Spectral Measure Research Articles

Band Selection via Band Density Prominence Clustering for Hyperspectral Image Classification

Band clustering has been widely used for hyperspectral band selection (BS). However, selecting an appropriate band to represent a band cluster is a key issue. Density peak clustering (DPC) provides an effective means for this purpose, referred to as DPC-based BS (DPC-BS). It uses two indicators, cluster density and cluster distance, to rank all bands for BS. This paper reinterprets cluster density and cluster distance as band local density (BLD) and band distance (BD) and also introduces a new concept called band prominence value (BPV) as a third indicator. Combining BLD and BD with BPV derives new band prioritization criteria for BS, which can extend the currently used DPC-BS to a new DPC-BS method referred to as band density prominence clustering (BDPC). By taking advantage of the three key indicators of BDPC, i.e., cut-off band distance bc, k nearest neighboring-band local density, and BPV, two versions of BDPC can be derived called bc-BDPC and k-BDPC, both of which are quite different from existing DPC-based BS methods in three aspects. One is that the parameter bc of bc-BDPC and the parameter k of k-BDPC can be automatically determined by the number of clusters and virtual dimensionality (VD), respectively. Another is that instead of using Euclidean distance, a spectral discrimination measure is used to calculate BD as well as inter-band correlation. The most important and significant aspect is a novel idea that combines BPV with BLD and BD to derive new band prioritization criteria for BS. Extensive experiments demonstrate that BDPC generally performs better than DPC-BS as well as many current state-of-the art BS methods.

Universality of oscillatory instabilities in fluid mechanical systems

Oscillatory instability emerges amidst turbulent states in experiments in various turbulent fluid and thermo-fluid systems such as aero-acoustic, thermoacoustic and aeroelastic systems. For the time series of the relevant dynamic variable at the onset of the oscillatory instability, universal scaling behaviors have been discovered in experiments via the Hurst exponent and certain spectral measures. By means of a center manifold reduction, the spatiotemporal dynamics of these real systems can be mapped to a complex Ginzburg–Landau equation with a linear global coupling. In this work, we show that this model is able to capture the universal behaviors of the route to oscillatory instability, elucidating it as a transition from defect to phase turbulence mediated by the global coupling.

Classification patterns in conversational English fricatives: Between- and within- speaker analyses

This study examines between- and within- speaker patterns in random forest classification models for fricatives in conversational English. Prior investigations on the categorization of fricatives have mostly focused on group-level analyses and careful speech. We use a corpus of sociolinguistic interview speech from Western Canadian English, which represents a more casual speech style, and we compare group-level results to the findings of classification models on individual speakers’ productions. The models use 23 different spectral, temporal, and amplitudinal measures to predict phonetic labels of the fricatives. Our results reveal that certain top-ranked predictors at the group level (e.g., spectral peak frequency, segment duration) are also important for fricative classification in the individual models. Other measures (e.g., midpoint kurtosis, RMS) show substantial variability in their relative prominence and play greater roles in individual- versus group-level modeling. We discuss the implications of these findings for our understanding of individual variation in connected speech and what the findings may imply about models of production and perception.

Creaky voice across language and gender: A study of Canadian English-French bilingual speech

This study addresses how non-contrastive creaky voice varies among languages and across speakers (as a function of gender). Spontaneous speech from 9 English-French bilingual speakers born and raised in Ontario/Québec was collected from publicly available online data sources, amounting to roughly 5 min of speech per speaker-language pair and 13 992 vowels total. This corpus will reach 40 speakers by the conference. Acoustic analysis consisted of pitch tracking in Praat, providing a proportion of unreliable f0 tracks for each vowel as well as one spectral slope measure (H1*-H2*) and two Harmonics-to-Noise Ratios (CPP and HNR05) as acoustic correlates of creaky voice. Statistical significance was tested using mixed-effects regression models, with fixed effects of language, gender, and utterance position, and maximal by-word and by-speaker random effects. The main results for gender show that men's vowels have more unreliable f0 tracks, lower H1*-H2*, lower HNR05 and somewhat lower CPP, suggesting that male speakers are creakier overall. Regarding language, English displays more unreliable pitch tracking compared to French, providing some evidence for language-dependent vocal settings. Other acoustic correlates of creak, however, do not show consistent cross-linguistic differences.

Dissociations between spontaneous electroencephalographic features and the perturbational complexity index in the minimally conscious state.

