives the necessary and sufficient conditions for the above network to be stable for unspecified fixed boundaries.

This paper gives a new sufficient condition for cellular neural networks with delay (DCNNs) to be completely stable. The result is a generalization of two existing stability conditions for DCNNs, and also contains a complete stability condition for standard CNNs as a special case. Our new sufficient condition does not require the uniqueness of equilibrium point of DCNNs and is independent of the length of delay.

Cellular Neural Networks (CNNs) have been developed as a high-speed parallel signal-processing platform. In this paper, a generalized two-layer cellular neural network model is proposed for image processing, in which two templates are introduced between the two layers. We found from the simulations that the two-layer CNNs efficiently behave compared to the single-layer CNNs for the many applications of image processing. For examples, simulation problems such as linearly non-separable task--logic XOR, center point detection and object separation, etc. can be efficiently solved with the two-layer CNNs. The stability problems of the two-layer CNNs with symmetric and/or special coupling templates are also discussed based on the Lyapunov function technique. Its equilibrium points are found from the trajectories in a phase plane, whose results agree with those from simulations.

This paper presents an efficient graph-based evolutionary optimization technique called Evolutionary Graph Generation (EGG) and its extension to a parallel version. A new version of parallel EGG system is based on a coarse-grained model of parallel processing and can synthesize heterogeneous networks of various different components efficiently. The potential capability of parallel EGG system is demonstrated through the design of current-mode logic circuits.

We have demonstrated synchronization of chaos in a pair of one-way coupled Colpitts oscillators by both experiment and numerical simulation. We have investigated parameter regions for achieving chaos-synchronization when one of the internal parameters is mismatched between the master and slave oscillators, and clarify the tolerance of parameter regions for synchronization against parameter mismatching.

In this paper we treat a novel adaptation strength according to neighborhood ranking of self-organizing neural networks with the objective of avoiding the initial dependency of reference vectors, which is related to the strength in the neural-gas network suggested by Martinetz et al. The present approach exhibits the effectiveness in the average distortion compared to the conventional technique through numerical experiments. Furthermore the present approach is applied to image data and the validity in employing as an image coding system is examined.

In this work we study the performance of a distributed GA that incorporates in its core parallel cooperative-competitive genetic operators. A series of controlled experiments are conducted using various large and difficult 0/1 multiple knapsack problems to test the robustness of the distributed GA. Simulation results verify that the proposed distributed GA compared with a canonical distributed GA significantly gains in search speed and convergence reliability with less communication cost for migration.

Feature subset selection is an important preprocessing task for pattern recognition, machine learning or data mining applications. A Genetic Algorithm (GA) with a fuzzy fitness function has been proposed here for finding out the optimal subset of features from a large set of features. Genetic algorithms are robust but time consuming, specially GA with neural classifiers takes a long time for reasonable solution. To reduce the time, a fuzzy measure for evaluation of the quality of a feature subset is used here as the fitness function instead of classifier error rate. The computationally light fuzzy fitness function lowers the computation time of the traditional GA based algorithm with classifier accuracy as the fitness function. Simulation over two data sets shows that the proposed algorithm is efficient for selection of near optimal solution in practical problems specially in case of large feature set problems.

The Belousov-Zhabotinsky (BZ) reaction provides us important clues in controlling 2D phase-lagged stable synchronous patterns in an excitable medium. Because of the difficulty in computing reaction-diffusion systems in large systems using conventional digital processors, we here propose a cellular-automaton (CA) circuit that emulates the BZ reaction. In the circuit, a two-dimensional array of parallel processing cells is responsible for fast emulation, and its operation rate is independent of the system size. The operations of the proposed CA circuit were demonstrated by using a simulation program with integrated circuit emphasis (SPICE).

