Using the two-dimensional nonlinear Schrödinger equation as a model example, we present general method for recovering nonlinearity of dispersive from its small-data scattering behavior. We prove that under very mild assumptions on nonlinearity, wave operator uniquely determines does map. Evaluating map well-chosen initial data, reduce problem to an inverse convolution problem, which solve by me...

We propose the use of self-defocusing nonlinearities to control nonlinear phase shifts in soliton fiber lasers. By analogy to dispersion management, we refer to this scheme as nonlinearity management. First we describe a map that can be regarded as a combination of nonlinearity management and dispersion management. The map is designed to support solitons in two segments of alternating sign of n...

7 High-order epistasis has been observed in many genotype-phenotype maps. These multi-way inter8 actions could have profound implications for evolution and may be useful for dissecting complex 9 traits. Previous analyses have assumed a linear genotype-phenotype map, and then applied a linear 10 high-order epistasis model to dissect epistasis. The assumption of linearity has not been tested 11 i...

Bistable responses of Fabry–Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, wit...

We present a framework for different approaches to finite-time Lyapunov exponent (FTLE) computation for 2D vector fields, based on the advection of seeding circles. On the one hand it unifies the popular flow map approach with techniques based on the evaluation of distinguished trajectories, such as renormalization. On the other hand it allows for the exploration of their order of approximation...

A substitution box (S-Box) is a crucial component of contemporary cryptosystems that provide data protection in block ciphers. At the moment, chaotic maps are being created and extensively used to generate these S-Boxes as map assists providing disorder resistance combat cryptanalytical attempts. In this paper, construction dynamic S-Box using cipher key proposed novel an innovative tweaking ap...

We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points by a fixed angle. For small values of the nonlinearity parameter, we compute the invariant measure and show that it has a singular density to first order in t...

We propose the Gaussian Error Linear Unit (GELU), a high-performing neural network activation function. The GELU nonlinearity is the expected transformation of a stochastic regularizer which randomly applies the identity or zero map, combining the intuitions of dropout and zoneout while respecting neuron values. This connection suggests a new probabilistic understanding of nonlinearities. We pe...

We show from an elementary symmetry analysis that, in dispersion-compensated systems for which a lossless model is valid, nonlinearity requires a chirp-free point at the center of symmetry (if such exists) of the map for any kind of unique periodic solution. We also present an example of a more-complex map when the periodic solution is not unique.