JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Current issue
Displaying 1-17 of 17 articles from this issue
• Yasufumi Hashimoto
2022 Volume 14 Pages 1-4
Published: 2022
Released on J-STAGE: January 27, 2022
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The unbalanced oil and vinegar signature scheme (UOV) is a signature scheme whose public key is a set of quadratic polynomials over a finite field. This scheme has been considered to be secure and efficient enough under suitable parameter selections. However, its key size is relatively large, and then various arrangements of UOV with smaller keys have been proposed. Hufu-UOV proposed by Tao in 2019 is one of such variants of UOV, whose keys are generated by circulant and Toeplitz matrices. In the present paper, we study the security of Hufu-UOV and propose an attack on it.

• Soujun Kitagawa, Daisuke Takahashi
2022 Volume 14 Pages 5-8
Published: 2022
Released on J-STAGE: February 02, 2022
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We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of expressions using shift operators and binary trees are applied for the derivation of solution.

• Jiro Akahori, Yui Furuichi, Kaori Okuma
2022 Volume 14 Pages 9-12
Published: 2022
Released on J-STAGE: February 03, 2022
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In the present paper, we introduce a variant of the numerical scheme called the deep solver of PDE. Our scheme is based on a non-linear version of the discrete-time Clark--Ocone formula, which describes the convergent expansion of the error terms. Our new scheme incorporates the higher-order error terms, which we conjecture to stabilize the stochastic gradient descent procedure, and also the irregularities in the driver and the terminal function of the associated forward-backward stochastic differential equation.

• Hisashi Kohashi, Harumichi Iwamoto, Takeshi Fukaya, Yusaku Yamamoto, T ...
2022 Volume 14 Pages 13-16
Published: 2022
Released on J-STAGE: February 26, 2022
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A performance prediction method for massively parallel computation is proposed. The method is based on performance modeling and Bayesian inference to predict elapsed time $T$ as a function of the number of used nodes $P$ ($T=T(P)$). The focus is on extrapolation for larger values of $P$ from the perspective of application researchers. The proposed method has several improvements over the method developed in a previous paper, and application to real-symmetric generalized eigenvalue problem shows promising prediction results. The method is generalizable and applicable to many other computations.

• Tomoaki Okayama
2022 Volume 14 Pages 17-20
Published: 2022
Released on J-STAGE: February 27, 2022
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Double-exponential formulas were proposed by Takahasi and Mori in 1974 as efficient numerical integration methods. They considered four typical cases: (i) integral on a finite interval, (ii) semi-infinite integral of algebraically decaying functions, (iii) semi-infinite integral of exponentially decaying functions, (iv) infinite integral of algebraically decaying functions, and they proposed a double-exponential formula for each case. This paper proposes a double-exponential formula for another case: (v) infinite integral of unilateral rapidly decreasing functions. A theoretical error analysis of the proposed formula is also given.

• Fuki Ito
2022 Volume 14 Pages 21-24
Published: 2022
Released on J-STAGE: March 02, 2022
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In this paper, we investigate optimal randomized algorithms of balanced AND-OR tree evaluation, with regards to query complexity. For balanced AND-OR trees, previous studies have made a good progress on the uniqueness of eigen-distributions, i.e., optimal mixed strategies determining an input (Suzuki & Nakamura 2012, Peng et. al. 2016). However, it has been considered that the dual problem, the uniqueness of optimal randomized algorithms, is rather difficult, and a new approach has been needed. By introducing a group-theoretical methods, we show that the uniqueness does not hold and there are uncountably many optimal randomized algorithms.

• Manabu Miyamoto, Keiichi Tanaka
2022 Volume 14 Pages 25-28
Published: 2022
Released on J-STAGE: March 02, 2022
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This study examines whether an alternative calculation approach exists for the asymptotic expansion of the probability density function of risky asset prices. We focus on the partial differential equation by using an eigenfunction expansion related to Hermite polynomials. We show that the expansion coefficients can be obtained by solving ordinary differential equations recursively and which order of Hermite polynomials appear in asymptotic expansion explicitly.

• Kansei Ushiyama, Shun Sato, Takayasu Matsuo
2022 Volume 14 Pages 29-32
Published: 2022
Released on J-STAGE: March 02, 2022
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Some continuous optimization methods can be regarded as numerical methods applied to ordinary differential equations, and attempts to derive and analyze optimization methods from this perspective have been made for quite a long time. In this study, along this line of research we point out a possibly overlooked simple fact that by carefully observing the relationship between the convergence of optimization methods and the stability of numerical methods, we can construct an efficient optimization method based on certain numerical methods with extremely wide stability domain.

