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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

It is important to study the global behavior of solutions to systems of ordinary differential equations describing the transmission dynamics of infectious disease. In this paper, we present a different approach from the Lyapunov function used in most of the study. This approach is based on the Poincaré compactification. We then apply the method to an SIR endemic model as a test case, and discuss its effectiveness and the potential applications of this approach. In addition, we refine the discussion of dynamics near the equilibrium, derive the asymptotic behavior, and mention its relation to the basic reproduction number.

Given two correlated systems, detecting causality between them from observed data is an important but challenging task. Combining two mathematical techniques, delay coordinate embedding and persistent homology, we propose a novel causal inference method for data comprising a pair of scalar time series that are observed from two possibly coupled deterministic dynamical systems. The idea is to encode the topology of the dynamics in the form of the persistent homology of the reconstructed attractors and compare the involved systems by a metric defined on the persistent homology.

We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that provides an upper bound on the expected value of the K-S test statistic when the distribution of the null hypothesis differs from the exact distribution. Furthermore, we proposed a second-level test based on the two-sample K-S test with an ideal empirical distribution as a candidate for improvement.

It is well-known that the trapezoidal formula is an accurate quadrature formula for the infinite integral of exponentially decaying functions. Even for the semi-infinite integral of exponentially decaying functions, the trapezoidal formula works accurately combined with a conformal map proposed by Lund. Another conformal map for this case was introduced by Muhammad and Mori, and their map worked better in all the numerical comparisons conducted so far. Therefore, the conformal map by Muhammad and Mori is expected to give better results in all instances than that by Lund. This paper proves the conjecture.

We discuss a particle system of 5 neighbors with two independent conserved densities. The mean momentum uniquely depends on a pair of the densities and a three-dimensional fundamental diagram is obtained. It shows the phase transition of behavior of asymptotic solution to the system. Moreover, we propose two other systems which have the similar unique dependency obtained numerically.

We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN formulation. In addition, since we treat a nonvacuum case, we review the evolution equations of the matter fields of a perfect fluid. To make the simulations stable, we propose a modified system, which decreases numerical errors in analysis, and we actually perform stable simulations with decreased numerical errors.

Numerical properties of the Poincaré integral invariant of the Toda lattice systems are investigated based on the discrete Fourier interpolation method. In the 1D Toda lattice, we show that the Poincaré integral invariant is conserved in a finite time interval in a symplectic time integration. In contrast, a conserved quantity of the 2D Toda lattice is conserved for a long time interval because of the interaction perpendicular to the lattice direction.

In this study we apply a modified optimality criteria method to density-based topology optimization analysis in static problems. The modified optimality criteria method was developed based on Newton's method and the optimality criteria method. Unlike the optimality criteria method, the modified optimality criteria method does not require the setting of weighting factors. We show the results of the respective density distributions obtained by the optimality criteria method and the modified optimality criteria method for a cantilever beam model. Finally, using the optimization of an automotive part, we demonstrate the industrial applicability of the modified optimality criteria method.

This paper presents some improved infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem, which comprises the Navier--Stokes equations for the flow in a two-dimensional flat torus under a special driving force. These estimations and the basic idea behind them play important roles in accurate enclosing of solutions for such type of nonlinear differential equations. Several comparisons of concrete values confirm the effectiveness of the presented approach.

In the last decade, there has been a growing concern in Japan about the proper use of resources related to emergency medical services, including ambulances. This letter proposes two new methods to optimize the ambulance deployment using a dynamic model, which precisely represents the sequential decision-making process of ambulances dispatched to each request. These methods give allocations to minimize the arrival times in all requests but differ in formulating objectives: one minimizes the average, and the other minimizes the maximum. A computer simulation is used to compare the performances of the two methods in terms of efficiency and fairness.

We propose a numerical method for computing the solutions of high-dimensional Markovian backward stochastic difference equations (BS$\Delta$Es), in which we apply a sparse grid quadrature/interpolation formula. This allows us to calculate the approximated solution accurately and efficiently, which we justify through a rigorous error analysis. Finally, we use a simple numerical experiment to demonstrate the performance of our method.

The square-root Vélu's formula ($\elu$'s formula) is known to be effective way to speed up the computations of higher-degree isogeny used for isogeny-based cryptosystems such as CSIDH and B-SIDH. The original formula was proposed using Montgomery curves, and Moriya et al. then extended it to Edwards curves without specific construction method. In this study, we explicitly show how to construct $\elu$'s formula on Edwards curves. In particular, we provide a method for adjusting for the differences between two resultants. We also compare the computational complexity with the original $\elu$'s formula and find that it is up to 8\% faster.

