In this paper, we shall construct mathematical theory based on the concept of set-valued mappings, suitable for available operation of network systems extraordinarily complicated and diversified on large scales. Fundamental conditions for availability of system behaviors of such network systems are clarified in a form of fixed point theorem for system of set-valued mappings.

This short paper is a written version of one part of the plenary address given at the November 1999 NOLTA symposium held at the Hilton Waikoloa Village in Hawaii. I was invited by Professor Shin'ichi Oishi, a general vice-chairman of the symposium, to give a survey of some of my own research. I was happy to do that--in the context of a description of what Bell Labs.' research environment was like in its math center in the 1960's, and why I feel that today's young researchers are often too constrained in that they are typically not encouraged to try to do really interesting work. Here the emphasis is on only the origins of input-output stability theory.

In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.

In this paper, in order to control uncertain chaotic system, an adaptive fuzzy control (AFC) scheme is developed for the multi-input/multi-output plants represented by the Takagi-Sugeno (T-S) fuzzy models. The proposed AFC scheme provides robust tracking of a desired signal for the T-S fuzzy systems with uncertain parameters. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the chaotic state tracks the state of the stable reference model (SRM) asymptotically with time for any bounded reference input signal. The suggested AFC design technique is applied to control of a uncertain Lorenz system based on T-S fuzzy model such as stabilization, synchronization and chaotic model following control (CMFC).

This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. 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. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. 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). The control method is applied to the approximation and control of chaotic dynamics generating various time series and even noisy time series by using one dimensional and higher dimensional system. As a result, if the noise level is relatively large, the method of the paper provides better control compared to conventional OGY method.

This paper deals with the approximation of multi-dimensional chaotic dynamics by using the multi-stage fuzzy inference system. The number of rules included in multi-stage fuzzy inference systems is remarkably smaller compared to conventional fuzzy inference systems where the number of rules are proportional to an exponential of the number of input variables. We also propose a method to optimize the shape of membership function and the appropriate selection of input variables based upon the genetic algorithm (GA). The method is applied to the approximation of typical multi-dimensional chaotic dynamics. By dividing the inference system into multiple stages, the total number of rules is sufficiently depressed compared to the single stage system. In each stage of inference only a portion of input variables are used as the input, and output of the stage is treated as an input to the next stage. To give better performance, the shape of the membership function of the inference rules is optimized by using the GA. Each individual corresponds to an inference system, and its fitness is defined by using the prediction error. Experimental results lead us to a relevant selection of the number of input variables and the number of stages by considering the computational cost and the requirement. Besides the GA in the optimization of membership function, we use the GA to determine the input variables and the number of input. The selection of input variable to each stage, and the number of stages are also discussed. The simulation study for multi-dimensional chaotic dynamics shows that the inference system gives better prediction compared to the prediction by the neural network.

The main objective of this work is to provide a deep understanding of the periodic behaviour corresponding to a homoclinic related to the Takens-Bogdanov (double-zero eigenvalue of the linearization matrix) and the periodic behaviour of the torus bifurcation related to the Hopf-Pitchfork bifurcation (a pair of imaginary eigenvalues and the third one zero) corresponding to some sections of a triple-zero eigenvalue bifurcation in the Chua's equation with a cubic nonlinearity.

Currently the long memory behavior is associated to stochastic processes. It can be modeled by different models such like the FARIMA processes, the k-factors GARMA processes or the fractal Brownian motion. On the other side, chaotic systems characterized by sensitivity to initial conditions and existence of an attractor are generally assumed to be close in their behavior to random white noise. Here we show why we can adjust a long memory process to well known chaotic systems defined in dimension one or in higher dimension. Using this new approach permits to characterize in another way the invariant measures associated to chaotic systems and to propose a way to make long term predictions: two properties which find applications in a lot of applied fields.

A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the heavy-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

We have experimentally observed chaotic oscillation of outputs in a diode-pumped Nd:YAG microchip laser array with an external Talbot mirror. The oscillation of chaotic output is observed at frequencies of sub MHz corresponding to the relaxation oscillation frequencies when the Talbot mirror is slightly tilted from the perfect alignment position with the internal cavity. Chaotic intermittent bursts also appear at frequencies of sub kHz due to longitudinal mode hopping. Synchronization of chaos is observed at these two different time scales. The generation of chaotic oscillations at sub MHz is confirmed by using numerical simulations. It is found that synchronized chaotic oscillations can be observed in the vicinity of the boundary of the injection locking range.

We propose hysteresis neural network solving combinatorial optimization problems, Box Puzzling Problem. Hysteresis neural network searches solutions of the problem with nonlinear dynamics. The output vector becomes stable only when it corresponds with a solution. This system does never become stable without satisfying constraints of the problem. After estimating hardware calculating time, we obtain that numerical calculating time increases extremely comparing with hardware time as problem's scale increases. However the system has possibility of limit cycle. Though it is very hard to remove limit cycle completely, we propose some methods to remove this phenomenon.

