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.

This paper is concerned with topology optimization methods with geometric constraints. Main results include the development of numerical methods with either a maximum thickness or a curvature constraint by combining the so-called diffusion-based level set methods with distance functions via elliptic equations. Numerical examples for two-material thermal conduction problems with these constraints will be presented.

This paper proposes a method for minimizing a Gerber–Shiu-like penalty function using a mini-batch stochastic projected gradient method (MBSPG) to determine optimal investment and reinsurance strategies. The Gerber–Shiu-like penalty function considers both the probability of ruin and the magnitude of loss when ruin occurs. To apply the MBSPG, we derive an unbiased estimator of the gradient via Malliavin calculus and establish Hölder continuity of the gradient. Numerical experiments demonstrate the effectiveness of our proposed method.

In this letter, we provide a complete characterization of Pell numbers that can be expressed as sums or differences of two Lucas numbers, using techniques based on linear forms in logarithms and reduction methods. This characterization distinguishes polynomial families and facilitates further applications, particularly in the classification of graphs via their spectral properties.

This study proves that the injectivity condition for the integral operator of the direct-indirect mixed Burton–Miller (BM) boundary integral equation (BIE) for Helmholtz transmission problems is identical to that for the ordinary BM BIE for Helmholtz transmission problems with a transmissive circular inclusion. Although some numerical methods based on the direct-indirect mixed BM BIE can be computed faster than the ordinary BM BIE, its well-posedness has been unclear. This study resolves a part of the well-posedness, namely the injectivity of the integral operator with a transmissive circular inclusion.

We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable trajectories, i.e., the edge of chaos. Despite its usefulness, it is generally difficult to derive analytically. In this study, we reveal the transition boundaries by leveraging the Markov chain Monte Carlo algorithm coupled directly with the numerical integration of nonlinear differential/difference equation. It is demonstrated that a posteriori modeling for parameter subspace along the edge of chaos determines an inherent constrained dynamical system to flexibly activate or de-activate the chaotic trajectories.

This paper reports that symmetries, which are known in the theory of integrable systems, naturally appeared in the classical linear theory of deformations of thin shells. Our result shows that if the governing equation of the middle surface of a shell becomes ‘exactly solvable’, infinitely many ‘nice’ deformations exist.

This paper presents a theorem of existence for an optimum point and methods to obtain component-wise verified solutions in constrained convex programming. The proposed method is based on the continuous Newton method and Kantorovich's theorem and slightly modifies Oishi and Tanabe's theorem for linear programming. Moreover, a theorem of existence for an optimum point for convex quadratic programming problems (CQPs) was also formulated. The CQP can be rewritten as linear complementarity problems (LCPs). A method to use component-wise verified solution method for LCPs is also presented. Numerical examples show that the proposed method is effective.

The block conjugate gradient (Bl-CG) method is an effective iterative solver for large sparse symmetric positive definite linear systems with multiple right-hand sides. Variable preconditioning, in which different preconditioners can be applied to each iteration, is a versatile approach for improving the convergence of iterative solvers. However, the convergence properties are obscure when variable preconditioning is used. In this study, we present a simple analysis of the error norm behavior of the Bl-CG method with variable preconditioning. Numerical experiments are conducted to demonstrate the convergence analysis.

In this letter, we establish a recurrence relation for the characteristic polynomial of alternating-oriented tetragonal comb graphs. Using this relation, we express the polynomial in terms of Chebyshev polynomials of the second kind. This formulation allows us to explicitly determine the eigenvalues of the graphs. Furthermore, we analyze the geometric structure of the spectra in the complex plane and propose conjectures on generalized comb graphs involving higher-order polygons and various gluing configurations.

Parallel-in-time methods for time-dependent problems have risen to prominence over the past decade as massively parallel computers push core counts into the millions. Among them, the block ϵ-circulant (BEC) preconditioned solver achieves outstanding convergence, yet the preconditioner itself dominates the solver runtime. We propose a mixed-precision strategy that uses single precision for BEC preconditioning and double precision elsewhere, thereby reducing the solver runtime especially on CPU-GPU systems. On an NVIDIA GH200 cluster, the mixed-precision BEC-GMRES solver achieves a 1.42× speedup for two-dimensional advection-diffusion problems without significant loss of accuracy.

In this paper, we propose an algorithm to enumerate genus-4 superspecial hyperelliptic curves whose automorphism groups are isomorphic to the quaternion group. By implementing this algorithm with Magma (W. Bosma, J. Symbolic Comput., 1997), we successfully obtain the number of isomorphism classes of such curves in every characteristic 7 ≤ p < 10000. Interestingly, the experimental results lead us to the conjecture that there exist exactly [p/48] isomorphism classes of such curves if p ≡ 1, 7 (mod 8), whereas such curves do not exist if p ≡ 3, 5 (mod 8).