Spectral Measure Research Articles

A novel methodology for gamma-ray spectra dataset procurement over varying standoff distances and source activities

The adoption of machine learning approaches for gamma-ray spectroscopy has received considerable attention in the literature. Many studies have investigated the deployment of various algorithm architectures to a specific task. However, little attention has been afforded to the development of the datasets leveraged to train the models. Such training datasets typically span a set of environmental or detector parameters to encompass a problem space of interest to a user. Variations in these measurement parameters will also induce fluctuations in the detector response, including expected pile-up and ground scatter effects. Fundamental to this work is the understanding that 1) the underlying spectral shape varies as the measurement parameters change and 2) the statistical uncertainties associated with two spectra impact their level of similarity. While previous studies attribute some arbitrary discretization to the measurement parameters for the generation of their synthetic training data, this work introduces a principled methodology for efficient spectral-based discretization of a problem space. A signal-to-noise ratio (SNR) respective spectral comparison measure and a Gaussian Process Regression (GPR) model are used to predict the spectral similarity across a range of measurement parameters. This innovative approach effectively showcased its capability by dividing a problem space, ranging from 5 cm to 100 cm standoff distances and 5 μCi–100 μCi of 137Cs, into three unique combinations of measurement parameters. The findings from this work will aid in creating more robust datasets, which incorporate many possible measurement scenarios, reduce the number of required experimental test set measurements, and possibly enable experimental training data collection for gamma-ray spectroscopy.

PaRaVis: An automatic Python graphical package for ensemble analysis of plant beta diversity using remote sensing proxies

The ongoing impacts of climatic changes, coupled with intensified human activities, are leading to a significant loss of plant diversity, prompting urgent calls for comprehensive monitoring of forest ecosystems. This is particularly concerning in regions with the encroachment of human activities into forest zones, and inadequate regulations that primarily view forests as a source of timber without fully accounting for their critical roles in biodiversity. These issues highlight the need for effective geospatial approaches to support conservation strategies and sustained monitoring of plant diversity. The majority of remote sensing studies of plant diversity have focused on alpha-diversity, while beta-diversity plays an important role in providing a comprehensive picture of biodiversity patterns across scales. Among various remote sensing proxies, Rao's Q index stands out as a reliable metric to quantify beta-diversity using multispectral remote sensing indices. However, a holistic approach that can incorporate multiple remote sensing indices and enable comparative analysis using graphical means with computational efficiency is lacking. In response, we developed PaRaVis, an open-source Python-based graphical package for deriving spectral diversity from multispectral remote sensing datasets as a proxy for functional diversity using Rao's Q index. This tool encompasses all the necessary steps for parallelized computation, visualization, and analysis of Rao's index from either single or multiple multispectral indices. It is capable of calculating and visualizing 75 vegetation indices (VIs), from a raster scene, followed by calculating Rao's Q both unidimensionally and multidimensionally in parallel. PaRaVis also offers features for visualizing, analyzing, and comparing Rao's Q outputs using statistical performance diagnostics. It provides a unique means to infer diversity patterns in space and time and is therefore invaluable for researchers or organizations involved with plant diversity monitoring, especially those with limited data analysis or computer programming experience. To demonstrate the tool's effectiveness, we analyzed plant diversity patterns using satellite-derived spectral heterogeneity measures in forest sites within the Hyrcanian Forests of Iran and sites located in Germany. The first case study focused on UNESCO Natural Heritage sites. Our analysis revealed that employing EVI, SR3, and TCI indices as inputs for the multidimensional Rao's Q yielded higher performance in monitoring more heterogeneous forests compared to the unidimensional mode. In the second case study, we utilized field Species Richness and Shannon-Wiener diversity indices to evaluate PaRaVis and our method. We found that using a multi-temporal, multi-index approach enhances the results compared to multi-seasonal and classical Rao based on single time.

A Multitask Network Robustness Analysis System Based on the Graph Isomorphism Network.

