Slope Of Power Spectral Density Research Articles

Flicker Noise in Resistive Gas Sensors-Measurement Setups and Applications for Enhanced Gas Sensing.

We discuss the implementation challenges of gas sensing systems based on low-frequency noise measurements on chemoresistive sensors. Resistance fluctuations in various gas sensing materials, in a frequency range typically up to a few kHz, can enhance gas sensing by considering its intensity and the slope of power spectral density. The issues of low-frequency noise measurements in resistive gas sensors, specifically in two-dimensional materials exhibiting gas-sensing properties, are considered. We present measurement setups and noise-processing methods for gas detection. The chemoresistive sensors show various DC resistances requiring different flicker noise measurement approaches. Separate noise measurement setups are used for resistances up to a few hundred kΩ and for resistances with much higher values. Noise measurements in highly resistive materials (e.g., MoS2, WS2, and ZrS3) are prone to external interferences but can be modulated using temperature or light irradiation for enhanced sensing. Therefore, such materials are of considerable interest for gas sensing.

Sensor-Based Assessment of Variability in Daily Physical Activity and Frailty

Introduction: Frailty is a common geriatric syndrome associated with decline in physiological reserve. While several digital biomarkers of daily physical activity (DPA) have been used in frailty assessment, the association between DPA variability and frailty is still not clear. The goal of this study was to determine the association between frailty and DPA variability. Methods: This is an observational cross-sectional study conducted between September 2012 and November 2013. Older adults (≥65 years), without any severe mobility disorder, and the ability to walk 10 m (with or without an assistive device) were eligible for the study. DPA including sitting, standing, walking, lying, and postural transition were recorded for 48 h continuously. DPA variability was analyzed from two perspectives: (i) DPA duration variability in terms of coefficient of variation (CoV) of sitting, standing, walking, and lying down durations; and (ii) DPA performance variability in terms of CoV of sit-to-stand (SiSt) and stand-to-sit (StSi) durations and stride time (i.e., slope of power spectral density – PSD). Results: Data was analyzed from 126 participants (44 non-frail, 60 pre-frail, and 22 frail). For DPA duration variability, CoV of lying and walking duration was significantly larger among non-frail compared to pre-frail and frail groups (p < 0.03, d = 0.89 ± 0.40). For DPA performance variability, StSi CoV and PSD slope were significantly smaller for non-frail compared to pre-frail and frail groups (p < 0.05, d = 0.78 ± 0.19). Conclusion: Lower DPA duration variability in pre-frail and frail groups may be attributed to the set daily routines frail older adults tend to follow, compared to variable physical activity routines of non-frail older adults. Higher DPA performance variability in the frail group may be attributed to reduced physiological capabilities toward walking for longer durations and the reduced muscle strength in the lower extremities, leading to incosistency in performing postural transitions.

Slope of the power spectral density flattens at low frequencies (200Hz) in human electroencephalogram.

The power spectral density (PSD) of the brain signals is characterized by two distinct features: oscillations, which are represented as distinct "bumps," and broadband aperiodic activity, that reduces in power with increasing frequency and is characterized by the slope of the power falloff. Recent studies have shown a change in the slope of the aperiodic activity with healthy aging and mental disorders. However, these studies analyzed slopes over a limited frequency range (<100Hz). To test whether the PSD slope is affected over a wider frequency range with aging and mental disorder, we analyzed the slope till 800Hz in electroencephalogram data recorded from elderly subjects (>49years) who were healthy (n = 217) or had mild cognitive impairment (MCI; n = 11) or Alzheimer's Disease (AD; n = 5). Although the slope reduced up to ~ 150Hz with healthy aging (as shown previously), surprisingly, at higher frequencies (>200Hz), it increased with age. These results were observed in all electrodes, for both eyes open and eyes closed conditions, and for different reference schemes. However, slopes were not significantly different in MCI/AD subjects compared with healthy controls. Overall, our results constrain the biophysical mechanisms that are reflected in the PSD slopes in healthy and pathological aging.

Maternal hair cortisol predicts periodic and aperiodic infant frontal EEG activity longitudinally across infancy.

