Slope Of Power Spectrum Research Articles

A Systematic Analysis of Star Cluster Disruption by Tidal Shocks. II. Predicting Star Cluster Dissolution Rates from a Time-series Analysis of Their Tidal Histories

Most of the dynamical mass loss from star clusters is thought to be caused by the time variability of the tidal field (“tidal shocks”). Systematic studies of tidal shocks have been hampered by the fact that each tidal history is unique, implying both a reproducibility and a generalization problem. Here we address these issues by investigating how star cluster evolution depends on the statistical properties of its tidal history. We run a large suite of direct N-body simulations of clusters with tidal histories generated from power spectra of a given slope and with different normalizations, which determine the timescales and amplitudes of the shocks, respectively. At fixed normalization (i.e., the same median tidal field strength), the dissolution timescale is nearly independent of the power spectrum slope. However, the dispersion in dissolution timescales, obtained by repeating simulations for different realizations of statistically identical tidal histories, increases with the power spectrum slope. This result means that clusters experiencing high-frequency shocks have more similar mass-loss histories than clusters experiencing low-frequency shocks. The density–mass relationship of the simulated clusters follows a power law with slope between 1.08 and 1.45, except for the lowest normalizations (for which clusters effectively evolve in a static tidal field). Our findings suggest that star cluster evolution can be described statistically from a time-series analysis of its tidal history, which is an important simplification for describing the evolution of the star cluster population during galaxy formation and evolution.

Differentiating neurodegenerative diseases based on EEG complexity

Neurodegenerative diseases are common causes of impaired mobility and cognition in the elderly. Among them, tauopathies and α-synucleinopathies were considered. The neurodegenerative processes and relative differential diagnosis were addressed through a qEEG non-linear analytic method. Study aims were to test accuracy of the power law exponent β applied to EEG in differentiating neurodegenerative diseases and to explore differences in neuronal connectivity among different neurodegenerative processes based on β. N = 230 patients with a diagnosis of tauopathy or α-synucleinopathy and at least one artifact-free EEG recording were selected. Periodogram was applied to EEG signal epochs from continuous recordings. Power law exponent β was determined by the slope of the signal power spectrum versus frequency in logarithmic scale. A data-driven clustering based on β values was performed to identify independent subgroups. Data-driven clustering based on β differentiated tauopathies (overall lower β values) from α-synucleinopathies (higher β values) with high sensitivity and specificity. Tauopathies also presented lower values in the correlation coefficients matrix among frontal sites of recording. In conclusion, significant differences in β values were found between tauopathies and α-synucleinopathies. Hence, β is proposed as a possible biomarker of differential diagnosis and neuronal connectivity.

X-ray flux and spectral variability of the blazar OJ 287 with Suzaku

ABSTRACT We present analyses of Suzaku XIS light curves and spectra of the BL Lac object OJ 287 with observations positioned primarily around proposed recurrent optical outbursts. The first two observations were performed in 2007 April 10–13 (epoch 1) and 2007 November 7–9 (epoch 2) that, respectively, correspond to a low and a high optical state and which, within the binary supermassive black hole model for OJ 287, precede and follow the impact flare. The last three observations, made consecutively during 2015 May 3–9 (epoch 3), were during the post-impact state of the 2013 disc impact and are the longest continuous X-ray observation of OJ 287 taken before the optical outburst in 2015 December. Intraday variability is found in both the soft (0.5–2 keV) and hard (2–10 keV) bands. The discrete correction function analysis of the light curves in both bands peaks at zero lag during epochs 2 and 3, indicating that the emission in both bands was cospatial and emitted from the same population of leptons. Power spectral densities of all three light curves are red noise dominated, with a rather wide range of power spectrum slopes. These X-ray spectra are overall consistent with power laws but with significantly different spectral indices. In the 2015 observations the X-ray spectrum softens during the flare, showing an obvious soft X-ray excess that was not evident in the 2007 observations. We discuss the implications of these observations on the jet, the possible accretion disc, and the binary supermassive black hole model proposed for the nearly periodic optical flaring of OJ 287.