The analysis of spontaneous electroencephalogram (EEG) is a cornerstone in the assessment of patients with disorders of consciousness (DoC). Although preserved EEG patterns are highly suggestive of consciousness even in unresponsive patients, moderately or severely abnormal patterns are difficult to interpret. Indeed, growing evidence shows that consciousness can be present despite either large delta or reduced alpha activity in spontaneous EEG. Quantifying the complexity of EEG responses to direct cortical perturbations (perturbational complexity index [PCI]) may complement the observational approach and provide a reliable assessment of consciousness even when spontaneous EEG features are inconclusive. To seek empirical evidence of this hypothesis, we compared PCI with EEG spectral measures in the same population of minimally conscious state (MCS) patients (n= 40) hospitalized in rehabilitation facilities. We found a remarkable variability in spontaneous EEG features across MCS patients as compared with healthy controls: in particular, a pattern of predominant delta and highly reduced alpha power-more often observed in vegetative state/unresponsive wakefulness syndrome (VS/UWS) patients-was found in a non-negligible number of MCS patients. Conversely, PCI values invariably fell above an externally validated empirical cutoff for consciousness in all MCS patients, consistent with the presence of clearly discernible, albeit fleeting, behavioural signs of awareness. These results confirm that, in some MCS patients, spontaneous EEG rhythms may be inconclusive about the actual capacity for consciousness and suggest that a perturbational approach can effectively compensate for this pitfall with practical implications for the individual patient's stratification and tailored rehabilitation.

Solution theory to semilinear stochastic equations of Schrödinger type on curved spaces I: operators with uniformly bounded coefficients

We study the Cauchy problem for Schrödinger type stochastic semilinear partial differential equations with uniformly bounded variable coefficients, depending on the space variables. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy data, and on the spectral measure associated with the noise, such that the Cauchy problem admits a unique function-valued mild solution in the sense of Da Prato and Zabczyc.

On Fourier expansions for systems of ordinary differential equations with distributional coefficients

We study the spectral theory for the first-order system Ju′+qu=wf of differential equations on the real interval (a,b) where J is a constant, invertible, skew-hermitian matrix and q and w are matrices whose entries are distributions of order 0 with q hermitian and w non-negative. Specifically, we construct a generalized Weyl-Titchmarsh m-function with corresponding spectral measure τ and a generalized Fourier transform after imposing certain conditions on J, q, and w. Different conditions are motivated and studied in the later sections. A Fatou-type identity needed for our result is recorded in the appendix.

IMN4NPD: An Integrated Molecular Networking Workflow for Natural Product Dereplication.

Molecular networking has emerged as a standard approach for natural product (NP) discovery. However, the current pipeline based on molecular networks tends to prioritize larger clusters comprising multiple nodes. To address this issue, we present the integrated molecular networking workflow for NP dereplication (IMN4NPD). This approach not only expedites the rapid dereplication of extensive clusters within the molecular network but also places specific emphasis on self-looped or pairs of nodes, which are often overlooked by the current methods. By amalgamating the outputs from various computational tools, we efficiently dereplicate compounds falling into specific categories and provide annotations for both large cluster nodes and self-looped or pair of nodes within the molecular network. Furthermore, we have incorporated several fundamentally distinct similarity algorithms, namely, Spec2Vec and MS2DeepScore, for constructing the t-SNE network. Through comparison with modified cosine similarity, we have observed that integrating additional diverse spectral similarity measures, the resulting t-SNE network enhanced the ability to dereplicate NPs. Demonstrating the use case of an ethanol extract of Plumula nelumbinis, we illustrate that an integration of multiple computational solutions with IMN4NPD aids the dereplication, especially self-looped nodes, and in the discovery of novel compounds in NPs.

Multitaper Spectrum Analysis of Consonants Produced by Patients With Dentofacial Disharmonies.

This study investigates differences in American English consonants produced by patients who present with various dentofacial disharmonies (DFDs), including severe overbites (Class II), underbites (Class III), and anterior open bites. Previous studies have found that patients with these malocclusion types all produce lingual sibilants and plosives with increased spectral center of gravity and increased spectral variance relative to controls. This result is puzzling since some DFD groups differ from controls in opposite ways, and it is also difficult to interpret because spectral moment measures are affected by a wide range of speech and nonspeech factors. To better understand the articulatory basis of these differences, we apply articulatorily interpretable spectral measures derived from multitaper spectra. We find that all groups of DFD patients produce /s ʃ t tʃ/ with midfrequency spectral peaks that are less prominent than those of the control group, but peak frequency measures are largely the same across all groups. We conclude that the DFD patients differ more in sibilant noise source properties than in front cavity filter properties.

