Spectral Measure Research Articles

This research study delves into the spectral characteristics and energy measures associated with fuzzy graphs. We present the fuzzy geodetic spectrum and fuzzy detour spectrum, which capture the spectral properties of fuzzy graphs under geodetic and detour constraints. In addition, we propose and derive novel expressions for the fuzzy geodetic-Laplacian and detour-Laplacian energies, incorporating both upper and lower bounds. Towards the end, a real-world application of fuzzy geodetic-Laplacian energy pertaining to illegal immigration and human trafficking is described. It emphasizes its potential to improve decision-making measures, allowing more effective and coordinated crime prevention and resolution initiatives.

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a noncommutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understanding localization in non-Hermitian settings.

Multiple sclerosis (MS) is a chronic neuro-degenerative and inflammatory disease causing motor, sensory, and cognitive deficits, including impairments in working memory and attention. These cognitive deficits may arise from an imbalance between excitatory and inhibitory neural activity due to synaptic loss. Recent studies suggest that the aperiodic 1/f slope, a neural marker reflecting excitation/inhibition (E/I) balance, could serve as a biomarker for cognitive control. This study examines 1/f slope modulation during cognitive tasks in people with MS and healthy controls to investigate its potential as a paradigm-independent marker of cognitive control. We analyzed the Magnetoencephalography (MEG) data collected from 126 participants: 44 healthy controls (HCs), 61 people with MS not treated with benzodiazepines (pwMS(BZDn)), and 21 pwMS treated with benzodiazepines (pwMS(BZDp)). Participants performed an auditory oddball task and a visual-verbal n-back working memory task. After preprocessing MEG data, we used the specparam (formerly FOOOF) algorithm to extract the aperiodic 1/f slope from power spectral densities across 42 cortical parcels. Through this analysis, we observed significant steepening in the 1/f slope following stimulus onset for all stimulus types, with non-standard stimuli (targets and distractors) producing more pronounced effect (i.e., steeper slopes following stimulus onset). Compared to HCs, people with MS treated with benzodiazepines showed attenuated slope steepening in response to distractor stimuli, consistent with benzodiazepine-related impairments in inhibitory control. Moreover, unlike HCs, pwMS exhibited less steepening of 1/f slope response to distractors versus targets, indicating deficient phasic inhibition. Finally, in both HCs and pwMS(BZDn), the 1/f slope modulation was positively correlated across the auditory oddball and n-back tasks, pointing to a consistent, paradigm-independent neural mechanism. Taken together, these findings demonstrate that the aperiodic 1/f slope is a sensitive, paradigm-independent marker of cognitive control and E/I balance. The attenuated slope steepening in response to distractors in pwMS highlights disruptions in inhibitory neural processes underlying their cognitive deficits. These findings underscore the value of aperiodic spectral measures to deepen our understanding of cognitive impairments in MS.

Detection and rehabilitation of age-related motor skills impairment: Neurophysiological biomarkers and perspectives.

Abstract In this paper, we extend a criterion of Sodin on the convergence of graph spectral measures to regular graphs of growing degree. As a result, we show that for a sequence of random ‐regular graphs with vertices, if and tends to infinity, the normalized spectral measure converges almost surely in ‐Wasserstein distance to the semicircle distribution for any . This strengthens a result of Dumitriu and Pal. Many of the results are also extended to unitary‐colored regular graphs. For example, we give a short proof of the weak convergence to the Kesten–McKay distribution for the normalized spectral measures of random ‐lifts. This result is derived by generalizing a formula of Friedman involving Chebyshev polynomials and non‐backtracking walks.