Feature subset selection basically depends on the design of a criterion function to measure the effectiveness of a particular feature or a feature subset and the selection of a search strategy to find out the best feature subset. Lots of techniques have been developed so far which are mainly categorized into classifier independent filter approaches and classifier dependant wrapper approaches. Wrapper approaches produce good results but are computationally unattractive specially when nonlinear neural classifiers with complex learning algorithms are used. The present work proposes a hybrid two step approach for finding out the best feature subset from a large feature set in which a fuzzy set theoretic measure for assessing the goodness of a feature is used in conjunction with a multilayer perceptron (MLP) or fractal neural network (FNN) classifier to take advantage of both the approaches. Though the process does not guarantee absolute optimality, the selected feature subset produces near optimal results for practical purposes. The process is less time consuming and computationally light compared to any neural network classifier based sequential feature subset selection technique. The proposed algorithm has been simulated with two different data sets to justify its effectiveness.

This paper describes the implementation of a proposed image filter into a Discrete-Time Cellular Neural Network (DT-CNN). The three stages that compose the filter are described, showing that the resultant filter is capable of (1) erasing or detecting several concentric shapes simultaneously, (2) thresholding and (3) thinning of gray-scale images. Because the DT-CNN has to fill certain conditions for this filter to be implemented, it becomes a modified version of a DT-CNN. Those conditions are described and also experimental results are clearly shown.

A high quality speech synthesis technique based on the wavelet subband analysis of speech signals was newly devised for enhancing the naturalness of synthesized voiced consonant speech. The technique reproduces a speech characteristic of voiced consonant speech that shows unvoiced feature remarkably in the high frequency subbands. For mixing appropriately the unvoiced feature into voiced speech, a noise inclusion procedure that employed the discrete wavelet transform was proposed. This paper also describes a developed speech synthesizer that employs several random fractal techniques. These techniques were employed for enhancing especially the naturalness of synthesized purely voiced speech. Three types of fluctuations, (1) pitch period fluctuation, (2) amplitude fluctuation, and (3) waveform fluctuation were treated in the speech synthesizer. In addition, instead of a normal impulse train, a triangular pulse was used as a simple model for the glottal excitation pulse. For the compensation for the degraded frequency characteristic of the triangular pulse that overdecreases than the spectral -6 dB/oct characteristic required for the glottal excitation pulse, the random fractal interpolation technique was applied. In order to evaluate the developed speech synthesis system, psychoacoustic experiments were carried out. The experiments especially focused on how the mixed excitation scheme effectively contributed to enhancing the naturalness of voiced consonant speech. In spite that the proposed techniques were just a little modification for enhancing the conventional LPC (linear predictive coding) speech synthesizer, the subjective evaluation suggested that the system could effectively gain the naturalness of the synthesized speech that tended to degrade in the conventional LPC speech synthesis scheme.

This paper is concerned with the controller synthesis for feedback systems with saturation based on the LPV system representation. The LPV system representation, combined with use of the detailed structure of saturation nonlinearity, enables us to reduce the conservativeness. In this paper, we develop a new iterative algorithm for designing a linear time-invariant controller which locally stabilizes the nonlinear closed-loop system and achieves the prescribed quadratic control performance. The present design method provides an explicit expression for a guaranteed domain of attraction, and maximizes the estimated region of the plant states for which the stability and the prescribed quadratic performance are satisfied. A numerical example shows the effectiveness of the present design method.

We consider a network consisting of phase locked loops coupled one another through frequency dividers. When the network structure is rotationally symmetric, spatially periodic simple patterns in terms of the phase of the PLLs are formed. The patterns determine the lock-in frequency of the network. The stability of the pattern is determined by the spatially distributed simple coupling weight patterns. Therefore, a signal with which the network synchronizes is indirectly selected by the weight patterns when several signals are simultaneously applied to the network. The selectivity plays an important role in an intelligent network model.

We show some results concerning the number of solutions of the equation y+Ax=b (y^Tx=0, y0, x0) which plays a central role in the dc analysis of transistor circuits. In particular, we give sufficient conditions for the equation to possess exactly 2^l (ln) solutions, where n is the dimension of the vector x.

In this paper, we present a numerical method with guaranteed accuracy to solve initial value problems (IVPs) of normal form simultaneous first order ordinary differential equations (ODEs) which have wide domain. Our method is based on the algorithm proposed by Kashiwagi, by which we can obtain inclusions of exact values at several discrete points of the solution curve of ODEs. The method can be regarded as an extension of the Lohner's method. But the algorithm is not efficient for equations which have wide domain, because the error bounds become too wide from a practical point of view. Our purpose is to produce tight bounds even for such equations. We realize it by combining Kashiwagi's algorithm with the mean value form. We also consider the wrapping effects to obtain tighter bounds.