Robust portfolio selection with subjective risk aversion under dependence uncertainty

This paper solves the robust portfolio decision problem with subjective risk aversion under dependence uncertainty. We use spectral risk measures to capture investors’ subjective risk aversion while constructing mixture R-vine copula uncertainty with R-vine copula change-point detection to characterize dependence uncertainty. We introduce worst-case spectral risk measures (WSRM) and formulate portfolio decision problems with WSRM as risk measures. We conduct an empirical study using eight global stock indices. The results demonstrate that our robust portfolio outperforms two other portfolios without incorporating dependence uncertainty or considering dependence uncertainty constructed only through common economic crisis information in static and dynamic investments encompassing the full out-of-sample period and crisis periods across different risk aversion levels. The performance of our dynamic robust portfolio increases with investors’ risk aversion levels. Our robust portfolio strategy can help investors with diverse risk preferences achieve substantial profits and enable those with high-risk aversion to reap the rewards of their risk aversion.

Extremes for stationary regularly varying random fields over arbitrary index sets

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point processes of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature (Basrak and Planinić in Bernoulli 27(2):1371–1408, 2021; Stehr and Rønn-Nielsen in Extremes 24(4):753–795, 2021). However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure (Wu and Samorodnitsky in Stochastic Process Appl 130(7):4470–4492, 2020) except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space (Segers et al. in Extremes 20:539–566, 2017), the Υ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Upsilon$$\\end{document}-spectral tail measure provides a natural extension that describes the clustering effect in full generality.

On spectral measures and convergence rates in von Neumann’s Ergodic theorem

On spectral measures and convergence rates in von Neumann’s Ergodic theorem

On an uncountable family of graphs whose spectrum is a Cantor set

For each p\geq 1 , the star automaton group \mathcal{G}_{S_p} is an automaton group which can be defined starting from a star graph on p+1 vertices. We study Schreier graphs associated with the action of the group \mathcal{G}_{S_p} on the regular rooted tree T_{p+1} of degree p+1 and on its boundary \partial T_{p+1} . With the transitive action on the n -th level of T_{p+1} is associated a finite Schreier graph \Gamma^{p}_{n} , whereas there exist uncountably many orbits of the action on the boundary, represented by infinite Schreier graphs which are obtained as the limits of the sequence \{\Gamma_{n}^{p}\}_{n\geq 1} in the Gromov–Hausdorff topology. We obtain an explicit description of the spectrum of the graphs \{\Gamma_{n}^{p}\}_{n\geq 1} . Then, by using amenability of \mathcal{G}_{S_p} , we prove that the spectrum of each infinite Schreier graph is the union of a Cantor set of zero Lebesgue measure, which is the Julia set of the quadratic map f_{p}(z) = z^{2}-2(p-1)z -2p , and a countable collection of isolated points supporting the Kesten–Neumann–Serre spectral measure. We also give a complete classification of the infinite Schreier graphs up to isomorphism of unrooted graphs, showing that they may have 1 , 2 or 2p ends, and that the case of 1 end is generic with respect to the uniform measure on \partial T_{p+1} .

An Inverse Spectral Problem for Non-Self-Adjoint Jacobi Matrices

Abstract We consider the class of bounded symmetric Jacobi matrices $J$ with positive off-diagonal elements and complex diagonal elements. With each matrix $J$ from this class, we associate the spectral data, which consists of a pair $(\nu ,\psi )$. Here $\nu $ is the spectral measure of $|J|=\sqrt {J^{*}J}$ and $\psi $ is a phase function on the real line satisfying $|\psi |\leq 1$ almost everywhere with respect to the measure $\nu $. Our main result is that the map from $J$ to the pair $(\nu ,\psi )$ is a bijection between our class of Jacobi matrices and the set of all spectral data.

Efficient image fusion method using improved Bi-dimensional Empirical Mode Decomposition

ABSTRACT Several transformations are used in image fusion to extract the different image spatial details. In this paper, an improved version of the BEMD (Bi-dimensional Empirical Mode Decomposition) is proposed and is used to propose an image fusion method aiming to have the high spatial resolution of the panchromatic image PAN and the spectral resolution of the multispectral image MS in the same fused image. The proposed improved BEMD permits to avoid using injection models that are used in image fusion for preserving the spectral signatures in the fused image. Mainly, we propose a new 2D extrema points extraction for BEMD. One of the most important characteristics of the proposed BEMD components is that they are more faithful to the EMD components; their local behaviour being of pure oscillating 2D mono-components with zero mean values. Comparisons, among predecessor methods with qualitative evaluation and various spectral and spatial quantitative measures, show the effectiveness and efficiency of the proposed image fusion method. In addition, this fusion method is computationally fast and can be used to quickly merge a massive volume of data.