Toward mapping turbulence in the intra-cluster medium

Context. Future X-ray observatories with high spectral resolution and imaging capabilities will enable measurements and mappings of emission line shifts in the intracluster medium (ICM). Such direct measurements can serve as unique probes of turbulent motions in the ICM. Determining the level and scales of turbulence will improve our understanding of the galaxy cluster dynamical evolution and assembly, together with a more precise evaluation of the non thermal support pressure budget. This will allow for more accurate constraints to be placed on the masses of galaxy clusters, among other potential benefits. Aims. In this view, we implemented the methods presented in the previous instalments of our work to characterising the turbulence in the intra-cluster medium in a feasibility study with the X-ray Integral Field Unit (X-IFU) on board the future European X-ray observatory, Athena. Methods. From idealized mock observations of a toy model cluster, we reconstructed the second-order structure function built with the observed velocity field to constrain the turbulence. We carefully accounted for the various sources of errors to derive the most realistic and comprehensive error budget within the limits of our approach. With prior assumptions on the dissipation scale and power spectrum slope, we constrained the parameters of the turbulent power spectrum model through the use of Markov chain Monte Carlo (MCMC) sampling. Results. With a very long exposure time, a favourable configuration, and a prior assumption of the dissipation scale, we were able to retrieve the injection scale, velocity dispersion, and power spectrum slope, with 1σ uncertainties for better than ∼15% of the input values. We demonstrated the efficiency of our carefully set framework to constrain the turbulence in the ICM from high-resolution X-ray spectroscopic observations, paving the way for more in-depth investigation of the optimal required observing strategy within a more restrictive observational setup with the future Athena/X-IFU instrument.

Low tube voltage and deep-learning reconstruction for reducing radiation and contrast medium doses in thin-slice abdominal CT: a prospective clinical trial.

To investigate the feasibility of low-radiation dose and low iodinated contrast medium (ICM) dose protocol combining low-tube voltage and deep-learning reconstruction (DLR) algorithm in thin-slice abdominal CT. This prospective study included 148 patients who underwent contrast-enhanced abdominal CT with either 120-kVp (600 mgL/kg, n = 74) or 80-kVp protocol (360 mgL/kg, n = 74). The 120-kVp images were reconstructed using hybrid iterative reconstruction (HIR) (120-kVp-HIR), while 80-kVp images were reconstructed using HIR (80-kVp-HIR) and DLR (80-kVp-DLR) with 0.5 mm thickness. Size-specific dose estimate (SSDE) and iodine dose were compared between protocols. Image noise, CT attenuation, and contrast-to-noise ratio (CNR) were quantified. Noise power spectrum (NPS) and edge rise slope (ERS) were used to evaluate noise texture and edge sharpness, respectively. The subjective image quality was rated on a 4-point scale. SSDE and iodine doses of 80-kVp were 40.4% (8.1 ± 0.9 vs. 13.6 ± 2.7 mGy) and 36.3% (21.2 ± 3.9 vs. 33.3 ± 4.3 gL) lower, respectively, than those of 120-kVp (both, p < 0.001). CT attenuation of vessels and solid organs was higher in 80-kVp than in 120-kVp images (all, p < 0.001). Image noise of 80-kVp-HIR and 80-kVp-DLR was higher and lower, respectively than that of 120-kVp-HIR (both p < 0.001). The highest CNR and subjective scores were attained in 80-kVp-DLR (all, p < 0.001). There were no significant differences in average NPS frequency and ERS between 120-kVp-HIR and 80-kVp-DLR (p ≥ 0.38). Compared with the 120-kVp-HIR protocol, the combined use of 80-kVp and DLR techniques yielded superior subjective and objective image quality with reduced radiation and ICM doses at thin-section abdominal CT. Scanning at low-tube voltage (80-kVp) combined with the deep-learning reconstruction algorithm may enhance diagnostic efficiency and patient safety by improving image quality and reducing radiation and contrast doses of thin-slice abdominal CT. Reducing radiation and iodine doses is desirable; however, contrast and noise degradation can be detrimental. The 80-kVp scan with the deep-learning reconstruction technique provided better images with lower radiation and contrast doses. This technique may be efficient for improving diagnostic confidence and patient safety in thin-slice abdominal CT.

