Given a vector p_i of floating-point numbers with exact sum s, we present a new algorithm with the following property: Either the result is a faithful rounding of s, or otherwise the result has a relative error not larger than eps^Kcond(∑p_i) for K to be specified. The statements are also true in the presence of underflow, the computing time does not depend on the exponent range, and no extra memory is required. Our algorithm is fast in terms of measured computing time because it allows good instruction-level parallelism. A special version for K=2, i.e., quadruple precision is also presented. Computational results show that this algorithm is more accurate and faster than competitors such as XBLAS.

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Revealing how lower organisms solve complicated problems is a challenging research area, which could reveal the evolutionary origin of biological information processing. Here we report on the ability of a single-celled organism, true slime mold, to find a smart solution of risk management under spatio-temporally varying conditions. We designed test conditions under which there were three food-locations at vertices of equilateral triangle and a toxic light illuminated the organism on alternating halves of the triangle. We found that the organism behavior depended on the period of the repeated illumination, even though the total exposure time was kept the same . A simple mathematical model for the experimental results is proposed from a dynamical system point of view. We discuss our results in the context of a strategy of risk management by Physarum.

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Feature extraction and selection are key factors in model reduction, classification and pattern recognition problems. This is especially important for input data with large dimensions such as brain recording or multiview images, where appropriate feature extraction is a prerequisite to classification. To ensure that the reduced dataset contains maximum information about input data we propose algorithms for feature extraction and classification. This is achieved based on orthogonal or nonnegative tensor (multi-array) decompositions, and higher order (multilinear) discriminant analysis (HODA), whereby input data are considered as tensors instead of more conventional vector or matrix representations. The developed algorithms are verified on benchmark datasets, using constraints imposed on tensors and/or factor matrices such as orthogonality and nonnegativity.

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Fatigued monetary bills adversely affect the daily operation of automated teller machines (ATMs). In order to make the classification of fatigued bills more efficient, the development of an automatic fatigued monetary bill classification method is desirable. We propose a new method by which to estimate the fatigue level of monetary bills from the feature-selected frequency band acoustic energy pattern of banking machines. By using a supervised self-organizing map (SOM), we effectively estimate the fatigue level using only the feature-selected frequency band acoustic energy pattern. Furthermore, the feature-selected frequency band acoustic energy pattern improves the estimation accuracy of the fatigue level of monetary bills by adding frequency domain information to the acoustic energy pattern. The experimental results with real monetary bill samples reveal the effectiveness of the proposed method.

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In this paper we consider region-to-region interaction in the brain from a dynamical systems viewpoint, and explain it by proposing a simple model at a mesoscale level. The model is characterized by the following two points: (1) Spatio-temporal patterns of neural activities corresponding to some sort of ‘attractors’ in a local region are symbolically represented by simple limit-cycle orbits, and (2) dynamical inter-region coupling is realized as a form of mutual excitation among these orbits. By numerical simulations, we show how the phase transition between the activation state and the resting state in the real brain can be explained from this dynamical systems viewpoint.

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It is well known that it is an ill-posed problem to decide whether a function has a multiple root. For example, an arbitrarily small perturbation of a real polynomial may change a double real root into two distinct real or complex roots. In this paper we describe a computational method for the verified computation of a complex disc to contain exactly k roots of a univariate nonlinear function. The function may be given by some program. Computational results using INTLAB, the Matlab toolbox for reliable computing, demonstrate properties and limits of the method.

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On reflexive real Banach spaces, a fixed point theorem in weak topology for successively recurrent system of fuzzy-set-valued nonlinear mapping equations and its application to ring nonlinear network systems are theoretically discussed in detail. An arbitrarily-level likelihood signal estimation is established, here.

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In this paper, a numerical method is presented for verifying the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations. Taking into account every error of numerical computations such as the discretization error and the rounding error, this method also provides mathematically guaranteed error bounds between approximations obtained by numerical computations and the exact solution whose existence is proven by the numerical existence theorem, which is based on the Newton-Kantorovich theorem. Finally, illustrative numerical results are presented for showing the usefulness of the method.

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A fast verified automatic integration algorithm is proposed for calculating univariate integrals over finite intervals. This algorithm is based on the double exponential formula proposed by Takahasi and Mori. The double exponential formula uses a certain trapezoidal rule. This trapezoidal rule is determined by fixing two parameters, the width h of a subdivision of a finite interval and the number n of subdivision points of this subdivision. A theorem is presented for calculating h and n as a function of a given tolerance of the verified numerical integration of a definite integral. An efficient a priori method is also proposed for evaluating function calculation errors including rounding errors of floating point calculations. Combining these, a fast algorithm is proposed for verified automatic integration. Numerical examples are presented for illustrating effectiveness of the proposed algorithm.

