Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For the global convergence of homotopy methods, it is a necessary condition that a given initial solution is the unique solution to the homotopy equation. According to the conventional criterion, such an initial solution, however, is restricted in some very narrow region. In this paper, considering the circuit interpretation of homotopy equations, we prove theorems on the uniqueness of an initial solution for globally convergent homotopy methods. These theorems give new criteria extending the region wherein any desired initial solution satisfies the uniqueness condition.

Affine arithmetic is a kind of interval arithmetic defined by Stolfi et al. In affine arithmetic, it is difficult to realize the efficient nonlinear binomial operations. The purpose of this letter is to propose a new dividing method which is able to supply more suitable evaluation than the old dividing method. And this letter also shows the efficiency of the new dividing method by numerical examples.

The array-enhanced coherence resonance (AECR) in the diffusively coupled active rotators is investigated and its analysis with the nonlinear Fokker-Planck equation is presented. By considering the nonlinear Fokker-Planck equation of the rotators, it is found that the time-periodic solution exists in some parameter range. By solving the equation of a rotator and the Fokker-Planck equation simultaneously, the behavior of a rotator in the system with infinite number of rotators is considered, and it is found that AECR also takes place in this infinite system. Thus it is concluded that AECR is caused by the time-periodic solution of the probability density induced by noise.

This paper investigates the use of chaotic pulsewidth modulation (CPWM) scheme for electronic ballasts to eliminate visible striations (appearance of black and white bands along the lamp tube) in fluorescent lamps. As striations can be eliminated by superimposing a small amount of dc current or low frequency ac current to the electrodes to produce composite current waveform through the lamp, the underlying principle of this work is based on the fact that the power spectral density of the lamp current will be rich of low-frequency harmonics at the output of inverters switching with CPWM. Most importantly, the lamp life will not be affected with chaotic switchings, because the lamp current crest factor is found to be similar to the one with standard pulsewidth modulation (PWM) and the lamp current does not have dc component. The effectiveness of eliminating striations is confirmed experimentally with a T8 36W prototype.

The radio wave intensity time series of the quasar is observed with the radio wave interferometer on the earth. External noise may superimpose with the radio wave on the path of wave propagation over the cosmological distance. In this paper, the effects of the superimposed noise on the radio wave intensity time series are discussed assuming nonlinear dynamics to apply on the time series. A convolution method is applied to the original observed radio wave intensity time series. Both the original and the convolution time series are analyzed by the Grassberger-Procaccia (GP) method with correlation integration and compared the results to estimate the presence and the effects of superimposed subtle noise. In addition, surrogate and Judd methods are applied to the radio wave intensity time series to increase the credibility of the results of the GP method. The effects of added random noise in Lorenz model are also analyzed with the GP method to estimate the above results.

A method for a genuinely multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. It is applied to EEG data from a psychological experiment, obtaining results which indicate a possible relevance of this method in the context of cognitive science as well as in other fields.

In this paper our recently introduced method called output distributional influence function (ODIF) is used for the evaluation of the robustness properties of the nonlinear filter class of morphological filters. Several examples of the ODIFs for the dilation, closing and clos-opening are given and explained carefully. For each of these morphological filters the effect of filter length is examined by using the ODIFs for the expectation and variance. The robustness properties of the filters are also compared to each other and the effect of the distribution of the contamination is investigated for the closing as an example of realistic filtering conditions.

We investigate the statistical features of both random- and chaos-based FM timing signals to ascertain their applicability to digital circuits and systems. To achieve such a goal, we consider both the case of single- and two-phase logic and characterize the random variable representing, respectively, the time lag between two subsequent rising edges or between two consecutive zero-crossing points of the modulated timing signal. In particular, we determine its probability density and compute its mean value and variance for cases which are relevant for reducing Electromagnetic emissions. Finally, we address the possible problems of performance degradation in a digital system driven by a modulated timing signal and to cope with this we give some guidelines for the proper choice of the statistical properties of the modulating signals.

