Dynamic characteristics of linear structural systems are governed by the natural frequencies and the mode-shapes. In this paper the statistical properties of the eigenvalues of linear dynamic systems are considered. It is assumed that the mass and the stiffness matrices are smooth, continuous and at least twice differentiable functions of a random parameter vector. The random parameter vector i...

Principal component analysis (PCA) is a widely used method for dimension reduction. In high dimensional data, the “signal” eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the “noise” eigenvalues. Therefore, popular tests based on the largest eigenvalue have little power to detect weak PCs. In the special case of the spiked model, certain...

Second order statistics estimates in the form of sample eigenvalues and sample eigenvectors give a sub optimal description of the population density. So far only attempts have been made to reduce the bias in the sample eigenvalues. However, because the sample eigenvectors differ from the population eigenvectors as well, the population eigenvalues are biased estimates of the variances along the ...

Principal Components Analysis (PCA) is the multivariate statistical technique employed to extract eigenvectors and eigenvalues from the contextual query co-occurrence matrix.

We report our current effort on extracting morphological features from neuronal dendrite patterns using the eigenvalues of their graph Laplacians and clustering neurons using those features into different functional cell types. Our preliminary results indicate the potential usefulness of such eigenvalue-based features, which we hope to replace the morphological features extracted by methods tha...

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, C. Padra, Appl. Numer. Math., 2012, for the approximation of Laplace eigenvalue problem with Crouzeix–Raviart non-conforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and ...

We discuss the leading asymptotics of eigenvalue splittings of & A + X2V in the limit as X + oo, and where V is a non-negative potential with several zeros. For example, if Eo(A), El(X) are the two lowest eigenvalues in .a situation where V has precisely two zeros, a and b, related by a symmetry, then lim,,, (A)-'ln[E,(X) Eo(h)] is given as the distance from a to b in a certain Riemann metric.

One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-do...

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way...