Early Structure Formation from Primordial Density Fluctuations with a Blue, Tilted Power Spectrum: High-redshift Galaxies

Recent observations by the James Webb Space Telescope (JWST) discovered unexpectedly abundant luminous galaxies at high redshift, posing possibly a severe challenge to popular galaxy formation models. We study early structure formation in a cosmological model with a blue, tilted power spectrum (BTPS) given by P(k)∝kms with m s > 1 at small length scales. We run a set of cosmological N-body simulations and derive the abundance of dark matter halos and galaxies under simplified assumptions on star formation efficiency. The enhanced small-scale power allows rapid nonlinear structure formation at z > 7, and galaxies with stellar mass exceeding 1010 M ⊙ can be formed by z = 9. Because of frequent mergers, the structure of galaxies and galaxy groups appears clumpy. The BTPS model reproduces the observed stellar mass density at z = 7–9, and thus eases the claimed tension between galaxy formation theory and recent JWST observations. The large-scale structure of the present-day Universe is largely unaffected by the modification of the small-scale power spectrum. We conduct a systematic study by varying the slope of the small-scale power spectrum to derive constraints on the BTPS model from a set of observations of high-redshift galaxies.

A voxel-level resting-state fMRI study on patients with alcohol use disorders based on a power spectrum slope analysis method.

Earlier neuroimaging investigations showed that abnormal brain activity in patients with alcohol use disorder (AUD) was frequency dependent. However, there is lacking of a comprehensive method to capture the amplitude of multi-frequency bands directly. Here, we used a new method, the power spectrum slope (PSS) to explore abnormal spontaneous activity of brain in patients with AUD. Thirty-three AUD patients and 29 healthy controls (HCs) enrolled in this study. The coefficient b and the power-law slope b' were calculated and compared between two groups. We also used the receiver operating characteristic (ROC) curve to examine the ability of the PSS analysis to distinguish between AUD and HCs. We next examined the correlation between PSS difference in the brain areas and the severity of alcohol dependence. Thirty AUD patients and 26 HCs were retained after head motion correction. The two metrics of PSS values increased in the left precentral gyrus in AUD patients. The area under the curve values of PSS differences in the specific brain area were respectively 0.836 and 0.844, with sensitivities of 86.7% and 83.3% and specificities of 73.1% and 76.9%. The Michigan Alcoholism Screening Test (MAST) and Alcohol drinking scale (ADS) scores were not significantly correlated with the PSS values in the specific brain area. As a novel method, the PSS can well detect abnormal local brain activity in the AUD patients and may offer new insights for future fMRI studies.

Developing Topics.