Despite various measures across different engineering and social systems, network robustness remains crucial for resisting random faults and malicious attacks. In this study, robustness refers to the ability of a network to maintain its functionality after a part of the network has failed. Existing methods assess network robustness using attack simulations, spectral measures, or deep neural networks (DNNs), which return a single metric as a result. Evaluating network robustness is technically challenging, while evaluating a single metric is practically insufficient. This article proposes a multitask analysis system based on the graph isomorphism network (GIN) model, abbreviated as GIN-MAS. First, a destruction-based robustness metric is formulated using the destruction threshold of the examined network. A multitask learning approach is taken to learn the network robustness metrics, including connectivity robustness, controllability robustness, destruction threshold, and the maximum number of connected components. Then, a five-layer GIN is constructed for evaluating the aforementioned four robustness metrics simultaneously. Finally, extensive experimental studies reveal that 1) GIN-MAS outperforms nine other methods, including three state-of-the-art convolutional neural network (CNN)-based robustness evaluators, with lower prediction errors for both known and unknown datasets from various directed and undirected, synthetic, and real-world networks; 2) the multitask learning scheme is not only capable of handling multiple tasks simultaneously but more importantly it enables the parameter and knowledge sharing across tasks, thus preventing overfitting and enhancing the performances; and 3) GIN-MAS performs multitasks significantly faster than other single-task evaluators. The excellent performance of GIN-MAS suggests that more powerful DNNs have great potentials for analyzing more complicated and comprehensive robustness evaluation tasks.

Graph-Based Electroencephalography Analysis in Tinnitus Therapy.

Tinnitus is the perception of sounds like ringing or buzzing in the ears without any external source, varying in intensity and potentially becoming chronic. This study aims to enhance the understanding and treatment of tinnitus by analyzing a dataset related to tinnitus therapy, focusing on electroencephalography (EEG) signals from patients undergoing treatment. The objectives of the study include applying various preprocessing techniques to ensure data quality, such as noise elimination and standardization of sampling rates, and extracting essential features from EEG signals, including power spectral density and statistical measures. The novelty of this research lies in its innovative approach to representing different channels of EEG signals as new graph network representations without losing any information. This transformation allows for the use of Graph Neural Networks (GNNs), specifically Graph Convolutional Networks (GCNs) combined with Long Short-Term Memory (LSTM) networks, to model intricate relationships and temporal dependencies within the EEG data. This method enables a comprehensive analysis of the complex interactions between EEG channels. The study reports an impressive accuracy rate of 99.41%, demonstrating the potential of this novel approach. By integrating graph representation and deep learning, this research introduces a new methodology for analyzing tinnitus therapy data, aiming to contribute to more effective treatment strategies for tinnitus sufferers.

Estimates and higher-order spectral shift measures in several variables

In recent years, higher-order trace formulas of operator functions have attracted considerable attention to a large part of the perturbation theory community. In this direction, we prove estimates for traces of higher-order derivatives of multivariate operator functions with associated scalar functions arising from multivariate analytic function space and, as a consequence, derive higher-order spectral shift measures for pairs of tuples of commuting contractions under Hilbert-Schmidt perturbations. These results substantially extend the main results of [26], where the estimates were proved for traces of first and second-order derivatives of multivariate operator functions. In the context of the existence of higher-order spectral shift measures, our results extend the relative results of [6,20] from a single-variable to a multivariate case under Hilbert-Schmidt perturbations. Our results rely crucially on heavy uses of explicit expressions of higher-order derivatives of operator functions and estimates of the divided difference of multivariate analytic functions, which are developed in this paper, along with the spectral theorem of tuple of commuting normal operators. In conclusion, we explore the significance of our results and provide relevant examples.

Spectrality of infinite convolutions and random convolutions

In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis. Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize spectrality of infinite convolutions generated by a sequence of admissible pairs. Then we delve into the analysis of the integral periodic zeros set. Finally, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions in some special cases.

Consistent spectral approximation of Koopman operators using resolvent compactification

Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The extraction of approximate Koopman or transfer operator eigenfunctions (and the associated eigenvalues) from an unknown system is nontrivial, particularly if the system has mixed or continuous spectrum. In this paper, we describe a spectrally accurate approach to approximate the Koopman operator on L 2 for measure-preserving, continuous-time systems via a ‘compactification’ of the resolvent of the generator. This approach employs kernel integral operators to approximate the skew-adjoint Koopman generator by a family of skew-adjoint operators with compact resolvent, whose spectral measures converge in a suitable asymptotic limit, and whose eigenfunctions are approximately periodic. Moreover, we develop a data-driven formulation of our approach, utilizing data sampled on dynamical trajectories and associated dictionaries of kernel eigenfunctions for operator approximation. The data-driven scheme is shown to converge in the limit of large training data under natural assumptions on the dynamical system and observation modality. We explore applications of this technique to dynamical systems on tori with pure point spectra and the Lorenz 63 system as an example with mixing dynamics.