Maternal stress is known to be an important factor in shaping child development, yet the complex pattern of associations between stress and infant brain development remains understudied. To better understand the nuanced relations between maternal stress and infant neurodevelopment, research investigating longitudinal relations between maternal chronic physiological stress and infant brain function is warranted. In this study, we leveraged longitudinal data to disentangle between- from within-person associations of maternal hair cortisol and frontal electroencephalography (EEG) power at three time points across infancy at 3, 9, and 15months. We analyzed both aperiodic power spectral density (PSD) slope and traditional periodic frequency band activity. On the within-person level, maternal hair cortisol was associated with a flattening of frontal PSD slope and an increase in relative frontal beta. However, on the between-person level, higher maternal hair cortisol was associated with steeper frontal PSD slope, increased relative frontal theta, and decreased relative frontal beta. The within-person findings may reflect an adaptive neural response to relative shifts in maternal stress levels, while the between-person results demonstrate the potentially detrimental effects of chronically elevated maternal stress. This analysis offers a novel, quantitative insight into the relations between maternal physiological stress and infant cortical function.

Wind Power Scenario Synthesis With Smoothing Effect Through Spectral Decomposition and Its Application to Flexible Resource Adequacy

We synthesize future scenarios of total wind power generation (WPG) of future wind farms by considering the smoothing effect, in which mid-term variability fades out, but periodicity and short-term variability remain as more geographically distributed wind farms are aggregated. First, we decompose the WPG into a periodic component (PC) and non-periodic component (NC). We design the future PC by modifying the standard deviation and mean of the current PC. Then, we assume that the NC can be decomposed into a variable component (VC), which is a source of mid-term variability, and an uncertain component (UC), which is a source of short-term variability. We separate the VC and UC in the frequency domain. We design the VC by modifying the slope of power spectral density (PSD) to represent the smoothing effect and the UC by synthesizing the PSD distribution to represent randomness. Based on our scenarios, we develop a new flexibility index and a novel recursive algorithm to calculate the required amount of future flexible resources and the value of the smoothing effect to maintain the flexible resource adequacy. Finally, we verify the smoothing effect and the amount of flexible resources by simulating the IEEE test network based on actual WPG in Texas and Australia.

Optical Variability of Eight FRII-type Quasars with 13 yr Photometric Light Curves

We characterize the optical variability properties of eight lobe-dominated radio quasars (QSOs): B2 0709+37, FBQS J095206.3+235245, PG 1004+130, [HB89] 1156+631, [HB89] 1425+267, [HB89] 1503+691, [HB89] 1721+343, and 4C +74.26, systematically monitored for a duration of 13 yr since 2009. The quasars are radio-loud objects with extended radio lobes that indicate their orientation close to the sky plane. Five of the eight QSOs are classified as giant radio quasars. All quasars showed variability during our monitoring, with magnitude variations between 0.3 and 1 mag for the least variable and the most variable QSOs, respectively. We performed both structure function (SF) analysis and power spectral density (PSD) analysis for the variability characterization and search for characteristic timescales and periodicities. As a result of our analysis, we obtained relatively steep SF slopes (α ranging from 0.49 to 0.75) that are consistent with the derived PSD slopes (∼2–3). All the PSDs show a good fit to single power-law forms, indicating a red-noise character of variability between timescales of ∼13 yr and weeks. We did not measure reliable characteristic timescales of variability from the SF analysis, which indicates that the duration of the gathered data is too short to reveal them. The absence of bends in the PSDs (change of slope from ≥1 to ∼0) on longer timescales indicates that optical variations are most likely caused by thermal instabilities in the accretion disk.

