Spectral Measure Research Articles

A new spectral measure of complexity and its capabilities for detecting signals in noise

This article is devoted to the improvement of signal recognition methods based on the information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the DFT. Lemmas on estimates of entropy, imbalance and statistical complexity in processing a time series of independent Gaussian quantities are proved. New concepts of one-dimensional and two-dimensional spectral complexities are proposed. The theoretical results obtained were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic when detecting a signal mixed with white noise at low signal-to-noise ratios.

Addition to the article “A new spectral measure of complexity and its capabilities for detecting signals in noise”

Note-addition to the article “A new spectral measure of complexity and its capabilities for detecting signals in noise”.

Orthogonal Fourier Analysis on domains

In this paper we go over the history of the Fuglede or Spectral Set Conjecture as it has developed over the last 30 years or so. We do not aim to be exhaustive and we do not cover important areas of development such as the results on the problem in classes of finite groups or the version of the problem that focuses on spectral measures instead of sets. The selection of the material has been strongly influenced by personal taste, history and capabilities. We are trying to be more descriptive than detailed and we point out several open questions.

Behavioral and neurophysiological signatures of cognitive control in humans and rats.

Deficits in cognitive control are implicated in numerous neuropsychiatric disorders. However, relevant pharmacological treatments are limited, likely due to weak translational validity of applicable preclinical models used. Neural indices derived from electroencephalography may prove useful in comparing and translating the effects of cognition-enhancing drugs between species. In the current study, we aimed to extend our previous cross-species results by examining if methylphenidate (MPH) modulates behavioral and neural indices of cognitive control in independent cohorts of humans and rats. We measured continuous electroencephalography data from healthy adults (n = 25; 14 female) and Long Evans rats (n = 22; 8 female) and compared both stimulus- and response-locked event-related potentials and spectral power measures across species, and their MPH-related moderation following treatment with vehicle (placebo) or 1 of 2 doses of MPH. Across both species, linear mixed effects modeling confirmed the expected Flanker interference effect on behavior (eg, accuracy) and response-related event-related potentials. Unexpectedly, in contrast to past work, we did not observe any task-related effects on the spectral power of rodents. Moreover, MPH generally did not modulate cognitive control of either species, although some species-specific patterns offer insight for future research. Collectively, these findings in independent human and rodent subjects replicate some of our previously reported behavioral and neurophysiological patterns partly consistent with the notion that similar neural mechanisms may regulate cognitive control in both species. Nonetheless, these results showcase an approach to accelerate translation using a coordinated between-species platform to evaluate pro-cognitive treatments.

Maximum likelihood estimation of elliptical tail

This study is focused on the efficient estimation of the elliptical tail. Initially, we derive the density function of the spectral measure of an elliptical distribution concerning a dominating measure on the unit sphere, which consequently leads to the density function of the elliptical tail. Subsequently, we propose a maximum likelihood estimation based on the derived density function class. The resulting maximum likelihood estimator (MLE) is proven to be consistent and asymptotically normal. Moreover, it is demonstrated that the MLE is asymptotically efficient, with the added advantage that its asymptotic covariance matrix can be feasibly estimated at a low computational cost. A simulation study and real data analysis are conducted to illustrate the efficacy of the proposed method.

A spectral dominance approach to large random matrices: Part II

This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We precise and extend some results of the first part. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the Dyson Brownian motion. We provide a regularizing result for those generalizations. We also show that several results of part I extend to cases in which there is no spectral dominance property. We then provide several modeling extensions of such models as well as several identities for the Dyson Brownian motion.

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the ‘rapid’ nature of the shoaling process, i.e. shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the length and angle of a shoal's slope. We investigate the effects of the shoaling process rapidness on the evolution of key statistical and spectral sea-state parameters. We let the wave field evolve over a slope with constant angle in all cases while we vary the slope length. Our results indicate that the non-equilibrium dynamics is not affected by the slope length, because further extending the slope length does not influence the magnitude of the statistical and spectral measures as long as the non-equilibrium dynamics dominates the wave evolution. Thus, the shoaling effect on rogue waves is deduced to be mainly driven by the slope magnitude rather than the slope length.

A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise

A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise

Addition to the Article “A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise”

Addition to the Article “A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise”

Remote Sensing Image Segmentation Based on Probabilistic Fuzzy Local Information Clustering

Abstract. In this paper, a remote sensing image segmentation based on probabilistic fuzzy local information clustering algorithm is proposed. First, assuming that the spectral measure within the same ground object follows the same probability distribution. The dissimilarity between pixel and object is modeled by the negative logarithm of the Gaussian probability density function. It can improve the noise sensitive problem caused by the Euclidean distance which can only describe the data with isotropic distribution. Then, in order to consider the effect of local spatial constraint, on the one hand, the probability measure is used to modify the local fuzzy factor to establish the dissimilarity measure with spatial constraints. On the other hand, the hidden Markov random field is used to model the prior probability model of pixel membership. Next, the entropy regularization term of the objective function is built by combining the Kullback-Leibler(KL) maximum entropy model to further improve the robustness and noise resistance. The qualitative and quantitative analysis of simulated image and different types of real remote sensing images show that the proposed algorithm can effectively overcome the above problems and further improve the accuracy of image segmentation to over 95%.

