PINK NOISE, 1/f<sup>α</sup>NOISE, AND THEIR EFFECT ON SOLUTIONS OF DIFFERENTIAL EQUATIONS

Stoyanov, Miroslav; Gunzburger, Max; Burkardt, John

doi:10.1615/int.j.uncertaintyquantification.2011003089

Cited by 26 publications

(21 citation statements)

References 13 publications

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“…Because the noise can be both large and correlated, the degree of correlation and strength of the noise signal can potentially mask the behavior of the true signal; this is called noise biasing. While white noise is uncorrelated (except for r ¼ 0), the noise within our system is correlated ("pink" noise with a 1/f power spectral density falloff) 45 and yields noise biasing (for r > 0). By performing cross-correlations of the separate data sets, the self-correlation from the noise is removed while the noise/signal effects from the cross terms are reduced.…”

Section: Resultsmentioning

confidence: 99%

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

et al. 2015

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A polyimide substrate was scribed using the stylus of an atomic force microscope, then covered with a nematic liquid crystal. The fiber from a near field scanning optical microscope was immersed into the liquid crystal and rastered approximately 80 nm above the surface, thereby obviating smearing effects that occur in thicker samples. By appropriate averaging of multiple data sets, a histogram of the "frozen-in" director deviation Δφ from the average easy axis was obtained, having a full-width-half-maximum of ∼0.02 rad. Additionally, the spatial autocorrelation function of Δφ was extracted, where the primary correlation length was found to be comparable to, but larger than, the liquid crystal's extrapolation length. A secondary characteristic length scale of a few μm was observed, and is thought to be an artifact due to material ejection during the scribing process. Our results demonstrate the utility of nanoscale imaging of the interface behavior inside the liquid crystal.

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Section: Resultsmentioning

confidence: 99%

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

et al. 2015

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“…f_alpha_gaussian (Stoyanov, Gunzburger, & Burkardt, 2011 To investigate the influence of similarity criteria and filter ranges in empirical data, we used 298 resting-state EEG data collected in the context of a larger assessment prior to task performance 299 and immediately following electrode preparation. 2.3 Calculation of standard and "modified" multiscale entropy 343 344…”

Section: Hypotheses and Current Study 227 228mentioning

confidence: 99%

Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What’s signal irregularity got to do with it?

Kosciessa

Kloosterman

Garrett³

2019

Preprint

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AbstractMultiscale Entropy (MSE) is used to characterize the temporal irregularity of neural time series patterns. Due to its’ presumed sensitivity to non-linear signal characteristics, MSE is typically considered a complementary measure of brain dynamics to signal variance and spectral power. However, the divergence between these measures is often unclear in application. Furthermore, it is commonly assumed (yet sparingly verified) that entropy estimated at specific time scales reflects signal irregularity at those precise time scales of brain function. We argue that such assumptions are not tenable. Using simulated and empirical electroencephalogram (EEG) data from 47 younger and 52 older adults, we indicate strong and previously underappreciated associations between MSE and spectral power, and highlight how these links preclude traditional interpretations of MSE time scales. Specifically, we show that the typical definition of temporal patterns via “similarity bounds” biases coarse MSE scales – that are thought to reflect slow dynamics – by high-frequency dynamics. Moreover, we demonstrate that entropy at fine time scales – presumed to indicate fast dynamics – is highly sensitive to broadband spectral power, a measure dominated by low-frequency contributions. Jointly, these issues produce counterintuitive reflections of frequency-specific content on MSE time scales. We emphasize the resulting inferential problems in a conceptual replication of cross-sectional age differences at rest, in which scale-specific entropy age effects could be explained by spectral power differences at mismatched temporal scales. Furthermore, we demonstrate how such problems may be alleviated, resulting in the indication of scale-specific age differences in rhythmic irregularity. By controlling for narrowband contributions, we indicate that spontaneous alpha rhythms during eyes open rest transiently reduce broadband signal irregularity. Finally, we recommend best practices that may better permit a valid estimation and interpretation of neural signal irregularity at time scales of interest.Author SummaryBrain signals exhibit a wealth of dynamic patterns that that are thought to reflect ongoing neural computations. Multiscale sample entropy (MSE) intends to describe the temporal irregularity of such patterns at multiple time scales of brain function. However, the notion of time scales may often be unintuitive. In particular, traditional implementations of MSE are sensitive to slow fluctuations at fine time scales, and fast dynamics at coarse time scales. This conceptual divergence is often overlooked and may lead to difficulties in establishing the unique contribution of MSE to effects of interest over more established spectral power. Using simulations and empirical data, we highlight these issues and provide evidence for their relevance for valid practical inferences. We further highlight that standard MSE and traditional spectral power are highly collinear in our example. Finally, our analyses indicate that spectral filtering can be used to estimate temporal signal irregularity at matching and intuitive time scales. To guide future studies, we make multiple recommendations based on our observations. We believe that following these suggestions may advance our understanding of the unique contributions of neural signal irregularity to neural and cognitive function across the lifespan.

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“…To assess the performance of the detection statistics under noisy conditions, we generated independent sequences of white Gaussian noise to simulate electronic noise (using MATLAB TM , The MathWorks Inc.), and pink (1/f) Gaussian noise [13] to simulate low frequency trends observed in PPG recordings. These sequences were scaled and added to the infant PPG data to generate a Signal-to-Noise Ratio (SNR) that ranged from -20 to 20 dB.…”

Section: Robustness With Noisy Datamentioning

confidence: 99%

A new movement artifact detector for photoplethysmographic signals

Robles-Rubio

Brown

Kearney

2013

2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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Oximeters are commonly used in abbreviated cardiorespiratory studies (ACS) to monitor blood oxygen saturation and heart rate using the photoplethysmography (PPG) signal. These data are prone to movement artifacts, especially in infants who move or need to be handled often. Therefore segments of PPG data contaminated by movement artifact must be detected as a first stage of analysis. In ACS this identification is generally done manually, by having an expert visually assess the quality of the signal. This is subjective and very time consuming, especially for long data records. For this reason we present a novel detector of PPG movement artifacts that uses moving average filters to remove trends, reduce the effect of white noise, and notch filter pulse-related information. The normalized root mean square of the filtered signal is then used as a detection statistic. We demonstrate its detection properties using a data set from infants recovering from anesthesia, and show that it performs better than other automated methods based on entropy or higher-order statistics. Furthermore, the new method is more robust than the other methods in the presence of large noise.

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PINK NOISE, 1/f^αNOISE, AND THEIR EFFECT ON SOLUTIONS OF DIFFERENTIAL EQUATIONS

Cited by 26 publications

References 13 publications

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What’s signal irregularity got to do with it?

A new movement artifact detector for photoplethysmographic signals

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PINK NOISE, 1/fαNOISE, AND THEIR EFFECT ON SOLUTIONS OF DIFFERENTIAL EQUATIONS

Cited by 26 publications

References 13 publications

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What’s signal irregularity got to do with it?

A new movement artifact detector for photoplethysmographic signals

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Resources

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PINK NOISE, 1/f^αNOISE, AND THEIR EFFECT ON SOLUTIONS OF DIFFERENTIAL EQUATIONS