The present paper describes a numerical solution to topology optimization problems of domains in which boundary value problems of partial differential equations are defined. Density raised to a power is used instead of the characteristic function of the domain. A design variable is set by a function on a fixed domain which is converted to the density by a sigmoidal function. Evaluation of derivatives of cost functions with respect to the design variable appear as stationary conditions of the Lagrangians. A numerical solution is constructed by a gradient method in a design space for the design variable.

View full abstract

We have proposed a block sparse approximate inverse with cutoff (BSAIC) preconditioner for relatively dense matrices. The BSAIC preconditioner is effective for semi-sparse matrices which have relatively large number of nonzero elements. This method reduces the computational cost for generating the preconditioning matrix, and overcomes the performance bottlenecks of SAI using the blocked version of Frobenius norm minimization and the drop-threshold schemes (cutoff) for semi-sparse matrices. However, a larger parameter of cutoff leads to a less effective preconditioning matrix with a large number of iterations. We analyze this convergence deterioration in terms of eigenvalues, and describe a deflation-type method which improves the convergence.

View full abstract

The LUJ2D algorithm is a recently proposed numerical solution method for non-orthogonal joint diagonalization problems appearing in signal processing. The original LUJ2D algorithm attains low performance on modern microprocessors since it is dominated by cache ineffective operations. In this study, we propose a cache efficient implementation of the LUJ2D algorithm. The experimental results show that the proposed implementation is about 1.8 times faster than the original one, achieving 21\% of the peak performance on the Opteron 1210 processor using one core.

View full abstract

The IDR($s$) proposed by Sonneveld and Gijzen is an efficient method for solving large nonsymmetric linear systems. In this paper, QMRIDR($s$), a new variant of the IDR($s$) method is presented. In this method, the irregular convergence behavior of IDR($s$) is remedied and both the fast and smooth convergence behaviors are expected. Numerical experiments are reported to show the performance of our method.

View full abstract

A new eigenvector-following approach for finding a saddle point without the Hessian matrix is described. The most important feature of the proposed approach is to rely not only on the lowest as in the case of a conventional approach, but also on higher, albeit less accurate, eigensolutions which are available when the Davidson method is employed. The proposed approach is shown to be more efficient than the conventional one by application to diffusion of a Zn interstitial atom in an InP supercell.

View full abstract

Simulations are performed in order to make comparisons among five methods of U.S. Congressional apportionment. Specifically, the probability is estimated under each method of apportionment that the number of Representatives allocated to a state is equal to the number obtained by rounding off the quota of that state to the nearest integer. According to the Webster method, numerical evidence shows that the probability is 97.6 percent on average.

View full abstract

A singular nonlinear partial differential equation (PDE) is introduced, which can be interpreted as the evolution of the risk preference in the optimal investment problem under the random risk process. The unknown quantity is related to the Arrow-Pratt coefficient of relative risk aversion with respect to the optimal value function. We show the existence of monotone traveling wave solutions and the nonexistence of non-monotone such solutions, which are suitable from the standpoint of financial economics.

View full abstract

This paper treats a winner determination problem of a Vickrey-Clarke-Groves mechanism based single-item multi-unit auction. For this problem, two simple 2-approximation algorithms are proposed. One is a linear time algorithm using a linear knapsack problem. The other is a greedy type algorithm. In addition, a fully polynomial time approximation algorithm based on a dynamic programming is described. Computational experiments verify availabilities of our algorithms by comparing computational times and approximation ratios.

View full abstract

There are various types of orthogonal wavelet families with order parameters. In this paper we introduce a new family of wavelets which converges in $L^q$ to the Shannon wavelet as the order parameter $n$ increases. In particular, we shall give a symmetric orthogonal scaling function whose time-bandwidth product is near $1/2$.

View full abstract

We consider the numerical integration of the modified Camassa-Holm equation, which has been recently proposed by McLachlan and Zhang (2009) as a generalization of the prominent Camassa-Holm equation. We present nonlinear and linear finite difference schemes for the modified equation that preserve two invariants at a same time. We also show some numerical examples of the presented schemes, where it is found that certain solutions of the mCH can behave like solitons.

View full abstract

We consider structure-preserving integration of the Ostrovsky equation, which for example models gravity waves under the influence of Coriolis force. We find a multi-symplectic formulation, and derive a finite difference discretization based on the formulation and by means of the Preissman box scheme. We also present a numerical example, which shows the effectiveness of this scheme.

View full abstract

We consider solutions of Sakaki-Kakei equations of type 1, 2, 7 and 12, which are irreversible two dimensional systems. We first obtain their conserved quantities, and reduce them to one dimensional nonautonomous systems. We next show that the equations of type 2 and 7 are transformed to arithmetic-harmonic mean equation, and obtain their general solutions. We finally show that the equations of type 1 and 12 are related to the solvable chaotic system proposed by Umeno. We also show that their iteration maps have self semiconjugacy, and obtain their particular solutions which are expressed in terms of lemniscate elliptic function.

View full abstract

The aim of this article is to examine self-exciting effect and/or mutually exciting effect on rating migrations. First, we examine with self-exciting/mutually exciting intensity models whether such effect can be observed for rating migrations in Japanese enterprises. Second, we analyze which explanatory variable is more significant to the jump of the intensity via model selection with Akaike information criterion (AIC).