We study a class of nonlinear dynamical systems to develop efficient algorithms. As an efficient algorithm, interior point method based on Newton's method is well-known for solving convex programming problems which include linear, quadratic, semidefinite and l_p-programming problems. On the other hand, the geodesic of information geometry is represented by a continuous Newton's method for minimizing a convex function called divergence. Thus, we discuss a relation between information geometry and convex programming in a related family of continuous Newton's method. In particular, we consider the α-projection problem from a given data onto an information geometric submanifold spanned with power-functions. In general, an information geometric structure can be induced from a standard convex programming problem. In contrast, the correspondence from information geometry to convex programming is slightly complicated. We first present there exists a same structure between the α-projection and semidefinite programming problems. The structure is based on the linearities or autoparallelisms in the function space and the space of matrices, respectively. However, the α-projection problem is not a form of convex programming. Thus, we reformulate it to a l_p-programming and the related ones. For the reformulated problems, we derive self-concordant barrier functions according to the values of α. The existence of a polynomial time algorithm is theoretically confirmed for the problem. Furthermore, we present the coincidence with the gradient vectors for the divergence and a modified barrier function. These results connect a part of nonlinear and algorithm theories by the discreteness of variables.

This paper presents a novel image coding scheme based on separate coding of region and residue sources. In a subband image coding scheme, quantization errors in each subimage spread over the reconstructed image and result in a blurring or a boundary artifact. To obtain high compression ratio without considerable degradation, an input image, in our scheme, is separated into region and residue sources which are coded using different coding schemes. The region source is coded by adaptive arithmetic coder. The residue source is coded using multiresolution subimages generated by applying a subband filter. Each block in the subimages is predicted by an affine transformation of blocks in lower resolution subimages. Experimental results show that a high coding efficiency is achieved using the proposed scheme, especially in terms of the subjective visual quality and PSNR at low bit-rate compression.

This paper presents a multimedia architecture extension design for a 200-MHz, 1.6-GOPS embedded RISC processor. The datapath architecture of the processor which realizes parallel execution of data transfer and SIMD (single instruction stream multiple data stream) parallel arithmetic operations is designed. Four SIMD parallel 16-bit MAC (multiply-accumulation) instructions are introduced with a symmetric rounding scheme which maximizes the accuracy of the 16-bit accumulation. This parallel 16-bit MAC on a 64-bit datapath is shown to be efficiently utilized for DSP applications such as the correlation and the matrix-vector multiplications in the multimedia RISC processor. By using the parallel MAC instruction with the symmetric rounding scheme, a 2D-IDCT which satisfies the IEEE1180 can be implemented in 202 cycles.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear continuous-time stochastic systems. To be able to treat the stochastic signal estimation problem, a performance criterion, extended from the criterion in the H filtering problem by introducing the stochastic expectation, is newly introduced in this paper. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in the Krein spaces is obtained as a result. For γ²<, the estimation accuracies of the fixed-point smoother and the filter are superior to the recursive least-squares (RLS) Wiener estimators previously designed in the transient estimation state. Here, γ represents a parameter in the proposed criterion. This paper also presents the fixed-point smoother and the filter using the state-space parameters from the devised estimators using the covariance information.

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of an upper bound on the worst-case infinite horizon cost function at each time instant. It is shown that the mean square stability of the proposed control system is guaranteed under some matrix inequality conditions on the terminal weighting matrices. The proposed controller is obtained using semidefinite programming.

A general tracking control problem for mobile robots is proposed and solved using the backstepping technique. A global result is given for the kinematic steering system to make the tracking error approaching to zero asymptotically. Based on our efforts, the proposed controller can solve both the tracking problem and the regulation problem of mobile robots. In particular, mobile robots can now globally follow any differentiable with bounded velocities path such as a straight line, a circle and the path approaching to the origin using the proposed controller. Moreover, the problem of back-into-garage parking is also solved by our approach. Some interesting simulation results are given to illustrate the effectiveness of the proposed tracking control laws.

In this paper, a simple chaotic circuit using two RC phase shift oscillators and a diode is proposed and analyzed. By using a simpler model of the original circuit, the mechanism of generating chaos is explained and the exact solutions are derived. The exact expression of the Poincare map and its Jacobian matrix make it possible to confirm the generation of chaos using the Lyapunov exponents and to investigate the related bifurcation phenomena.

We present a design strategy to reduce power demands in application-specific, heterogeneous multiprocessor systems with interdependent subtasks. This power reduction scheme can be used with a randomised search such as a genetic algorithm where multiple trial solutions are tested. The scheme is applied to each trial solution after allocation and scheduling have been performed. Power savings are achieved by equally expanding each processor's execution time with a corresponding reduction in their respective operating voltage. Lowest cost solutions achieve average reductions of 24% while minimum power solutions average 58%.

