The study explores algorithms for evaluating matrix φ functions, focusing on the scaling and squaring method, which combines approximation formulas with double-angle relations. Despite its effectiveness, the method's optimal degree of the formula remains underexplored due to the computational burden of matrix multiplications within the relations. To address this, we propose an alternative method that achieves equivalence to these relations without the extensive use of matrix multiplications. Furthermore, we determine the optimum degree for the approximation formula.

We extend the analysis of regulatory networks, represented by differential equations, to account for time delays, which are often critical in modeling biological systems such as gene regulatory networks. Building on the framework of Fiedler et al. (2013), who identified determining nodes influencing long-term network dynamics based solely on the network structure, we introduce a novel method for incorporating time delays into this analysis. Our approach enhances the precision of studying complex biological systems by providing a more accurate representation of dynamic interactions over time.

Exploiting the arbitrariness of inverse ultradiscretization, we introduce a hybrid model that combines the optimal velocity (OV) and the slow-to-start (s2s) models while enforcing the no-overtaking constraint as a discrete-time equation. The ultradiscretization of the new model coincides with the us2s–OV model, which also prohibits overtaking. Furthermore, in the continuum limit, the new model reduces to the s2s–OV model multiplied by a step function.

In this paper, we propose a new algorithm for high-precision matrix multiplication. When the accuracy of results from standard floating-point arithmetic is unsatisfactory, high-precision computation methods can be considered. Examples of such methods include pair arithmetic (PA) by Lange and Rump and double-word arithmetic (DW) by Bailey. In this study, we design a high-precision computation method that cleverly uses fused multiply-add (FMA) operations less costly than PA or DW. We also demonstrate its performance through numerical experiments.

A fast computation method and implementation techniques for computing the matrix inverse square root are presented. We demonstrate that the rational approximation method outperforms others in terms of the number of floating-point operations and its rounding error using the sum of resolvents computation is similar to that of the eigenvalue decomposition method. Moreover, the internal and external parallelism of the sum of resolvents computation can be effectively utilized by implementation for both CPU and GPU.

In this study, we employed machine learning to predict the presence or absence of defects in structures, using acceleration response waveforms from a hammering test. The loss function was defined by the binary cross-entropy error, and several numerical experiments were performed to predict defects by changing the acceleration response waveforms. These acceleration response waveforms were used as input data, enabling the supervised machine learning model to output the presence or absence of defects.

This study shows that the extended entropic chaos degree (EECD) can quantify the chaos of the Lorenz and Rössler equations under an adequate finite partition {A_i} of the domain. The Lyapunov exponent (LE) is often used to quantify chaos in dynamical systems. However, computing the LE is challenging when information about these systems is limited to time-series observational data. The EECD is a modified version of the original entropic chaos degree and is used as a criterion for measuring the strength of chaos from the perspective of information dynamics. The EECD can be directly computed from time-series data.

One-way functions play fundamental role in public-key cryptography. In this paper, one-way functions proposed by Anshel and Goldfeld in 1997 are reformulated, and their computational complexity and applications are discussed. Their one-way functions are constructed using L-functions associated with elliptic curves defined over the rational number field. Their functions are unique and also have potential applications in post-quantum cryptography.

Understanding the quantitative changes in marine ecosystems caused by factors such as climate change, is essential for conserving biodiversity. Marine ecosystem models can help forecast these changes. However, the parameter identification in a highly accurate forecasting model requires collecting oceanographic data and expert tuning. In this study, we applied grid search and Bayesian optimization to hyperparameter optimization to reduce the model building costs and further confirmed that the optimal parameter values can be systematically derived using both methods. The two-step Bayesian optimization, which classifies parameters based on ecosystem characteristics, proved to be the most effective.

This paper presents a fast H-matrices-based boundary integral equation method that can be applied to various wave-related problems. We propose an efficient algorithm for convolution in time direction for the intermediate domain between P- and S-waves using the exponentiation notation of the integral kernel. Furthermore, lattice H-matrices are used to address computational inefficiencies in parallel environments due to the hierarchical structure of H-matrices. 3D stress wave propagation simulations confirm the accuracy of the method.

We consider finite difference schemes for the Cahn–Hilliard equation, which describes spinodal decomposition. For this equation, stable numerical schemes can be designed by the discrete variational derivative method, but their spatial accuracy remained second-order, and it was difficult to improve under the standard boundary conditions. In this letter, we show that the discrete variational derivative method can be extended via the idea of summation-by-parts operators, by which we can construct spatially high-order schemes retaining the desired dissipation property. We also show numerical experiments to confirm the higher-order accuracy.

This paper describes density-based topology optimization for multi-objective problem using a modified optimality criteria (OC) method. Multi-objective problems include strain energy minimization and von Mises stress minimization. The update equation for topology optimization is a map-based modified OC method, which is a modification of the modified OC method. The linear weighted sum method was employed for multi-objective optimization, and the effects of the weights of the linear weighted sum method on the optimal design results was presented.