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.