We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic midpoint rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations...

Nonlinear Schrödinger (NLS) equations have attracted the attention of the physical and mathematical community for over four decades. NLS equations arise in such diverse fields as deep water waves [4, 25], plasma physics [24], fiber optics [11], and Bose-Einstein condensation [17]. The basic method for solving the NLS initial-value problem is the inverse scattering transform (IST) method [2–4, 6...

BACKGROUND Neocortical lesions (NLs) are an important pathological component of multiple sclerosis (MS), but their visualization by magnetic resonance imaging (MRI) remains challenging. OBJECTIVES We aimed at assessing the sensitivity of multi echo gradient echo (ME-GRE) T2*-weighted MRI at 7.0 Tesla in depicting NLs compared to myelin and iron staining. METHODS Samples from two MS patients...

BACKGROUND Biodegradable polymers have increasingly been recognized for various biological applications in recent years. Here we examined the immunostimulatory activities of the novel poly(aspartic acid) conjugated with L-lysine (PLA). METHODS PLA was synthesized by conjugating L-lysine to aspartic acid polymer. PLA-nanoliposomes (PLA-NLs) were prepared from PLA using a microfluidizer. The im...

In this study we tested the hypothesis that magainin, a peptide known to form pores in bacterial cell membranes, can increase skin permeability by disrupting stratum corneum lipid structure. We further hypothesized that magainin's enhancement requires co-administration with a surfactant chemical enhancer to increase magainin penetration into the skin. In support of these hypotheses, exposure to...

If the initial condition for the Korteweg-deVries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the Nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and implications have been discussed only in asides. In this note, we attempt a more focused and comprehensive discussion including such as is...

The vertebrate nuclear pore complex (NPC) harbors an approximately 10-nm diameter diffusion channel that is large enough to admit 50-kD polypeptides. We have analyzed the permeability properties of the Saccharomyces cerevisiae nuclear envelope (NE) using import (NLS) and export (NES) signal-containing green fluorescent protein (GFP) reporters. Compared with wild-type, passive export rates of a ...

The Hedgehog (Hh) family of secreted proteins governs many key developmental processes by regulating Ci/Gli transcription factors at multiple levels including nuclear-cytoplasmic shuttling. Here, we investigate the mechanism underlying the regulation of Ci/Gli subcellular localization by identifying and characterizing a novel nuclear localization sequence (NLS) in the N-terminal conserved domai...

This paper considers the problem of estimating the parameters of chirp signals with randomly time-varying amplitude. Two methods for solving this problem are presented. First, a nonlinear least-squares approach (NLS) is proposed. It is shown that by minimizing the NLS criterion with respect to all samples of the time-varying amplitude, the problem reduces to a two-dimensional maximization probl...

In this paper, we consider the logistic regression model with an integrated regressor driven by a general linear process. In particular, we derive the limit distributions of the nonlinear least squares (NLS) estimators and their t-ratios of the parameters in the model. It is shown that the NLS estimators are generally not efficient. Moreover, the t-ratios for the level parameters have limit dis...