The diffusion tensor is typically assumed to be positive definite. However, noise in the measurements may cause the eigenvalues of the tensor estimate to be negative, thereby violating this assumption. Negative eigenvalues in diffusion tensor imaging (DTI) data occur predominately in regions of high anisotropy and may cause the fractional anisotropy (FA) to exceed unity. Two constrained least s...

A procedure is described for computing range and orientation invariant spectral signatures of buried unexploded ordnance (UXO) from electromagnetic induction (EMI) data. The normalized eigenvalues of the magnetic polarizability tensor that characterizes the target response are used as the orientation-invariant spectral signatures. It is shown that the eigenvalues can be normalized with respect ...

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. T...

The purpose in this paper is to compute the eigenvalues of SturmLiouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A ...

The propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear Schrrdinger equation (NLS). When considering realistic fibers one must examine perturbed NLS equations, with the particular perturbation depending on the physical situation that is being modeled. A common example is the complex Ginzburg-Landau equation (CGL), which is a dissipative perturbation...

We are interested in a nonlinear boundary value problem for (|u′′|p−2u′′)′′ = λ|u|p−2u in [0,1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n− 1 zero points in (0,1). Eigenvalues of the ...

The nonlinear stability of two populations diffusing in a common bounded domain with nonlinear density-dependent dispersal of a general type is studied, under Robin boundary conditions. The stability and instability of the positive equilibrium are studied by the linear eigenvalues method. The nonlinear stability is studied with the Lyapunov direct method. In a particular case, global stability ...