• Koki Nitta, Toshiki Sasaki, Nobito Yamamoto
2022 Volume 14 Pages 33-36
Published: 2022
Released on J-STAGE: March 16, 2022
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In Terasaka et al. JSIAM Lett. (2020), we have proposed numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria using non-linear transformations by up to third degree polynomials. In the present study, we extend these methods by proving that polynomials of an arbitrary degree can be applied to define the transformations and show an example problem where we have to use a fifth-degree polynomial to construct local Lyapunov functions.

• Shunpei Terakawa, Takaharu Yaguchi
2022 Volume 14 Pages 37-40
Published: 2022
Released on J-STAGE: March 16, 2022
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We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although it is known that symplectic integrators are suitable for discretizing Hamiltonian systems, the composition of Hamiltonian systems may not be Hamiltonian. In this paper, focusing on a property of Hamiltonian systems, that is, the conservation of the symplectic form, we provide a condition under which two Hamiltonian systems coupled with interactions compose a Hamiltonian system.

• Ryunosuke Oshiro, Ken'ichiro Tanaka
2022 Volume 14 Pages 41-44
Published: 2022
Released on J-STAGE: April 06, 2022
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The choice of the norm on a space of functions over a graph is important to obtain a good quadrature. In this study, we consider numerical integration on an undirected and unweighted graph. Existing studies have defined various kinds of norms, which define a kind of smoothness" of functions over a graph. In this study, we used the norm defined by [Seto, Suda and Taniguchi, Linear Algebra Appl. (2014)]. and kernel quadrature techniques, the Frank--Wolfe and away-steps Frank--Wolfe method. We obtain a theoretical guarantee of the convergence of the away-steps Frank--Wolfe method.

• Masaru Shintani, Ken Umeno
2022 Volume 14 Pages 45-48
Published: 2022
Released on J-STAGE: April 06, 2022
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The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

• Masaru Shintani, Ken Umeno
2022 Volume 14 Pages 49-52
Published: 2022
Released on J-STAGE: April 06, 2022
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We propose a new dynamic pricing algorithm based on the universal exponential law of booking curves in services with reservations. The algorithm includes a parametric learning model which makes it possible to simulate the effect of changes in prices on quantity demanded from historical data continuously for practical use. Furthermore, we show an example, where some real data in a hotel applies for the learning model. Our proposed algorithm with the learning model, which can dynamically update the optimum parameters, is envisaged to be utilized as a practical dynamic pricing strategy.

• Shuto Kawai, Shun Sato, Takayasu Matsuo
2022 Volume 14 Pages 53-56
Published: 2022
Released on J-STAGE: May 11, 2022
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We consider a conservative scheme for the Ostrovsky equation proposed in Yaguchi et al. (J. Comput. Appl. Math., 2010), whose mathematical analysis has been left open. In this letter, we first show the existence of numerical solutions. We then establish an $L^2$ convergence estimate, which can in turn imply an $H^1$ estimate by a supplementary $L^\infty$ boundedness argument. We also point out that the scheme can be implemented in a differential form, which is much cheaper in computational cost.

• Yoshiki Jikumaru
2022 Volume 14 Pages 57-60
Published: 2022
Released on J-STAGE: May 11, 2022
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In this paper, we propose piecewise linear constant anisotropic mean curvature (CAMC) curves and surfaces based on a variational characterization. These curves (resp. surfaces) are equilibrium for the anisotropic energy amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the non-minimal case) the area (resp. volume) to one side of the curves (resp. surfaces). Our discrete CAMC surfaces are a generalization of discrete CMC surfaces defined by the variational principle. We also show a stability result of discrete CAMC surfaces including the result for discrete CMC surfaces.

• Mikio Murata
2022 Volume 14 Pages 61-64
Published: 2022
Released on J-STAGE: May 15, 2022
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We proposed a method for generating cellular automata from reaction-diffusion equations automatically. Tropical discretization is a method that uses positive discretization and ultradiscretization. The tropical discretization is used to create a cellular automaton from the competitive diffusion equation in this paper. It has been demonstrated that constructed difference equations, ultradiscrete equations, and cellular automata have a similar property to competitive diffusion equations in that the order of the solutions is conserved.