Standard Spectral Methods Research Articles

Alpha coherence is a network signature of cognitive recovery from disorders of consciousness.

Alpha (8-12 Hz) frequency band oscillations are among the most informative features in electroencephalographic (EEG) assessment of patients with disorders of consciousness (DoC). Because interareal alpha synchrony is thought to facilitate long-range communication in healthy brains, coherence measures of resting-state alpha oscillations may provide insights into a patients capacity for higher-order cognition beyond channel-wise estimates of alpha power. In multi-channel EEG, global coherence methods may be used to augment standard spectral analysis methods by both estimating the strength and identifying the structure of coherent oscillatory networks. We performed global coherence analysis in 95 separate clinical EEG recordings (28 healthy controls and 33 patients with acute or chronic DoC, 25 of whom returned for follow-up) collected between two academic medical centers. We found that posterior alpha coherence is associated with recovery of higher-level cognition. We developed a measure of network organization, based on the distance between eigenvectors of the alpha cross-spectral matrix, that detects recovery of posterior alpha networks. In patients who have emerged from a minimally conscious state, we showed that coherence-based alpha networks are reconfigured prior to restoration of alpha power to resemble those seen in healthy controls. This alpha network measure performs well in classifying recovery from DoC (AUC = 0.78) compared to common representations of functional connectivity using the weighted phase lag index (AUC = 0.50 - 0.57). Lastly, we observed that activity within these alpha networks is suppressed during positive responses to task-based EEG command-following paradigms, supporting the potential utility of this biomarker to detect covert cognition. Our findings suggest that restored alpha networks may represent a sensitive early signature of cognitive recovery in patients with DoC. Therefore, network detection methods may augment the utility of EEG assessments for DoC.

An algorithm for correction of atmospheric scattering dilution effects in volcanic gas emission measurements using skylight differential optical absorption spectroscopy

Differential Optical Absorption Spectroscopy (DOAS) is commonly used to measure gas emissions from volcanoes. DOAS instruments measure the absorption of solar ultraviolet (UV) radiation scattered in the atmosphere by sulfur dioxide (SO2) and other trace gases contained in volcanic plumes. The standard spectral retrieval methods assume that all measured light comes from behind the plume and has passed through the plume along a straight line. However, a fraction of the light that reaches the instrument may have been scattered beneath the plume and thus has passed around it. Since this component does not contain the absorption signatures of gases in the plume, it effectively “dilutes” the measurements and causes underestimation of the gas abundance in the plume. This dilution effect is small for clean-air conditions and short distances between instrument and plume. However, plume measurements made at long distance and/or in conditions with significant atmospheric aerosol, haze, or clouds may be severely affected. Thus, light dilution is regarded as a major error source in DOAS measurements of volcanic degassing. Several attempts have been made to model the phenomena and the physical mechanisms are today relatively well understood. However, these models require knowledge of the local atmospheric aerosol composition and distribution, parameters that are almost always unknown. Thus, a practical algorithm to quantitatively correct for the dilution effect is still lacking. Here, we propose such an algorithm focused specifically on SO2 measurements. The method relies on the fact that light absorption becomes non-linear for high SO2 loads, and that strong and weak SO2 absorption bands are unequally affected by the diluting signal. These differences can be used to identify when dilution is occurring. Moreover, if we assume that the spectral radiance of the diluting light is identical to the spectrum of light measured away from the plume, a measured clean air spectrum can be used to represent the dilution component. A correction can then be implemented by iteratively subtracting fractions of this clean air spectrum from the measured spectrum until the respective absorption signals on strong and weak SO2 absorption bands are consistent with a single overhead SO2 abundance. In this manner, we can quantify the magnitude of light dilution in each individual measurement spectrum as well as obtaining a dilution-corrected value for the SO2 column density along the line of sight of the instrument. This paper first presents the theory behind the method, then discusses validation experiments using a radiative transfer model, as well as applications to field data obtained under different measurement conditions at three different locations; Fagradalsfjall located on the Reykjanaes peninsula in south Island, Manam located off the northeast coast of mainland Papua New Guinea and Holuhraun located in the inland of north east Island.