Alzheimer's disease is characterized by cortical hyperexcitability in the early stages, which may be attributed to the intricate interplay between tau and amyloid β pathologies. To combat the propagation of tau pathology and cognitive decline, it may be beneficial to maintain a high degree of functional brain network segregation. Additionally, the use of non-invasive brain stimulation techniques to alter cortical excitability could help alleviate cognitive deficits. However, it is unclear how these interventions are related to tau or amyloid biomarkers. In this study, 530 participants aged 40 to 65 from the Barcelona Brain Health Initiative cohort were analyzed to investigate the connection between plasma concentration of tau phosphorylated at amino acid 181 (pTau181), cortical excitability, and segregation of functional brain networks. Participants had functional magnetic resonance imaging (fMRI), electroencephalography (EEG), and pTau181 available. A subset of 47 participants also underwent transcranial magnetic stimulation with concurrent EEG (TMS-EEG). Cortical excitability was assessed using the one-over-f slope of the EEG power spectrum (1/f-slope) and evoked response to a TMS perturbation (TEP) of the left prefrontal cortex (L-PFC) between 160-240ms post single-pulse TMS. The degree of segregation between major functional networks was measured from fMRI data using the system segregation statistic. A generalized linear model with a gamma distribution (Table 1) revealed that steeper 1/f-slope correlated with higher pTau181 concentration, particularly in participants older than 53 years of age (Figure 1.A), or system segregation below 0.28 (Figure 1.B). A multiple linear regression within the TMS-EEG subsample (Table 2) revealed that the TEP response correlated positively with pTau181 as age increased, and that this model, despite including a smaller sample size, better explained pTau181 concentrations. The study shows that cortical excitability is related to pTau181 based on age and system segregation. The TEP response is a more sensitive marker than unperturbed EEG metrics in explaining the relation between excitability and pTau181 concentrations. Combined TMS with EEG could potentially be an inexpensive and scalable approach for early identification and longitudinal tracking of middle-aged adults at risk for cognitive decline and dementia.

The WISDOM of power spectra: how the galactic gravitational potential impacts a galaxy’s central gas reservoir in simulations and observations

ABSTRACT Observations indicate that the central gas discs are smoother in early-type galaxies than their late-type counterparts, while recent simulations predict that the dynamical suppression of star formation in spheroid-dominated galaxies is preceded by the suppression of fragmentation of their interstellar media. The mass surface density power spectrum is a powerful tool to constrain the degree of structure within a gas reservoir. Specifically here, we focus on the power spectrum slope and aim to constrain whether the shear induced by a dominant spheroidal potential can induce sufficient turbulence to suppress fragmentation, resulting in the smooth central gas discs observed. We compute surface density power spectra for the nuclear gas reservoirs of fourteen simulated isolated galaxies and twelve galaxies observed as part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project. Both simulated and observed galaxies range from disc-dominated galaxies to spheroids, with central stellar mass surface densities, a measure of bulge dominance, varying by more than an order of magnitude. For the simulations, the power spectra steepen with increasing central stellar mass surface density, thereby clearly linking the suppression of fragmentation to the shear-driven turbulence induced by the spheroid. The WISDOM observations show a different (but potentially consistent) picture: while there is no correlation between the power spectrum slopes and the central stellar mass surface densities, the slopes scatter around a value of 2.6. This is similar to the behaviour of the slopes of the simulated galaxies with high central stellar mass surface densities, and could indicate that high shear eventually drives incompressible turbulence.

The spectral slope as a marker of excitation/inhibition ratio and cognitive functioning in multiple sclerosis.

Multiple sclerosis (MS) is a neurodegenerative disease characterized by neuronal and synaptic loss, resulting in an imbalance of excitatory and inhibitory synaptic transmission and potentially cognitive impairment. Current methods for measuring the excitation/inhibition (E/I) ratio are mostly invasive, but recent research combining neurocomputational modeling with measurements of local field potentials has indicated that the slope with which the power spectrum of neuronal activity captured by electro- and/or magnetoencephalography rolls off, is a non-invasive biomarker of the E/I ratio. A steeper roll-off is associated with a stronger inhibition. This novel method can be applied to assess the E/I ratio in people with multiple sclerosis (pwMS), detect the effect of medication such as benzodiazepines, and explore its utility as a biomarker for cognition. We recruited 44 healthy control subjects and 95 pwMS who underwent resting-state magnetoencephalographic recordings. The 1/f spectral slope of the neural power spectra was calculated for each subject and for each brain region. As expected, the spectral slope was significantly steeper in pwMS treated with benzodiazepines (BZDs) compared to pwMS not receiving BZDs (p = .01). In the sub-cohort of pwMS not treated with BZDs, we observed a steeper slope in cognitively impaired pwMS compared to cognitively preserved pwMS (p = .01) and healthy subjects (p = .02). Furthermore, we observed a significant correlation between 1/f spectral slope and verbal and spatial working memory functioning in the brain regions located in the prefrontal and parietal cortex. In this study, we highlighted the value of the spectral slope in MS by quantifying the effect of benzodiazepines and by putting it forward as a potential biomarker of cognitive deficits in pwMS.

