A min–max spanning tree is a spanning tree minimizing the maximum weight of its edges. Sepasian and Monabbati (2017) introduced the problem of upgrading the maximum edge weight of a min–max spanning tree. Each edge weight can be decreased by paying a cost, and the objective is to minimize the maximum weight of a min–max spanning tree within a given budget. They designed a polynomial algorithm and a faster algorithm for a special case. In this paper, we extend their algorithm to matroids. Further, we show that the algorithm for the special case is applicable to a more general case.

Recently, proximal Newton-type methods with metrics restricted to diagonal matrices have been proposed for solving composite optimization problems whose objective function is the sum of a smooth function and a possibly nonsmooth function. Although the effectiveness of one of them, the proximal diagonal Newton method (PDNM), has been reported theoretically and numerically, only 𝒪(1/k) sublinear convergence rate has been obtained at best for non-strongly convex problems. We propose an accelerated variant of the PDNM, which achieves the convergence rate of 𝒪(1/k²).

Because of a declining birth rate and an aging population, intergenerational inequality in the public pension system has become one of the most serious social issues, especially in Japan. This paper examines whether it is possible to address intergenerational inequality while maintaining the current pay-as-you-go system in Japan’s National Pension scheme. The study employs agent-based modeling simulation to investigate two settings related to financial resources: (i) changes in the ratio of insurance premiums to taxes, and (ii) the ratio of consumption tax to income tax.

In this paper, we perform a roundoff error analysis of an integration-based method for computing the matrix sign function recently proposed by Nakaya and Tanaka. The method expresses the matrix sign function using an integral representation and computes the integral numerically by the double-exponential formula. While the method has large-grain parallelism and works well for well-conditioned matrices, its accuracy deteriorates when the input matrix is ill-conditioned or highly nonnormal. We investigate the reason for this phenomenon by a detailed roundoff error analysis.

In this study, a method was developed for estimating defects in concrete from test data generated by hammering a concrete plate using machine learning. A neural network was constructed based on a self-attention network to estimate the three-dimensional position and size of the defects placed within the concrete plate. The scalograms generated from the acceleration responses were used as the input. Identification was also conducted using data augmentation, in which we evaluated the effect of the number of training data items on identification accuracy.

This paper describes level-set based topology optimization for bi-linear type elasto-plastic problems. The geometric complexity can be controlled by the value of the regularization factor τ defined by the phase-field method, and the application of this method to bi-linear elasto-plastic models aims to improve the reliability of structural designs. In this study, a comparison is carried out for the final topologies in elastic and bi-linear elasto-plastic models using 2D and 3D cantilever beam models; we also provide reliable design considerations.

Advances in experimental technologies have induced the need for 3D cell data analysis. However, we lack a simple method that directly analyzes 3D data. 2D methods are insufficient when cells overlap orthogonal to slices. Experimental constraints sometimes make the step size of slices greater than a pixel in each slice. We present a 3D figure detection technology using persistent homology usable even in the above situations. Also, the parameters have clear geometric meanings. Thus, our method serves as an easy-to-use 3D cell detection technology that directly uses 3D data and respects experimental constraints.

A sequence of solutions generated by a continuous optimization method can be associated with a solution trajectory of the continuous dynamical system obtained by the continuous limit of step sizes being 0. Such dynamical systems can contain Hessians even when the original optimization methods do not. In this paper, we show the convergence rate of such dynamical systems via the method of Lyapunov functions and argue their optimality.

A chaotic dynamical system is one in which the system obeys deterministic laws but its future and past are difficult to predict. In this study, we observed and discussed the behavior of orbits of coupled two nonchaotic dynamical systems when they are coupled. As a result, a chaotic synchronization phenomenon, in which the orbits of the two dynamical systems synchronize completely with chaotic natures, was observed under certain conditions. We clarified the conditions under which the phenomenon occurs by analytically deriving the conditional Lyapunov exponent, Cauchy Laws with ergodic theory.

Numerical properties of the momentum conservation law for Hamiltonian partial differential equations are investigated based on a symplectic time integration. In the nonlinear Klein–Gordon system, it is shown that the critical value of the coefficient of the dispersion term is nearly proportional to the inverse square of the total grid number. The result is consistent with the scale invariance of the equation of motion. On the other hand, in the nonlinear Schrödinger-type system, the critical value of the coefficient does not follow the scale invariance of the equation of motion.

In this study, we developed a mixed-integer programming model that can help maximize the profit of the gas-fired power generation business in Japan. Owing to the practical constraints of liquefied natural gas (LNG) cargo, LNG tank, and power generating unit, Japanese gas-fired power producers are currently unable to effectively utilize the futures market. By using this model, power producers can calculate the optimal futures position and the number of spot LNG cargoes to buy/sell in response to the daily changing forward spark spread. The numerical simulation shows that the optimal electricity futures position decreases in a step-wise manner against the electricity futures price.

