Journal Article•
Mathematical Analysis of Random Noise-Conclusion
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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TL;DR: A variety of statistical properties have been developed for the number of solutions of an equation as mentioned in this paper, including a variety of properties related to the probability of finding a solution to an equation.
Abstract: A variety of statistical properties have been developed for the number of solutions of an equation
23 citations
TL;DR: In this article, the wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the liquid and its partial pressure in the surrounding gas phase.
Abstract: The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first-order transition in the adsorbed film thickness, which we term “Wenzel prewetting”, occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting.
23 citations
TL;DR: In this paper, the authors present results for the statistical properties of the fluctuating radial transport caused by low-frequency electrostatic turbulence in a toroidal plasma with no toroidal transform, and they find strongly intermittent features in the flux signal obtained as the product of fluctuating density and the E???B/B2-velocity.
Abstract: Turbulent plasma transport due to low-frequency electrostatic fluctuations in a toroidal plasma is studied experimentally. The data are obtained in a magnetized toroidal plasma with no toroidal transform. The plasma is generated by a discharge from a hot electron emitting filament and diagnosed by conventional Langmuir probes measuring densities by electron or ion saturation currents and floating potentials. We present results for the statistical properties of the fluctuating radial transport caused by low-frequency electrostatic turbulence in the device. The turbulent plasma flux is identified as the product of the fluctuating density and the E???B/B2-velocity. Even though the probability densities of the fluctuating electric fields and plasma densities are close to Gaussians, we find strongly intermittent features in the flux signal obtained as the product of these two fluctuating quantities. A conditional statistical analysis gives insight in detail of the turbulent transport. The intermittency studies are extended by analyzing the excess statistics, i.e. the average duration of time intervals in the flux signal spent above a given reference level. We find that this analysis offers a very effective measure for intermittency effects. In our case, the signal is characterized by an excess of temporally narrow, large amplitude bursts, when compared with an equivalent Gaussian random signal.
23 citations
TL;DR: This chapter focuses on the filters that are designed to identify maxima of the first derivative of the signal.
Abstract: Publisher Summary There are three approaches to deal with the problem of edge detection: the region approach, the template-matching approach, and the filtering approach. Filters are designed to identify the locations of maximal image energy or to respond in a predetermined way when the first or the second derivative of the signal becomes maximal. This chapter focuses on the filters that are designed to identify maxima of the first derivative of the signal. To be able to tell whether a filter has good signal-to-noise ratio or not, without trying it in practice, the expressions of the filter response to the signal and to the noise separately needs to be calculated.
23 citations
TL;DR: In this article, a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes is considered.
Abstract: We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study the point process N b + of upcrossings of some level b. Our main result shows that a suitably scaled point process N b + ( (b)t), t 0, converges, as b!1, weakly to a geometrically compound Poisson process. We also prove a version of Rice’s formula relating the stationary density of the process to level crossing intensities. This formula provides an interpretation of the scaling factor (b). While our proof of the limit theorem requires additional assumptions, Rice’s formula holds whenever the (stationary) overall intensity of jumps is nite.
23 citations