Spectral Measure Research Articles

On the chain structure in the de Branges spaces

We study indivisible intervals and the monotonicity of the growth of the exponential type in the chains of de Branges subspaces in terms of the spectral measure. We prove that for spectral measures supported on Z, there exist at most two subspaces of the same type, which then bound an indivisible interval. Furthermore, in this case, we study possible locations of the indivisible intervals.

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing orthostatic syncope in response to prolonged postural stress, and in healthy controls. The spectral measures of total, causal and instantaneous coupling between HP and SAP, and between MAP and CBFV, are averaged in the low-frequency band of the spectrum to focus on specific rhythms, and over all frequencies to get time-domain measures. The analysis of cardiovascular interactions indicates that postural stress induces baroreflex involvement, and its prolongation induces baroreflex dysregulation in syncope subjects. The analysis of cerebrovascular interactions indicates that the postural stress enhances the total coupling between MAP and CBFV, and challenges cerebral autoregulation in syncope subjects, while the strong sympathetic activation elicited by prolonged postural stress in healthy controls may determine an increased coupling from CBFV to MAP during late tilt. These results document that the combination of time-domain and spectral measures allows us to obtain an integrated view of cardiovascular and cerebrovascular regulation in healthy and diseased subjects.

URLLC Shadowing Estimation in eMBB-uRLLC Multiplexing for Geospatially Correlated PPP Channel

This letter investigates eMBB-uRLLC multiplexing in which the eMBB users’ channel feedback is exploited for the uRLLC channel condition estimation. This approach allows instant and reliable transmission without acquiring the user’s CSI, which is especially advantageous in intermittent uRLLC traffic transmissions. This letter introduces two channel estimators for a geospatially-correlated channel and derives their estimation errors. Then, we propose an eMBB-uRLLC multiplexing algorithm based on the estimates and provide transmission reliability and spectral efficiency measures under adaptive modulation and coding. Simulation results confirm the effectiveness of the proposed approach in different propagation environments.

Female adolescent singing voice characteristics: an exploratory study using LTAS and inverse filtering

Background and Aim: To date, little research is available that objectively quantifies female adolescent singing-voice characteristics in light of the physiological and functional developments that occur from puberty to adulthood. This exploratory study sought to augment the pool of data available that offers objective voice analysis of female singers in late adolescence. Methods: Using long-term average spectra (LTAS) and inverse filtering techniques, dynamic range and voice-source characteristics were determined in a cohort of vocally healthy cis-gender female adolescent singers (17 to 19 years) from high-school choirs in Aotearoa New Zealand. Non-parametric statistics were used to determine associations and significant differences. Results: Wide intersubject variation was seen between dynamic range, spectral measures of harmonic organisation (formant cluster prominence, FCP), noise components in the spectrum (high-frequency energy ratio, HFER), and the normalised amplitude quotient (NAQ) suggesting great variability in ability to control phonatory mechanisms such as subglottal pressure (Psub), glottal configuration and adduction, and vocal tract shaping. A strong association between the HFER and NAQ suggest that these non-invasive measures may offer complimentary insights into vocal function, specifically with regard to glottal adduction and turbulent noise in the voice signal. Conclusion: Knowledge of the range of variation within healthy adolescent singers is necessary for the development of effective and inclusive pedagogical practices, and for vocal-health professionals working with singers of this age. LTAS and inverse filtering are useful non-invasive tools for determining such characteristics.

Impacts of anterior-posterior jaw disproportions on speech of dentofacial disharmony patients.

Articulation problems impact communication, development, and quality of life, and are diagnosed in 73-87% of patients with Class II Dentofacial Disharmony (DFD). We evaluated whether differences exist in stop (/t/ or/k/), fricative (/s/ or/ʃ/), and affricate (/tʃ/) consonant sounds of Class II DFD subjects, and whether extent of malocclusion correlates with severity of speech distortion. We hypothesized that Class II patients display milder distortions than Class III and anterior open bite (AOB), as Class II patients can posture into a Class I occlusion. Audio and orthodontic records were collected from DFD patients (N = 53-Class II, 102-Class III, 72-Controls) who were pursuing orthodontics and orthognathic surgery. A speech pathologist perceptually scored speech. Acoustic differences in recordings were measured using Spectral Moment Analysis. When Class II subjects were compared to controls, significant differences were found for the centroid frequency (M1) of the /s/ sound and the spectral spread (M2) of /t/, /tʃ/, and /s/ sounds, with pairwise significance for controls relative to Class II AOB and all Class II subjects. Class II AOB subjects had higher M1 and M2 values than patients with Class II closed bites and Class I controls for most sounds. When comparing across anterior-posterior (AP) groups, differences exist between controls, Class II and III DFD subjects for M1 of /t/, /tʃ/, and/ʃ/ and M2 for /t/, /tʃ/, /s/, and /ʃ/ sounds. Using linear regression, correlations between Class II and III severity and spectral measures were found for /t/ and /tʃ/ sounds. Class II and III patients have a higher prevalence of qualitative distortions and spectral changes in consonants compared to controls, but Class II spectral shifts are smaller and affect fewer sounds than in Class III and AOB cohorts. Linear correlations between AP discrepancy and spectral change suggest causation and that treatment may improve articulation problems.

Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree

The Hausdorff dimension of spectral measure for the graph Laplacian is shown exactly in terms of an intermittency function. The intermittency function can be estimated by using one-dimensional discrete Schrödinger operator method.

Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with the dimension, and the perturbation matrix is drawn from one of several different random matrix ensembles. We establish a number of non-asymptotic results for the eigenvalues of this model, including a local law and a rate of convergence in Wasserstein distance of the empirical spectral measure to its limiting distribution. In addition, we define the classical locations of the eigenvalues and prove a rigidity result showing that, on average, the eigenvalues concentrate closely around their classical locations. While proving these results we also establish a number of auxiliary results that may be of independent interest, including a quantitative version of the Tao–Vu replacement principle, a general least singular value bound that applies to adversarial models, and a description of the limiting empirical spectral measure for random multiplicative perturbations.

Divergence of mock Fourier series for spectral measures

In this paper, we study divergence properties of the Fourier series on Cantor-type fractal measure, also called the mock Fourier series. We give a sufficient condition under which the mock Fourier series for doubling spectral measure is divergent on a set of strictly positive measure. In particular, there exists an example of the quarter Cantor measure whose mock Fourier sums are not almost everywhere convergent.

Patterns in Foliar Isotopic Nitrogen, Percent Nitrogen, and Site Index for Managed Forest Systems in the United States

Patterns in foliar nitrogen (N) stable isotope ratios (δ15N) have been shown to reveal trends in terrestrial N cycles, including the identification of ecosystems where N deficiencies limit forest ecosystem productivity. However, there is a gap in our understanding of within-species variation and species-level response to environmental gradients or forest management. Our objective is to examine the relationship between site index, foliar %N, foliar δ15N and spectral reflectance for managed Douglas-fir (Pseudotsuga menziesii) and loblolly pine (Pinus taeda) plantations across their geographic ranges in the Pacific Northwest and the southeastern United States, respectively. Foliage was measured at 28 sites for reflectance using a handheld spectroradiometer, and further analyzed for δ15N and N concentration. Unlike the prior work for grasslands and shrubland species, our results show that foliar δ15N and foliar %N are not well correlated for these tree species. However, multiple linear regression models suggest a strong predictive ability of spectroscopy data to quantify foliar δ15N, with some models explaining more than 65% of the variance in the δ15N. Additionally, moderate to strong explanations of variance were found between site index and foliar δ15N (R2 = 0.49) and reflectance and site index (R2 = 0.84) in the Douglas-fir data set. The development of relationships between foliar spectral reflectance, δ15N and measures of site productivity provides the first step toward mapping canopy δ15N for these managed forests with remote sensing.

EEG-based methods for recovery prognosis of patients with disorders of consciousness: A systematic review

ObjectiveDisorders of consciousness (DoC) are acquired conditions of severely altered consciousness. Electroencephalography (EEG)-derived biomarkers have been studied as clinical predictors of consciousness recovery. Therefore, this study aimed to systematically review the methods, features, and models used to derive prognostic EEG markers in patients with DoC in a rehabilitation setting. MethodsWe conducted a systematic literature search of EEG-based strategies for consciousness recovery prognosis in five electronic databases. ResultsThe search resulted in 2964 papers. After screening, 15 studies were included in the review. Our analyses revealed that simpler experimental settings and similar filtering cut-off frequencies are preferred. The results of studies were categorised by extracting qualitative and quantitative features. The quantitative features were further classified into evoked/event-related potentials, spectral measures, entropy measures, and graph-theory measures. Despite the variety of methods, features from all categories, including qualitative ones, exhibited significant correlations with DoC prognosis. Moreover, no agreement was found on the optimal set of EEG-based features for the multivariate prognosis of patients with DoC, which limits the computational methods applied for outcome prediction and correlation analysis to classical ones. Nevertheless, alpha power, reactivity, and higher complexity metrics were often found to be predictive of consciousness recovery. ConclusionsThis study’s findings confirm the essential role of qualitative EEG and suggest an important role for quantitative EEG. Their joint use could compensate for their reciprocal limitations. SignificanceThis study emphasises the need for further efforts toward guidelines on standardised EEG analysis pipeline, given the already proven role of EEG markers in the recovery prognosis of patients with DoC.

