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"A well-known and thoroughly studied phenomenon in nonlinear wave propagation is that of modulation instability (MI). MI is usually approached as a perturbation to a pump, and its analysis is based on preserving only ter...

"The Generalized Nonlinear Schrödinger Equation (GNLSE) finds several applications, especially in describing pulse propagation in nonlinear fiber optics. A well-known and thoroughly studied phenomenon in nonlinear wave ...

A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in high-dimensional feature spa...

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Economic inequality is a social phenomenon with several facets, all of which are signifificant when it comes to multidimensional measurement. When income is used as the fundamental variable of analysis to measure economi...

"In this Letter, we present, for the first time, to the best of our knowledge, the modulation instability (MI) gain spectrum of waveguides with an arbitrary frequency-dependent nonlinear coefficient ensuring strict energ...

"This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim, the notion of re...

"This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of outputmaps. With this aim the notion of redu...

"We propose an original, simple, and direct method for the simultaneous estimation of the selfsteepening parameter and the fractional Raman contribution in fiber optics. Our proposal is based on the dependence of the mod...

"In this work, it is shown that the output sequence of a well-known cryptographic generator, the so-called self-shrinking generator, can be obtained from a simple linear model based on cellular automata. In fact, such a ...

"We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadban...

"We study the properties of a soliton crystal, a bound state of several optical pulses that propagate with a fixed temporal separation through the optical fibres of the proposed approach for generation of optical frequen...

"We revisit modulation instability in optical fibers, including all relevant effects, such as higher-order dispersion terms, self-steepening, and the Raman response. Our analysis allows us to calculate the spectral evolu...

Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact repr...

We present here a framework for the study of molecular variation within a single species. Information on DNA haplotype divergence is incorporated into an analysis of variance format, derived from a matrix of squared-dist...

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningfu...

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems...

Preface to the Classics Edition Preface Acknowledgments Glossary of Symbols Introduction Part I. Background Material. 1. Sample Problems 2. Linear Algebra 3. Analysis Part II. Nonconstructive Existence Theorems. 4. Gradi...

Previous article Next article An Algorithm for Least-Squares Estimation of Nonlinear ParametersDonald W. MarquardtDonald W. Marquardthttps://doi.org/10.1137/0111030PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport Ci...

Basic Prerequisite Knowledge. Fitting a Straight Line by Least Squares. Checking the Straight Line Fit. Fitting Straight Lines: Special Topics. Regression in Matrix Terms: Straight Line Case. The General Regression Situa...

Data Analysis Using Regression and Multilevel/Hierarchical Models, first published in 2007, is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression an...

Preface 1. Introduction. Problems to be considered Characteristics of 'real-world' problems Finite-precision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. What is not possible Newto...

A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and pres...

The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formu...