Abstract: Condition numbers for infinite-dimensional optimization, as defined in Zolezzi (2002, 2003), are shown to exhibit a stable behavior when employing finite-dimensional solution methods of the Ritz type, in particular finite elements. The same behavior is shown to hold in connection with the so called extended Ritz method.

Based on the univariate t-statistic from an invariant representation of multi-variate data, we propose a new quantile-quantile (Q-Q) plot to detect non-multinormality in high-dimensional data analysis. Acceptance regions for the Q-Q plot are provided by the theory of quantile processes. Using the acceptance regions, we perform a Monte Carlo study on the power of the Q-Q plot. It turns out that ...

In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximizes information about a ‘relevance’ variable, Y , while constraining the information encoded about the original data, X . Unfortunately however, the IB method is computationally demanding when data are high-d...

Motivated by contact resistance on the front side of a crystalline silicon solar cell, we formulate and analyse a two-dimensional mathematical model for electron flow across a poorly conducting (glass) layer situated between silver electrodes, based on the driftdiffusion (Poisson-Nernst-Planck) equations. We devise and validate a novel spectral method to solve this model numerically. We find th...

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed and low rank representation based subspace clustering is a very promising and efficient subspace clustering algorithm. Low rank representation method seeks ...

In recent years, 3D face recognition has obtained much attention. Using 2D face image as probe and 3D face data as gallery is an alternative method to deal with computation complexity, expensive equipment and fussy pretreatment in 3D face recognition systems. In this paper we propose a learning based 2D-3D face matching method using the CCA to learn the mapping between 2D face image and 3D face...

Tomographic phase microscopy (TPM) facilitates three-dimensional imaging of live cells based on quantitative measurement of the distribution of the refractive index, but without the need for specific staining. However, the limited imaging speed and the anisotropic resolution of the reconstructed refractive index map remain major obstacles to the extension and further application of TPM. To addr...

In this paper, we will present a novel face recognition algorithm using 3D geometric information of the face, which is acquired using parallel stereo vision. Firstly, we present an effective method of detecting facial feature, which mainly depends on the facial skin color information in the YCbCr color space. We define the feature points for the facial feature and compute the depth data of each...