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.
In 2015, Gower and Richtárik presented a unifying framework for a variety of randomized iterative algorithms for consistent linear systems. The framework includes the randomized Kaczmarz method that exponentially converges in the mean square whenever the system is consistent. For noisy linear systems corresponding to inconsistent systems, the randomized Kaczmarz method computes an approximate solution within a fixed distance depending on the norm of the noise vector. We extend this error analysis to a general framework in inconsistent systems in a similar manner to Gower and Richtárik, and verify this theoretical analysis in numerical experiments.
HMFEv is a new multivariate signature scheme proposed at PQCrypto 2017. This is a vinegar variant of multi-HFE (Chen et al., 2008). While the original multi-HFE is known to be insecure against the direct attack (Huang et al., 2015), the min-rank attack (Bettale et al., 2013) and the attack using a diagonalization approach (Hashimoto, 2017), HMFEv is considered to be secure enough against these attacks. However, the security against the high-rank attack had not been studied at all. In the present paper, we study the structure of HMFEv and discuss its security against the high-rank attack.
We show that plane curves in the centroaffine geometry admit a flow which is described by the defocusing modified KdV equation. We establish a correspondence between this flow and the KdV flow in the equicentroaffine geometry. We also present an explicit formula for the KdV flow in terms of the $\tau$ function.
This paper formulates and solves the shape optimization problem for the body of a musical instrument such as an acoustic guitar. A coupling system consisting of a linear elastic body surrounded by a compressible fluid is used to define the frequency response problem with respect to an external force applied to the bridge of an acoustic guitar. The acoustic power on an outer boundary within a given frequency range is defined as the objective cost function. The solution of the shape optimization problem is constructed using the $H^1$ gradient method. A numerical example is used to validate this approach.
Lung cancer is the leading cause of cancer death. Dimerization and phosphorylation of the receptor tyrosine kinase are involved in the malignant progression of cancers and drug resistance. Focusing on the EGFR-ErbB3 dimerization, we build a mathematical model using ordinary differential equations (ODEs). By classifying the molecules into two groups, we sum molecular ODEs into two groups and solve them explicitly. From these solutions, all molecule concentrations and their equilibria can be derived theoretically. Based on the theoretical solutions, we determine the dimerization behavior and a key parameter. Our model can be applied to similar dimerization networks.
A numerical method is considered herein for solving the problem of coefficient identification in a linear partial differential equation used to detect damages in steel-concrete composite beams. To identify the numerically unknown coefficient, an iterating algorithm based on the adjoint method is presented. The $H^1$ gradient method is applied to set the search direction in our algorithm. The search direction is selected based on the solution to the weak equation with a bilinear form in the $H^2$ Sobolev space. The effectiveness of our method is confirmed via numerical experiments.
We investigate the performance of the parallel block Jacobi method for the symmetric eigenvalue problem with dynamic ordering both theoretically and experimentally. First, we present an improved global convergence theorem of the method that takes into account the effect of annihilating multiple blocks at once. Next, we compare the dynamic ordering with two representative parallel cyclic orderings experimentally and show that the former can speedup the convergence for ill-conditioned matrices considerably with little extra cost.
We propose a max-plus equation as an extension of $1+1$D cellular automaton of four neighbors. It has two conserved quantities and one monotonically decreasing quantity which are max-plus analogues of those of the binary cellular automaton. It is interesting that one of the quantities is global and defined by the maximum value of dependent variable. We show proofs about their conservation and monotonicity using max-plus formulas.
We propose a simple and fast numerical method for solving an evolution equation for closed flame/smoldering fronts, equivalent to the Kuramoto-Sivashinsky equation in a scale. Comparison of numerical results and an experiment suggests that our model equation is valid for not only propagating gas-phase flame fronts but also expanding smoldering fronts over thin solids.
A novel procedure for designing invariant-preserving numerical schemes for Poisson and Nambu systems is proposed. Such systems include important physical problems such as the Korteweg--de Vries equation and the shallow water equations, where often some physical invariants control the dynamics of the solutions. By the new procedure, numerical schemes that preserve one or two such invariants can be constructed. The key is a clever discretization of the brackets. Numerical results for the shallow water equations using a fully discretized extension of the legendary Arakawa--Lamb scheme confirm the validity of our procedure.
The Lanczos-Phillips algorithm is a method to compute the Cholesky decomposition of Hankel matrices. This algorithm can compute the Chebyshev continued fraction from a given set of moments faster than the qd algorithm. Moreover, a new algorithm to compute the Perron continued fraction is presented with the help of orthogonal polynomials. The Cholesky decomposition of Toeplitz matrices plays a key role.
Tensor renormalization group (TRG) is a coarse-graining algorithm for approximating the partition function using a tensor network in the field of elementary particle physics. Although the computational cost of TRG can be reduced using a randomized singular value decomposition, its computation time is still large. In this paper, we propose a cost-efficient cutoff method for calculating TRG by truncating small tensor elements. Numerical experiments showed that the proposed method is faster than the conventional one without degrading accuracy.
This paper presents an approach to designing a fish-like linear elastic body whose vibration mode becomes a swimming mode similar to that observed in real fish. To determine the shape of the elastic body, a shape optimization problem is formulated using the squared error norm between the solution of a frequency response and the swimming mode as the cost function and solved by a method based on the $H^1$ gradient method. The body is excited by body forces located at assigned places. The frequency is set around the natural frequency of the eigenmode, mostly in accordance with the swimming mode.
When observing a collection of ranked items, we may be interested in the questions of why and how one item is ranked over another. This paper presents a method for discovering the knowledge about the rank of the items from consumer reviews. We formulate the questions of interest as a single biconvex minimization problem which has a relationship with SVM(Support Vector Machines). To facilitate the process of knowledge discovery, we propose a two-stage learning algorithm for discovering knowledge from small data. Finally, we evaluate the method by showing our simulation and experiment results.
In this study, numerical studies for a maximally stiff structure based on the topology optimization theory and the FEM are carried out, and the result of several practical tensile tests for the optimized structure was shown. The specimens for tensile testing were made using 3D printer. The numerical studies included filtering radius based examination. The thickness of the optimized model was also investigated, assuming the displacement of the optimized model to be the same as that of the initial model.
Contour-integral based eigensolvers have been proposed for efficiently exploiting the performance of massively parallel computational environments. In the algorithms of these methods, inner linear systems need to be solved and its calculation time becomes the most time-consuming part for large-scale problems. In this paper, we consider applying a contour-integral based method to a large dense problem in conjunction with a block Krylov subspace method as an inner linear solver. Comparison of parallel performance with the contour-integral based method with a direct linear solver and a ScaLAPACK's eigensolver is shown using matrices from a practical application.