This study proposes an integrable discretization of linear and logistic equations at random intervals with higher-order accuracy. We approximate the exponential function by rational functions using the Padé approximation of any degree and employ them to increase accuracy. We design a new integrable discretization of the linear equations under random intervals with higher-order accuracy. The logistic equation can be discretized through dependent variable transformation while maintaining integrability.

Numerical integrators which conserve invariants of original differential equations are called conservative integrators. While most of them are computationally expensive, a cheaper class is the projection methods, where conservation is realized by simple projections. However, such methods do not necessarily preserve affine invariance originally held in differential equations. In this study, we point out several affine-invariant projections and discuss how the affine invariance affects the quality of numerical solutions.

Numerical simulation of the one-dimensional advection equations is known to be difficult with discontinuous initial states. The initial shape undergoes distortion due to high-frequency fluctuations, exemplifying a prevalent challenge in discretizing dynamics: the violation of conservation laws. In addressing this issue, our study introduces a topological regularization method for numerical simulations, leveraging persistent homology. The effectiveness of our approach is demonstrated through numerical simulations of the one-dimensional advection equation with a rectangular initial state. The results highlight the potential of our method to improve the accuracy and fidelity of simulations, especially in scenarios where maintaining topological conservation is critical.

Generative Adversarial Networks (GANs) are the architecture of significant interest in the field of data generation using machine learning. Attempts have been made in the past to generate time-series data using GANs. In this study, we generated time series following a generalized Boole transformation using GANs and investigated how well the generated data preserved the characteristics of the original time series from both a dynamic and statistical perspective. Additionally, we examined the impact of the distribution followed by the random noise input to the GAN’s generator on the pseudo time series.

This paper presents a fast wavefield evaluation method for two-dimensional wave scattering problems. The proposed method is based on a modified version of proxy-surface-accelerated interpolative decomposition, making it effective even if the evaluation points are near the boundary. The commonly known fast multipole method requires the use of direct evaluations near the boundaries of scatterers because the analytical expansion of kernel functions does not converge. On the one hand, the proposed method does not require the analytical expansion of kernel functions. The validity and effectiveness of the proposed method are demonstrated using numerical examples.

Some isogeny-based cryptosystems use addition and doubling on the Jacobian over genus-2 sextic and non-monic hyperelliptic curves. In this study, we generalized some formulae for quintic and monic curves to sextic curves using projective coordinates and then compared them. For sextic curves and projective coordinates, the formulae based on Lange’s were faster than those based on Costello–Lauter’s, in contrast to quintic curves. The formulae based on Lange’s take 64M + 6S for addition and 59M + 9S for doubling, where M and S denote the computational costs of multiplication and squaring, respectively.

This study introduces a novel algorithm designed to facilitate the accurate generation of domain triangulation for certain n-dimensional simplex domains. Traditional mesh generators employing floating-point arithmetic often encounter rounding errors, leading to a discrepancy between the generated domain triangulation and the intended geometric domain. Our algorithm introduces strategic perturbations to the triangulation nodes. This ensures that boundary nodes are precisely aligned on the domain boundary, thereby preserving the domain’s geometric integrity. Furthermore, this paper highlights the algorithm’s significance in enhancing the precision and reliability of high-precision eigenvalue computations for differential operators through practical mesh generation examples.

In this paper, we report the behavior of solutions of the one-dimensional Cahn–Hilliard equation with dynamic boundary conditions, where the time evolution on the boundary is induced by the boundary derivative. By studying the time evolution from a certain initial value, we find that as the time constant on the boundary asymptotically approaches a certain value, the relaxation to a stable stationary solution slows down at a logarithmic rate. This phenomenon is not observed in the case of the Neumann boundary condition.

Lundin and Stenger applied the Sinc approximation combined with the single-exponential (SE) transformation to approximate derivatives over the finite interval (−1,1), and provided its theoretical error analysis. In this study, we improve their approximation formula by replacing the SE transformation with the double-exponential (DE) transformation. The replacement has already been proposed for the first-order derivative, and an error analysis has also been provided. This study proposes the approximation and provides its rigorous convergence analysis for any order derivative.

In the aquaculture industry, damage occurs because of a sudden decrease in salinity concentration. Therefore, the demand for real-time forecasting has increased. Forecasting through machine learning is increasing; however, observation stations at the target site are not always present. Therefore, we predicted the flow field at the target site through data assimilation (DA) using a method combining the Kalman filter and finite element method. In this study, we used the predicted values with DA for long short-term memory and improved the prediction accuracy.