Objective: Conduct a mega-analysis of two complementary measures of resting-state functional magnetic resonance imaging (rsfMRI) dynamics-amplitude of low-frequency fluctuation (ALFF) and low-frequency spectral entropy (lfSE)-in mood and psychosis-spectrum disorders to evaluate group differences and clinical symptom associations.Design: ALFF and lfSE were calculated at the node-level by filtering data from 0.01 Hz to 0.08 Hz, regressing demographic variables, and harmonizing sites. Group differences were assessed using the Wilcoxon signed test. Symptom associations were evaluated with Spearman's rho. Analyses were conducted at both whole-brain and network levels, with sensitivity analyses to evaluate the impact of frequency brands.Setting: Four independent open-source case-control datasets with resting-state functional magnetic resonance imaging were used: the Center for Biomedical Research Excellence, the Human Connectome Project for Early Psychosis, the Strategic Research Program for Brain Sciences, and the UCLA Consortium for Neuropsychiatric Phenomics.Participants: Included participants had a mood disorder (bipolar, dysthymia, or major depressive disorder, n=228, aged 38.31 ± 12.56 years), a psychosis-spectrum disorder (early psychosis, schizophrenia spectrum disorder, or mood disorder with psychotic symptoms, n=318, aged 29.8 ± 13.21 years), or a healthy control (n=535, aged 39.89 ± 15.3 years).Main outcomes and Measures: To identify group differences and symptom associations in mood and psychosis-spectrum disorders using ALFF and lfSE.Results: ALFF in psychosis-spectrum was significantly lower than mood disorders and controls (q's<0.001) at the whole-brain and network levels. lfSE in controls was significantly lower than both psychosis-spectrum and mood disorders at the whole-brain and network levels (q's<0.001). Whole-brain ALFF is positively associated with mood symptoms (rho=0.27, p<0.05). Whole-brain lfSE is negatively associated with positive (rho=-0.13, p<0.05) and mood (rho=-0.38, p<0.01) symptoms. A greater sensitivity of group differences and symptom associations to frequency ranges was observed in mood disorders. ALFF is sensitive to medication.Conclusions and Relevance: Widespread, global differences in ALFF and lfSE underly psychosis-spectrum and mood disorders. lfSE may be applicable for wider use in fMRI. Differences in spectral measures of brain dynamics may represent shared and distinct markers of mental health.

Anthropogenic noise may affect the spectral and temporal structures of contact calls in wild non-human primates. However, most studies have compared groups living at varying distances from noise sources, while few have focused on the relationship between specific noise types and vocalizations at the individual level, which is necessary to examine vocal plasticity. We aimed to clarify the effects of background noise on the acoustic characteristics of coo calls of Japanese macaques on an individual basis; thus, we examined the effects of noise levels, behavioral context, and number of individuals in proximity on the duration and spectral measure of calls. We conducted focal observations of adult female Japanese macaques, and recorded coo calls and background noise levels. We analyzed 128 calls from nine subjects and found that the start and mean frequencies of coo calls were higher at higher noise levels. The call duration and frequency modulations were higher when the number of individuals in proximity was lower and the end frequency was higher during foraging and moving. These findings suggest that different factors affect the acoustic characteristics of the coo calls of Japanese macaques simultaneously. The most intense background noise sources were typically low-frequency sources that overlapped the frequency bands of the calls. Hence, they exerted a profound influence on call acoustics, which is consistent with the results of previous studies. Within-individual adjustments to ambient noise indicate vocal plasticity, enabling efficient signal transmission to the receiver.

Distinct neurodynamics of functional brain networks in Alzheimer's disease and frontotemporal dementia as revealed by EEG.

We investigate the interplay between parity-time-symmetry (PT-symmetry) breaking and localization transitions in non-Hermitian spin chains with an Aubry-André potential and competing Dzyaloshinskii-Moriya (DM) interactions. While prior studies (e.g., [S. Longhi, Phys. Rev. Lett. 122, 237601 (2019)0031-900710.1103/PhysRevLett.122.237601]) suggest a universal alignment of PT transitions and delocalization, our analysis of next-nearest-neighbor DM couplings reveals a critical deviation: the two phenomena decouple in certain parameter regimes, despite coinciding for nearest-neighbor interactions. Through eigenvalue analysis and inverse/normalized participation ratios (IPR/NPR), we identify three distinct phases: (i) extended states (weak potential), (ii) localized states (strong potential), and (iii) an intermediate hybrid phase unique to next-nearest-neighbor DM couplings. To unravel the dynamical fingerprints of these phases, we track the time-dependent density propagation, long-time survival probability, and phase-sensitive Loschmidt echo. The density evolution exhibits ballistic spreading in extended phases versus localized confinement, while the survival probability's decay rate, exponential in localized regimes versus algebraic in extended ones, serves as a clear phase discriminator. Notably, quenches between phases induce distinct dynamical signatures, with the Loschmidt echo sharply reflecting phase boundaries through its decay profile. These results establish dynamical metrics as indispensable tools for characterizing non-Hermitian phase transitions beyond spectral or localization measures.

