We address the two novel types of point processes on the multidimensional sphere proposed by Beltrán and Etayo. First, for the point process on the odd-dimensional sphere introduced by Beltrán and Etayo (Constr. Approx., 2018), we give an explicit form of the expectation of the p-frame potential of the process and investigate its asymptotic behavior. Second, for the point processes, termed generalized spherical ensemble, on the even-dimensional sphere introduced by Beltrán and Etayo (J. Math. Anal. Appl., 2019), we provide an upper bound of the expectation of the p-frame potential of the process.

The Sinc approximation is known to yield quite accurate results for double-exponentially decaying functions. To date, this approximation has been successfully applied to derivatives, initial value problems, boundary value problems, and so forth. However, an error analysis of the approximation of the m-th derivatives has not been explicitly given, except in the case of m = 1. This study provides an error analysis for all positive integers m.

Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second variation of the area is nonnegative for all volume-preserving variations satisfying the given boundary condition. In this paper, we examine the stability of CMC hypersurfaces in general Euclidean space possibly having boundaries on two parallel hyperplanes. We reveal the stability of equilibrium hypersurfaces without self-intersection for the first time in all dimensions. The analysis is assisted by numerical computations.

An anisotropic double crystal (double crystal in short) is a mathematical model of a simplest multi-crystal. It consists of two connected regions in the space enclosing two prescribed volumes that contact each other. Its energy is the integral of an energy density over the surface, and the energy density depends on the normal direction of the surface at each point. A double crystal is a critical point of this energy. We derive a geometric characterization of double crystals. In a plane, for a certain energy density function, we classify the double crystals in terms of symmetry and the given areas.

In a projection-based model reduction, a Galerkin-type projection is frequently used to generate a reduced matrix. However, the stability may not be preserved and the computational effort for generating the projection is not negligible. In this study, we use random projections to reduce an original large-scale matrix. We show that the stability of the reduced matrix is guaranteed with high probability and that the matrix can be obtained efficiently.

The scattering transform network (STN) has a similar structure as that of a convolutional neural network. We propose a novel Monogenic Wavelet Scattering Network (MWSN) for 2D texture image classification through a cascade of monogenic wavelet filtering with nonlinear modulus and averaging operators by replacing the 2D Morlet wavelet filtering in the standard STN. Our MWSN can extract useful hierarchical and directional features with interpretable coefficients. Using the CUReT texture image database, we demonstrate the superior performance of our MWSN over the standard STN. This performance improvement can be explained by the natural extension of 1D analyticity to 2D monogenicity.

Consider two coaxial round circles with the same radius. A mathematical model of a tiny liquid drop trapped between them are constant mean curvature (CMC) surfaces because a CMC surface is a critical point of the area for all variations that preserve the enclosed volume and satisfy given boundary condition. A CMC surface is said to be stable if the second variation of the area for any such variation is nonnegative. In this paper, we judge the stability of one period of the so-called unduloid between two consecutive bulges rigorously for the first time.

We perform numerical calculations for the magnetic Hele-Shaw (HS) problem with a time-dependent gap using the method of fundamental solutions (MFS). In general, lifting the upper plate of an HS cell destabilizes the interface between the viscous fluid in the cell and the air surrounding it. We set the magnetic field generated by passing electric current, which is through at the center of the cell and perpendicular to the plate. Previous studies have suggested that the magnetic field suppresses interface instability between the magnetic fluid and air. We have succeeded in reproducing the suppression effect numerically using MFS.

We apply persistent homology to figure counting/detecting. This paper includes the theoretical construction, the numerical experiments, and the applications to real images. In the theoretical construction, we define some geometric concepts, formulate the counting problem, and prove the theorem that gives the threshold value for distinguishing noise and figures. We use the Rips and Čech complexes and compare the two complexes. In the numerical experiments, we count several model images. Finally, we apply our method to real images.

By combining independent component analysis (ICA) with a chaotic dynamical system of orthogonality, it is potential to construct a communication system that enables data transmission and reception at the chip rate, and achieves high speed and potentially large capacity. As ICA communication is a kind of novel digital wireless technology, in this study, we successfully confirmed the transmission of bit data using chaotic spreading sequence at the chip rate. Also further evaluations of its performance by simulation and the comparison of code-division multiple access with the same chaotic spreading sequence are performed.