Due to phase lock caused by a saddle-node bifurcation, the states of limit cycles for a tropically discretized Sel’kov model become equivalent to those for its ultradiscretized max-plus model. This property is essentially the same as the case of the negative feedback model, and existence of a general mechanism for ultradiscretization of the limit cycles is suggested. Furthermore, we find the logarithmic dependence of the time to pass the bottleneck for phase drift motion in the vicinity of the bifurcation point. This dependency can be understood as a consequence of the piecewise linearization by applying the ultradiscrete limit.

Numerical computation for eigenvalue decomposition plays a crucial role in many scientific fields, and highly accurate eigenpairs are required in certain domains. A novel method was proposed in this study for the iterative refinement of the eigenpair of a real symmetric matrix, which is based on the Ogita–Aishima method and uses compact WY representation. The proposed method can refine the accuracy of a partial eigenpair without using a full eigenvector matrix. Numerical examples illustrate the convergence of residuals, and a large-memory computer is not required for refinement.

The discrete relativistic Toda equation is derived from the compatibility condition of the spectral transformations of the Laurent biorthogonal polynomials. The ultradiscrete version of this equation is regarded as a time evolution of the soliton cellular automaton, a new kind of box-ball system. In the time evolution of this automaton, not only balls but also some boxes move. We introduce 10-arc lines for the automaton and obtain the conserved quantities corresponding to soliton sizes.

In this study, we show that a weak key exists with a high probability in Strongly Asymmetric Algorithm-5 (SAA-5), a post-quantum key agreement protocol based on matrix operations on finite field 𝔽_p. It has been claimed that only an exhaustive attack is possible for recovering a secret shared key. We propose a polynomial time recovery attack on the weak keys using the prime factorization of p – 1, the rank of matrices used in the protocol, and the Chinese remainder theorem. We also report the results of numerical experiments on SAA-5 using Magma against the recommended parameters, which can be recovered within a short time.

In 2004, Demaine et al. showed that if P is a simply connected polygonal region in the plane, then for any piecewise-C² folded state (f, λ) of P, there exists a folding motion from P to (f, λ). In this paper, we show that if P is not simply connected, then the conclusion of the theorem does not necessarily hold; in fact, there exists an annulus P in ℝ² such that there exist piecewise-C² folded states of P which do not admit folding motions. The theorem is proved using an argument from a branch of low-dimensional topology called knot theory.

In this paper, we introduce a novel Quantum Least-Squares Monte Carlo (QLSM) algorithm for solving backward stochastic differential equations (BSDEs). The QLSM algorithm leverages quantum computing to enhance the efficiency of traditional least-squares Monte Carlo methods. We present the detailed procedure of the QLSM method and an evaluation of its accuracy and computational cost. This approach has significant potential for applications in mathematical finance, particularly in pricing complex financial derivatives and risk management.

Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in turbulence studies, we demonstrate that SVD for an artificial matrix with multi-scale structures reproduces the power-law-like distribution in the singular value spectrum with several orthogonal modes. Then, MFSVD is applied to practical turbulence field data produced by numerical simulations. It is clarified that relative errors in the reproduction of quadratic nonlinear quantities in multi-field turbulence converge remarkably faster than the single-field case, which requires thousands of modes to converge.

This study presents a numerical solution to the shape design problem in a viscous flow field that considers fluid–structure interactions. The square error integrals between the actual flow velocity distributions and the target distributions used to control the flow velocity of the subdomain in the viscous flow field are used as the objective functional. The adjoint variable method is used. A shape derivative is derived for this problem. Furthermore, the H¹ gradient method is used to perform reshaping. A numerical analysis program is developed for the problem using FreeFEM, and its validity is confirmed using the numerical results of 2D problems.

In this study, we present a shape optimization analysis of a corrugated wing to improve the lift force. We solved the shape optimization problem using the adjoint variable method. Owing to shape optimization analysis, the corrugated wing, considered as the initial shape, deformed to a shape pointing downward at the trailing edge, which increased the lift force by a factor of 1.4. Furthermore, we applied the deep reinforcement learning method, Double Deep Q-Network, to the trailing edge of the wing, which is one of the parts of the sensitivity concentration, and further increased the lift force by 5.6%.

This paper presents a density-based topology optimization for two-layer material structure problems along with a design method for maximally stiff structures using machine learning. We applied a modified optimality criteria method to two-layer structure problems to investigate the effects of arbitrary parameters on optimal topology. In addition, we formulated a design method for maximally stiff structures using machine learning to reduce computational costs.