Components of the two-sided Kolmogorov–Smirnov test in signal detection problems with Gaussian white noise

1991 ◽  
Vol 29 (3) ◽  
pp. 325-335 ◽  
Author(s):  
Holger Drees ◽  
Hartmut Milbrodt
2008 ◽  
Vol 08 (02) ◽  
pp. L229-L235 ◽  
Author(s):  
LEI ZHANG ◽  
JUN HE ◽  
AIGUO SONG

Recently, it was reported that some saturation nonlinearities could effectively act as noise-aided signal-noise-ratio amplifiers. In the letter we consider the signal detection performance of saturation nonlinearities driven by a sinusoidal signal buried in Gaussian white noise. It is showed that the signal detection statistics still undergo a nonmonotonic evolution as noise is raised. We also particularly show that an improvement of the SNR in terms of the first harmonic does not imply the possibility to improve the signal detection performance through stochastic resonance. The study might also complement other reports about stochastic resonance in saturation nonlinearities.


1999 ◽  
Vol 19 (4) ◽  
pp. 452-459 ◽  
Author(s):  
Cole A. Giller ◽  
Mustapha R. Hatab ◽  
Angela M. Giller

Although transcranial Doppler ultrasound (TCD) has been used to detect oscillations in CBF, interpretation is severely limited, since only blood velocity and not flow is measured. Oscillations in vessel diameter could, therefore, mask or alter the detection of those in flow by TCD velocities. In this report, the authors use a TCD-derived index of flow to detect and quantify oscillations of CBF in humans at rest. A flow index (FI) was calculated from TCD spectra by averaging the intensity weighted mean in a beat-by-beat manner over 10 seconds. Both FI and TCD velocity were measured in 16 studies of eight normal subjects at rest every 10 seconds for 20 minutes. End tidal CO2 and blood pressure were obtained simultaneously in six of these studies. The TCD probe position was meticulously held constant. An index of vessel area was calculated by dividing FI by velocity. Spectral estimations were obtained using the Welch method. Spectral peaks were defined as peaks greater than 2 dB above background. The frequencies and magnitudes of spectral peaks of FI, velocity, blood pressure, and CO2 were compared with t tests. The Kolmogorov-Smirnov test was used to further confirm that the data were not white noise. In most cases, three spectral peaks (a, b, c) could be identified, corresponding to periods of 208 ± 93, 59 ± 31, and 28 ± 4 (SD) seconds for FI, and 196 ± 83, 57 ± 20, and 28 ± 6, (SD) seconds for velocity. The magnitudes of the spectral peaks for FI were significantly greater ( P < 0.02) than those for velocity. These magnitudes corresponded to variations of at least 15.6%, 9.8%, and 6.8% for FI, and 4.8%, 4.2%, and 2.8% for velocity. The frequencies of the spectral peaks of CO2 were similar to those of FI with periods of 213 ± 100, 60 ± 46, and 28 ± 3.6 (SD) seconds. However, the CO2 spectral peak magnitudes were small, with an estimated maximal effect on CBF of (±) 2.5 ± 0.98, 1.5 ± 0.54, and 1.1 ± 0.31 (SD) percent. The frequencies of the blood pressure spectral peaks also were similar, with periods of 173 ± 81, 44 ± 8, and 26 ± 2.5 (SD) seconds. Their magnitudes were small, corresponding to variations in blood pressure of (±) 2.1 ± 0.55, 0.97 ± 0.25, and 0.72 ± 0.19 (SD) percent. Furthermore, coherence analysis showed no correlation between CO2 and FI, and only weak correlations at isolated frequencies between CO2 and velocity, blood pressure and velocity, or blood pressure and FI. The Kolmogorov-Smirnov test distinguished our data from white noise in most cases. Oscillations in vessel flow occur with significant magnitude at three distinct frequencies in normal subjects at rest and can be detected with a TCD-derived index. The presence of oscillations in blood velocity at similar frequencies but at lower magnitudes suggests that the vessel diameters oscillate in synchrony with flow. Observed variations in CO2 and blood pressure do not explain the flow oscillations. Ordinary TCD velocities severely underestimate these oscillations and so are not appropriate when small changes in flow are to be measured.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammadreza Azimi ◽  
Seyed Ahmad Rasoulinejad ◽  
Andrzej Pacut

AbstractIn this paper, we attempt to answer the questions whether iris recognition task under the influence of diabetes would be more difficult and whether the effects of diabetes and individuals’ age are uncorrelated. We hypothesized that the health condition of volunteers plays an important role in the performance of the iris recognition system. To confirm the obtained results, we reported the distribution of usable area in each subgroup to have a more comprehensive analysis of diabetes effects. There is no conducted study to investigate for which age group (young or old) the diabetes effect is more acute on the biometric results. For this purpose, we created a new database containing 1,906 samples from 509 eyes. We applied the weighted adaptive Hough ellipsopolar transform technique and contrast-adjusted Hough transform for segmentation of iris texture, along with three different encoding algorithms. To test the hypothesis related to physiological aging effect, Welches’s t-test and Kolmogorov–Smirnov test have been used to study the age-dependency of diabetes mellitus influence on the reliability of our chosen iris recognition system. Our results give some general hints related to age effect on performance of biometric systems for people with diabetes.


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