Hyperscanning approaches mark a shift from single- to two-person neuroscience, enabling a more profound understanding of the neural mechanisms underlying interpersonal synchronization. In this context, functional near-infrared spectroscopy (fNIRS) has emerged as a valuable tool for measuring brain activity in a natural, unconstrained environment. While interpersonal synchrony using fNIRS hyperscanning has been well-studied using statistical association analysis, establishing causal relationships that elucidate the direction of influence remains challenging. This study aimed to investigate the feasibility of determining the direction of influence in dyadic interactions. Since the ground truth of such direction is not available in a natural setting, we validated our approach in an experimental setup in which we controlled the direction of influence between two subjects by assigning them the roles of "Model" and "Imitator" of specified motor tasks. A total of 22 participants, hence 11 dyads, completed the task in a within-subject design. We adapted concepts from spectral causal effect decomposition theories to formulate a new measure of the direction and intensity of influence. The results demonstrate that the direction of influence in fNIRS data can be detected with an accuracy in the range of 62%-71%. Furthermore, the proposed spectral causality measure was shown to significantly reduce spurious causal relationships due to the confounding effects of physiological processes and measurement artifacts compared to time domain causal analysis.

Quantitative electroencephalography characteristics in delirium with various etiologies: A multicenter study.

Abstract We establish higher-order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator of the contractions and significantly enlarging the set of admissible functions. We also derive higher-order trace formulas for maximal dissipative operators under relaxed assumptions and new simplified trace formulas for unitary and resolvent comparable self-adjoint operators. The respective spectral shift measures are absolutely continuous and, in the case of contractions, the set of admissible functions for the nth-order trace formula on the unit circle includes the Besov class $B^n_{\infty , 1}(\mathbb {T})$ . Both aforementioned properties are new in the mentioned generality.

The Poincaré plot was introduced as a tool to analyze heart rate variations caused by arrhythmias. Later, it was applied to time series with normal beats. The plot shows the relationship between the inter-beat interval (IBI) of one beat to the next. Several parameters were developed to characterize this relationship. The short and long axis of the fitting ellipse, SD1 and SD2, respectively, their ratio, and their product are used. The difference between the IBI of a beat and m beats later are also studied, SD1(m) and SD2(m). We studied the mathematical relations between heart rate variability measures and the Poincaré measures in the time (standard deviation of IBI, SDNN, root mean square of successive differences, RMSSD) and frequency domain (power in low and high frequency band, and their ratio). We concluded that SD1 and SD2 do not provide new information compared to SDNN and RMSSD. Only the correlation coefficient r(m) provides new information for m > 1. Novel findings are that ln(SD2(m)/SD1(m)) = tanh−1(r(m)), which is an approximately normal distributed transformation of r(m), and that SD1(m) and SD2(m) can be calculated by multiplying the power spectrum by a weighing function that depends on m, revealing the relationship with spectral measures, but also the relationship between SD1(m) and SD2(m). Both lagged parameters are extremely difficult to interpret compared to low and high frequency power, which are more closely related to the functioning of the autonomic nervous system.

