In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system by using the self-adjoint extension theory of functional analysis, we deduce the general condition for the appearance of chaos. The prediction is confirmed by numerically examining the statistical properties of energy spectrum of rectangular billiards with multiple point interactions inside. The dependence of the level statistics on the strength as well as the number of the scatterers is displayed.

Synchronization between two fully stretching piecewise affine Markov maps in the usual master-slave configuration has been proven to be possible in some interesting 2-dimensional and 3-dimensional cases. Aim of this contribution is to make a further step in the study of this phenomenon by showing that, if the two systems synchronize, the probability of having a certain synchronization time is bounded from above by an exponentially vanishing distribution. This result gives some formal ground to the numerical evidence shown in [2].

We here consider an extension of the validity of classical criteria ensuring the robustness of the statistical features of discrete time dynamical systems with respect to implementation inaccuracies and noise. The result is achieved by proving that, whenever a discrete time dynamical system is robust, all the discrete time dynamical systems topologically conjugate with it are also robust. In particular, this result offer an explanation for the stochastic robustness of the logistic map, which is confirmed by the reported experimental measurements.

In this study, a coupled chaotic circuits network is realized by real circuit elements. By using a simple circuit converting generating spatial patterns to digital signal, irregular self-switching phenomenon of the appearing patterns can be observed as real physical phenomenon.

A numerical method is proposed for efficiently locating fold bifurcation points of periodic orbits of high-dimensional differential-equation systems. This method is an extension of the subspace shooting method (or the Newton-Picard shooting method) that locates periodic orbits by combining the conventional shooting method and the brute-force method. Fold bifurcation points are located by combining a variant of the subspace shooting method with a fixed parameter value and the secant method for searching the parameter value of the bifurcation point. The target in the subspace-shooting part is an (not necessarily periodic) orbit represented by a Poincare mapping point which is close to the center manifold and satisfies the eigenvalue condition for the bifurcation. The secant-search part finds the parameter value where this orbit becomes periodic. Avoiding the need for differentiating the Poincare map with respect to the bifurcation parameter and exploiting several properties of the center manifold, the proposed method is both robust and easy to implement.

In order to demodulate a Differential Chaos Shift Keying (DCSK) signal, the energy carried by the received chaotic signal must be determined. Since a chaotic signal is not periodic, the energy per bit carried by the chaotic signal can only be estimated, even in the noise-free case. This estimation has a non-zero variance that limits the attainable data rate. In this paper the DCSK technique is combined with frequency modulation in order to overcome the estimation problem and to improve the data rate of DCSK modulation.

The naturalness of normal sustained vowels is considered to be attributable to the fluctuations observed in the steady part where speech signal is seemingly almost periodic. There always exist two kinds of involuntary fluctuations in the steady part of sustained vowels, even if the sustained vowels are phonated as steadily as possible. One is pitch period fluctuation and the other is waveform fluctuation. In this study, frequency analyses on these fluctuations were conducted in order to investigate their general characteristics. The results of the analyses suggested that the frequency characteristics of the fluctuations were possible to be approximated as 1/f^β-like, which is regarded as the specific feature of random fractal. Therefore, a procedure based on random fractal generation methods was proposed in order to produce these fluctuations for the improvement of the voice quality of synthesized sustained vowels. A series of psychoacoustic experiments was also conducted to evaluate the proposed technique. Experimental results indicated that the proposed technique was effective for synthesized sustained vowels to be perceived as human-like. Unlike the sustained vowels which were synthesized without pitch period fluctuation nor waveform fluctuation, the synthesized sustained vowels which contained the fluctuations were not perceived as buzzer-like, which is the major problem of the voice quality of synthesized sustained vowels. However, it was also found that both of the fluctuations were not always the acoustic cues for the naturalness of normal sustained vowels. The synthesized sustained vowels which contained the fluctuations whose frequency characteristics were the same as that of white noise were perceived as noise-like, which is not at all the voice quality of normal sustained vowels. The results of psychoacoustic experiments indicated that the frequency characteristics of the fluctuations, which are possible to be modeled as 1/f^β-like, were the significant factors for the naturalness of normal sustained vowels.

This paper gives two kinds of functions for which Uesaka's Conjecture, stating that the globally optimum (not a local minimum) of a quadratic function F(x)=-(1/2)x^tAx in the n-dimensional hypercube may be obtained by solving a differential equation, holds true, where n denotes the dimension of the vector x. Uesaka stated in his paper that he proved the conjecture only for n=2. This corresponds to a very special case of this paper. The results of this paper suggest that the conjecture really holds for a wide class of quadratic functions and therefore support the conjecture partially.

Though response of neurons is mainly decided by synaptic events, the length of a time window for the neuronal response has still not been clarified. In this paper, we analyse the time window within which a neuron processes synaptic events, on the basis of the Hodgkin-Huxley equations. Our simulation shows that an active membrane property makes neurons' behavior complex, and that a few milliseconds is plausible as the time window. A neuron seems to detect coincidence synaptic events in such a time window.