Pressure fluctuations in a gas-solid fluidized bed at temperatures up to 1650 °C

Fluidized beds operating at ultra-high temperatures have great application potential for synthesizing essential materials and chemicals, but they are relatively unexplored. This study, for the first time, investigates fluidization characteristics at temperatures up to 1650 °C by measurement and analysis of pressure fluctuations in a laboratory fluidized bed of 30 mm diameter with corundum particles of an average size of 900 μm. Standard statistical and spectral methods are used to analyze pressure fluctuation signals and characterize fluidization behavior based on the effect of temperature on pressure fluctuation parameters, including the probability density function, standard deviation, autocorrelation, power spectra density, amplitude, dominant frequency, and average cycle frequency. The results indicate that, for the coarse corundum particles used in this study, fluidization behavior inverts at a crucial temperature of approximately 1400 °C. Below this temperature, gas–solid flows in the bed are predominantly controlled by gas bubble movements. In this temperature range, periodicity and maximum amplitude decrease and dominant frequency increases with temperature. Above 1400 °C, interparticle forces, such as van der Waals and viscous forces, are significantly strengthened due to changes in the structural and physiochemical properties of solid materials. The greatly enhanced interparticle forces at ultra-high temperatures promote the dominance of microstructured flows over the overall pressure fluctuations, making interparticle forces the controlling factor influencing gas–solid flows in fluidized beds at ultra-high temperatures. These findings provide a better understanding of ultra-high temperature fluidized beds and can promote their research and development for industrial applications.

Extended Tromograph Surveys for a Full Experimental Characterisation of the San Giorgio Cathedral in Ragusa (Italy).

Geophysical surveys are widely used to reconstruct subsoil seismo-stratigraphic structures with a non-invasive approach. In this study the geophysical surveys were carried out with the aim to characterise the San Giorgio Cathedral in Ragusa (Italy) and the area on which it is built from a dynamic point of view. A 3D subsoil model was realised through the integration of two active (i.e., seismic tomography and multichannel analysis of surface waves) and one passive seismic technique (horizontal to vertical spatial ratio). The instrumentation used for the latter method consists of a tromograph (Tromino®), which is also employed for the characterisation of the building, focusing on the façade and the dome, by means of an ambient vibration test, processed through the standard spectral ratio and frequency domain decomposition methods. Integration of the 3D model, showing the distribution of areas with different physicomechanical characteristics, enables identifying anomalies that are likely attributable to the remains of the ancient Byzantine church of San Nicola. Four lower modes mainly involving the two investigated macroelements are identified. The experimental results outline the advantages of the use of the tromograph both for soil and structural characterisation, especially for massive masonry buildings located in areas with high seismic hazard.

Finite element model updating with quantified uncertainties using point cloud data

AbstractWhile finite element (FE) modeling is widely used for ultimate strength assessments of structural systems, incorporating complex distortions and imperfections into FE models remains a challenge. Conventional methods typically rely on assumptions about the periodicity of distortions through spectral or modal methods. However, these approaches are not viable under the many realistic scenarios where these assumptions are invalid. Research efforts have consistently demonstrated the ability of point cloud data, generated through laser scanning or photogrammetry-based methods, to accurately capture structural deformations at the millimeter scale. This enables the updating of numerical models to capture the exact structural configuration and initial imperfections without the need for unrealistic assumptions. This research article investigates the use of point cloud data for updating the initial distortions in a FE model of a stiffened ship deck panel, for the purposes of ultimate strength estimation. The presented approach has the additional benefit of being able to explicitly account for measurement uncertainty in the analysis. Calculations using the updated FE models are compared against ground truth test data as well as FE models updated using standard spectral methods. The results demonstrate strength estimation that is comparable to existing approaches, with the additional advantages of uncertainty quantification and applicability to a wider range of application scenarios.

Disordered systems insights on computational hardness

In this review article we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked tensor model and the generalized linear model. We discuss the random (non-planted) versions of these problems as prototypical optimization problems, as well as the planted versions (with a hidden solution) as prototypical problems in statistical inference and learning. Based on ideas from physics, many of these problems have transitions where they are believed to jump from easy (solvable in polynomial time) to hard (requiring exponential time). We discuss several emerging ideas in theoretical computer science and statistics that provide rigorous evidence for hardness by proving that large classes of algorithms fail in the conjectured hard regime. This includes the overlap gap property, a particular mathematization of clustering or dynamical symmetry-breaking, which can be used to show that many algorithms that are local or robust to changes in their input fail. We also discuss the sum-of-squares hierarchy, which places bounds on proofs or algorithms that use low-degree polynomials such as standard spectral methods and semidefinite relaxations, including the Sherrington–Kirkpatrick model. Throughout the manuscript we present connections to the physics of disordered systems and associated replica symmetry breaking properties.