Millimeter Light Curves of Sagittarius A* Observed during the 2017 Event Horizon Telescope Campaign

The Event Horizon Telescope (EHT) observed the compact radio source, Sagittarius A* (Sgr A*), in the Galactic Center on 2017 April 5–11 in the 1.3 mm wavelength band. At the same time, interferometric array data from the Atacama Large Millimeter/submillimeter Array and the Submillimeter Array were collected, providing Sgr A* light curves simultaneous with the EHT observations. These data sets, complementing the EHT very long baseline interferometry, are characterized by a cadence and signal-to-noise ratio previously unattainable for Sgr A* at millimeter wavelengths, and they allow for the investigation of source variability on timescales as short as a minute. While most of the light curves correspond to a low variability state of Sgr A*, the April 11 observations follow an X-ray flare and exhibit strongly enhanced variability. All of the light curves are consistent with a red-noise process, with a power spectral density (PSD) slope measured to be between −2 and −3 on timescales between 1 minute and several hours. Our results indicate a steepening of the PSD slope for timescales shorter than 0.3 hr. The spectral energy distribution is flat at 220 GHz, and there are no time lags between the 213 and 229 GHz frequency bands, suggesting low optical depth for the event horizon scale source. We characterize Sgr A*’s variability, highlighting the different behavior observed just after the X-ray flare, and use Gaussian process modeling to extract a decorrelation timescale and a PSD slope. We also investigate the systematic calibration uncertainties by analyzing data from independent data reduction pipelines.

Aperiodic electrophysiological activity in preterm infants is linked to subsequent autism risk.

Approximately 7% of preterm infants receive an autism spectrum disorder (ASD) diagnosis. Yet, there is a significant gap in the literature in identifying prospective markers of neurodevelopmental risk in preterm infants. The present study examined two electroencephalography (EEG) parameters during infancy, absolute EEG power and aperiodic activity of the power spectral density (PSD) slope, in association with subsequent autism risk and cognitive ability in a diverse cohort of children born preterm in South Africa. Participants were 71 preterm infants born between 25 and 36weeks gestation (34.60±2.34weeks). EEG was collected during sleep between 39 and 41weeks postmenstrual age adjusted (40.00±0.42weeks). The Bayley Scales of Infant Development and Brief Infant Toddler Social Emotional Assessment (BITSEA) were administered at approximately 3 years of age adjusted (34±2.7 months). Aperiodic activity, but not the rhythmic oscillatory activity, at multiple electrode sites was associated with subsequent increased autism risk on the BITSEA at three years of age. No associations were found between the PSD slope or absolute EEG power and cognitive development. Our findings highlight the need to examine potential markers of subsequent autism risk in high-risk populations other than infants at familial risk.

Properties of Magnetic Field Fluctuations in Long-Lasting Radial IMF Events from Wind Observation

Long-lasting radial interplanetary magnetic field (IMF) intervals in which IMF points along the solar wind velocity for several hours have many interesting properties. We investigate the average parameters and the behavior of magnetic field fluctuations within 419 such radial intervals. The power spectral density (PSD) calculated over 1-h intervals of a radial IMF is compared with PSDs in adjacent regions prior to and after the radial IMF. We concentrate on (1) the power of IMF fluctuations, (2) the median slopes of PSDs in both inertial and kinetic ranges, (3) the proton temperature and its anisotropy, and (4) the occurrence rate of wavy structures and their polarization. We have shown that the fluctuation amplitude is low in the radial IMF intervals in both magnetohydrodynamic (MHD) and kinetic ranges, and the spectral power increases with the cone angle in the MHD range. We discuss this effect in the light of present knowledge on plasma turbulence and peculiarities of observations of magnetic field variations under the radial background magnetic field. We found that in the radial IMF events, the proton temperature is more isotropic, the occurrence rate of waves is higher, and the waves have no preferred polarization in the frequency range from 0.1 to 1 Hz. It suggests that the radial IMF structure leads to a different development of turbulence than the typical Parker-spiral structure.

Origins of subdiffractional contrast in optical coherence tomography.

We demonstrate that OCT images quantify subdiffractional tissue structure. Optical coherence tomography (OCT) measures stratified tissue morphology with spatial resolution limited by the temporal coherence length. Spectroscopic OCT processing, on the other hand, has enabled nanoscale sensitive analysis, presenting an unexplored question: how does subdiffractional information get folded into the OCT image and how does one best analyze to allow for unambiguous quantification of ultrastructure? We first develop an FDTD simulation to model spectral domain OCT with nanometer resolution. Using this, we validate an analytical relationship between the sample statistics through the power spectral density (PSD) of refractive index fluctuations and three measurable quantities (image mean, image variance, and spectral slope), and have found that each probes different aspects of the PSD (amplitude, integral and slope, respectively). Finally, we found that only the spectral slope, quantifying mass scaling, is monotonic with the sample autocorrelation shape.