The hippocampus is thought to play an important role in the transformation from short-term memory into long-term memory, which is called consolidation. The physiological phenomenon of synaptic change called LTP or LTD has been studied as a basic mechanism for learning and memory. The neural network mechanism of the consolidation, however, is not clarified yet. The authors' approach is to construct information processing theory in learning and memory, which can explain the physiological data and behavioral data. This paper proposes a dynamical hippocampal model which can store and recall spatial input patterns. The authors assume that the primary functions of hippocampus are to store episodic information of sensory signals and to keep them for a while until the neocortex stores them as a long-term memory. On the basis of the hippocampal architecture and hypothetical synaptic dynamics of LTP/LTD, the authors construct a hippocampal model. This model considers: (1) divergent connections, (2) the synaptic dynamics of LTP and LTD based on pre- and postsynaptic coincidence, and (3) propagation of LTD. Computer simulations show that this model can store and recall its input spatial pattern by self-organizing closed activating pathways. By the backward propagation of LTD, the synaptic pathway for a specific spatial input pattern can be selected among the divergent closed connections. In addition, the output pattern also suggests that this model is sensitive to the temporal timing of input signals. This timing sensitivity suggests the applicability to spatio-temporal input patterns of this model. Future extensions of this model are also discussed.

We present a cascade neural network for blind source extraction. We propose a family of unconstrained optimization criteria, from which we derive a learning rule that can extract a single source signal from a linear mixture of source signals. To prevent the newly extracted source signal from being extracted again in the next processing unit, we propose another unconstrained optimization criterion that uses knowledge of this signal. From this criterion, we then derive a learning rule that deflates from the mixture the newly extracted signal. By virtue of blind extraction and deflation processing, the presented cascade neural network can cope with a practical case where the number of mixed signals is equal to or larger than the number of sources, with the number of sources not known in advance. We prove analytically that the proposed criteria both for blind extraction and deflation processing have no spurious equilibria. In addition, the proposed criteria do not require whitening of mixed signals. We also demonstrate the validity and performance of the presented neural network by computer simulation experiments.

This paper describes an efficient simulation algorithm for the spatiotemporal pattern analysis of the continuous-time neural networks with the multivalued logic (multivalued continuous-time neural networks). The multivalued transfer function of neuron is approximated to the stepwise constant function which is constructed by the sum of the step functions with the different thresholds. By this approximation, the dynamics of the network can be formulated as a stepwise constant linear differential equation at each timestep and the optimal timestep for the numerical integration can be obtained analytically. Finally, it is shown that the proposed method is much faster than a variety of conventional simulators.

An asynchronous pulse neural network model which is suitable for VLSI implementation is proposed. The model neuron can function as a coincidence detector as well as an integrator depending on its internal time-constant relative to the external one, and show complex dynamical behavior including chaotic responses. A network with the proposed neurons can process spatio-temporal coded information through dynamical cell assemblies with functional synaptic connections.

In the design of nonlinear reliable controllers, one major issue is to solve for the solutions of the Hamilton-Jacobi inequality. In general, it is hard to obtain a closed form solutions due to the nonlinear nature of the inequality. In this paper, we seek for the existence conditions of quadratic type positive semidefinite solutions of Hamilton-Jacobi inequality. This is achieved by taking Taylor's series expansion of system dynamics and investigating the negative definiteness of the associated Hamilton up to fourth order. An algorithm is proposed to seek for possible solutions. The candidate of solution is firstly determined from the associated algebraic Riccati inequality. The solution is then obtained from the candidate which makes the truncated fourth order polynomial of the inequality to be locally negative definite. Existence conditions of the solution are explicitly attained for the cases of which system linearization possesses one uncontrollable zero eigenvalue and a pair of pure imaginary uncontrollable eigenvalues. An example is given to demonstrate the application to reliable control design problem.

Modeling error is the major concerning issue in the trajectory estimation. This paper formulates the dynamic model of a reentry vehicle in reentry phase for identification with an unmodeled acceleration input covering possible model errors. Moreover, this work presents a novel on-line estimation approach, adaptive filter, to identify the trajectory of a reentry vehicle from a single radar measured data. This proposed approach combines the extended Kalman filter and the recursive least-squares estimator of input with the hypothetical testing scheme. The recursive least-squares estimator is provided not only to extract the magnitude of the unmodeled input but to offer a testing criterion to detect the onset and presence of the input. Numerical simulation demonstrates the superior capabilities in accuracy and robustness of the proposed method. In real flight analysis, the adaptive filter also performs an excellent estimation and prediction performances. The recommended trajectory estimation method can support defense and tactical operations for anti-tactical ballistic missile warfare.