Characterization of chronic lung allograft dysfunction phenotypes using spectral and intrabreath oscillometry.

Background: Chronic lung allograft dysfunction (CLAD) is the major cause of death beyond 2 years after lung transplantation and develops in 50% of all patients by 5 years post-transplant. CLAD is diagnosed on the basis of a sustained drop of 20% for at least 3 months in the forced expiratory volume (FEV1), compared to the best baseline value achieved post-transplant. CLAD presents as two main phenotypes: bronchiolitis obliterans syndrome (BOS) is more common and has better prognosis than restrictive allograft syndrome (RAS). Respiratory oscillometry is a different modality of lung function testing that is highly sensitive to lung mechanics. The current study investigated whether spectral and intrabreath oscillometry can differentiate between CLAD-free, BOS- and RAS-CLAD at CLAD onset, i.e., at the time of the initial 20% drop in the FEV1. Methods: A retrospective, cross-sectional analysis of 263 double lung transplant recipients who underwent paired testing with oscillometry and spirometry at the Toronto General Pulmonary Function Laboratory from 2017 to 2022 was conducted. All pulmonary function testing and CLAD diagnostics were performed following international guidelines. Statistical analysis was conducted using multiple comparisons. Findings: The RAS (n = 6) spectral oscillometry pattern differs from CLAD-free (n = 225) by right-ward shift of reactance curve similar to idiopathic pulmonary fibrosis whereas BOS (n = 32) has a pattern similar to obstructive lung disease. Significant differences were found in most spectral and intrabreath parameters between BOS, RAS, and time-matched CLAD-free patients. Post-hoc analysis revealed these differences were primarily driven by BOS instead of RAS. While no differences were found between CLAD-free and RAS patients with regards to spectral oscillometry, the intrabreath metric of reactance at end-inspiration (XeI) was significantly different (p < 0.05). BOS and RAS were differentiated by spectral oscillometry measure R5, and intrabreath resistance at end expiration, ReE (p < 0.05 for both). Conclusion: Both spectral and intrabreath oscillometry can differentiate BOS-CLAD from CLAD-free states while intrabreath oscillometry, specifically XeI, can uniquely distinguish RAS-CLAD from CLAD-free. Spectral and intrabreath oscillometry offer complementary information regarding lung mechanics in CLAD patients to help distinguish the two phenotypes and could prove useful in prognostication.

Tree Detection and Species Classification in a Mixed Species Forest Using Unoccupied Aircraft System (UAS) RGB and Multispectral Imagery

Information on tree species and changes in forest composition is necessary to understand species-specific responses to change, and to develop conservation strategies. Remote sensing methods have been increasingly used for tree detection and species classification. In mixed species forests, conventional tree detection methods developed with assumptions about uniform tree canopy structure often fail. The main aim of this study is to identify effective methods for tree delineation and species classification in an Australian native forest. Tree canopies were delineated at three different spatial scales of analysis: (i) superpixels representing small elements in the tree canopy, (ii) tree canopy objects generated using a conventional segmentation technique, multiresolution segmentation (MRS), and (iii) individual tree bounding boxes detected using deep learning based on the DeepForest open-source algorithm. Combinations of spectral, texture, and structural measures were tested to assess features relevant for species classification using RandomForest. The highest overall classification accuracies were achieved at the superpixel scale (0.84 with all classes and 0.93 with Eucalyptus classes grouped). The highest accuracies at the individual tree bounding box and object scales were similar (0.77 with Eucalyptus classes grouped), highlighting the potential of tree detection using DeepForest, which uses only RGB, compared to site-specific tuning with MRS using additional layers. This study demonstrates the broad applicability of DeepForest and superpixel approaches for tree delineation and species classification. These methods have the potential to offer transferable solutions that can be applied in other forests.

Scale-free and oscillatory spectral measures of sleep stages in humans.

