The author once defined the Ω-matrix and showed that it played an important role for estimating the number of solutions of a resistive circuit containing active elements such as CCCS's. The Ω-matlix is a generalization of the wellknown P-matrix. This paper gives the necessary and sufficient conditions for the Ω-matrix.

In this paper, we propose a novel SPICE oriented steady-state analysis of nonlinear circuits based on the circuit partition technique. Namely, a given circuit is partitioned into the linear and nonlinear subnetworks by the application of the substitution theorem. Each subnetwork is solved using SPICE simulator by the different techniques of AC analysis and transient analysis, respectively, whose steady-state reponse is found by an iteration method. The novel points of our algorithm are as follows: Once the linear subnetworks are solved by AC analysis, each subnetwork is replaced by a simple equivalent RL or RC circuit at each frequency component. On the other hand, the reponse of nonlinear subnetworks are solved by transient analysis. If we assume that the sensitivity circuit is approximated at the DC operational point, the variational value will be also calculated from a simple RL ro RC circuit. Thus, our method is very simple and can be also applied to large scale circuits, effciently. To improve the convergency, we introduce a compensation technique which is usefully applied to stiff circuits containing components such as diodes and transistors.

This paper describes a waveform relaxationbased coupled lossy transmission line circuit simulator DESIRE3T+. First, the generalized method of characteristics (GMC) is reviewed, which replaces a lossy transmission line with an equivalent disjoint network. Next, the generalized line delay window (GLDW) partitioning technique is proposed, which accelerates the transient analysis of the circuits including transmission lines replaced by GMC model. Finally GMC model and GLDW technique are implemented in hte relaxation-based circuit simulator DESIRE3T+ which can analyze bipolar transistor circuits by using the dynamic decomposition technique, and the performance is estimated.

Bifurcation Phenomena observed in a circuit containing two Josephson junctions coupled by a resistor are investigated. This circuit model has a mechanical analogue: Two damped pendula linked by a clutch exchanging kinetic energy of each pendulum. In this paper, firstly we study equilibria of the system. Bifurcations and topological properties of the equilibria are clarified. Secondly we analyze periodic solutions in the system by using suitable Poincare mapping and obtain a bifurcation diagram. There are two types of limit cycles distinguished by whether the motion is in S¹R³ or T²R², since at most two cyclic coordinates are included in the state space. There ia a typical structure of tangent bifurcation for 2-periodic solutions with a cusp point. We found chaotic orbits via the period-doubling cascade, and a long-period stepwise orbit.

In this study, we investigate two oscillators which have the same natural frequency, mutually coupled by N-type piecewise-linear negative resistor. In this system, according to the negative range of the coupling negative resistor, the various inter-esting synchronization phenomena which are in-phase, opposite phase and doublemode-like oscillations are observed. Especially, we show doublemode-like oscillations that are not observed until now in mutually coupled van der Pol oscillators with the smooth cubic characteristics, although the ones with same natural frequencies are coupled. And we show the differences of the phenomena between two oscillators coupled by the smooth cubic negative resistor and the ones coupled by the piecewise-linear negative resistor.

We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.

We consider a ring of n Rayleigh oscillators coupled hybridly. Using the symmetrical property of the system we demonstrate the degeneracy of the Hopf bifurcation of the equilibrium at the origin. The degeneracy implies the exstence and stability of the n-phase oscillation. We discuss some consequences of the perturbation of the symmetry. Then we study the case n = 3. We show the bifurcation diagram of the equilibria and of hte periodic solutions. Especially, we analyze the mechanism for the symmetry breaking bifurcation of the fully symmetric solution. We report and explain the occurrence of both chaotic attractors and repellors and show two types of symmetry recovering crisis they undergo.

In this study, some oscillators with different oscillation frequencies, N - 1 oscillators have the same oscillation frequency and only the Nth oscillator has different frequency, coupled by a resistor are investigated. At first we consider nonresonance. By carrying out circuit experiments and computer calculations, we observe that oscillation of the Nth oscillator stops in some range of the frequency ratio and that others are synchronized as if the Nth oscillator does not exist. These phenomena are also analyzed theoretically by using the averaging method. Secondly, we investigate the resonance region where the fiequency ratio is nearly equal to 1. For this region we can observe interesting double-mode oscillation, that is, synchronization of envelopes of the double-mode oscillation and change of oscillation amplitude of the Nth oscillator.

Synchronization and chaos of the oscillator circuit that is composed of two Duffing-Rayleigh oscillators coupled by resistor are investigated. The characteristic feature of this system is that the cubic nonlinear restoring force of each oscillator. The restoring force causes the Neimark-Sacker bifurcation with various synchronizations in the parameter plane. We clarify the bifurcation structure related with this nonlinear phenomenon, and study the chaotic state and its bifurcation process. Especially, we deals with the case that the symmetrical property is broken by changing system parameters.