There are so many methods of calculating the cylindrical function Z_ν(x), but it seems that there is no method of calculating Z_ν(x) in the region of νx and |ν|»1 with high accuracy. The asymptotic series presented by Watson, et al. are frequently used for the numerical calculation of cylindrical function Z_ν(x) where νx and |ν|»1. However, the function B_m(εx) included in the m'th term of the asymptotic series is known only for m5. Hence, the asymptotic series can not give sufficiently accurate values of the cylindrical functions. The authors attempt to develop programs for the numerical calculation of the cylindrical functions using this asymptotic series. For this purpose, we must know the function B_m(εx) of arbitrary m. We developed a method of calculating B_m(εx) for arbitrary m, and then succeeded in calculating the cylindrical functions in the region νx with high precision.

When we search from a huge amount of documents, we often specify several keywords and use conjunctive queries to narrow the result of the search. Though the searched documents contain all keywords, positions of the keywords are usually not considered. As a result, the search result contains some meaningless documents. It is therefore effective to rank documents according to proximity of keywords in the documents. This ranking is regarded as a kind of text data mining. In this paper, we propose two algorithms for finding documents in which all given keywords appear in neighboring places. One is based on plane-sweep algorithm and the other is based on divide-and-conquer approach. Both algorithms run in O(n log n) time where n is the number of occurrences of given keywords. We run the algorithms on a large collection of html files and verify its effectiveness.

In this paper, we consider the problem of active learning, and give a necessary and sufficient condition of sample points for the optimal generalization capability. By utilizing the properties of pseudo orthogonal bases, we clarify the mechanism of achieving the optimal generalization capability. We also show that the condition does not only provide the optimal generalization capability but also reduces the computational complexity and memory required to calculate learning result functions. Based on the optimality condition, we give design methods of optimal sample points for trigonometric polynomial models. Finally, the effectiveness of the proposed active learning method is demonstrated through computer simulations.

Given a graph G=(V,E), five distinct vertices u₁,u₂,u₃,u₄,u₅ V and five natural numbers n₁,n₂,n₃,n₄,n₅ such that Σ⁵_i=1n_i=|V|, we wish to find a partition V₁,V₂,V₃,V₄,V₅ of the vertex set V such that u_i V_i, |V_i|=n_i and V_i induces a connected subgraph of G for each i, 1i5. In this paper we give a simple linear-time algorithm to find such a partition if G is a 5-connected internally triangulated plane graph and u₁,u₂,u₃,u₄,u₅ are located on the outer face of G. Our algorithm is based on a "5-canonical decomposition" of G, which is a generalization of an st-numbering and a "canonical ordering" known in the area of graph drawings.

Solutions based on error-correcting codes for the blacklisting problem of a broadcast distribution system have been proposed by Kumar, Rajagopalan and Sahai. In this paper, detailed analysis of the solutions is presented. By choosing parameters properly in their constructions, we show that the performance is improved significantly.

Software defined radio (SDR) is receiving much attention as the key technology to realize the next generation wireless communication system. This paper proposes the concept of system diversity on SDR and investigates the effectiveness of system diversity by using a concrete simulation model. System diversity allows the wireless communication system being used to be dynamically changed in addition to the signal processing algorithm or modulation/coding scheme being used. To clarify the validity of system diversity, we examine a system simulation model consisting of three wireless communication systems; algorithms are introduced to show how system diversity can be controlled using the QoS parameters of received signal level, data transmission rate, and channel capacity. The process by which system diversity switching is triggered is elucidated, and a practical example is introduced. Simulation results confirm that system diversity offers higher performance in terms of data throughput and system channel capacity than existing wireless communication systems. Finally, a comprehensive algorithm is described that protects existing single-mode traffic from being degraded by SDR switching.

A positive integer code EXE_b,h,d(b1, h1,d0) is proposed. Its codeword for a positive integer n consists of three kinds of information: (1) how many times the number of n's digits can be subtracted by the terms of a progression including a geometric progression, (2) the rest of the subtractions, and (3) given value of the positive integer n. EXE_b,h,d is a non-recursive type code. It is an asymptotically optimal code (for d1) and preserves the lexicographic,length, and number orders (for bh+2). Some examples of EXE_b,h,d are also presented. Their codeword lengths are found to be shorter than the Amemiya and Yamamoto code CE_k except for small positive integers.

In this paper we show that the neuron filter is effective for relaxing the coefficient sensitiveness of the Hopfield neural network for combinatorial optimization problems. Since the parameters in motion equation have a significant influence on the performance of the neural network, many studies have been carried out to support determining the value of the parameters. However, not a few researchers have determined the value of the parameters experimentally yet. We show that the use of the neuron filter is effective for the parameter tuning, particularly for determining their values experimentally through simulations.