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: KZ(SZ) plots of DSP from noise, simulated data and single ion channel recordings showed that DSPs with false negative CP could be distinguished and showed that filtering had a significant effect on the normality of data and so filtering should be taken into account when calculating statistics.
Abstract: Change point detectors (CPDs) are used to segment recordings of single molecules for the purpose of kinetic analysis. The assessment of the accuracy of CPD algorithms has usually been based on testing them with simulated data. However, there have not been methods to assess the output of CPDs from real data independent of simulation. Here we present one method to do this based on the assumption that the elementary kinetic unit is a stationary period (SP) with a normal distribution of samples, separated from other SPs by change points (CPs). Statistical metrics of normality can then be used to assess SPs detected by a CPD algorithm (detected SPs, DSPs). Two statistics in particular were found to be useful, the z-transformed skew (S
Z) and z-transformed kurtosis (K
Z). K
Z(S
Z) plots of DSP from noise, simulated data and single ion channel recordings showed that DSPs with false negative CP could be distinguished. Also they showed that filtering had a significant effect on the normality of data and so filtering should be taken into account when calculating statistics. This method should be useful for analyzing single molecule recordings where there is no simple model for the data.
3 citations
TL;DR: In this article, the power spectrum of the acoustical noise generated by turbulent flow in closed systems is evaluated and used as a forcing function to determine the mechanical response and fatigue lifetime of the solid boundaries in the various volumes contained in the closed system.
3 citations
TL;DR: A new computational model to generate Rayleigh channels that completely match the authors' anticipation-fully uncorrelated or fully correlated channels is introduced, and a design method to reduce the number of sinusoids is proposed to achieve reduced computational cost of the system.
Abstract: Assessing the performance of communication system is critical in system design in mobile communication study. Numerous methodologies have been employed to facilitate the assessment, amongst which generation of multiple fading channels is widely used and thus of great interest to us. Specifically, multiple Rayleigh fading channels are extensively utilized in simulation of the following: MIMO channels, amplify-and-forward fading channels, frequency-selective channels, etc. The existing model to generate Rayleigh fading channels is the sum of sinusoids SOS. However, the SOS model is flawed, as it sometimes generates impure correlated channels. That is, a small fraction of correlated channels are generated when we anticipate uncorrelated or vice versa. In this paper, on the basis of the concept of SOS, we introduce a new computational model to generate Rayleigh channels that completely match our anticipation-fully uncorrelated or fully correlated channels. Additionally, we also propose a design method to reduce the number of sinusoids, thus we achieve reduced computational cost of the system. Simulation results and comparison analysis indicate that, with reduced computational cost, our method is able to produce pure Rayleigh fading channels- 100% uncorrelated or the opposite.Copyright © 2013 John Wiley & Sons, Ltd.
3 citations
TL;DR: Generation of random test signals and some other applications in the fields of reliability and queueing theory as well as in those of biomedical and nuclear engineering are briefly discussed.
3 citations
TL;DR: In this paper, the authors studied the latitudinal distribution and evolution of sunspot areas of solar cycles 12, 13, 14, 15, 16, and 18 for both even and odd cycles.
Abstract: We study the latitudinal distribution and evolution of sunspot areas of Solar Cycles 12 – 23 (SC12–23) and sunspot groups of Solar Cycles 8 – 23 (SC8–23) for even and odd cycles. The Rician distribution is the best-fit function for both even and odd sunspots group latitudinal occurrence. The mean and variance for even northern/southern butterfly wing sunspots are 14.94/14.76 and 58.62/56.08, respectively, and the mean and variance for odd northern/southern wing sunspots are 15.52/15.58 and 61.77/58.00, respectively. Sunspot groups of even cycle wings are thus at somewhat lower latitudes on average than sunspot groups of the odd cycle wings, i.e. about 0.6 degrees for northern hemisphere wings and 0.8 degrees for southern hemisphere wings. The spatial analysis of sunspot areas between SC12–23 shows that the small sunspots are at lower solar latitudes of the Sun than the large sunspots for both odd and even cycles, and also for both hemispheres. Temporal evolution of sunspot areas shows a lack of large sunspots after four years (exactly between 4.2 – 4.5 years), i.e. about 40% after the start of the cycle, especially for even cycles. This is related to the Gnevyshev gap and is occurring at the time when the evolution of the average sunspot latitudes crosses about 15 degrees. The gap is, however, clearer for even cycles than odd ones. Gnevyshev gap divides the cycle into two disparate parts: the ascending phase/cycle maximum and the declining phase of the sunspot cycle.
3 citations
Cites background from "Mathematical Analysis of Random Noi..."
...The PDF of the Rician distribution is defined as fZ (z) = z σ2 exp ( − ( z2 + ν2 ) σ2 ) I0 (zν σ2 ) , r ≥ 0, (6) where I0 is the modified Bessel function of the first kind with zeroth order (Rice, 1945; Taluktar and Lawing, 1991)....
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...The Rice distribution, Rician distribution, is the probability distribution related to the Rayleigh distribution but with non-zero mean (Rice, 1945)....
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