The diversity and variability of star formation histories in models of galaxy evolution

ABSTRACT Understanding the variability of galaxy star formation histories (SFHs) across a range of time-scales provides insight into the underlying physical processes that regulate star formation within galaxies. We compile the SFHs of galaxies at z = 0 from an extensive set of models, ranging from cosmological hydrodynamical simulations (Illustris, IllustrisTNG, Mufasa, Simba, EAGLE), zoom simulations (FIRE-2, g14, and Marvel/Justice League), semi-analytic models (Santa Cruz SAM) and empirical models (UniverseMachine), and quantify the variability of these SFHs on different time-scales using the power spectral density (PSD) formalism. We find that the PSDs are well described by broken power laws, and variability on long time-scales (≳1 Gyr) accounts for most of the power in galaxy SFHs. Most hydrodynamical models show increased variability on shorter time-scales (≲300 Myr) with decreasing stellar mass. Quenching can induce ∼0.4−1 dex of additional power on time-scales &amp;gt;1 Gyr. The dark matter accretion histories of galaxies have remarkably self-similar PSDs and are coherent with the in situ star formation on time-scales &amp;gt;3 Gyr. There is considerable diversity among the different models in their (i) power due to star formation rate variability at a given time-scale, (ii) amount of correlation with adjacent time-scales (PSD slope), (iii) evolution of median PSDs with stellar mass, and (iv) presence and locations of breaks in the PSDs. The PSD framework is a useful space to study the SFHs of galaxies since model predictions vary widely. Observational constraints in this space will help constrain the relative strengths of the physical processes responsible for this variability.

Severe Magnetic Fluctuations in the Near‐Earth Magnetotail: Spectral Analysis and Dependence on Solar Activity

AbstractMagnetic fluctuations in the near‐Earth magnetotail are an important signature of substorm onset. In a previous statistical study, we reported their occurrence rates, spatial distributions, and relationship with plasma flows. In the present study, we investigated their spectral properties using 11 years of measurements from the Time History of Events and Macroscale Interactions during Substorms mission for 2008–2018. We found 10,848 severe magnetic fluctuation events with , where σB and are the standard deviation and average, respectively, of the magnetic field intensity for the local proton gyroperiod. The occurrence rates of severe magnetic fluctuations show no clear dependence on the F10.7 index in one solar cycle. We extracted 36 dipolarization events with severe magnetic fluctuations. In the power spectral density (PSD) of the magnetic fluctuations during dipolarizations, the steepness of the spectral slope increased with increasing frequency in almost all the events. The average PSDs are shown sorted by (a) distance to the neutral sheet and (b) ambient magnetic field intensity. In all groups, the slopes of the average PSDs increased abruptly from below ∼10−1.3 Hz (0.05 Hz) to above ∼10−1.3 Hz, which is close to the gyrofrequency of O+ ions. It is the first time that a change of slope near the proton gyrofrequency (frequency range: 0.05–1 Hz) was found in cases of larger ambient magnetic field intensity, implying that the magnetic fluctuations were relatively strong near the proton gyrofrequency. These results suggest that the magnetic fluctuations contribute to the nonmagnetohydrodynamic effect in the ion motion.

PKS 2155-304: A Case Study of Blazar Variability Power Spectrum at the Highest Energies and on the Longest Timescales

We present the results of our Power Spectral Density (PSD) analysis for the BL Lac object PKS 2155−304, utilizing the nightly-binned long-term light curve from the decade-long monitoring, as well as the minute-binned intra-night light curve from the High Energy Stereoscopic Survey (H.E.S.S.; &gt;200 GeV). The source is unique for exhibiting the shortest flux-doubling timescale at Very High Energy (VHE) among its class and thus provides a rare opportunity to study the particle acceleration on the smallest spatial scales in blazar jets. The light curves are modeled in terms of the Continuous-Time Auto-Regressive Moving Average (CARMA) process. The combined long-term and intra-night PSD extends up to ∼6 decades in the temporal frequency range; unprecedented at the TeV energies for a blazar source. Our systematic approach reveals that PKS 2155−304 shows, on average, a complex shape of variability power spectrum, with more variability power on longer timescales. The long-term variability is best modeled by the CARMA(2,1) process, while the intra-night variability is modeled by a CARMA(1,0) process. We note that the CARMA(1,0) process refers to an Ornstein–Uhlenbeck process where the power-law PSD slope (PSD varies as a function of variability frequency to the power of the negative slope) changes from two to zero, above a certain “characteristic/relaxation” timescale. Even though the derived power spectrum of the intra-night light curve did not reveal a flattening, we speculate such relaxation must occur on timescales longer than a few hours for the source.