Magnetic field draping around clumpy high-velocity clouds in galactic halo

ABSTRACT Throughout the passage within the Galactic halo, high-velocity clouds (HVCs) sweep up ambient magnetic fields and form stretched and draped configurations of magnetic fields around them. Many earlier numerical studies adopt spherically symmetric uniform-density clouds as initial conditions for simplicity. However, observations demonstrate that HVCs are clumpy and turbulent. In this paper, we perform 3D magnetohydrodynamic simulations to study the evolution of clouds with initial density distributions described by power-law spatial power spectra. We systematically study the role of (i) the initial density structure, (ii) halo magnetic fields, and (iii) radiative cooling efficiency upon infalling HVCs. We find that (i) the clouds’ density structure regulates mixing and mass growth. Uniform clouds grow from the onset of the simulations, while clumpy clouds initially lose gas and then grow at later times. Along the same lines, the growth curve of clumpy clouds depends on the slope of the initial density power spectra. (ii) Magnetic fields suppress hydrodynamic instabilities and the growth of small-scale structures. As a result, magnetized clouds develop long filaments extended along the streaming direction, whereas non-magnetized clouds are fragmented into many small clumps. (iii) Efficient cooling keeps the main cloud body more compact and produces decelerated dense clumps condensed from the halo gas. This work potentially helps us understand and predict the observed properties of HVCs such as the detectability of magnetized clouds, the presence of decelerated HI structures associated with HVC complexes and small-scale features, and a possible link between the origin and the fate of HVCs.

A deep dive: Chandra observations of the NGC 4839 group falling into the Coma cluster

ABSTRACT Cosmological simulations of structure formation predict that galaxy clusters continue to grow and evolve through ongoing mergers with group-scale systems. During these merging events, the ram pressure applied by the intracluster medium acts to strip the gas from the infalling groups, forming large tails of stripped gas, which eventually become part of the main cluster. In this work, we present a detailed analysis of our new deep Chandra observations of the NGC 4839 group falling into the nearby Coma cluster, providing a unique opportunity to explore the way galaxy clusters in the local Universe continue to grow. Our analysis reveals a cold front feature at the leading head of the group, preceded by a bow shock of hot gas in front with a Mach number of ∼1.5. The power spectrum of surface brightness fluctuations in the tail shows that the slope gets less steep as the distance from the leading head increases, changing from $-2.35_{-0.06}^{+0.07}$ at the inner part of the tail to $-1.37_{-0.07}^{+0.09}$ at the outermost part of the tail. These values are shallower than the slope of the Kolmogorov 2D power spectrum, indicating that thermal conduction is being suppressed throughout the tail, enabling long-lived small-scale turbulence, which would typically be washed out if thermal conduction was not inhibited. The characteristic amplitude of surface brightness fluctuations in the tail suggests a mild level of turbulence with a Mach number in the range of 0.1–0.5, agreeing with that found for the infalling group in Abell 2142.