Modulation of neural oscillations in escitalopram treatment: a Canadian biomarker integration network in depression study

Current pharmacological agents for depression have limited efficacy in achieving remission. Developing and validating new medications is challenging due to limited biological targets. This study aimed to link electrophysiological data and symptom improvement to better understand mechanisms underlying treatment response. Longitudinal changes in neural oscillations were assessed using resting-state electroencephalography (EEG) data from two Canadian Biomarker Integration Network in Depression studies, involving pharmacological and cognitive behavioral therapy (CBT) trials. Patients in the pharmacological trial received eight weeks of escitalopram, with treatment response defined as ≥ 50% decrease in Montgomery–Åsberg Depression Rating Scale (MADRS). Early (baseline to week 2) and late (baseline to week 8) changes in neural oscillation were investigated using relative power spectral measures. An association was found between an initial increase in theta and symptom improvement after 2 weeks. Additionally, late increases in delta and theta, along with a decrease in alpha, were linked to a reduction in MADRS after 8 weeks. These late changes were specifically observed in responders. To assess specificity, we extended our analysis to the independent CBT cohort. Responders exhibited an increase in delta and a decrease in alpha after 2 weeks. Furthermore, a late (baseline to week 16) decrease in alpha was associated with symptom improvement following CBT. Results suggest a common late decrease in alpha across both treatments, while modulatory effects in theta may be specific to escitalopram treatment. This study offers insights into electrophysiological markers indicating a favorable response to antidepressants, enhancing our comprehension of treatment response mechanisms in depression.

Spectrality and non-spectrality of a class of Moran measures

Let {Mn}n=1∞∈M2(R) be a sequence of real expanding matrices and {Dn}n=1∞ be a sequence of digit sets withDn={(00),(anbn),(cndn)}, where |andn−bncn|=ϕ(n)∈Z, and letμ{Mn},{Dn}=δM1−1D1⁎δ(M1M2)−1D2⁎δ(M1M2M3)−1D3⁎⋯ be the associated Moran measure. This paper establishes a necessary and sufficient condition for μMn,Dn to be a spectral measure when each Mn is a diagonal matrix, and characterizes the structure of the spectrum Λ. Furthermore, we demonstrate that for any sequence of matrices {Mn}n=1∞ ∈ M2(Z) with det⁡(Mn)∉3Z, the space L2(μ{Mn},{Dn}) contains at most 9 mutually orthogonal exponential functions. The precise maximum cardinality of such functions is also determined.

Multi-modal and multi-level structure-specific spectral intensity measures for seismic evaluation of reinforced concrete frames

Multi-modal and multi-level structure-specific spectral intensity measures for seismic evaluation of reinforced concrete frames

Distinct Longitudinal Changes in EEG Measures Reflecting Functional Network Disruption in ALS Cognitive Phenotypes

Amyotrophic lateral sclerosis (ALS) is characterised primarily by motor system degeneration, with clinical evidence of cognitive and behavioural change in up to 50% of cases. We have shown previously that resting-state EEG captures dysfunction in motor and cognitive networks in ALS. However, the longitudinal development of these dysfunctional patterns, especially in networks linked with cognitive-behavioural functions, remains unclear. Longitudinal studies on non-motor changes in ALS are essential to further develop our understanding of disease progression, improve care and enhance the evaluation of new treatments. To address this gap, we examined 124 ALS individuals with 128-channel resting-state EEG recordings, categorised by cognitive impairment (ALSci, n = 25), behavioural impairment (ALSbi, n = 58), or non-impaired (ALSncbi, n = 53), with 12 participants meeting the criteria for both ALSci and ALSbi. Using linear mixed-effects models, we characterised the general and phenotype-specific longitudinal changes in brain network, and their association with cognitive performance, behaviour changes, fine motor symptoms, and survival. Our findings revealed a significant decline in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:\ heta\\:$$\\end{document}-band spectral power over time in the temporal region along with increased \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\gamma\\:}_{l}$$\\end{document}-band power in the fronto-temporal region in the ALS group. ALSncbi participants showed widespread β-band synchrony decrease, while ALSci participants exhibited increased co-modulation correlated with verbal fluency decline. Longitudinal network-level changes were specific of ALS subgroups and correlated with motor, cognitive, and behavioural decline, as well as with survival. Spectral EEG measures can longitudinally track abnormal network patterns, serving as a candidate stratification tool for clinical trials and personalised treatments in ALS.

Advances, challenges, and prospects of electroencephalography-based biomarkers for psychiatric disorders: a narrative review.