Medidas espectrais e cepstrais em mulheres com disfonia comportamental

ABSTRACT Purpose To investigate whether there are differences in cepstral and spectral acoustic measures between women with behavioral dysphonia with and without laryngeal lesions and verify whether there is a correlation between such measures and the auditory-perceptual evaluation of voice quality. Methods The sample comprised 78 women with behavioral dysphonia without laryngeal lesions (BDWOL) and 68 with behavioral dysphonia with laryngeal lesions (vocal nodules) (BDWL). Cepstral peak prominence (CPP), cepstral peak prominence-smoothed (CPPS), spectral decrease, and H1-H2 (difference between the amplitude of the first and second harmonics) were extracted. They were submitted to the auditory-perceptual evaluation (APE) of the grade of hoarseness (GH), roughness (RO), breathiness (BR), and strain (ST). Results BDWL women had higher H1-H2 values and lower CPP and CPPS values than BDWOL women. More deviant voices had lower CPP and CPPS values. Breathy voices had lower CPP and CPPS values and higher H1-H2 values than rough ones. There was a weak negative correlation between CPP and RO, a moderate negative correlation with GH, and a strong negative correlation with BR. CPPS had a moderate negative correlation with GH, RO, and BR. H1-H2 had a weak positive correlation with BR. There was a weak positive correlation between spectral decrease and ST. Conclusion H1-H2, CPP, and CPPS were different between BDWOL and BDWL women. Furthermore, cepstral and spectral measures were correlated with the different APE parameters.

Classes of completely monotone and Bernstein functions defined by convexity properties of their spectral measures

<abstract><p>We were interested in Bernstein and Lévy measures having certain convexity-type properties. The convexity-type properties were an extension of the harmonic convexity property considered in <sup>[<xref ref-type="bibr" rid="b9">9</xref>]</sup>. We characterized the corresponding completely monotone and Bernstein functions. We hope this paper can aid with understanding the analogous properties and open questions presented in <sup>[<xref ref-type="bibr" rid="b8">8</xref>,<xref ref-type="bibr" rid="b9">9</xref>]</sup>.</p></abstract>

Estimation of Spectral Risk Measure for Left Truncated and Right Censored Data

Estimation of Spectral Risk Measure for Left Truncated and Right Censored Data

Spectral peak analysis and intrinsic neural timescales as markers for the state of consciousness

Resting state EEG in patients with disorders of consciousness (DOC) is characterized by an increase of power in the delta frequency band and a concurrent decrease in the alpha range, equivalent to a weakening or disappearance of the alpha peak. Prolongation of Intrinsic Neural Timescales (INTs) is also associated with DOCs. Together, this raises the question whether the decreased alpha peak relates to the prolonged INTs and, importantly, how that can be used for diagnosing the state of consciousness in DOC individuals. Analyzing resting state EEG recordings from both healthy subjects and DOC patients, we measure INTs through autocorrelation window (ACW) and utilize peak analysis to quantify the weakening of the alpha peak. First, we replicate previous findings of prolonged ACW in DOC patients. We then identify significantly lower alpha peak measures in DOC compared to controls. Interestingly, spectral peaks shift from the alpha to the theta range in several DOC subjects while such change is absent in healthy controls. Next, our study reveals a close relationship between ACW and alpha peak in both healthy and DOC subjects, a correlation that holds for theta peaks in DOC. Further, the prolonged ACW correlates with the state of consciousness, as quantified by the Coma Recovery Scale-Revised (CRS-R), and mediates the relationship between theta peak and CRS-R. Finally, through split analyses and machine learning, we show that ACW and alpha peak measures conjointly distinguish healthy controls and DOC patients with high accuracy (95.5%). In conclusion, we demonstrate that the prolongation of ACW, together with spectral peak measures, holds promise to serve as additional EEG biomarkers for diagnosing the state of consciousness in DOC subjects.

Kernel-based estimation of spectral risk measures

Kernel-based estimation of spectral risk measures