Chaos degree is proposed as a measure of chaos that can be computed from a data series. It is known that the value of chaos degree is unstable under the influence of partition. Therefore, one of mathematical interests is whether chaos degree has a limit value or not when the number of partitions is infinite. In this study, we analytically derived the limit values of chaos degree for asymmetric tent maps, and found that the limit values differ significantly when the parameter is an irrational and rational number.

Numerical simulations of the semilinear Klein–Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein–Gordon equation. The disparity between the two forms is the discretization of the differential term. We show that one of the forms has higher numerical stability and second-order numerical accuracy with respect to the grid, and we explain the reason for the instability of the other form.

This paper presents a numerical method for quasi-static contact problems with the Coulomb friction. The method is based on the primal-dual algorithm for convex optimization. As a noteworthy feature, this method is free from solutions of linear equations systems; it consists of matrix-vector multiplications, vector additions, and projections of vectors onto the friction cone. Numerical experiments show that this method requires smaller computational cost compared with a regularized and smoothed Newton method for complementarity problems.

The problem of solving a system of multivariate quadratic equations over a finite field is known to be hard in general. However, there have been several algorithms of solving the system of quadratic equations efficiently when the number of variables is sufficiently larger than the number of equations (e.g., Kipnis et al., Eurocrypt 1999; Thomae and Wolf, PKC 2012; Cheng et al., PQCrypto 2014; and Furue et al., PQCrypto 2021). In the present paper, we propose a new algorithm that is available if the number of variables is smaller than that required in the previously given algorithms.

In 2020, through his work on a numerical evaluation for the aromaticity, the second author conjectured that the eigenvalues of a directed graph corresponding to polyacen (linearly connected r hexagons) would draw ⌊(r+1)/2⌋ hexagons on the complex plane. In this letter, we would like to introduce operations on directed graphs and prove his conjecture in a general form.

Isogeny-based cryptography is a promising candidate for post-quantum cryptography. Speeding up the isogeny computation of large prime degrees up to several thousands is a main research topic in isogeny-based cryptography. The currently most efficient method for computing isogenies is the square-root Vélu's formulas. In this paper, we propose an efficient variant of the square-root Vélu's formulas by introducing an optimal index system using a redundant integer representation. Our index system improves the isogeny computation in 44% of 367 primes between 97 and 2689 and is approximately 6.6% faster for primes 1279 and 2687.

In this study, we apply density-based topology optimization using the modified optimality criteria (OC) method to a support yoke. The modified OC method was developed by incorporating the concept of Newton’s method into the OC method. Our proposed method is less dependent on setting the move-limit, so it is employed in the update equation for topology optimization. This paper discusses the effect of the penalization parameter used in the solid isotropic material with penalization method on updates using the modified OC method. We also give a mathematical proof of the convergence properties for the modified OC method.

A numerical verification method is proposed to prove the existence of time-global solutions of complex ordinary differential equations (ODEs), which should be inscribed within a circle with a specified radius r. A conservative quantity is assumed to exist and is calculated to construct the verification conditions. We use a numerical example with a series expansion on the right side of the ODEs to demonstrate how to find such a conservative quantity and how to apply our method.

Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions under which the dynamical structures of the original continuous dynamical systems are retained in their discretized dynamical systems, and the types of fixed points are identified if they change due to discretization. We also discuss stability of the fixed points in the discrete dynamical systems. The obtained general results are applied to Sel’kov model and Lengyel–Epstein model.

It is known that a reduced matrix obtained by Gaussian random projections preserves the stability of an original matrix in a probabilistic manner. However, due to unknown constants appearing in a probability concentration inequality, the exact value of the probability when stability is preserved, or the condition for the dimension of the reduced matrix to preserve stability with high probability, is not known. In this study, we derive the stable probability of the reduced matrix obtained by Gaussian random projections by presenting a variant of the theorem used for the existing research without unknown constants.

The double-exponential formula is a quadrature formula that applies the trapezoidal formula to the infinite integral of double-exponentially decaying functions. Its high efficiency has been recognized since the 1970s, and in 1997, it was demonstrated that the formula is optimal in some sense. To achieve its best performance, its mesh size and truncation numbers are optimally selected depending on a given positive integer. However, existing selection formulas are not optimal. In this paper, we propose optimal selection formulas for the mesh size and truncation numbers, giving a far better error bound than the existing one.

