We present a method to linearize, without approximation, specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the are expressed by scalar functions that defined quotient linear eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) contains solutions NEPv. Due characterization MEPs in terms generalized this provides direct way co...

 Abstract—Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such systems, we propose a nonlinear modal decoupling (NMD) approach inversely constructing as many decoupled nonlinear oscillators as the system’s oscillation modes so that individual decoupled oscillators can be easily analyzed to infer...

Post-nonlinear (PNL) independent component analysis (ICA) is a generalisation of ICA where the observations are assumed to have been generated from independent sources by linear mixing followed by component-wise scalar nonlinearities. Most previous PNL ICA algorithms require the post-nonlinearities to be invertible functions. In this paper, we present a variational Bayesian approach to PNL ICA ...

The search for universally applicable nonlinearities in blind signal separation has produced nonlinearities that are optimal for a given distribution, as well as nonlinearities that are most robust against model mismatch. This paper shows yet another justification for the score function, which is in some sense a very robust nonlinearity. It also shows that among the class of parameterizable non...

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural networks. The framework readily integrates into existing stochastic neural n...

Frequency-resolved photon correlations have proven to be a useful resource unveil nonlinearities hidden in standard observables such as the spectrum or (color-blind) correlations. In this manuscript, we analyze frequency-resolved of photons being emitted from an optomechanical system where light is nonlinearly coupled quantized motion mechanical mode resonator, but quantum nonlinear response ty...

This paper presents a nonlinear analytical model for micromechanical silicon ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and ele...

We compute the production of cosmic rays in dynamical superbubble produced by a cluster massive stars. Stellar winds, supernova remnants and turbulence are found to accelerate particles so efficiently that nonlinear feedback must be taken into account order ensure energy balance is not violated. High do scatter on escape quickly after each explosion, which makes both their intensity inside bubb...

In this paper, we study the spatial disorder of coupled discrete nonlinear Schrödinger (CDNLS) equations with piecewise-monotone nonlinearities. By the construction of horseshoes, we show that the CDNLS equation possesses a hyperbolic invariant Cantor set on which it is topological conjugate to the full shift on N symbols. The CDNLS equation exhibits spatial disorder, resulting from the strong ...

A system identification method in the frequency-domain is proposed for a servomechanism with nonlinearities. A linear part of the servomechanism is identified exactly without distortion due to inherent nonlinearities through the proposed method. Parameters of the nonlinearities, including both Coulomb and viscous friction, are identified by the use of limit cycle analysis and describing functio...