The cardio-music synchrogram, which is a visualization tool that helps us observe the phase synchronization between heartbeats and beats of music, is originated in cardio-respiratory synchrogram. In this paper, we proposed a novel statistical method for detecting synchronization periods in cardio-music synchrogram (CMS), and reported the synchronization periods of the cardiac activity for 8 subjects in a listening experiments. Our approach focused on the difference between the statistical distributions of the correlation coefficient calculated for the CMS in a control experiment and in the CMS in the listening experiment.

Probabilistic encryption becomes more and more important since its ability to against chosen-ciphertext attack. Applications like online voting schemes and one-show credentials are based on probabilistic encryption. Research on good probabilistic encryptions are on going, while many good deterministic encryption schemes are already well implemented and available in many systems. To convert any deterministic encryption scheme into a probabilistic encryption scheme, a randomized media is needed to apply on the message and carry the message over as an randomized input. In this paper, nonlinear codes obtained by certain mapping from linear error-correcting codes are considered to serve as such carrying media. Binary nonlinear codes obtained by Gray mapping from ₄-linear codes are discussed as example for a such scheme.

We consider the problem of constructing nonlinear dynamical systems that realize an arbitrary prescribed tree sources. We give a construction of dynamical systems by using piecewise-linear maps. Furthermore, we examine the obtained dynamical system to show that the structure of the memory of tree sources is characterized with some geometrical property of the constructed dynamical systems. Using a similar method, we also construct a dynamical system generating an arbitrary prescribed reverse tree source and show that the obtained dynamical system has some interesting geometrical property explicitly reflecting the tree structure of the memory of the reverse tree source.

Let us introduce n ( 2) nonlinear 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,(i = 1,2,,n 0), such that f_i() . Moreover, let us introduce n fuzzy-set-valued nonlinear mappings F_i: X_i-1 X_i {a family of all non-empty closed compact fuzzy subsets of X_i}. Here, we have a fixed point theorem on the recurrent system of β-level fuzzy-set-valued mapping equations: x_i F_iβ(x_i-1,f_i(x_i-1)), (i = 1,2,,n 0), where the fuzzy set F_i is characterized by a membership function µ_Fi(x_i): X_i [0,1], and the β-level set F_iβ of the fuzzy set F_i is defined as F_iβ {ξ_i X_i | µ_Fi(ξ_i) β}, for any constant β (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.

This paper proposes a new approach to fuzzy inference system for modeling nonlinear systems based on measured input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the extended kernel method. The extended kernel method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. Especially, the process of linear transformation is needed in order to solve difficulty determining the type of kernel function which presents the nonlinear mapping in according to nonlinear system. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated results of the proposed technique are illustrated by examples involving benchmark nonlinear systems.

NK-Landscapes are stochastically generated fitness functions on bit strings, parameterized with N bits and K epistatic interactions between bits. The term epistasis describes nonlinearities in fitness functions due to changes in the values of interacting bits. Empirical studies have shown that the overall performance of random bit climbers on NK-Landscapes is superior to the performance of some simple and enhanced genetic algorithms (GAs). Analytical studies have also lead to suggest that NK-Landscapes may not be appropriate for testing the performance of GAs. In this work we study the effect of selection, drift, mutation, and recombination on NK-Landscapes for N = 96. We take a model of generational parallel varying mutation GA (GA-SRM) and switch on and off its major components to emphasize each of the four processes mentioned above. We observe that using an appropriate selection pressure and postponing drift make GAs quite robust on NK-Landscapes; different to previous studies, even simple GAs with these two features perform better than a random bit climber (RBC+) for a broad range of classes of problems (K 4). We also observe that the interaction of parallel varying mutation with crossover improves further the reliability of the GA, especially for 12 < K < 32. Contrary to intuition, we find that for small K a mutation only evolutionary algorithm (EA) is very effective and crossover may be omitted; but the relative importance of crossover interacting with varying mutation increases with K performing better than mutation alone (K > 12). This work indicates that NK-Landscapes are useful for testing each one of the major processes involved in a GA and for assessing the overall behavior of a GA on complex non-linear problems. This study also gives valuable guidance to practitioners applying GAs to real world problems of how to configure the GA to achieve better results as the non-linearity and complexity of the problem increases.