Uniform color spaces are very important in color engineering, image source coding and multimedia information processing. In spite of many efforts have been paid on the subject, however, construction of an exact uniform color space seems difficult until now. Existing approaches mainly used local and heuristic approximations. Moreover, there seemed also certain confusion in definitions of the uniform spaces. In this paper we discuss the issue from a point of view of global Riemannian geometry. The equivalence between global and local definitions of uniform space are shown. Then both an exact and a simplified algorithm are presented to uniformize either a part or the totality of a color space. These algorithms can be expected to find applications in optimal quantization of color information.

The paper deals with the estimation method of system equations of dynamic behavior of an input-pricing mechanism by using the Genetic Programming (GP) and its applications. The scheme is similar to recent noise reduction method in noisy speech which is based on the adaptive digital signal processing for system identification and subtraction estimated noise. We consider the dynamic behavior of an input-pricing mechanism for a service facility in which heterogeneous self-optimizing customers base their future join/balk decisions on their previous experiences of congestion. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The string used for the GP is extended to treat the rational form of system functions. The condition for the Li-Yorke chaos is exploited to ensure the chaoticity of the approximated functions. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted (x(t))), then we impose the input u(t) so that x_f= (t+1)=(x(t))+u(t) where x_f is the fixed point. Then, the next state x(t+1) of targeted dynamic system f(x(t)) is replaced by x(t+1)+u(t). We extend ordinary control method based on the GP by imposing the input u(t) so that the deviation from the targeted level x_L becomes small enough after the control. The approximation and control method are applied to the chaotic dynamics generating various time series based on several queuing models and real world data. Using the GP, the control of chaos is straightforward, and we show some example of stabilizing the price expectation in the service queue.

A new blind restoration method applying Real-coded genetic algorithm (RcGA) will be proposed, and this method will be proven valid for the blurred image restoration with unidentified degradation in the experiments. In this restoration method, the degraded and blurred image is going to get restricted to the images possible to be expressed in the point spread function (PSF), then the restoration filter for this degraded image, which is also the 2-dimentional inverse filter, will be searched among several points applying RcGA. The method will enable to seek efficiently among vast solution space consists of numeral coefficient filters. And perceiving the essential features of the spectrum in the frequency space, an evaluation function will be proposed. Also, it will be proposed to apply the Rolling-ball transform succeeding an appropriate Gaussian degrade function against the dual degraded image with blur convoluting impulse noise. By above stated features of this restoration method, it will enable to restore the degraded image closer to the original within a practical processing time. Computer simulations verify this method for image restoration problem when the factors causing image distortions are not identified.

The cooperative and competitive network suitable for circuit realization is presented, based on the network proposed by Amari and Arbib. To ensure WTA process, the output function of the original network is replaced with the piecewise linear function and supplying the inputs as pulse waveforms is obtained. In the SPICE simulations, it is confirmed that the network constructed by operational amplifiers attains WTA process, even if the scale of the network becomes large.

ZCZ sets are families of sequences, whose periodic auto/cross-correlation functions have zero correlation zone at the both side of the zero-shift. They can provide approximately synchronized CDMA systems without intra-cell interference for cellular mobile communications. This paper presents ternary ZCZ sets achieving a mathematical bound, and investigates the average interference parameters for the sets in order to evaluate inter-cell interference. It is shown that they can provide AS-CDMA systems with efficiency frequency usage.

In previous work we have proposed a steganographic technique for gray scale images called BPCS-Steganography. We also apply this technique to full color images by decomposing the image into its three color component images and treating each as a gray scale image. This paper proposes a method to apply BPCS-Steganography to palette-based images. In palette-based images, the image data can be decomposed into color component images similar to those of full color images. We can then embed into one or more of the color component images. However, even if only one of the color component images is used for embedding, the number of colors in the palette after embedding can be over the maximum number allowed. In order to represent the image data in palette-based format, color quantization is therefore needed. We cannot change the pixel values of the color component image that contains the embedded information, but can only change the pixel values of the other color component images. We assume that the degrading of the color component2 image with information embedded is smaller than that of the color component images that are used for color reduction. We therefore embed secret information into the G component image, because the human visual system is more sensitive to changes the luminance of a color, and G has the largest contribution to luminance of the three color components. In order to reduce the number of colors, the R and B component images are then changed in a way that minimizes the square error.