A neural network emulator for the Lyman-α forest 1D flux power spectrum

ABSTRACT The Lyman-α forest offers a unique avenue for studying the distribution of matter in the high redshift universe and extracting precise constraints on the nature of dark matter, neutrino masses, and other ΛCDM extensions. However, interpreting this observable requires accurate modelling of the thermal and ionization state of the intergalactic medium, and therefore resorting to computationally expensive hydrodynamical simulations. In this work, we build a neural network that serves as a surrogate model for rapid predictions of the one-dimensional Lyman-α flux power spectrum (P1D), thereby making Bayesian inference feasible for this observable. Our emulation technique is based on modelling P1D as a function of the slope and amplitude of the linear matter power spectrum rather than as a function of cosmological parameters. We show that our emulator achieves sub-percent precision across the full range of scales (k∥ = 0.1 – $4\, \mathrm{Mpc}^{-1}$) and redshifts (z = 2 – 4.5) considered, and also for three ΛCDM extensions not included in the training set: massive neutrinos, running of the spectral index, and curvature. Furthermore, we show that it performs at the 1 per cent level for ionization and thermal histories not present in the training set and performs at the percent level when emulating down to $k_{\parallel }=8\, \mathrm{Mpc}^{-1}$. These results affirm the efficacy of our emulation strategy in providing accurate predictions even for cosmologies and reionization histories that were not explicitly incorporated during the training phase, and we expect it to play a critical role in the cosmological analysis of the DESI survey.

Rotation measure structure functions with higher-order stencils as a probe of small-scale magnetic fluctuations and its application to the Small and Large Magellanic Clouds

ABSTRACTMagnetic fields and turbulence are important components of the interstellar medium (ISM) of star-forming galaxies. It is challenging to measure the properties of the small-scale ISM magnetic fields (magnetic fields at scales smaller than the turbulence driving scale). Using numerical simulations, we demonstrate how the second-order rotation measure (RM, which depends on thermal electron density, ne, and magnetic field, b) structure function can probe the properties of small-scale b. We then apply our results to observations of the Small and Large Magellanic Clouds (SMC and LMC). First, using Gaussian random b, we show that the characteristic scale, where the RM structure function flattens is approximately equal to the correlation length of b. We also show that computing the RM structure function with a higher-order stencil (more than the commonly-used two-point stencil) is necessary to accurately estimate the slope of the structure function. Then, using Gaussian random b and lognormal ne with known power spectra, we derive an empirical relationship between the slope of the power spectrum of b, ne, and RM. We apply these results to the SMC and LMC and estimate the following properties of small-scale b: correlation length (160 ± 21 pc for the SMC and 87 ± 17 pc for the LMC), strength (14 ± 2 $\mu {\rm G}$ for the SMC and 15 ± 3 $\mu {\rm G}$ for the LMC), and slope of the magnetic power spectrum (−1.3 ± 0.4 for the SMC and −1.6 ± 0.1 for the LMC). We also find that ne is practically constant over the estimated b correlation scales.

The Cygnus Allscale Survey of Chemistry and Dynamical Environments: CASCADE

Context. While star formation on large molecular cloud scales and on small core and disk scales has been investigated intensely over the past decades, the connection of the large-scale interstellar material with the densest small-scale cores has been a largely neglected field. Aims. We wish to understand how the gas is fed from clouds down to cores. This covers dynamical accretion flows as well as the physical and chemical gas properties over a broad range of spatial scales. Methods. Using the IRAM facilities NOEMA and the IRAM 30 m telescope, we mapped large areas (640 arcmin2) of the archetypical star formation complex Cygnus X at 3.6 mm wavelengths in line and continuum emission. The data were combined and imaged together to cover all accessible spatial scales. Results. The scope and outline of The Cygnus Allscale Survey of Chemistry and Dynamical Environments (CASCADE) as part of the Max Planck IRAM Observatory Program (MIOP) is presented. We then focus on the first observed subregion in Cygnus X, namely the DR20 star formation site, which comprises sources in a range of evolutionary stages from cold pristine gas clumps to more evolved ultracompact Hii regions. The data covering cloud to cores scales at a linear spatial resolution of &lt;5000 au reveal several kinematic cloud components that may be part of several large-scale flows around the central cores. The temperature structure of the region is investigated by means of the HCN/HNC intensity ratio and compared to dust-derived temperatures. We find that the deuterated DCO+ emission is almost exclusively located toward regions at low temperatures below 20 K. Investigating the slopes of spatial power spectra of dense gas tracer intensity distributions (HCO+, H13CO+, and N2H+), we find comparatively flat slopes between −2.9 and −2.6, consistent with high Mach numbers and/or active star formation in DR20. Conclusions. This MIOP large program on star formation in Cygnus X provides unique new data connecting cloud with core scales. The analysis of the DR20 data presented here highlights the potential of this program to investigate in detail the different physical and chemical aspects and their interrelations from the scale of the natal molecular cloud down to the scale of accretion onto the individual protostellar cores.