View full abstract

In 2004, Akiyama and Goto proposed an algebraic surface public-key cryptosystem (ASC04) which is based on the hardness of finding sections on fibered algebraic surfaces. In 2007, Uchiyama and Tokunaga gave an efficient attack, which is called the reduction attack, against ASC04 under some condition of a public-key of the scheme. In 2008, Iwami proposed its improved attack. In this paper, we point out a flaw in Iwami's attack and propose a generalized reduction attack. The attack is based on Iwami's attack, and the flaw is fixed. We also discuss our experiments of the attack.

View full abstract

In this research, we revamp the approach of Buraschi and Jackwerth (2001), especially, in the derivation of the pricing-kernel and the data-handling technique and then empirically analyze the consistency of the DVMs introduced in Mawaribuchi, Miyazaki and Okamoto (2009) to the dynamics of the cross-sectional option returns. The implication attained from our quantitative analyses is that even in the trending and volatile market, we could build the equity models that are rational to the dynamics of the cross-sectional option market prices within the framework of the complete model without incorporating the additional stochastic variable such as jump or stochastic volatility.

View full abstract

The performance of some nonlinear eigenvalue problem solvers can be increased by setting parameters that are based on rough estimates of the desired eigenvalues. In the present paper, we propose a stochastic method for estimating the eigenvalue density for nonlinear eigenvalue problems of analytic matrix functions. The proposed method uses unbiased estimation of the matrix traces and contour integrations. Its performance is evaluated through the numerical experiments.

View full abstract

In this paper, we present a method for reconstructing the dipole sources inside the human brain from radial Magnetoencephalography data measured on the part of the boundary which encloses the source. Combining the proposed method with the direct method provides a good initial solution for an optimization-based algorithm. The method is verified with the numerical simulations, phantom experiments, and a somatosensory evoked field data analysis.

View full abstract

The IDRstab method is often more effective than both IDR($s$) and BiCGstab($\ell$) for solving large nonsymmetric linear systems. However the computational costs for vector updates are expensive on the original implementation of IDRstab. In this paper, we propose a variant of IDRstab to reduce the computational cost; vector updates are saved. Numerical experiments demonstrate the efficiency of our variant of IDRstab for sparse linear systems.

View full abstract

The present paper describes the result of the error estimation of a numerical solution to topology optimization problems of domains in which boundary value problems are defined. In the previous paper, we formulated a problem by using density as a design variable, presented a regular solution, and called it the H1 gradient method. The main result in this paper is the proof of the first order convergence in the H1 norm of the solution in the H1 gradient method with respect to the size of the finite elements if first order elements are used for the design and state variables.

View full abstract

A copula function makes a bridge between multivariate joint distributions and univariate marginal distributions, and provides a flexible way of describing nonlinear dependence among random circumstances. We introduce a new family of bivariate copulas which evolves according to the discrete process of heat equation. We prove the convergence of solutions as well as the measure of dependence. Numerical experiments are also performed, which shows that our procedure works substantially well.

View full abstract

Sinc-Nyström methods for Fredholm integral equations of the second kind have been independently proposed by Muhammad et al. and Rashidinia-Zarebnia. They also gave error analyses, but the results did not claim the convergence of their schemes in a precise sense. This is because in their error estimates there remained an unestimated term: the norm of the inverse of the coefficient matrix of the resulting linear system. In this paper, we estimate the term theoretically to complete the convergence estimate of their methods. Furthermore, we also prove the boundedness of the condition number of each coefficient matrix.

View full abstract

In this paper, we present a modified version with variable coefficients of the $(2+1)$ dimensional Korteweg-de Vries, or \textit{Calogero-Bogoyavlenskii-Schiff} equation, derived by applying the Painlevé test. Its Lax pair with a non-isospectral condition in $(2+1)$ dimensions is also given. Moreover a transformation which links the form with variable coefficients to the canonical one is shown.

View full abstract

We present a parallel algorithm for incremental orthogonalization, where the vectors to be orthogonalized are given one by one at each step. It is based on the compact WY representation and always produces vectors that are orthogonal to working accuracy. Moreover, it has large granularity and can be parallelized efficiently. When applied to the GMRES method, this algorithm reduces to a known algorithm by Walker. However, our formulation makes it possible to apply the algorithm to a wider class of incremental orthogonalization problems, as well as to analyze its accuracy theoretically. Numerical experiments demonstrate accuracy and scalability of the algorithm.

View full abstract

We present an intensity based credit rating migration model and execute empirical analyses on forecasting the number of downgrades in some credit portfolios. The framework of the model is based on so-called top-down approach. We firstly model economy-wide rating migration intensity with a self-exciting stochastic process. Next, we characterize the downgrade intensity for the underlying sub-portfolio with some thinning model specified by the distribution of credit ratings in the sub-portfolio. The results of empirical analyses indicate that the model is to some extent consistent with downgrade data of Japanese firms in a sample period.

View full abstract

Anonymity is an important security requirement for protocols such as voting schemes. It is often guaranteed by using anonymous channels such as mixnets. In this paper, we present a technique for automatically verifying the anonymity of protocols that use anonymous channels by using Proverif, a tool for the automatic verification of security protocols. We use this technique to verify the voting scheme developed by Fujioka, Okamoto, and Ohta.

View full abstract