Wind energy relevant characteristics of turbulence over boreal forests

Turbulence statistics from three tall meteorological masts and LES in forested landscapes are compared to standard turbulence models used for wind turbine design. The comparison is split into different atmospheric conditions to highlight the impact of stratification on the character of turbulence. The aim of the work is to clarify to which extent standard turbulence models are accurate over forested regions. To this end, different spectral measures such as power spectra and coherence are examined as well as vertical profiles of turbulence characteristics relevant to the design and siting of wind turbines. The measurements are used to investigate vertically separated 2-point statistics and the LES to investigate laterally separated statistics. The results show that in neutral stratification and for smaller separation distances, in the order of half a radius, the standard turbulence models apply, but in non-neutral stratification, particularly in stable conditions and for larger separations the disparity between observations and standard turbulence grow. This effect is mainly attributed to the effect of stratification, while features in the turbulence statistics specifically related to the forest cover is absent at heights relevant to wind energy. The results of the study are expected to be of interest for turbine design purposes as well as wind resource estimation and wind modelling in forested areas.

Quantitative electroencephalography in cerebral amyloid angiopathy

ObjectiveWe investigated whether quantitative electroencephalography (qEEG) correlates with cognition and cortical superficial siderosis (cSS) in cerebral amyloid angiopathy. MethodsWe included patients with sporadic (sCAA) and hereditary Dutch-type CAA (D-CAA). Spectral measures and the phase lag index (PLI) were analyzed on qEEG. Cognition was assessed with the MoCA and cSS presence was scored on 3T-MRI. Linear regression analyses were performed to investigate these qEEG measures and cognition. Independent samples T-tests were used to analyze the qEEG measure differences between participants with and without cSS. ResultsWe included 92 participants (44 D-CAA; 48 sCAA). A lower average peak frequency (β[95 %CI] = 0.986[0.252–1.721]; P = 0.009) and a higher spectral ratio (β[95 %CI] = −0.918[−1.761–−0.075]; P = 0.033) on qEEG correlated with a lower MoCA score, irrespective of a history of symptomatic intracerebral hemorrhage (sICH). The PLI showed no correlation to the MoCA. qEEG slowing was not different in those with or without cSS. ConclusionsSpectral qEEG (but not PLI) reflects cognitive performance in patients with CAA with and without a history of sICH. We found no association between qEEG slowing and cSS. SignificanceqEEG could be a valuable biomarker, especially in challenging cognitive testing situations in CAA, and a potential predictive tool in future studies.

TransExION: a transformer based explainable similarity metric for comparing IONS in tandem mass spectrometry

Small molecule identification is a crucial task in analytical chemistry and life sciences. One of the most commonly used technologies to elucidate small molecule structures is mass spectrometry. Spectral library search of product ion spectra (MS/MS) is a popular strategy to identify or find structural analogues. This approach relies on the assumption that spectral similarity and structural similarity are correlated. However, popular spectral similarity measures, usually calculated based on identical fragment matches between the MS/MS spectra, do not always accurately reflect the structural similarity. In this study, we propose TransExION, a Transformer based Explainable similarity metric for IONS. TransExION detects related fragments between MS/MS spectra through their mass difference and uses these to estimate spectral similarity. These related fragments can be nearly identical, but can also share a substructure. TransExION also provides a post-hoc explanation of its estimation, which can be used to support scientists in evaluating the spectral library search results and thus in structure elucidation of unknown molecules. Our model has a Transformer based architecture and it is trained on the data derived from GNPS MS/MS libraries. The experimental results show that it improves existing spectral similarity measures in searching and interpreting structural analogues as well as in molecular networking.Scientific ContributionWe propose a transformer-based spectral similarity metrics that improves the comparison of small molecule tandem mass spectra. We provide a post hoc explanation that can serve as a good starting point for unknown spectra annotation based on database spectra.

Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on Zd -covers, thus proving a strong form of Krickeberg mixing. We also prove that the spectral measures around 0 of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.

Spectrality of homogeneous Moran measures on the plane

LetM=ρ1−1a0ρ2−1 be a real upper triangular expanding matrix and D=00,d10,d2d3 be a three-element real digit set with d1d3≠0 , and let {nk}k=1∞ be a sequence of positive integers with upper bound. The infinite convolutions μM,D,{nk}=δM−n1D∗δM−(n1+n2)D∗⋯∗δM−(n1+⋯+nk)D∗⋯ converges weakly to a Borel probability measure (homogeneous Moran measure). In this paper, we study the existence of exponential orthonormal basis for L2(μM,D,{nk}). A necessary and sufficient condition for μM,D,{nk} to be a spectral measure is established.

A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability.

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of clear spectral representation. We embed into the linear parametric framework for computing GC from a driver X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of arterial pressure and cerebral blood flow obtained in syncope subjects and healthy controls. Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to orthostasis in syncope subjects, likely related to impaired cerebral autoregulation. The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect pathophysiological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled processes in both physiological and clinical investigations.

Differential spectral characteristics of the Spanish fricative /s/ in the articulation of individuals with dysarthria and apraxia of speech

PurposeThis study examines whether there are differences in the speech of speakers with dysarthria, speakers with apraxia and healthy speakers in spectral acoustic measures during production of the central-peninsular Spanish alveolar sibilant fricative /s/. MethodTo this end, production of the sibilant was analyzed in 20 subjects with dysarthria, 8 with apraxia of speech and 28 healthy speakers. Participants produced 12 sV(C) words. The variables compared across groups were the fricative's spectral amplitude difference (AmpD) and spectral moments in the temporal midpoint of fricative execution. ResultsThe results indicate that individuals with dysarthria can be distinguished from healthy speakers in terms of the spectral characteristics AmpD, standard deviation (SD), center of gravity (CoG) and skewness, the last two in context with unrounded vowel, while no differences in kurtosis were detected. Participants with AoS group differ significantly from healthy speaker group in AmpD, SD and CoG and Kurtosis, the first one followed unrounded vowel and the latter two followed by rounded vowels. In addition, speakers with apraxia of speech group returned significant differences with respect to speakers with dysarthria group in AmpD, CoG and skewness. ConclusionsThe differences found between the groups in the measures studied as a function of the type of vowel context could provide insights into the distinctive manifestations of motor speech disorders, contributing to the differential diagnosis between apraxia and dysarthria in motor control processes.

Spectral Density Estimation for a Class of Spectrally Correlated Processes

We study the estimation problem of the spectral density function for harmonizable non‐stationary processes. More precisely, we consider spectrally correlated processes whose spectral measure has the support contained in the union of unknown lines with possibly non‐unit slopes. We propose the frequency‐smoothed periodogram along the estimated support line as an estimator of the spectral density function. We show the mean‐square consistency of the proposed estimator. Additionally, we discuss the estimation of the support line in a specific model with its applications in locating a moving source. Finally, we present simulations confirming the proven results.

Validation of Raman spectroscopic models to verify the origin of Australian beef grown under different production systems

Verification of beef production systems and authentication of origin is becoming increasingly important as consumers base purchase decisions on a greater number of perceived values including the healthiness and environmental impact of products. Previously Raman spectroscopy has been explored as a tool to classify carcases from grass and grain fed cattle. Thus, the aim of the current study was to validate Partial Least Squares Discriminant Analysis (PLS-DA) models created using independent samples from carcases sampled from northern and southern Australian production systems in 2019, 2020 and 2021. Validation of the robustness of discrimination models was undertaken using spectral measures of fat from 585 carcases which were measured in 2022 using a Raman handheld device with a sample excised for fatty acid analysis. PLS-DA models were constructed and then employed to classify samples as either grass or grain fed in a two-class model. Overall, predictions were high with accuracies of up to 95.7% however, variation in the predictive ability was noted with models created for southern cattle yielding an accuracy of 73.2%. While some variation in fatty acids and therefore models can be attributed to differences in genetics, management and diet, the impact of duration of feeding is currently unknown and thus further work is warranted.