Neural networks for Vector Quantization (VQ) such as K-means, Neural-Gas (NG) network and Kohonen's Self-Organizing Map (SOM) have been proposed. K-means, which is a "hard-max" approach, converges very fast. The method, however, devotes itself to local search, and it easily falls into local minima. On the other hand, the NG and SOM methods, which are "soft-max" approaches, are good at the global search ability. Though NG and SOM exhibit better performance in coming close to the optimum than that of K-means, the methods converge slower than K-means. In order to the disadvantages that exist when K-means, NG and SOM are used individually, this paper proposes hybrid methods such as NG-K, SOM-K and SOM-NG. NG-K performs NG adaptation during short period of time early in the learning process, and then the method performs K-means adaptation in the rest of the process. SOM-K and SOM-NG are similar as NG-K. From numerical simulations including an image compression problem, NG-K and SOM-K exhibit better performance than other methods.

Brain subsystems have a high degree of information processing ability using nonlinear dynamics and although various neuron models and artificial neural networks have been investigated, the information processing functions of biological neural networks have not yet been clarified. Recently, various research efforts have confirmed that dendrites perform an important role in brain information processing. In this paper, we discuss the nonlinear characteristics of a hardware active dendrite model, in order to clarify information encoding and transmission via action potentials. That is to say, we show that our proposed model can reproduce the nonlinear characteristics of a biologically active dendrite. First, the hardware active dendrite model we propose is described. We next discuss the response characteristics for pulse stimuli using the model. As a result, when input pulses are applied to an active line, which is the basic structure of the dendrite model, it is shown clearly that backpropagation characteristics are acquired and that the characteristics are qualitatively in agreement with the characteristics of biological dendrites. Furthermore, we verify that the ratio of input to output frequency at the cell body is influenced by the backpropagation characteristics with two branches, which is the simplest structure in the active dendrite model. Thus, with backpropagation characteristics, the possibility that the model can carry out clearly the information processing of biological neural networks, is suggested.

Treating an averaged multiple-trials data or non-averaged single-trial data is a main approach in recent topics on applying independent component analysis (ICA) to neurobiological signal processing. By taking an average, the signal-to-noise ratio (SNR) is increased but some important information such as the strength of an evoked response and its dynamics will be lost. The single-trial data analysis, on the other hand, can avoid this problem but the SNR is very poor. In this study, we apply ICA to both non-averaged single-trial data and averaged multiple-trials data to determine the properties and advantages of both. Our results show that the analysis of averaged data is effective for seeking the response and dipole location of evoked fields. The non-averaged single-trial data analysis efficiently identifies the strength and dynamic component such as α-wave. For determining both the range of evoked strength and dipole location, an analysis of averaged limited-trials data is better option.

This study describes the feasibility of using the penalty-function nonlinear programming neural network method to find the optimal power generating output which minimizes both the costs of generating power and power transmission losses. This method depends on neural network technology in acquiring exterior penalty function. Employing nonlinear function in equality and inequality constraints, the model is established using a neural network and additional objective functions; these additional objective functions expand cost function by using an appropriate penalty function. In this study, a 26-busbar including six generators was used to test the penalty function nonlinear programming neural network method. A comparison with the sequential unconstrained minimization technique (SUMT) demonstrates the reliability and precision of the optimal solution obtained using the new method.

In this paper, a Compensatory Neuro-Fuzzy Network (CNFN) for nonlinear system control is proposed. The compensatory fuzzy reasoning method is using adaptive fuzzy operations of neural fuzzy network that can make the fuzzy logic system more adaptive and effective. An on-line learning algorithm is proposed to automatically construct the CNFN. They are created and adapted as on-line learning proceeds via simultaneous structure and parameter learning. The structure learning is based on the fuzzy similarity measure and the parameter learning is based on backpropagation algorithm. The advantages of the proposed learning algorithm are that it converges quickly and the obtained fuzzy rules are more precise. The performance of CNFN compares excellently with other various exiting model.