A mathematical model based on an optimization formulation is presented for perceptual clustering of dot patterns. The features in the present model are its nonlinearity enabling the model to reveal hysteresis phenomena and its scale invariance. The clustering of dots is given by the mutual linking of dots by virtual lines. Every dot is assumed to be perceived at locations displaced from their original places. It is exemplified with simulations that the model can produce a hierarchical clustering of dots by variation in thresholds for the wiring of virtual lines and also the model can additionally reproduce some geometrical illusions semiquantitatively. This model is further extended for perceptual grouping in line segment patterns and geometrical illusions obsrved in those patterns are reproduced by the extended model.

In this paper, Chay's bursting pancreatic β-cell model is updated to include a role for [Ca²⁺]_ER, the luminal calcium concentration in the endoplasmic reticulum (ER). The model contains a calcium current which is activated by voltage and inactivated by [Ca²⁺]_i. It also contains a cationic nonselective current (I_NS) that is activated by depletion of luminal Ca²⁺ in the ER. In this model, [Ca²⁺]_ER oscillates slowly, and this slow dynamic drives electrical bursting and the [Ca²⁺]_i oscillations. This model is capable of providing answers to some puzzling phenomena,which the previous models could not (e. g., why do single pancreatic β-cells burst with a low frequency while the cells in an islet burst with a much higher frequency ?). Verification of the model prediction that [Ca²⁺]_ER is a primary oscillator that drives electrical bursting and [Ca²⁺]_i oscillations in pancreatic β-cells awaits experimental testing. Experiments using fluorescent dyes such as mag-fura-2-AM could provide relevant information.

Conventional learning algorithms are considered to be a sort of estimation of the true recognition function from sample patterns. Such an estimation requires a good assumption on a prior distribution underlying behind learning data. On the other hand the human being sounds to be able to acquire a better result from an extremely small number of samples. This forces us to think that the human being might use a suitable prior (called presupposition here), which is an essential key to make recognition machines highly flexible. In the present paper we propose a framework for guessing the learner's presupposition used in his learning process based on his learning result. First it is pointed out that such a guess requires to assume what kind of estimation method the learner uses and that the problem of guessing the presupposition becomes in general ill-defined. With these in mind, the framework is given under the assumption that the learner utilizes the Bayesian estimation method, and a method how to determine the presupposition is demonstrated under two examples of constraints to both of a family of presuppositions and a set of recognition functions. Finally a simple example of learning with a presupposition is demonstrated to show that the guessed presupposition guarantees a better fitting to the samples and prevents a learning machine from falling into over learning.

Deterministic nonlinear prediction is applied to both artificial and real time series data in order to investigate orbital-instabilities, short-term predictabilities and long-term unpredictabilities, which are important characteristics of deterministic chaos. As an example of artificial data, bimodal maps of chaotic neuron models are approximated by radial basis function networks, and the approximation abilities are evaluated by applying deterministic nonlinear prediction, estimating Lyapunov exponents and reconstructing bifurcation diagrams of chaotic neuron models. The functional approximation is also applied to squid giant axon response as an example of real data. Two metnods, the standard and smoothing interpolation, are adopted to construct radial basis function networks; while the former is the conventional method that reproduces data points strictly, the latter considers both faithfulness and smoothness of interpolation which is suitable under existence of noise. In order to take a balance between faithfulness and smoothness of interpolation, cross validation is applied to obtain an optimal one. As a result, it is confirmed that by the smoothing interpolation prediction performances are very high and estimated Lyapunov exponents are very similar to actual ones, even though in the case of periodic responses. Moreover, it is confirmed that reconstructed bifurcation diagrams are very similar to the original ones.

The capability of generalization is the most desirable property of a learning system. It is well known that to achieve good generalization, the complexity of the system should match the intrinsic complexity of the problem to be learned. In this work, introduction of fractal connection structure in nonlinear learning systems like multilayer perceptrons as a means of improving its generalization capability in classification problems has been investigated via simulation on sonar data set in underwater target classification problem. It has been found that fractally connected net has better generalization capability compared to the fully connected net and a randomly connected net of same average connectivity for proper choice of fractal dimension which controlls the average connectivity of the net.

This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.