Model-based investigation of elasticity and spectral exponent from atomic force microscopy and electrophysiology in normal versus Schizophrenia human cerebral organoids.

The physiological origin of the aperiodic signal present in the electrophysiological recordings, called l/f neural noise, is unknown; nevertheless, it has been associated with health and disease. The power spectrum slope, -α in 1/fα, has been postulated to be related to the dynamic balance between excitation (E) and inhibition (I). Our study found that human cerebral organoids grown from induced pluripotent stem cells (iPSCs) from Schizophrenia patients (SCZ) showed structural changes associated with altered elasticity compared to that of the normal cerebral organoids. Furthermore, mitochondrial drugs modulated the elasticity in SCZ that was found related to the changes in the spectral exponent. Therefore, we developed an electro-mechanical model that related the microtubular-actin tensegrity structure to the elasticity and the 1/fα noise. Model-based analysis showed that a decrease in the number and length of the constitutive elements in the tensegrity structure decreased its elasticity and made the spectral exponent more negative while thermal white noise will make α = 0.. Based on the microtubularactin model and the cross-talk in structural (elasticity) and functional (electrophysiology) response, aberrant mitochondrial dynamics in SCZ are postulated to be related to the deficits in mitochondrial-cytoskeletal interactions for long-range transport of mitochondria to support synaptic activity for E/I balance. Clinical Relevance-Our experimental data and modeling present a structure-function relationship between mechanical elasticity and electrophysiology of human cerebral organoids that differentiated SCZ patients from normal controls.

Reliability and Validity of Power Spectrum Slope (PSS): A Metric for Measuring Resting-State Functional Magnetic Resonance Imaging Activity of Single Voxels.

Methods that capture the features of single voxels of resting-state fMRI (RS-fMRI) could precisely localize the abnormal spontaneous activity and hence guide precise brain stimulation. As one of these metrics, the amplitude of low-frequency fluctuation (ALFF) has been used in numerous studies, however, it is frequency-dependent and the division of frequency bands is still controversial. Based on the well-accepted power law of time series, this study proposed an approach, namely, power spectrum slope (PSS), to characterize the RS-fMRI time series of single voxels. Two metrics, i.e., linear coefficient b and power-law slope b’ were used and compared with ALFF. The reliability and validity of the PSS approach were evaluated on public RS-fMRI datasets (n = 145 in total) of eyes closed (EC) and eyes open (EO) conditions after image preprocessing, with 21 subjects scanned two times for test–retest reliability analyses. Specifically, we used the paired t-test between EC and EO conditions to assess the validity and intra-class correlation (ICC) to assess the reliability. The results included the following: (1) PSS detected similar spatial patterns of validity (i.e., EC–EO differences) and less test–retest reliability with those of ALFF; (2) PSS linear coefficient b showed better validity and reliability than power-law slope b’; (3) While the PPS showed less validity in most regions, PSS linear coefficient b showed exclusive EC–EO difference in the medial temporal lobe which did not show in ALFF. The power spectrum plot in the parahippocampus showed a “cross-over” of power magnitudes between EC and EO conditions in the higher frequency bands (>0.1 Hz). These results demonstrated that PSS (linear coefficient b) is complementary to ALFF for detecting the local spontaneous activity.

