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.