The required building blocks of CMOS fuzzy chips capable of performing as adaptive fuzzy systems are described in this paper. The building blocks are designed with mixed-signal current-mode cells that contain low-resolution A/D and D/A converters based on current mirrors. These cells provide the chip with an analog-digital programming interface. They also perform as computing elements of the fuzzy inference engine that calculate the output signal in either analog or digital formats, thus easing communication of the chip with digital processing environments and analog actuators. Experimental results of a 9-rule prototype integrated in a 2. 4-µm CMOS process are included. It has a digital interface to program the antecedents and consequents and a mixed-signal output interface. The proposed design approach enables the CMOS realization of low-cost and high-inference fuzzy systems able to cope with complex processes through adaptation. This is illustrated with simulated results of an application to the on-line identification of a nonlinear dynamical plant.

Related with accuracy, computational complexity and so on, quality of computing for the so-called homotopy method has been discussed recently. In this paper, we shall propose an estimation method with interval analysis of region in which unique solution path of the homotopy equation is guaranteed to exist, when it is applied to a certain class of uniquely solvable nonlinear equations. By the estimation, we can estimate the region a posteriori, and estimate a priori an upper bound of the region.

This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.

A reconfiguration method for processor array is proposed in this paper. In the method, genetic algorithm (GA) is used for searching effective spare arrangement, which leads to successful reconfiguration. The effectiveness of the method is demonstrated by computer simulations.

This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, F_p-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.

The most basic cross-talk minimization problem is to assign given n intervals to n parallel tracks where the cross-talk is defined between two intervals assigned to the adjacent tracks with the amount linear to parallel running length. This paper solves the problem for the case when any pair of intervals intersects and the objective is to minimize the sum of cross-talks. We begin the discussion with the fact that twice the sum of lengths of n/2 shortest intervals is a lower bound. Then an interval set that attains this lower bound is characterized with a simple assignment algorithm. Some additional considerations provide the minimum cross-talk for the other interval sets. The main procedure is to sort the intervals twice with respect to the length of left and right halves of intervals.

Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.

This paper proposes a simple learning algorithm that can realize any boolean function using the three-layer binary neural networks. The algorithm has flexible learning functions. 1) moving "core" for the inputs separations,2) "don't care" settings of the separated inputs. The "don't care" inputs do not affect the successive separations. Performing numerical simulations on some typical examples, we have verified that our algorithm can give less number of hidden layer neurons than those by conventional ones.

Conventional approaches to neural network training do not consider possibility of selecting training samples dynamically during the learning phase. Neural network is simply presented with the complete training set at each iteration of the learning. The learning can then become very costly for large data sets. Huge redundancy of data samples may lead to the ill-conditioned training problem. Ill-conditioning during the training causes rank-deficiencies of error and Jacobean matrices, which results in slower convergence speed, or in the worst case, the failure of the algorithm to progress. Rank-deficiencies of essential matrices can be avoided by an appropriate selection of training exemplars at each iteration of training. This article presents underlying theoretical grounds for dynamic sample selection (DSS), that is mechanism enabling to select a subset of training set at each iteration. Theoretical material is first presented for general objective functions, and then for the objective functions satisfying the Lipschitz continuity condition. Furthermore, implementation specifics of DSS to first order line search techniques are theoretically described.

Computational expensiveness of the training techniques, due to the extensiveness of the data set, is among the most important factors in machine learning and neural networks. Oversized data set may cause rank-deficiencies of Jacobean matrix which plays essential role in training techniques. Then the training becomes not only computationally expensive but also ineffective. In [1] the authors introduced the theoretical grounds for dynamic sample selection having a potential of eliminating rank-deficiencies. This study addresses the implementation issues of the dynamic sample selection based on the theoretical material presented in [1]. The authors propose a sample selection algorithm implementable into an arbitrary optimization technique. An ability of the algorithm to select a proper set of samples at each iteration of the training has been observed to be very beneficial as indicated by several experiments. Recently proposed approaches to sample selection work reasonably well if pattern-weight ratio is close to 1. Small improvements can be detected also at the values of the pattern-weight ratio equal to 2 or 3. The dynamic sample selection approach, presented in this article, can increase the convergence speed of first order optimization techniques, used for training MLP networks, even at the value of the pattern-weight ratio (E-FP) as high as 15 and possibly even more.

This article shows that a multivalued logic defined as juxtaposition of Boolean binary logics can use all of inference chain, induction and deduction that are important in realization of intelligent inference systems.

In this paper, we propose an adaptive lattice-transversal joint (LTJ) filter structure that is quite suitable for the practical implementation of the acoustic echo canceller. The structure maintains fast convergence of the lattice structure and low computational complexity of the transversal structure simultaneously. It is particularly more efficient in memory usage than any other existing fast-convergent algorithm for the acoustic echo cancellation.

This letter presents a new algorithm for improving the Signal to Noise Ratio (SNR) of complex sinusoidal signals contaminated by additive Gaussian noises using sum of Higher-Order Statistics (HOS). We conduct some computer simulations to show that the proposed algorithm can improve the SNR more than 7 dB compared with the conventional coherent integration when the SNR of the input signal is -10 dB.