It is shown that bounded impulse action can be combined with usual bang-bang control input to minimize the performance index. Especially for unstable oscillators, the size of controllable region can be increased. We present results on how to minimize the performance index using both ordinary bang-bang control and impulse actions with a recharge constraint on impulse firing. Following the maximum principle and necessary conditions induced from usual perturbation arguments, the mixed control input (bang-bang and impulse actions) is represented in adjoint state and then state variable feedback form. Simulation results show how the switch curves can be used to determine the optimal control value.

Analog Hopfield neural networks (HNNs) have so far been used to solve many kinds of optimization problems, in particular, combinatorial problems such as the TSP, which can be described by an objective function and some equality constraints. When we solve a minimization problem with equality constraints by using HNNs, however, the constraints are satisfied only approximately. In this paper we propose a circuit which rigorously realizes the equality constraints and whose energy function corresponds to the prescribed objective function. We use the SPICE program to solve circuit equations corresponding to the above circuits. The proposed method is applied to several kinds of optimization problems and the results are very satisfactory.

In this paper, we present an output feedback controller using a fuzzy controller and observer for nonlinear systems with unknown time-delay. Recently, Cao et al. proposed a stabilization method for the nonlinear time-delay systems using a fuzzy controller when the time-delay is known. In general, however, it is impossible to know or measure this time-varying delay. The proposed method requires only the upper bound of the derivative of the time-delay. We represent the nonlinear system with the unknown time-delay by Takagi-Sugeno (T-S) fuzzy model and design the fuzzy controller and observer for the systems using the parallel distributed compensation (PDC) scheme. In addition, we derive the sufficient condition for the asymptotic stability of the equilibrium point by applying Lyapunov-Krasovskii theorem to the closed-loop system and solve the condition in the formulation of LMI. Finally, computer simulations are included to demonstrate the effectiveness of the suggested method.

A nonlinear circuit described by the forced Duffing's equation is known to display a rich variety of dynamical behavior. Coupling two Duffing's circuits by a linear resistor, we conclude that combinatorial resonances occur on weak coupling condition. In a coupled system, although symmetrical properties are usually observed, breaking of symmetry can lead to much more complex nonlinear resonant phenomena. In this paper, we discuss asymmetry in four cases of perturbation on parameters. Many bifurcation diagrams are presented. Comparing with symmetrical cases, we analyze the combinatorial resonances in coupled Duffing's circuit completely.

In this paper, we propose new physical design techniques to reduce crosstalk noise and crosstalk-induced delay variations caused in a nanometer-scale system-on-a-chip (SoC). We have almost eliminated the coupling effect between signal wires by simply optimizing parameters for the automatic place and route methodology. Our approach consists of two techniques, (1) A 3-D optimization technique for tuning the routing grid configuration both in the horizontal and vertical directions. (2) A co-optimization technique for tuning the cell utilization ratio and the routing grid simultaneously. Experiments on the design of an image processing circuit fabricated in a 0.13 µm CMOS process with six layers of copper interconnect show that crosstalk noise is almost eliminated. From the results of a static timing analysis considering the worst-case crosstalk condition, the longest path delay is decreased by about 15% maximum if technique (1) is used, and by about 7% maximum if technique (2) is used. The 7-15% delay reduction has been achieved without process improvement, and this reduction corresponds to between 1/4 and 1/2 generation of process progress.

The concept of an Ω-matrix was introduced by Nishi in order to estimate the number of solutions of a resistive circuit containing active elements. He gave a finite characterization by means of four conditions which are all satisfied if and only if the matrix under investigation is an Ω-matrix. In this note we show that none of the four conditions can be omitted.

We show that the necessary and sufficient condition for the existence of a balanced bowtie decomposition of the complete multigraph λK_n is n 5 and λ(n-1) 0 (mod 12). Decomposition algorithms are also given.