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In investments, it is not easy to identify traders'behavior from stock prices, and agent systems may help us. This paper deals with discriminant analyses of stock prices using multifractality of time series generated via multi-agent systems and interpolation based on Wavelet Transforms. We assume five types of agents where a part of agents prefer forecast equations or production rules. Then, it is shown that the time series of artificial stock price reveals as a multifractal time series whose features are defined by the Hausedorff dimension D(h). As a result, we see the relationship between the reliability (reproducibility) of multifractality and D(h) under sufficient number of time series data. However, generally we need sufficient samples to estimate D(h), then we use interpolations of multifractal times series based on the Wavelet Transform.

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To illuminate the synchronization phenomena between heartbeat and music, the effects of a sedative music of variable tempo on heart rates were investigated. In the experiment, nine subjects were exposed to the sedative music with having changes in its tempo. The tempo gradually increases, decreases, or stands stable in the music (hereafter these experimental condition are named as Up, Down, and Flat condition). With regard to the analysis of synchronization, we introduced our formerly developed Cardio-Music Synchrogram, which was used to extract statistically significant synchronization period between heartbeat and music. As a result, it was suggested that the sedative music in Down condition induced synchronization more frequently than Flat and Up conditions.

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We analyze stationary phase tracking error of delay-locked loops (DLL) in direct spread code division multiple access (DS-CDMA) using Markovian spreading sequences. The phase tracking error is caused by noise generated inside of DLLs by multiple access interferences. When binary Markovian sequences are used, the noise is not considered as white Gaussian noise. This makes analysis of the tracking error difficult. In this paper, we describe DLLs by stochastic difference equations and derive forward evolutional equations of the probability distribution of the states of DLLs. Applying path integral analysis to the evolutional equations, we obtained stationary distribution. We found from the distribution that Markovian spreading sequences with negative eigenvalue were effective in decreasing stationary phase tracking error of not only a type of DLL in asynchronous CDMA but also DLLs in chip-synchronous CDMA.

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We consider discretized piecewise-monotone-increasing Markov transformations and give an algorithm, called the bounded monotone truth-table algorithm, for generating all full-length sequences which are based on the discretized transformations. The algorithm is efficient in the sense that it guarantees to generate all full-length sequences without computing their total number. Additionally it is applicable to generation of all de Bruijn sequences.

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This paper describes a method of implementing RadauIIA and LobattoIIIA of implicit Runge-Kutta formulas into circuit simulators for nonlinear circuits as numerical integration. These implicit Runge-Kutta methods have high orders and are A-stable. Equivalent circuits at discrete time for linear and nonlinear elements are proposed. Circuits at times between past and present time are needed in addition to the equivalent circuit at present time. Solutions at intermediate and present times must be estimated simultaneously. So, the size of equivalent circuit becomes larger than the numerical integration in conventional circuit simulators. However, since the orders of these algorithms are high, this problem is solved by using larger time step for numerical integration compared to conventional methods to save calculation time. The implicit Runge-Kutta and conventional methods are compared in terms of accuracy and computational costs using example circuits.

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This paper presents a low voltage CMOS full-wave rectifier for transcutaneous power transmission in low power battery-less devices such as biomedical implants. By using a simple comparator-controlled switch which needs a small supply voltage, the lowest input voltage amplitude can be reduced to 0.7V with a standard CMOS 0.18µm process. With only one comparator, the proposed design dramatically reduces the power loss and the production cost. In combination with current offset which minimize the reverse current of the rectifier under different input amplitudes, the proposed rectifier can achieve a maximum peak voltage conversion efficiency of more than 93% and a power efficiency of approximately 87%.

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This paper proposes a novel error-correcting scheme using chaotic dynamics for noncoherent chaos communications. In our proposed system, two successive chaotic sequences are generated from the same chaotic map; the second sequence is generated with an initial value which is the last value of the first sequence. In this case, successive chaotic sequences having the same chaotic dynamics are created. This feature gives the receiver additional information to correctly recover the information data and thus improves the bit error performance of the receiver. As results of the computer simulation, we confirm that the advantage gained in BER performance of the proposed error-correcting method is about 1-1.5 dB compared to conventional method. In addition, we achieve that the proposed error-correcting scheme is performed without the new additional redundancy code by using the chaotic dynamics.

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Identification of a region in biological sequences, motif extraction problem (MEP) is solved in bioinformatics. However, the MEP is an NP-hard problem. Therefore, it is almost impossible to obtain an optimal solution within a reasonable time frame. To find near optimal solutions for NP-hard combinatorial optimization problems such as traveling salesman problems, quadratic assignment problems, and vehicle routing problems, chaotic search, which is one of the deterministic approaches, has been proposed and exhibits better performance than stochastic approaches. In this paper, we propose a new alignment method that employs chaotic dynamics to solve the MEPs. It is called the Chaotic Motif Sampler. We show that the performance of the Chaotic Motif Sampler is considerably better than that of the conventional methods such as the Gibbs Site Sampler and the Neighborhood Optimization for Multiple Alignment Discovery.

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