Abstract. We propose a verified numerical multiple integration based on the composite Gauss-Legendre quadrature whose division number of individual remainders is fewer than that of individual main terms. By combining remainder terms partially, the number of calculations for higher-order differentials, which take a long time to compute, can be reduced. Thus, a computation time of the proposed method decrease. In addition, to utilize a product cubature rule, the number of high-order differentials in remainder terms of multiple integration can be reduced. We illustrate the effectiveness of the proposed method using examples in two and three dimensions.

Abstract. This paper proposes a method using quantifier elimination to search circuit-constant range of high-voltage analog circuits. Quantifier elimination is a method which solves equivalent logical expression even with free variables involved by removing quantifier symbol included in first-order predicate logic. Because the method is able to search the circuit-constant range in a guarantee stable operation, it is suitable for safely redesigning past assets of high-voltage analog circuits. In this paper, circuit-constant values are determined using the proposed method, and its effectiveness is examined through experiment of high-voltage analog circuits.

Abstract. We propose a novel method for analyzing operational risk loss data. In this method, the marginal distribution of multidimensional operational risk loss data are formulated by a discrete distribution, the dependency is formulated by a D-vine t-copula, and parameters are estimated simultaneously with Markov chain Monte Carlo(MCMC) via the Bayesian method. Numerical experiments confirmed the practicality of the proposed method.

Abstract. The SIR and SEIR models, which are expressed by the differential equation, describe the short time epidemic of infectious diseases deterministically. However, in real, the pattern of the infection spread is unintentionally, therefore we need to consider the random fluctuation to catch the dynamics of populations. In this paper, we proposed the small diffusion SEIR model and derive the asymptotic distribution of estimators. We simulate in software R to demonstrate our theory.