A. Einstein

Bio: A. Einstein is an academic researcher. The author has contributed to research in topics: Einstein & Autocorrelation. The author has an hindex of 1, co-authored 1 publications receiving 22 citations.

Method for the determinination of the statistical values of observations concerning quantities subject to irregular fluctuations

Abstract: Albert Einstein introduces the concepts of the autocorrelation and cross-correlation functions and proves that automatic instruments can be devised for their experimental determination. However, the main point of the paper is that he introduces the concept of a power spectrum (without the use of this term, which - like "correlation function" and "stationary"- do not appear until much later) and elucidates its physical meaning. He also indicates two possible ways of calculating such spectra from experimental data. The stress Einstein laid on the importance of the spectrum of power (of "intensity," as he called it) of fluctuating time series F(t) shows a striking physical intuition since no applications existed for this concept in 1914.

New forms of Levinson and Schur algorithms

Abstract: The Levinson and Schur solutions to the adaptive filtering and parameter estimation problem of recursive least squares processing are described. Unnormalized versions of a newly developed Schur RLS adaptive filter are presented. A systolic array of the Schur RL adaptive filter is devised and its performance is illustrated with a typical example. The classical Levinson and Schur algorithms drop out as special cases of the more general Levinson and Schur RLS adaptive filtering algorithms. The recently introduced split Levinson and Schur algorithms, which are obtained by exploiting the symmetry in the Toeplitz-structured extended normal equations, are reviewed. >

Nonlinear function approximation over high-dimensional domains

Abstract: An algorithm is disclosed for constructing nonlinear models from high-dimensional scattered data. The algorithm progresses iteratively adding a new basis function at each step to refine the model. The placement of the basis functions is driven by a statistical hypothesis test that reveals geometric structure when it fails. At each step the added function is fit to data contained in a spatio-temporally defined local region to determine the parameters, in particular, the scale of the local model. The proposed method requires no ad hoc parameters. Thus, the number of basis functions required for an accurate fit is determined automatically by the algorithm. The approach may be applied to problems including modeling data on manifolds and the prediction of financial time-series. The algorithm is presented in the context of radial basis functions but in principle can be employed with other methods for function approximation such as multi-layer perceptrons.

Applications of optical coherence theory

Abstract: Over the last century, classical optical coherence has developed from a few vaguely related concepts into a standing along branch of optics and, more broadly, electromagnetics, that has resulted in a number of groundbreaking discoveries concerning the nature of light, its evolution and interaction with matter. While the theoretical developments of this field have been well documented in a number of excellent monographs and review articles, its applications have never been properly summarized. In this review we cover broadly employed, currently developing, and yet untapped practical outcomes of optical coherence theory used in other fields of science, technology, and medicine.

On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation

Abstract: The Kraichnan-Leith-Batchelor scenario of a dual cascade, consisting of an upscale pure energy cascade and a downscale pure enstrophy cascade, is an idealization valid only in an infi nite domain in the limit of in finite Reynolds number. In realistic situations there are double cascades of energy and enstrophy located both upscale and downscale of injection, as long as there are cascades. We outline the statistical theory governing the double cascades and predict the form of the energy spectrum. We show that in general the twin conservation of energy and enstrophy imply the presence of two constant fluxes in each inertial range. This gives rise to a more complicated energy spectrum, which cannot be predicted using dimensional arguments as in the classical theory.