Owing to a lack of appropriate biomarkers for accurate diagnosis and treatment, psychiatric disorders cause significant distress and functional impairment, leading to social and economic losses. Biomarkers are essential for diagnosing, predicting, treating, and monitoring various diseases. However, their absence in psychiatry is linked to the complex structure of the brain and the lack of direct monitoring modalities. This review examines the potential of electroencephalography (EEG) as a neurophysiological tool for identifying psychiatric biomarkers. EEG noninvasively measures brain electrophysiological activity and is used to diagnose neurological disorders, such as depression, bipolar disorder (BD), and schizophrenia, and identify psychiatric biomarkers. Despite extensive research, EEG-based biomarkers have not been clinically utilized owing to measurement and analysis constraints. EEG studies have revealed spectral and complexity measures for depression, brainwave abnormalities in BD, and power spectral abnormalities in schizophrenia. However, no EEG-based biomarkers are currently used clinically for the treatment of psychiatric disorders. The advantages of EEG include real-time data acquisition, noninvasiveness, cost-effectiveness, and high temporal resolution. Challenges such as low spatial resolution, susceptibility to interference, and complexity of data interpretation limit its clinical application. Integrating EEG with other neuroimaging techniques, advanced signal processing, and standardized protocols is essential to overcome these limitations. Artificial intelligence may enhance EEG analysis and biomarker discovery, potentially transforming psychiatric care by providing early diagnosis, personalized treatment, and improved disease progression monitoring.

Influence of Carnatic Vocal Training on Voice Measures in Males

Introduction: Training is an integral part of learning any skill. The vocal training helps singers attain proficiency as they are the most demanding vocal group of all professional voice users. Hence, it is necessary to evaluate the influence of training on the singer’s voice. The current study objective was to investigate the influence of vocal training on voice measures (acoustic and aerodynamic) between male Carnatic singers with lower (6 months–5 years) and higher (6–10 years) training using novel task “mkaram” along with lyrical task. Methods: Group 1 consisted of 30 trained male Carnatic singers with lower vocal training, and group 2, thirty trained male singers with higher training in the age of 18–45 years. The acoustic (frequency-related parameter, cepstral, spectral, perturbation, and noise) and aerodynamic measures (maximum phonation time and s/z ratio) of voice were obtained. The test-retest reliability was conducted on a sample of 10% of the population from each group, with a 2-week interval between the tests. Cross-sectional study design was applied. Results: The statistical analysis revealed significantly decreased frequency-related parameters (semitones) such as the mean fundamental frequency, lowest fundamental frequency, highest fundamental frequency at the low register and the highest fundamental frequency at the middle register in group 2 during “mkaram” task (p ≤ 0.05). Similarly, one of the spectral-related measures 1st harmonic-2nd harmonic (dB) during lyrical task and one of the noise-related measure harmonic-to-noise ratio (dB) at the middle register during “mkaram” task showed a significant decrease in group 2 compared to group 1 (p ≤ 0.05). Test-retest reliability revealed that most of the parameters had “acceptable to excellent” internal consistency (Cronbach’s α >0.7 to 1). Conclusion: Few frequency and noise measures during “mkaram” task and a spectral measure during lyrical task showed to be sensitive in distinguishing the impact of vocal training on the voices of male Carnatic singers. The higher vocal training was found to help the singers to perform more efficiently with enhanced vocal range particularly in the low register and to some extent in the middle register. Indeed, the study highlighted the positive effects of vocal training on male Carnatic singers.

Spectral packing decomposition of CMV matrices through power-law subordinacy

This note gives a classification for the spectral measures of CMV matrices, which are special unitary five-diagonal matrices related to orthogonal polynomials on the unit circle, with respect to packing measures.

Another look at residual dynamic mode decomposition in the regime of fewer snapshots than dictionary size

Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues associated with finite truncations of Koopman operators (e.g., Extended Dynamic Mode Decomposition), such as spurious eigenvalues. Spectral properties computed by ResDMD include spectra, pseudospectra, spectral measures, Koopman mode decompositions, and dictionary verification. In scenarios where the number of snapshots is fewer than the dictionary size, particularly for exact DMD and kernelized Extended DMD, ResDMD has traditionally been applied by dividing snapshot data into a training set and a quadrature set. We demonstrate how to eliminate the need for two datasets through a novel computational approach of solving a dual least-squares problem. We analyze these new residuals for exact DMD and kernelized Extended DMD, demonstrating ResDMD’s versatility and broad applicability across various dynamical systems, including those modeled by high-dimensional and nonlinear observables. The utility of these new residuals is showcased through three diverse examples: the analysis of a cylinder wake, the study of airfoil cascades, and the compression of transient shockwave experimental data. This approach not only simplifies the application of ResDMD but also extends its potential for deeper insights into the dynamics of complex systems.

Chaotic Measures as an Alternative to Spectral Measures for Analysing Turbulent Flow

Chaotic Measures as an Alternative to Spectral Measures for Analysing Turbulent Flow

Spectral structure of a class of self-similar spectral measures with product form digit sets

Spectral structure of a class of self-similar spectral measures with product form digit sets