Power spectra of sleep electroencephalograms (EEG) comprise two main components: a decaying power-law corresponding to the aperiodic neural background activity, and spectral peaks present due to neural oscillations. “Traditional” band-based spectral methods ignore this fundamental structure of the EEG spectra and thus are susceptible to misrepresenting the underlying phenomena. A fitting method that attempts to separate and parameterize the aperiodic and periodic spectral components called “fitting oscillations and one over f” (FOOOF) was applied to a set of annotated whole-night sleep EEG recordings of 251 subjects from a wide age range (4–69 years). Most of the extracted parameters exhibited sleep stage sensitivity; significant main effects and interactions of sleep stage, age, sex, and brain region were found. The spectral slope (describing the steepness of the aperiodic component) showed especially large and consistent variability between sleep stages (and low variability between subjects), making it a candidate indicator of sleep states. The limitations and arisen problems of the FOOOF method are also discussed, possible solutions for some of them are suggested.

Temporal and spectral characteristics of conversational versus read fricatives in American English.

The present study compares the production of fricatives in conversational versus read speech in American English. The goal is to examine which parameters contribute to the identification of fricatives across the two speech styles. The study surveys over 162 000 fricative tokens from the Buckeye Corpus [Pitt, Johnson, Hume, Kiesling, and Raymond (2005). Speech Commun. 45, 89-95] and the TIMIT Corpus [Zue and Seneff (1996). Recent Research towards Advanced Man-Machine Interface through Spoken Language (Elsevier, Amsterdam, the Netherlands), pp. 515-525]. A total of 18 different temporal and spectral measures are tested, including segment duration, preceding and following phone duration, spectral moments (at onset, midpoint, and/or offset), spectral peak frequency, etc. Results show that segment duration and midpoint spectral moments make the most prominent contribution to the categorization of fricatives for both speech styles. Spectral measures are more important for conversational speech, whereas duration plays a greater role for read speech. At the same time, the magnitude of the differences across speech styles is often low and many of the observed effects may be attributable to methodological differences across the corpora. Results may indicate that reduction of fricatives in conversational speech is more limited compared to the reduction of other types of speech sounds, such as plosives.

The tonal system of Hengyang Xiang

Hengyang belongs to the Hengzhou branch of Xiang Chinese; it contrasts six tones: high rising (45), falling-rising (213), low-rising (24), low level (11), mid level (33), and low-mid (22). Liu (2010) found that the falling-rising (213) and the low-rising (24) tones have merged to become a distinct low-dipping tone (214), as in Mandarin. This merger is attributed to language contact and influence from Mandarin, because it is mostly observed in frequent words and has a stronger tendency among younger populations (Liu, 2010). However, it is unclear whether this tone merger is complete, because previous reports conflict as to the number of tones in the tonal system of Hengyang (Zhong, 2011; Li, 1986; Huang, 2013). This study investigates the tonal system in Hengyang using acoustic analyses to capture the tonal differences in pitch and voice quality characteristics including spectral tilt and periodicity measures. We recorded ten participants reading monosyllabic words. The participants were from four age groups ranging from 21 to 60 years old (21–30, 31–40, 41–50, and 51–60 years old). We hypothesize that the tone merger occurs more often in frequently used words and for younger speakers. The findings will depict the acoustic spaces of Hengyang tones and show whether the merged tonal patterns are associated with particular words and/or age groups. The discussion will emphasize how language contact gives rise to tonal neutralization and sound change.

Knowledge-Based Prediction of Network Controllability Robustness.

Network controllability robustness (CR) reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network after a sequence of node-removal or edge-removal attacks. Traditionally, the CR is determined by attack simulations, which is computationally time-consuming or even infeasible. In this article, an improved method for predicting the network CR is developed based on machine learning using a group of convolutional neural networks (CNNs). In this scheme, a number of training data generated by simulations are used to train the group of CNNs for classification and prediction, respectively. Extensive experimental studies are carried out, which demonstrate that 1) the proposed method predicts more precisely than the classical single-CNN predictor; 2) the proposed CNN-based predictor provides a better predictive measure than the traditional spectral measures and network heterogeneity.