Bi-fractal feature of bi-Gaussian stratified surfaces

Abstract Surface serves as the fingerprint of a component. Researchers have observed the bi-fractal feature of a surface roughness. The increasing number of researchers attempting to model the roughness from a bi-Gaussian stratified perspective provides the possibility of understanding the bi-fractal mechanism. Engineering (two-process and worn surfaces) and simulated surfaces are selected to establish a database of bi-Gaussian stratified surfaces. The bi-fractal feature of these bi-Gaussian stratified surfaces is analyzed, finding that the upper Gaussian component of a bi-Gaussian stratified feature reduces the power spectral density (PSD) and partially diverges the slope of the logarithmic PSD to render a bi-fractal behavior. The proportion of the components plays a greater role than the ratio of the component root-mean-square values.

Long-term optical monitoring of TeV emitting blazars

We present ten years of R-band monitoring data of 31 northern blazars which were either detected at very high-energy (VHE) gamma rays or listed as potential VHE gamma-ray emitters. The data comprise 11 820 photometric data points in the R-band obtained in 2002–2012. We analyzed the light curves by determining their power spectral density (PSD) slopes assuming a power-law dependence with a single slope β and a Gaussian probability density function (PDF). We used the multiple fragments variance function (MFVF) combined with a forward-casting approach and likelihood analysis to determine the slopes and perform extensive simulations to estimate the uncertainties of the derived slopes. We also looked for periodic variations via Fourier analysis and quantified the false alarm probability through a large number of simulations. Comparing the obtained PSD slopes to values in the literature, we find the slopes in the radio band to be steeper than those in the optical and gamma rays. Our periodicity search yielded one target, Mrk 421, with a significant (p &lt; 5%) period. Finding one significant period among 31 targets is consistent with the expected false alarm rate, but the period found in Mrk 421 is very strong and deserves further consideration.

Signature of inverse Compton emission from blazars

Blazars are classified into high, intermediate and low energy peaked sources based on the location of their synchrotron peak. This lies in infra-red/optical to ultra-violet bands for low and intermediate peaked blazars. The transition from synchrotron to inverse Compton emission falls in the X-ray bands for such sources. We present the spectral and timing analysis of 14 low and intermediate energy peaked blazars ob- served with XMMNewton spanning 31 epochs. Parametric fits to X-ray spectra helps constrain the possible location of transition from the high energy end of the syn- chrotron to the low energy end of the inverse Compton emission. In seven sources in our sample, we infer such a transition and constrain the break energy in the range 0.6 10 keV. The Lomb-Scargle periodogram is used to estimate the power spectral density (PSD) shape. It is well described by a power law in a majority of light curves, the index being flatter compared to general expectation from AGN, ranging here between 0.01 and 1.12, possibly due to short observation durations resulting in an absence of long term trends. A toy model involving synchrotron self-Compton (SSC) and exter- nal Compton (EC; disk, broad line region, torus) mechanisms are used to estimate magnetic field strength 6 0.03 - 0.88 G in sources displaying the energy break and infer a prominent EC contribution. The timescale for variability being shorter than synchrotron cooling implies steeper PSD slopes which are inferred in these sources.

How Far Is Quasar UV/Optical Variability from a Damped Random Walk at Low Frequency?