In this paper, we construct a natural errors-in-variables regression model corresponding to the total least squares (TLS) problem with linear equations constraints and prove strong consistency of the estimation. The presented asymptotic theory in the statistical sense is a generalization of the consistency analysis of an estimation with the use of ordinary total least squares for basic errors-in-variables regression models.

This paper focuses on reducing the computation time for problems in 3D volumetric model reconstruction using the extended CSRBF method. Since the most time-consuming part of the application is solving a saddle point problem with multiple right-hand sides, it is important that this problem be solved in the shortest time possible. Recently, we have proposed an approach for solving saddle point problems using the associated block structure. In this paper, we apply the proposed approach to the problem of 3D volumetric model reconstruction. Through numerical experiments, the performance of the proposed approach is evaluated by comparing it with conventional approaches.

Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODEs. However, since such ODEs can achieve any convergence rate by time rescaling, the correspondence is not as straightforward as usually expected, and deriving new methods through ODEs is not quite direct. In this letter, we pay attention to stability restriction in discretizing ODEs and show that acceleration by time rescaling basically implies deceleration in discretization; they balance out so that we can define an attainable unique convergence rate which we call ``essential convergence rate''.

In data assimilation, state estimation is not straightforward when the observation operator is unknown. This study proposes a method for composing a surrogate operator when the true operator is unknown. A neural network is used to improve the surrogate model iteratively to decrease the difference between the observations and the results of the surrogate model. A twin experiment suggests that the proposed method outperforms approaches that tentatively use a specific operator throughout the data assimilation process.

Dynamical properties of the two limit cycles in a ultradiscrete Sel'kov model are analytically investigated. We construct a Poincaré map for the limit cycles and reveal their stabilities; one is attracting and the other is repelling. Basins for the limit cycles are identified. It is found that the basin of the repelling limit cycle has self-similar structure. We also review the Poincaré map from the viewpoint of integrable system theory.

We numerically generate a stochastic process called ``Brownian house-moving,'' which is a Brownian bridge that stays between its starting point and its terminal point. To construct this process, statements are prepared on the weak convergence of conditioned Brownian bridges. We also study the sample path properties of Brownian house-moving and the decomposition formula for its distribution. Using this decomposition formula and a Monte Carlo sampling technique for a BES$(3)$-bridge, we are able to numerically generate Brownian house-moving at discrete times.

The multivariate quadratic (MQ) polynomial problem involves finding solutions to a system of MQ equations. The construction of an efficient algorithm for solving the MQ problem is an important research topic in the security evaluation of multivariate public key cryptosystems. Gröbner basis computation is often used to solve the MQ problem; the F₄ algorithm is a representative algorithm for computing Gröbner bases. In this article, we examine a polynomial selection strategy for efficiently solving the MQ problem using the F₄ algorithm.

The Lyapunov function plays an important role in the stability theory of dynamical systems. Its counterpart for discrete dynamical systems is not studied so much, though importance of such systems is increasing. In this letter, an attempt is made to construct a discrete analog of the Lyapunov function for the competitive Lotka-Volterra equation. For this purpose, a discrete logarithmic function is defined and its effectiveness is shown.

Vector-valued fuzzy cellular automata (VFCA) are dynamical systems that are the continuous counterparts of cellular automata (CA). As such, continuous-valued traffic-flow models can be defined as VFCA that conserve the number of particles. In this study, a VFCA-based traffic model with obstacles on the road is presented. The proposed VFCA model exhibits asymptotic behavior, in the fundamental diagram, similar to a totally asymmetric simple-exclusion process. This observation was also investigated using the mean-field theory by comparing the equations of the two models.

In this paper, we perform an error analysis of the truncated Taylor series expansion method for computing matrix exponential by taking into account both the truncation error and the rounding error. The derived error bound will be useful to determine the order of expansion or computing precision required to attain the prespecified error level. We also consider mixed-precision computation and give a criterion to determine the order after which lower precision arithmetic can be used without affecting the overall accuracy.

This paper proposes a data analysis method using persistent homology and nonnegative matrix factorization. A concatenated persistence image technique is used to extract coexisting structures from the persistence diagrams of different dimensions hidden behind the data. To demonstrate the potential of our method, we apply the method to 3D voxel data of iron ore sinters obtained by X-ray computed tomography. The analysis successfully captures the coexistence structures in these iron ore sinters.