A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linearPT -symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet...

This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in infinite-dimensional Hilbert space. approach is both motivated works for total variation, where interesting results on and relation variation flow have been proven previously, recent finite-dimensional polyhedral semi-norms, gradient f...

Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function Q is an established measure quantifying the quality of a community, being identified as a set of nodes having high modularity. In our terminology, a set of nodes with positive modularity is called a module and a set that maximizes Q is thus called leading module...

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Appl...

In the paper kernel evolving neural network and its learning algorithm are investigated. The proposed system solves the problem of finding the eigenvectors and the corresponding principal components in on-line mode in an environment where hidden in the experimental data interdependencies are nonlinear and can change throw time.

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduct...

In this paper, we present a family of domain decomposition based on an Aitken like acceleration of the Schwarz method seen as an iterative procedure with linear rate of convergence. This paper is a generalization of the method first introduced at the 12 International Conference on Domain Decomposition that was restricted to regular Cartesian grids. The potential of this method to provide scalab...

In this paper, a method for obtaining nonlinear sti ness coe cients in modal coordinates for geometrically nonlinear nite-element models is developed. The method requires application of a nite-element program with a geometrically nonlinear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of ...

It is recently shown in [1, 2] that the exact analytical solution of a rigid body controlled by a linear feedback law may directly be written down in terms of eigenvalues and eigenvectors. However, this control has been computed in previous work [3] for the regulation of satellite angular momentum when the flywheels are at rest. Therefore, the method will here be extended to deal with the struc...

We present an efficient implementation of volumetric nonlinear anisotropic image diffusion on modern programmable graphics processing units (GPUs). We avoid the computational bottleneck of a time consuming eigenvalue decomposition in R. Instead, we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining t...