We report the exact analysis of asymptotic behavior for some stochastic cellular automata with a quadratic conserved quantity. There exists a reduction from the cellular automaton with a quadratic conserved quantity to that with a primary through a transformation of variable. Exact analysis about the asymptotic behavior is made utilizing this relation.

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Tracy and Widom showed that the level spacing function of the Gaussian unitary ensemble is related to a particular solution of the fourth Painlevé equation. We reconsider this problem from the viewpoint of Hirota's bilinear method in soliton theory and present another proof. We also consider the asymptotic behavior of the level spacing function as s→ ∞, and its relation to the “Clarkson-McLeod solution” to the Painlevé IV equation.

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The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing a equivalence class of cyclic permutations to the initial values. We proved that the graphs are bi-directional and that they are composed of several arrays of complete graphs connected at one of their vertices. The condition for the graphs to be bi-directional is studied for general discrete equations.
MSC2010: 37K10, 37P05, 37P25, 37J35

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The roundoff error accumulation in the iterative use of the fast Fourier transform (FFT) is discussed. By using numerical simulations of partial differential equations, we numerically show that the roundoff error in the iterative use of the FFT tends to be accumulated. To avoid a lack of precision, we present numerical simulations in which a quadruple precision floating point number is used, which ensures sufficient precision against the accumulation of the roundoff errors in the FFT.

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We discuss several methods to simulate interval arithmetic operations using floating-point operations with fixed rounding mode. In particular we present formulas using only rounding to nearest and using only chop rounding (towards zero). The latter was the default and only rounding on GPU (Graphics Processing Unit) and cell processors, which in turn are very fast and therefore attractive in scientific computations.

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In this paper, we develop an accurate and efficient algorithm for solving ill-conditioned linear systems. For this purpose, we propose two preconditioning methods that are based on LU factorization. One is the method using the inverse of an LU factor. The other is the method using the residual of an LU factorization. The latter method requires less computational cost than the former one. Using an LU factorization with the iterative refinement, we can accurately solve a linear system Ax =b for $\kappa(A) \lesssim u^{-1}$, where u is the relative rounding error unit in working precision. If we use the proposed algorithm with accurate dot product, we can obtain an accurate approximate solution for ill-conditioned linear systems beyond the limit of the working precision. Results of numerical experiments show that the proposed algorithm can work for $\kappa(A) \lesssim u^{-2}$ in reasonable computing time.

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This paper is concerned with the embedding constant of the Sobolev type inequality for fractional derivatives on $\Omega\subset\mathbb{R}^{N}~(N\in\mathbb{N})$. The constant is explicitly described using the analytic semigroup over L²(Ω) generated by the Laplace operator. Some numerical examples of estimating the embedding constant are also provided.

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Remarkable hardware robustness of deep learning is revealed from an error-injection analysis performed using a custom hardware model implementing parallelized restricted Boltzmann machines (RBMs). RBMs used in deep belief networks (DBNs) demonstrate robustness against memory errors during and after learning. Fine-tuning has a significant impact on the recovery of accuracy under the presence of static errors that may modify structural data of RBMs. The proposed hardware networks with fine-graded memory distribution are observed to tolerate memory errors, thereby resulting in a reliable deep learning hardware platform, potentially suitable to safety-critical embedded applications.

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This paper discusses the stochastic resonance (SR) effect in a binary communication system for subthreshold signal reception. We focus on the problem of no communication when received signal strength is below receiver sensitivity. Subthreshold signal reception requires a device that exhibits SR, such as a Schmitt trigger or a comparator. Previously, we proposed an alternative three-level device and demonstrated its high performance for subthreshold signal reception in an SR receiver. In the present study, we show that our proposed three-level device outperforms the three devices and discuss reasons for this superior performance. Contributions of our present paper are twofold: first, we analytically derive bit error rate (BER) performances of SR receivers installed with a Schmitt trigger and a comparator;second, we compare performances of the Schmitt trigger, comparator, and three-level device.

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This paper presents the theory and implementation of the non-linear control method of Input to Output Linearization (IOL) for boost DC-DC switching power converters operating in continuous inductor current mode. The paper examines the non-linear and non-minimum phase nature of boost converters. The limitations of IOL control on boost converters have been outlined. It has been shown that these limitations are overcome by addressing the non-minimum phase nature in boost converters. Using analytical and experimental methods, it is demonstrated that IOL control scheme compensates the non-linear boost converter to achieve wide range of output voltages with excellent response to load and duty cycle variations.

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