Consonantal contrasts in Hnaring Lutuv

Hnaring is a dialect of Lutuv, a member of the South Central branch of Tibeto-Burman spoken by 15 000 to 18 000 people in Chin State in western Burma and in refugee communities worldwide (community estimates, Eberhard et al., 2022; Salaz and Raymer, 2020). Like many other Tibeto-Burman languages, Lutuv features an extensive consonantal inventory, with three-way contrasts for labial and coronal stops and two-way contrasts for dorsals, laryngeal contrasts for sibilant and lateral affricates (/ts, tsʰ/, /tl, tlʰ/), and voicing contrasts for sonorants /r, r̥, l, l̥, n, n̥, m, m̥/. Of special note is the high degree of variability observed in the instantiation of voiceless sonorants, which can include alternately ordered phases of aspiration, frication, and/or voicing. For example, voiceless laterals can be realized in at least four ways ([lʰ, ʰl, ɬ, l̥]); rhotics alternate between rhotic and sibilant productions ([ʰr, rʰ, ʃ]); and nasals show phasing and voicing differences [ʰm, mʰ, m̥, m⌢m̥]. Using both wordlist data and naturalistic speech from a conversational corpus collected during Summer 2022, this study presents a suite of temporal and spectral measures for Hnaring Lutuv consonants and combines qualitative and quantitative data to characterize the observed variation.

The Brown measure of the free multiplicative Brownian motion

The free multiplicative Brownian motion b_{t} is the large-N limit of the Brownian motion on mathsf {GL}(N;mathbb {C}), in the sense of *-distributions. The natural candidate for the large-N limit of the empirical distribution of eigenvalues is thus the Brown measure of b_{t}. In previous work, the second and third authors showed that this Brown measure is supported in the closure of a region Sigma _{t} that appeared in the work of Biane. In the present paper, we compute the Brown measure completely. It has a continuous density W_{t} on overline{Sigma }_{t}, which is strictly positive and real analytic on Sigma _{t}. This density has a simple form in polar coordinates: Wt(r,θ)=1r2wt(θ),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} W_{t}(r,\ heta )=\\frac{1}{r^{2}}w_{t}(\ heta ), \\end{aligned}$$\\end{document}where w_{t} is an analytic function determined by the geometry of the region Sigma _{t}. We show also that the spectral measure of free unitary Brownian motion u_{t} is a “shadow” of the Brown measure of b_{t}, precisely mirroring the relationship between the circular and semicircular laws. We develop several new methods, based on stochastic differential equations and PDE, to prove these results.

Neural Network-Based Subduction Ground Motion Model and Its Application to New Zealand and the Andaman and Nicobar Islands

ABSTRACT A deep learning model is developed for the Next Generation Attenuation – Subduction database for predicting spectral accelerations and peak amplitude measures. The developed model satisfies the statistical criteria necessary for prediction. Standard deviations lie in 0.2864–0.3809, 0–0.2696, and 0.4514–0.7892, range for inter-event, -region, and intra-events, respectively. Transfer learning is applied to the New Zealand region. Probabilistic seismic hazard analysis is performed for the Andaman-Nicobar region and obtained a peak ground acceleration of 0.6–0.7 g and 0.4–0.5 g at the Andaman and the Nicobar Islands, respectively, for a 2475-year return period.

N-acetylcysteine treatment mitigates loss of cortical parvalbumin-positive interneuron and perineuronal net integrity resulting from persistent oxidative stress in a rat TBI model.

Traumatic brain injury (TBI) increases cerebral reactive oxygen species production, which leads to continuing secondary neuronal injury after the initial insult. Cortical parvalbumin-positive interneurons (PVIs; neurons responsible for maintaining cortical inhibitory tone) are particularly vulnerable to oxidative stress and are thus disproportionately affected by TBI. Systemic N-acetylcysteine (NAC) treatment may restore cerebral glutathione equilibrium, thus preventing post-traumatic cortical PVI loss. We therefore tested whether weeks-long post-traumatic NAC treatment mitigates cortical oxidative stress, and whether such treatment preserves PVI counts and related markers of PVI integrity and prevents pathologic electroencephalographic (EEG) changes, 3 and 6 weeks after fluid percussion injury in rats. We find that moderate TBI results in persistent oxidative stress for at least 6 weeks after injury and leads to the loss of PVIs and the perineuronal net (PNN) that surrounds them as well as of per-cell parvalbumin expression. Prolonged post-TBI NAC treatment normalizes the cortical redox state, mitigates PVI and PNN loss, and-in surviving PVIs-increases per-cell parvalbumin expression. NAC treatment also preserves normal spectral EEG measures after TBI. We cautiously conclude that weeks-long NAC treatment after TBI may be a practical and well-tolerated treatment strategy to preserve cortical inhibitory tone post-TBI.