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Journal Article•

Mathematical Analysis of Random Noise-Conclusion

01 Jan 1945-Bell System Technical Journal-Vol. 24, pp 46-156
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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Book Chapter•DOI•
Willard J. Pierson1•
TL;DR: In this paper, the authors describe the new theoretical developments, which give a more complete and more accurate description of the analysis, generation, propagation, and refraction of wind generated gravity waves.
Abstract: Publisher Summary The purpose of this chapter is to describe the new theoretical developments, which give a more complete and more accurate description of the analysis, generation, propagation, and refraction of wind generated gravity waves. A special path of development through hydrodynamic theory permits a link with time series theory that yields a realistic and practical description of actual ocean waves. This description explains the irregularity of these waves, it describes their short crestedness, and it illustrates the change from sea waves to swell waves. Because of the essential irregularity of actual wind generated gravity waves, the finer developments and the refinements of nonlinear theory have to be sacrificed. Linear theories are used in order to employ the principle of superposition to the best advantage. The irregularity and the marked variation in height from wave to wave in an actual wave record are explained before minor effects of nonlinearity can be taken into consideration. The plan of this chapter is to outline the many different kinds of inquiry pursued in classical hydrodynamics with reference to waves; to show that simple harmonic progressive waves must be selected as the link with time series theory; to show how Fourier integral theory leads more generally to time series theory; and finally, to show how a model of wind generated gravity waves can be constructed, which will explain many of the features of actual waves.

107 citations

Journal Article•DOI•
TL;DR: A thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector.
Abstract: A thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector. The pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive Monte Carlo simulations. Parameter optimization and computational budget aspects are discussed.

105 citations

Journal Article•DOI•
TL;DR: This work studies how threshold models and neocortical neurons transfer temporal and interneuronal input correlations to correlations of spikes and shows that pairs with different firing rates driven by common inputs in general exhibit asymmetric spike correlations.
Abstract: We study how threshold models and neocortical neurons transfer temporal and interneuronal input correlations to correlations of spikes. In both, we find that the low common input regime is governed by firing rate dependent spike correlations which are sensitive to the detailed structure of input correlation functions. In the high common input regime, the spike correlations are largely insensitive to the firing rate and exhibit a universal peak shape. We further show that pairs with different firing rates driven by common inputs in general exhibit asymmetric spike correlations.

103 citations

Journal Article•DOI•
TL;DR: In this article, a new scalar measure of persistence together with a companion estimator is proposed, which has the advantage of not requiring the specification and estimation of a model for the series under investigation.

103 citations

Journal Article•DOI•
TL;DR: The critical exponent of the intensity moment is computed from the Thorn-Arnol'd classification of caustics as catastrophes as discussed by the authors, and the results indicate that when N to infinity (Gaussian random medium) the exponents depend only on whether the waves propagate in two or three dimensions.
Abstract: The critical exponent of the intensity moment is computed from the Thorn-Arnol'd classification of caustics as catastrophes The caustics are studied on the torus whose coordinates are 16 N random phases theta 1 theta N for members of the ensemble describing the phase screen or inhomogeneous medium responsible for the disorder of the wave The results indicate that when N to infinity (Gaussian random medium) the exponents depend only on whether the waves propagate in two or three space dimensions

102 citations