NIST SP800-22 is a randomness test set applied for a set of sequences. Although SP800-22 is widely used, a rational criterion throughout all test items has not been shown. The main reason is that the dependency of test items has not been perfectly clear. In this paper, a certain scalar is computed for each sequence throughout all test items and make the histogram of the scalar. By comparing the histogram and the theoretical distribution under some assumptions, the dependency is visually shown. In addition, an algorithmic method to derive ``minimum set'' using the histogram is proposed.
We present here an estimation of a shallow water flow field based on ensemble Kalman filter FEM. With this technique, the stochastic distribution of the state variables is represented by the ensemble approximation, and the special distribution of the state variables is obtained using the FEM. The shallow water equation is employed as the governing equation, and the SUPG method, a discretization method within the FEM, is applied to discretize the governing equation. The influence of sample number on estimation accuracy and the effect of the advection term in the shallow water equation are investigated in an open-channel model.
Through empirical analysis, this note shows that the time intervals between the consecutive transactions of Nikkei 225 Futures in the Osaka Securities Exchange substantially follow identical Pareto distribution of type Ⅲ independently if the length of observation period is fixed at 15 minutes. This result is expected to give a possible suggestion when we develop a real time simulator of a stock market.
Some discrete inequalities such as the Sobolev inequality give useful a priori estimates for numerical schemes. Although they had been known for the simplest forward difference operator, those for central difference type opereators had been left open until quite recently in Kojima-Matsuo-Furihata (2016) a unified way to discuss them was found. Still, due to some technical reasons, the result was limited to a narrow range of central difference operators. In this paper, we provide a new proof that gives a complete answer regarding the discrete Sobolev inequality and the discrete Gagliardo-Nirenberg inequality with the nonlinear Schrödinger equation index.