Abstract Studies have shown that UV/optical light curves of quasars can be described using the prevalent damped random walk (DRW) model, also known as the Ornstein–Uhlenbeck process. A white noise power spectral density (PSD) is expected at low frequency in this model; however, a direct observational constraint to the low-frequency PSD slope is difficult due to the limited lengths of the light curves available. Meanwhile, quasars show scatter in their DRW parameters that is too large to be attributed to uncertainties in the measurements and dependence on the variation of known physical factors. In this work we present simulations showing that, if the low-frequency PSD deviates from the DRW, the red noise leakage can naturally produce large scatter in the variation parameters measured from simulated light curves. The steeper the low-frequency PSD slope, the larger scatter we expect. Based on observations of SDSS Stripe 82 quasars, we find that the low-frequency PSD slope should be no steeper than −1.3. The actual slope could be flatter, which consequently requires that the quasar variabilities should be influenced by other unknown factors. We speculate that the magnetic field and/or metallicity could be such additional factors.

Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect

AbstractEarth surface evolution, like many natural phenomena typified by fluctuations on a wide range of scales and deterministic smoothing, results in a statistically rough surface. We present theory demonstrating that scaling exponents of topographic and stratigraphic statistics arise from long‐time averaging of noisy surface evolution rather than specific landscape evolution processes. This is demonstrated through use of “elastic” Langevin equations that generically describe disturbance from a flat earth surface using a noise term that is smoothed deterministically via sediment transport. When smoothing due to transport is a local process, the geologic record self organizes such that a specific Sadler effect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presence or absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadler slopes captures the same smoothing feature combined with the presence of long‐range spatial correlation in topographic disturbance.

Multiwavelength Variability Study of the Classical BL Lac Object PKS 0735+178 on Timescales Ranging from Decades to Minutes

Abstract We present the results of our power spectral analysis for the BL Lac object PKS 0735+178, utilizing the Fermi-LAT survey at high-energy γ-rays, several ground-based optical telescopes, and single-dish radio telescopes operating at GHz frequencies. The novelty of our approach is that, by combining long-term and densely sampled intra-night light curves in the optical regime, we were able to construct for the first time the optical power spectrum of the blazar for a time domain extending from 23 years down to minutes. Our analysis reveals that: (1) the optical variability is consistent with a pure red noise, for which the power spectral density can be well approximated by a single power law throughout the entire time domain probed; (2) the slope of power spectral density at high-energy γ-rays (∼1) is significantly flatter than that found at radio and optical frequencies (∼2) within the corresponding time variability range; (3) for the derived power spectra, we did not detect any low-frequency flattening, nor do we see any evidence for cutoffs at the highest frequencies down to the noise floor levels due to measurement uncertainties. We interpret our findings in terms of a model where the blazar variability is generated by the underlying single stochastic process (at radio and optical frequencies), or a linear superposition of such processes (in the γ-ray regime). Along with the detailed PSD analysis, we also present the results of our extended (1998–2015) intra-night optical monitoring program and newly acquired optical photo-polarimetric data for the source.

Radio-to-γ-Ray, Broadband Variability Study of the Classical BL Lac Object PKS 0735+178

The power-law shape of the power spectral density (PSD) of blazar light curves— P ( ν k ) ∝ ν k − β , where ν k is the temporal frequency—indicates that blazar variability is, in general, of the colored-type noise ( β ≃ 1 − 3 ). A precise characterisation of PSD slopes, normalizations, or characteristic timescales (if any) manifesting as distinct features in the power spectra of blazars is important for constraining the physics of the emission and energy dissipation processes in relativistic jets. Here we present the results of the PSD analysis for the BL Lac object PKS 0735+178 at GeV (Fermi-LAT), optical (R-band), and radio (GHz band from UMRAO and OVRO programmes) frequencies, covering a broad range in variability timescales. The novelty of our approach is that in the optical regime, by combining the long-term and densely sampled R-band intra-night light curves, we constructed the PSD for time periods ranging from 23 years down to minutes. Our analysis reveals that: (1) the nature of processes generating flux variability at optical and radio frequencies is different from those operating at GeV photon energies ( β ∼ 2 and 1, respectively); (2) the main driver behind the optical variability is the same on timescales of years, months, days, and hours (a single power-law with β ∼ 2). We discuss our findings in the framework of a model where the overall blazar variability is generated by an underlying single stochastic process (radio and optical frequencies), or a linear superposition of such processes (γ-ray regime).