In this paper we present the analog architecture and the implementation of an on-chip learning Multi Layer Perceptron network. The learning algorithm is based on Back Propagation but it exhibits increased capabilities due to local learning rate management. A prototype chip (SLANP, Self-Learning Neural Processor) has been designed and fabricated in a CMOS 0.7 µm minimum channel length technology. We report the experimental results that confirm the functionality of the chip and the soundness of the approach. The SLANP performance compare favourably with those reported in the literature.

In loudspeaker-based 3D audio systems, there are some acoustic crosstalk cancellation methods to enlarge the 'sweet spot' around a fixed listener position. However, these methods have common defect that most of them can be applied only to the specific narrow frequency band. In this letter, we propose the more robust acoustic crosstalk cancellation method so that we can cancel the crosstalk signal in far wider frequency band and enlarge 'sweet spot. ' For this goal, we apply a sum and difference filter to the conventional three loudspeaker-based 3D audio system.

In this paper, for real-time automatic image transform based lip-reading under illumination variations, an efficient (smaller feature data size) and robust (better recognition under different lighting conditions) method is proposed. Image transform based approach obtains a compressed representation of image pixel values of speaker's mouth and is reported to show superior lip-reading performance. However, this approach inevitably produces large feature vectors relevant to lip information to require much computation time for lip-reading even when principal component analysis (PCA) is applied. To reduce the necessary dimension of feature vectors, the proposed method folded the lip image based on its symmetry in a frame image. This method also compensates the unbalanced illumination between the left and the right lip areas. Additionally, to filter out the inter-frame time-domain spectral distortion of each pixel contaminated by illumination noise, our method adapted the hi-pass filtering on the variations of pixel values between consecutive frames. In the experimental results performed on database recorded at various lighting conditions, the proposed lip-folding or/and inter-frame filtering reduced much the necessary number of feature data, principal components in this work, and showed superior recognition rate compared to the conventional method.

This paper addresses a high-order sliding mode control strategy for output tracking of nonholonomic mobile robots. First, we introduce the dynamic model of robots, driving motors and nonslipping kinematics constraint conditions. Second, we decompose the system into linear and nonlinear components via diffeomorphism and nonlinear input transformation. Also we consider parameter variations of robots and deduce the uncertain model of robots. Third, we design a high order sliding mode controller for output tracking of known and uncertain systems, respectively. Finally, we perform numerical simulations, demonstrating that the proposed high-order sliding mode control not only reduces the chattering problem of sliding mode systems, but also has certain robustness properties with respect to uncertainties of robots.

In this paper we analyze an asymptotic stability of nonlinear singularly perturbed systems and propose a composite control with gain scheduling where the fast controller is the gain scheduled controller and the slow state plays a role of slowly varying parameters in gain scheduling. Specifically, the slow controller is designed by the slow manifold to stabilize the reduced slow system. As a result, the slow manifold of the system is the same as the designed manifold.

A novel method for the primitive description of the multiprimitive texture is proposed. This method segments a texture by the watershed algorithm into fragments each of which contains one grain. The similar fragments are grouped by the cluster analysis in the feature space whose basis is the morphological size density. Each primitive is extracted as the grain of the central fragment in each cluster.

Fuzzy value is a fuzzy set on interval [0,1], whose α-cuts are all closed intervals for α [0,1], i.e., fuzzy value is a fuzzy number on [0,1]. In this note, we introduce three kinds of metrics d_i (i=1,2,3) into fuzzy-valued space m[0,1] and consider continuity of fuzzy-valued operations on metric spaces (m[0,1], d_i) (i=1,2,3). The obtained results will provide some theoretical bases for numeral calculation of fuzzy-valued operations.