Modulus of continuity for spectral measures of suspension flows over Salem type substitutions

Modulus of continuity for spectral measures of suspension flows over Salem type substitutions

Temporal, spectral and amplitude characteristics of the Greek fricative /s/ in hearing-impaired and normal-hearing speech

ABSTRACT Fricatives, and especially sibilants, are very frequently misarticulated by speakers with hearing loss. Misarticulations can result in phonemic contrast weakening or loss, compromising intelligibility. The present study focuses on the examination of acoustic characteristics of the Greek alveolar fricative /s/, an articulatorily demanding sound, produced by young adult speakers with profound hearing impairment and with normal hearing. An array of variables was examined using mixed-effects and random forest models aiming to assess the effectiveness of various measures in differentiating hearing-impaired and normal-hearing /s/ production. Significant differences were found in spectral and amplitude measures, but not in temporal measures. In hearing-impaired speech, spectral slope and RMS amplitude had significantly lower values, indicating a more distributed spectrum, suggestive of decreased flow velocity through the fricative constriction. Also, a trend for concentration of energy at lower frequencies was observed suggesting more posterior fricative articulation than normal. Moreover, measures capturing the variation of frequency and amplitude over time revealed different patterns of sibilance development across time than normal, denoting the production of a less well-formed or less sibilant /s/ by speakers with hearing impairment. The investigation of contextual effects on /s/ in hearing-impaired speech showed increased spectral variance, negative skewness and lower kurtosis in the labial (rounded) context /u/ in relation to the nonlabial contexts /i/ and /a/, indicating a more diffuse, less compact spectrum with concentration at high frequencies. Findings are discussed in relation to previous literature on fricative production by speakers with hearing impairment and normal hearing in Greek and other languages.

Identifying System Non-Linearities by Fusing Signal Bispectral Signatures

Higher-order statistics investigate the phase relationships between frequency components, an aspect which cannot be treated using conventional spectral measures such as the power spectrum. Among the widely used higher-order statistics, the bispectrum ranks prominently. By delving into higher-order correlations, the bispectrum offers a means of extracting additional merits and insights from frequency coupling, enhancing our understanding of complex signal interactions. This analytical approach overcomes the limitations of traditional methods, providing a more comprehensive view of the complex relationships within the frequency domain. In this paper, the extensive use of the bispectrum in various scientific and technical areas is firstly emphasized by presenting very recent applications. The main scope of this work is to investigate the consequences of various non-linearities in the creation of phase couplings. Specifically, the quadratic, the cubic and the logarithmic non-linearities are examined. In addition, simple recommendations are given on how the underlying nonlinearity could be detected. The total approach is novel, considering the capability to distinguish from the bispectral content if two non-linearities are simultaneously present.

Exploring an application-oriented land-based hyperspectral target detection framework based on 3D–2D CNN and transfer learning

Target detection based on hyperspectral images refers to the integrated use of spatial information and spectral information to accomplish the task of localization and identification of targets. There are two main methods for hyperspectral target detection: supervised and unsupervised methods. Supervision method refers to the use of spectral differences between the target to be tested and the surrounding background to identify the target when the target spectrum is known. In ideal situations, supervised object detection algorithms perform better than unsupervised algorithms. However, the current supervised object detection algorithms mainly have two problems: firstly, the impact of uncertainty in the ground object spectrum, and secondly, the universality of the algorithm is poor. A hyperspectral target detection framework based on 3D–2D CNN and transfer learning was proposed to solve the problems of traditional supervised methods. This method first extracts multi-scale spectral information and then preprocesses hyperspectral images using multiple spectral similarity measures. This method not only extracts spectral features in advance, but also eliminates the influence of complex environments to a certain extent. The preprocessed feature maps are used as input for 3D–2D CNN to deeply learn the features of the target, and then, the softmax method is used to output and obtain the detection results. The framework draws on the ideas of integrated learning and transfer learning, solves the spectral uncertainty problem with the combined similarity measure and depth feature extraction network, and solves the problem of poor robustness of traditional algorithms by model migration and parameter sharing. The area under the ROC curve of the proposed method has been increased to over 0.99 in experiments on both publicly available remote sensing hyperspectral images and measured land-based hyperspectral images. The availability and stability of the proposed method have been demonstrated through experiments. A feasible approach has been provided for the development and application of specific target detection technology in hyperspectral images under different backgrounds in the future.