A dynamics-based density profile for dark haloes – I. Algorithm and basic results

ABSTRACT The density profiles of dark matter haloes can potentially probe dynamics, fundamental physics, and cosmology, but some of the most promising signals reside near or beyond the virial radius. While these scales have recently become observable, the profiles at large radii are still poorly understood theoretically, chiefly because the distribution of orbiting matter (the one-halo term) is partially concealed by particles falling into haloes for the first time. We present an algorithm to dynamically disentangle the orbiting and infalling contributions by counting the pericentric passages of billions of simulation particles. We analyse dynamically split profiles out to 10 R200m across a wide range of halo mass, redshift, and cosmology. We show that the orbiting term experiences a sharp truncation at the edge of the orbit distribution. Its sharpness and position are mostly determined by the mass accretion rate, confirming that the entire profile shape primarily depends on halo dynamics and secondarily on mass, redshift, and cosmology. The infalling term also depends on the accretion rate for fast-accreting haloes but is mostly set by the environment for slowly accreting haloes, leading to a diverse array of shapes that does not conform to simple theoretical models. While the resulting scatter in the infalling term reaches 1 dex, the scatter in the orbiting term is only between 0.1 and 0.4 dex and almost independent of radius. We demonstrate a tight correspondence between the redshift evolution in Λ cold dark matter (ΛCDM) and the slope of the matter power spectrum. Our code and data are publicly available.

Electroencephalogram aperiodic power spectral slope can be reliably measured and predicts ADHD risk in early development.

The aperiodic exponent of the electroencephalogram (EEG) power spectrum has received growing attention as a physiological marker of neurodevelopmental psychopathology, including attention-deficit/hyperactivity disorder (ADHD). However, its use as a marker of ADHD risk across development, and particularly in very young children, is limited by unknown reliability, difficulty in aligning canonical band-based measures across development periods, and unclear effects of treatment in later development. Here, we investigate the internal consistency of the aperiodic EEG power spectrum slope and its association with ADHD risk in both infants (n=69, 1-month-old) and adolescents (n=262, ages 11-17 years). Results confirm good to excellent internal consistency in infancy and adolescence. In infancy, a larger aperiodic exponent was associated with greater family history of ADHD. In contrast, in adolescence, ADHD diagnosis was associated with a smaller aperiodic exponent, but only in children with ADHD who had not received stimulant medication treatment. Results suggest that disruptions in cortical development associated with ADHD risk may be detectable shortly after birth via this approach. Together, findings imply a dynamic developmental shift in which the developmentally normative flattening of the EEG power spectrum is exaggerated in ADHD, potentially reflecting imbalances in cortical excitation and inhibition that could contribute to long-lasting differences in brain connectivity.

Power spectrum slope confounds estimation of instantaneous oscillatory frequency

Oscillatory neural dynamics are highly non-stationary and require methods capable of quantifying time-resolved changes in oscillatory activity in order to understand neural function. Recently, a method termed ‘frequency sliding’ was introduced to estimate the instantaneous frequency of oscillatory activity, providing a means of tracking temporal changes in the dominant frequency within a sub-band of field potential recordings. Here, the ability of frequency sliding to recover ground-truth oscillatory frequency in simulated data is tested while the exponent (slope) of the 1/fx component of the signal power spectrum is systematically varied, mimicking real electrophysiological data. The results show that 1) in the presence of 1/f activity, frequency sliding systematically underestimates the true frequency of the signal, 2) the magnitude of underestimation is correlated with the steepness of the slope, suggesting that, if unaccounted for, slope changes could be misinterpreted as frequency changes, 3) the impact of slope on frequency estimates interacts with oscillation amplitude, indicating that changes in oscillation amplitude alone may also influence instantaneous frequency estimates in the presence of strong 1/f activity; and 4) analysis parameters such as filter bandwidth and location also mediate the influence of slope on estimated frequency, indicating that these settings should be considered when interpreting estimates obtained via frequency sliding. The origin of these biases resides in the output of the filtering step of frequency sliding, whose energy is biased towards lower frequencies precisely because of the 1/f structure of the data. We discuss several strategies to mitigate these biases and provide a proof-of-principle for a 1/f normalization strategy.