This study clarifies the relationship between trends in the number of corporate bankruptcies and trends in corporate managerial sentiment indicators. To this end, we perform an empirical study by modeling monthly bankruptcy counts with a generalized linear mixture model incorporated with business sentiment indices for covariates. The empirical results show that managerial sentiments efficiently explain trends in the number of corporate bankruptcies in Japan. In addition, the predictive power of the business condition index is equivalent to or greater than the prediction by macroeconomic variables in the sample period.

In this study, tidal current estimation analysis and calculation of tidal power generation potential are performed for a Tokyo Bay model using the extended Kalman filter FEM. When a calculation of tidal power generation potential was carried out as an application of the result of the tidal current estimation analysis, it was found that a similar pattern was observed in the linear and the non-linear system equations. The likely reason for this is that the calculation of the tidal power generation potential is performed by time integration.

Fuzzy cellular automaton (CA) is a dynamical system with a continuous state value embedding a CA with a discrete state value. We investigate a fuzzy CA obtained from an elementary CA of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.

In this paper, we attempt to provide an elementary introduction to the excursion risk theory by constructing a discrete-time analogue. The excursion risk theory is a theory of calculating risks in investments that use mean-reverting trading signals. We consider the case where the trading signal is a simple symmetric random walk (RW) and use the excursions of them to compute several quantities of risks in the investments. It may be said that this paper gives one way of applying the excursion theory of RWs that mathematicians have been studying for a long time to mathematical finance.

An application of the Bayesian optimization to an ordinary differential equation-based neural network is proposed. The loss function was considered as a black box function of the coefficients, and Bayesian optimization was applied to obtain desirable parameter values. The proposed method drastically simplifies the implementation because the adjoint method-based updating of coefficients is not required. Numerical experiments demonstrate that the performance of the proposed method is comparable to that of existing methods.

The images that our eyes perceive are slightly different from the objects. Images in visual space are illusions. However, they are indeed based on optics. In physical space, parallel lines never intersect. In visual space, however, parallel lines intersect at the vanishing point. This is not limited to the human eye; camera lenses produce images similarly. If visual space is spherical, the phenomenon of intersecting parallel lines is no mystery. This paper provides a new geometric model considering the intersection of parallel lines at vanishing points.

Multivariate polynomial public cryptography is a form of post-quantum cryptography that represents one of the candidates for next-generation cryptography. Solving a multivariate simultaneous system of quadratic equations (MQ problem) serves as the basis of security for multivariate public-key cryptography, and evaluating its computational complexity is an important topic. The hybrid approach is a method for solving MQ problems, which combines exhaustive search and Gröbner basis computation. We propose a new algorithm as an alternative to the hybrid approach, wherein the Gröbner basis computation is performed, the assignment calculation is performed subsequently, and the Gröbner basis computation is performed again.

Regulated egress, a method in which people are divided into several groups and each group is allowed to egress in turn, is used at large event venues to avoid congestion in the surrounding area. In this study, we developed an index that considers people’s egress time and congestion during the waiting period to evaluate regulated egress. Then, using simulation and theoretical analysis, we determined the appropriate number of groups to use when conducting regulated egress.

To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.

This paper presents a modified neural model for topic detection from a corpus and proposes a new metric to evaluate the detected topics. The new model builds upon the embedded topic model incorporating some modifications such as document clustering. Numerical experiments suggest that the new model performs favourably regardless of the document’s length. The new metric, which can be computed more efficiently than widely-used metrics such as topic coherence, provides variable information regarding the understandability of the detected topics.

The problem of finding solutions to a system of multivariate quadratic (MQ) algebraic equations, called the MQ problem, is important research for the security evaluation of multivariate public key cryptosystems. Algorithms for computing Gröbner bases are often used as tools for solving the MQ problem. M4GB algorithm is known as an efficient algorithm to compute Gröbner bases. M4GB stores many polynomials to efficiently compute Gröbner bases, which tends to increase space complexity, i.e., memory usage. In this article, we propose a technique to reduce memory usage of M4GB algorithm.

In 5G/6G, it is important for massive machine-type communications (mMTC) that each device’s signal does not interfere with others. The correlation properties of spreading codes in code division multiple access (CDMA) are important to achieve this. In this study, we propose a code that can be obtained by multiplying multiple primitive root codes to achieve mMTC and demonstrate that an appropriate set of codes achieves perfect orthogonality. Simulations of CDMA using the proposed codes show a significant decrease of bit error rate compared to Gold codes and random codes.