We propose a novel segmentation algorithm which combines an image segmentation method into small regions with chaotic neurodynamics that has already been clarified to be effective for solving some combinatorial optimization problems. The basic algorithm of an image segmentation is the variable-shape-bloch-segmentation (VB) which searches an opti-mal state of the segmentation by moving the vertices of quadran-gular regions. However, since the algorithm for moving vertices is based upon steepest descent dynamics, this segmentation method has a local minimum problem that the algorithm gets stuck at undesirable local minima. In order to treat such a problem of the VB and improve its performance, we introduce chaotic neurodynamics for optimization. The results of our novel method are compared with those of conventional stochastic dynamics for escaping from undesirable local minima. As a result, the better results are obtained with the chaotic neurodynamical image segmentation.

Gray scale images are represented by recurrent neural subnetworks which together with a competition layer create an associative memory. The single recurrent subnetwork N_i implements a stochastic nonlinear fractal operator F_i, constructed for the given image f_i. We show that under realstic assumptions F has a unique attractor which is located in the vicinity of the original image. Therefore one subnetwork represents one original image. The associative recall is implemented in two stages. Firstly, the competition layer finds the most invariant subnetwork for the given input noisy image g. Next, the selected recurrent subnetwork in few (5-10) global iterations produces high quality approximation of the original image. The degree of invariance for the subnetwork N_i on the inprt g is measured by a norm ||g-F_i(g)||. We have experimentally verified that associative recall for images of natural scenes with pixel values in [0, 255] is successful even when Gaussian noise has the standard deviation σ as large as 500. Moreover, the norm, computed only on 10% of pixels chosen randomly from images still successfuly recalls a close approximation of original image. Comparing to Amari-Hopfield associative memory, our solution has no spurious states, is less sensitive to noise, and its network complexity is significantly lower. However, for each new stored image a new subnetwork must be added.

In this paper, after the introduction of the definition of State Controlled Cellular Neural Networks (SC-CNNs), it is shown that they are able to generate complex dynamics of circuits showing strange behaviour. Theoretical propoitions are presented to fix the templates of the SC-CNNs in such a way as to exactly match the dynamic behaviour of the circuits considered. The easy and cheap implementation of the proposed SC-CNN devices is illustrated and a gallery of experimentally obtained strange attractors are shown to confirm the practical suitability of the outlined strategy.

Various applications of cellular neural network (CNN) are reported such as a feature extraction of the patterns, an extraction of the edges or corners of a figure, noise exclusion, searching in maze and so forth. In this paper, we propose a cellular neural network whose each cell has more than two output levels. By using the output function which has several saturated levels, each cell turns to have several output states. The multiple-valued CNN enhances its associative memory function so as to express various kinds of aspects. We report an application of the enhanced asscociative memory function to a diagnosis of the liver troubles.

Correspondence problem in road image sequence is discussed and a method to establish road correspondence from its perspective image sequence is suggested. The proposed method is mainly based on the features of turn angles of road edge points, while the turn angle for each edge point at one time can be computed from the frame based on the determination of matching points whin that frame. The turn angles will change from frame to frame according to the panning rotation of the camera and, each stationary edge point, the difference of turn angles between two frames equals the panning angle of the camera. Thus we develop an algorithm to estimate the value of panning angle of the camera by which correspondence in road image sequence can be established.

A method is presented for detecting impulsive noises in chaotic time series, based on a new nonlinear prediction algorithm. A multi-dimensional trajectory is reconstructed from a time series using delay coordinates. The future value of a point on the trajectory is predicted using a local approximation technique revised by adding the Biweight estimation method and then the prediction error is calculated. Impulsive noises are detected by examining the prediction errors for all points on the trajectory. The proposed method is applied to the time series of the pupil area and the refractive power of the lens in the human eye. The Lyapunov exponent analysis for thses time series is conducted. As a result, it is shown that the proposed method is effective in detecting impulsive noises caused by blinking in these time series.

This paper introduces signal-controlled time-series modeling based on arbitrarily chosen buliding blocks. Such modeling is used in the design of a nested-form transver-sal structure based on Almost-Symmetrical ARMA (AS-ARMA) building blocks. This structure can operate in the transient mode, in contrast to the commonly used linear line-enhancers based on an conventional ARMA, leading to practically sound processing of short-duration signals. It is shown that the proposed time-series modeling can be effectively applied towards the separation of superimposed signals of heavily overlapping spectra.

In the paper a new type of Multilayer Perceptron, developed in Quaternion Algebra, is adopted to realize short-time prediction of chaotic time series. The new introduced neural structure, based on MLP and developed in the hypercomplex quaternion algebra (HMLP) allows accurate results with a decreased network complexity with respect to the real MLP. The short term prediction of various chaotic circuits and systems has been performed, with particular emphasys to the Chua's circuit, the Saito's circuit with hyperchaotic behaviour and the Lorenz system. The accuracy of the prediction is evaluated through a correlation index between the actual predicted terms of the time series. A comparison of the performance obtained with both the real MLP and the hypercomplex one is also reported.

