In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier–Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori e...

The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually, the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein, which characterize the eigenvalue spectrum of the noise covariance matrix, and...

Modular structure is a typical structure that is observed in most of real networks. Diffusion dynamics in network is getting much attention because of dramatic increasing of the data flows via the www. The diffusion dynamics in network have been well analysed as probabilistic process, but the proposed frameworks still shows the difference from the real observations. In this paper, we analysed s...

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkin...

—Canonical correlation analysis (CCA) is a powerful tool for analyzing multi-dimensional paired data. However, CCA tends to perform poorly when the number of paired samples is limited, which is often the case in practice. To cope with this problem, we propose a semi-supervised variant of CCA named “semiCCA”that allows us to incorporate additional unpaired samples for mitigating over ttng. The p...

A tissue interaction model for skin organ pattern formation is presented. Possible spatially patterned solutions on rectangular domains are investigated. Linear stability analysis suggests that the model can exhibit pattern formation. A weakly nonlinear two-dimensional perturbation analysis is then carried out. This demonstrates that when bifurcation occurs via a simple eigenvalue, patterns suc...

In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions...

The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that eigenbranches that develop from the stable Lyapunov exponents of the free system also have a strong influence on the control properties, either by hybridization or by a crossing of branches whi...

We present a novel multitask learning framework called multitask generalized eigenvalue program (MTGEP), which jointly solves multiple related generalized eigenvalue problems (GEPs). This framework is quite general and can be applied to many eigenvalue problems in machine learning and pattern recognition, ranging from supervised learning to unsupervised learning, such as principal component ana...

Eigenvalue analysis plays an important role in understanding physical phenomena. However, if one deals with strongly nonnormal matrices or operators, the eigen-values alone may not tell the full story. A popular tool which can be useful to get more insight in the reliability or sensitivity of eigenvalues is "-pseudospectra. Apart from "-pseudospectra we consider other tools which might help to ...