Alzheimer's disease is the most prevalent neurodegenerative disorder leading to progressive cognitive decline and functional impairment. Although advanced neuroimaging and cerebrospinal fluid biomarkers have improved early detection, their high costs, invasiveness, and limited accessibility restrict universal screening. Quantitative electroencephalography (qEEG) offers a non-invasive and cost-effective alternative for assessing neurophysiological changes associated with AD. This review critically evaluates current evidence on EEG biomarkers, including spectral, connectivity, and complexity measures, discussing their pathophysiological basis, diagnostic accuracy, and clinical utility in AD. Limitations and future perspectives, especially in developing standardized protocols and integrating machine learning techniques, are also addressed.

Objective.Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an established therapy for Parkinson's disease (PD). Yet, optimizing lead placement and stimulation programming remains challenging. Current techniques rely on imaging and intraoperative microelectrode recordings (MER), while programming relies on trial-and-error clinical testing, which can be time-consuming. DBS-induced local evoked potentials (DLEP), also known as evoked resonant neural activity, have emerged as a potential alternative electrophysiological marker for mapping. However, direct comparisons with traditional spectral features, such as beta-band, high-frequency oscillations (HFOs), and aperiodic component are lacking.Approach.We evaluated DLEP across 39 STN DBS leads in 31 subjects with PD undergoing DBS surgery, using both a single-pulse and high-frequency (HF) burst stimulation paradigms. We developed a novel artifact-removal method to enable monopolar DLEP recovery, including estimating the DLEP amplitudes at stimulated contacts, further enhancing spatial sampling of DLEP. We evaluated spectral features and DLEP in respect to imaging-based and MER-based localization, and its predictive power for post-operative programming.Main results.DLEP showed great spatial consistency, maximizing within STN with 100% accuracy for single-pulse and 84.62% for burst stimulation, surpassing spectral measures including beta (89.74%) and HFO (82.05%). DLEP better correlated with clinical outcomes (single-pulsesρ= -0.33, HF burstsρ= -0.26), than spectral measures (betaρ= -0.25, HFOρ= 0.05). Furthermore, single-pulses at low-frequencies are sufficient for DLEP-based mapping.Significance.We show how DLEP provide higher STN-spatial specificity and correlation with postoperative programming compared to spectral features. To support clinical translation of DLEP, we developed two methods aimed to recover artifact-free DLEP and estimating DLEP amplitudes at stimulating contacts. DLEP appear distinct from beta and HFO activity, yet strongly tied to aperiodic spectral components, suggesting that DLEP amplitude reflects underlying STN excitability. This study highlights that DLEP are a robust and clinically valuable marker for DBS targeting and programming.

Abstract The paper deals with the spectral theory of a class of non-self-adjoint convolution operators whose entries are circulant matrices. We show that such operators are of scalar type and provide exact formulas for their spectral measures. The general case of operators defined on Banach spaces is also considered.

The co-ocurrence of phonological word-level stress and tone is cross-linguistically rare. Word-level stress is a complex cluster concept that involves a number of different dimensions making it a cross-linguistically challenging topic. This study investigates the status of stress and tone in an underdocumented language taking into consideration several dimensions that are known to interact with stress marking cross-linguistically. Central Pame is an Otomanguean language whose word prosodic system has been impressionistically described as one with stress and tone, with a three-way tonal contrast. This study presents the first quantitative investigation of the acoustic correlates duration, intensity, formant structure, spectral tilt, and fundamental frequency in the language. Results indicate that duration is longer in stressed than in deaccented syllables. Intensity and, to some degree, spectral tilt measures are also affected by stress. Additionally, we find evidence for a three-way tonal contrast marked with fundamental frequency and duration and which varies between female and male speakers.

The large degree scaling spectrum of spectral measures with consecutive digits

Spectra of the Sierpiński type spectral measure and their Beurling dimensions

In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality measure of these polynomials, as well as the spectral measure for the associated doubly infinite tridiagonal Jacobi matrix. Notably, while the orthogonality measure may include discrete mass points, the spectral measure(s) of the doubly infinite Jacobi matrix are absolutely continuous. Additionally, we uncover an intrinsic connection between these new orthogonal polynomials and Chebyshev polynomials through a nonlinear transformation of the polynomial variables.