Chaos shift keying (CSK) is a modulation method in digital communication systems using chaotically modulated signals. This paper proposes novel CSK which utilizes two types of chaotic synchronization called in-phase and anti-phase chaotic synchronization. In this method, binary signals are mapped into two phases of chaotic synchronization, and a transmitter generates a two-phase-shift-keyed chaotic signal. So it will be called chaotic phase shift keying (CPSK) in this paper. This method is simpler than that based on two pairs of different chaotic systems. We also discuss an effect of noise in transmission lines.

Electronic systems are progressively replacing mechanical devices or human operation for identifying people or objects in everyday-life applications. Especially, the contactless identification systems available today have several advantages, but they cannot handle easily several simultaneously present items. This paper describes a solution to this problem, based on blind source separation techniques. The effectiveness of this approach is experimentally demonstrated, especially by using a real-time DSP-based implementation of the proposed system.

In this paper, an extention for Haddad's method, which is the time-domain stability analysis on scalar nonlinear control systems, to multi-variable nonlinear control systems are proposed, and it is shown that these results are useful for the stability analysis of nonlinear control systems with various types of fuzzy controllers.

The dipole-dipole interaction in the quantum mechanical treatment of the matter-radiation dynamics, is shown to give rise to split energy levels reminiscent of the nonlinear coupled spectral features as well as a self-sustained coherent modes. Wiener's theory of nonlinear random processes is applied to the second harmonic generation (SHG), leading also to coupled spectral pulling and dipping features, due to the dual noise sources in the fundamental and the harmonic polarizations. Furthermore, the nonlinear spectral features are suggested to be applied to implement quantum (qubit) gates for computation.

We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.

In this paper, we propose a modified Hamming network which contains less connection numbers and faster convergence speed. Besides, the real weight of subnet can also be transformed into integer weight. As so it is suitable for the hardware implementation of VLSI.

A new type of noncausal stochastic model is proposed to represent a random image with double peak spectrum. The model based on the assumption that the double peak spectrum is expressed by a product of two spectra located at two symmetric positions in the 2D spatial frequency space. Estimation of model parameters is made by means of minimizing the "whiteness" which was proposed in authors' previous work. In a simulation for model estimation we make use of computer-generated random images with double peak spectrum. Comparing this with the estimation by a causal model, we demonstrate that the present method can better estimate not only the spectral peak location but also the spectral shape. The proposed model can be extend to an image model with multl-peak spectrum. However, Increase of parameters makes the model estimation more difficult We try a model with triple peak spectra since a real texture image usually possesses a spectral peak at the origin besides the two peaks. A result shows that the estimation of three spectral positions are good enough, but their spectral shapes are not necessarily satisfactory. It is expected that the estimation of multi-peaked spectral model can be made better by improving the process of minimizing the "whiteness."

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits The algorithm is based on the idea of "contraction" of the solution domain using a sign test. The proposed algorithm is efficient because many large super-regions containing no solution are eliminated in early steps.

It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2f^m). An [m(2^em - 1), em, 2^em-1m] code, a [3(2^2e - 1), 2e, 3・2^2e-1] code, a [2(2^2e - 1), 2, (2^2e+2 - 4)/3] code, a [3(2^2e - 1), 2, 2^2e+1 - 2] code, and a [3(2^2e - 1), 2(e+1), 3・2^2e-1 - 2] code are optimal and a [2(2^2e - 1), 2(e + 1), 2^2e - 2] code is quasi-optimal.

From a GF(q) sequence {a_i}_i0 with period qⁿ - 1 we can obtain new periodic sequences {a_i}_i0 with period qⁿ by inserting one symbol b GF(q) at the end of each period. Let b₀ = Σqⁿ-2 i=0 a_i. It Is first shown that the linear complexity of {a_i}_i0, denoted as LC({a_i}) satisfies LC({a_i}) = qⁿ if b -b₀ and LC({a_i}) qⁿ - 1 if b = -b₀ Most of known sequences are shown to satisfy the zero sum property, i.e., b₀ = 0. For such sequences satisfying b₀ = 0 it is shown that qⁿ - LC({a_i}) LC({a_i}) qⁿ - 1 if b = 0.

In this article, a new analogic CNN algorithm to extract features of postage stamps in gray-scale images Is introduced. The Gradient Controlled Diffusion method plays an important role in the approach. In our algorithm, it is used for smoothing and separating Arabic figures drawn with a color which is similar to the background color. We extract Arabic figures in postage stamps by combining Gradient Controlled Diffusion with nearest neighbor linear CNN template and logic operations. Applying the feature extraction algorithm to different test images it has been verified that it is also effective in complex segmentation problems