Digital watermarking systems are required to embed as much information as possible in a digital media without the perceptual distortion as well as to extract it correctly with high probabilities, even though the media is subjected to many kinds of operations. To this end, guided scrambling (GS) techniques, usually used for a recording channel, are applied to digital watermarking systems. A simple GS scheme can make the power of a watermark signal larger against the power of media noise under the condition of preserving the perceptual fidelity, resulting in smaller error probabilities of the retrieved watermark bits. In addition, watermarking systems based on the GS can have more robustness to some specified operations if the prior information on the operations is given to the embedder. JPEG compression is a good example of such an operation when still images are transmitted over the Internet. In order for watermark signals to be more tolerable to the known JPEG attack, the GS-based watermark embedder is informed of advance knowledge of the JPEG compression. Further, a configuration of the GS concatenated with turbo coding is introduced to lower the bit error rate more.

In many cryptographic applications, a large-order finite field is used as a definition field, and accordingly, many researches on a fast implementation of such a large-order extension field are reported. This paper proposes a definition field F_pm with its characteristic p a pseudo Mersenne number, the modular polynomial f(x) an irreducible all-one polynomial (AOP), and using a suitable basis. In this paper, we refer to this extension field as an all-one polynomial field (AOPF) and to its basis as pseudo polynomial basis (PPB). Among basic arithmetic operations in AOPF, a multiplication between non-zero elements and an inversion of a non-zero element are especially time-consuming. As a fast realization of the former, we propose cyclic vector multiplication algorithm (CVMA), which can be used for possible extension degree m and exploit a symmetric structure of multiplicands in order to reduce the number of operations. Accordingly, CVMA attains a 50% reduction of the number of scalar multiplications as compared to the usually adopted vector multiplication procedure. For fast realization of inversion, we use the Itoh-Tsujii algorithm (ITA) accompanied with Frobenius mapping (FM). Since this paper adopts the PPB, FM can be performed without any calculations. In addition to this feature, ITA over AOPF can be composed with self reciprocal vectors, and by using CVMA this fact can also save computation cost for inversion.

Complete complementary codes have the property that the sum of correlation functions of several sequences satisfies both ideal autocorrelation and cross-correlation values. Modulatable complete complementary codes (MCC codes), which is a type of periodic complete complementary codes, are suitable for spreading sequences of M-ary CDMA systems. In the present paper, we propose a new method for constructing MCC codes. Using this method, we can easily generate various MCC codes.

Power Line Communication (PLC) is very attractive for achieving high-rate in-home networks. Noise in power lines is modeled as a cyclostationary Gaussian process. In order to achieve reliable communication using power lines, effective measures including error control techniques need to be taken against this particular noise. This paper focuses its attention on an effect of turbo codes on PLC. We adopt two noise environments for examining the effect in terms of BER performance. The result of the examination provides that turbo codes have enough capability to limit the effect of the noise. It also provides that the effect depends on size of a channel interleaver. Since an effective SNR estimation scheme should be required to apply turbo codes to PLC, we also examine the effect of two SNR estimation schemes in terms of BER performance.

Distributed execution of a service often means that various places compete for the right to progress. If they exchange the right by explicit communication, there is a continuous flow of protocol messages. If the maximum transit delay of the communication medium is short, a better solution is to restrict progress of places to their individual time windows. The paper describes how to derive such time-sharing-based multi-party protocols for well-formed services specified in LOTOS/T+. The method is compositional with respect to the structure of the given service specification, supporting alternative, sequential, interrupt and parallel composition of services.

In this paper, we propose a delayed feedback guaranteed cost controller design method for uncertain linear systems with delays in states. Based on the Lyapunov method, an LMI optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. Numerical examples show the effectiveness of the proposed method.

A fast winner search method for VQ based on 2-pixel-merging sum pyramid is proposed in order to reject a codeword at an earlier stage to reduce the computational burden. The necessary search scope of promising codewords is meanwhile narrowed by using sorted real sums. The high search efficiency is confirmed by experimental results.