A new approach to identifying the local structure of multidimensional chaotic time series

The paper is devoted to the solution of the problems of mathematical supply of decision making during multichannel monitoring of large-scaled systems. The work also deals with space-time dynamics of multidimensional time series of different origins. Highly dynamical chaotic processes whose fine structure cannot be revealed by standard spectral methods are regarded. Technologies for dimension reduction based on data matrix representation on the first singular basis and multiple regression in projections’ space are developed.

Comparison of undirected frequency-domain connectivity measures for cerebro-peripheral analysis

Analyses of cerebro-peripheral connectivity aim to quantify ongoing coupling between brain activity (measured by MEG/EEG) and peripheral signals such as muscle activity, continuous speech, or physiological rhythms (such as pupil dilation or respiration). Due to the distinct rhythmicity of these signals, undirected connectivity is typically assessed in the frequency domain. This leaves the investigator with two critical choices, namely a) the appropriate measure for spectral estimation (i.e., the transformation into the frequency domain) and b) the actual connectivity measure. As there is no consensus regarding best practice, a wide variety of methods has been applied. Here we systematically compare combinations of six standard spectral estimation methods (comprising fast Fourier and continuous wavelet transformation, bandpass filtering, and short-time Fourier transformation) and six connectivity measures (phase-locking value, Gaussian-Copula mutual information, Rayleigh test, weighted pairwise phase consistency, magnitude squared coherence, and entropy). We provide performance measures of each combination for simulated data (with precise control over true connectivity), a single-subject set of real MEG data, and a full group analysis of real MEG data. Our results show that, overall, WPPC and GCMI tend to outperform other connectivity measures, while entropy was the only measure sensitive to bimodal deviations from a uniform phase distribution. For group analysis, choosing the appropriate spectral estimation method appears to be more critical than the connectivity measure. We discuss practical implications (sampling rate, SNR, computation time, and data length) and aim to provide recommendations tailored to particular research questions.

Evaluation of horizontal to vertical spectral ratio and standard spectral ratio methods for mapping shear wave velocity across anchorage, Alaska

The use of horizontal to vertical spectral ratios (HVSR) of earthquake ground motions has become a standard technique to characterize sites, especially those lacking subsurface measurements. Several studies have developed relationships between HVSR results and time-averaged shear-wave velocity in the upper 30 m (VS30). Other studies have utilized standard spectral ratios calculated from horizontal ground motion Fourier amplitude spectra to estimate VS30. Anchorage, Alaska (USA), has a network of strong-motion recording stations, many of which have no site-specific subsurface characterization. This study compares measured VS30 and HVSR results from 18 strong-motion stations to four regional models developed by others. A relationship between the 1 Hz band-averaged (0.5–2.5 Hz) spectral amplification results and VS30 is presented. VS30 estimates for the strong-motion stations are made, and a regional model is developed between HVSR and VS30, both in terms of fpeak (the frequency of the peak HVSR amplitude) and Apeak (the amplitude of the peak). In addition to the regional model, additional VS30 data from other sites in Anchorage, including 19 downhole VS30 measurements and 22 microtremor VS30 estimates from others, are used with the strong-motion station VS30 estimates to develop a VS30 contour map of Anchorage. The contouring represents the spatial distribution of the site classes of the local building code, which are based on VS30. This map may be incorporated into planning documents for future developments in the city.

Data Clustering and Graph Partitioning via Simulated Mixing

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by the computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spectral clustering, however they compromise on the accuracy of the spectral clustering to achieve faster speed. In this paper, we propose a novel spectral clustering algorithm based on a mixing process on a graph. Unlike the existing spectral clustering algorithms, our algorithm does not require computing eigenvectors. Specifically, it finds the equivalent of a linear combination of eigenvectors of the normalized similarity matrix weighted with corresponding eigenvalues. This linear combination is then used to partition the dataset into meaningful clusters. Simulations on real datasets show that partitioning datasets based on such linear combinations of eigenvectors achieves better accuracy than standard spectral clustering methods as the number of clusters increase. Our algorithm can easily be implemented in a distributed setting.

Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces

Abstract Numerical integration of the stiffness matrix in higher-order finite element (FE) methods is recognized as one of the heaviest computational tasks in an FE solver. The problem becomes even more relevant when computing the Gram matrix in the algorithm of the Discontinuous Petrov Galerkin (DPG) FE methodology. Making use of 3D tensor-product shape functions, and the concept of sum factorization, known from standard high-order FE and spectral methods, here we take advantage of this idea for the entire exact sequence of FE spaces defined on the hexahedron. The key piece to the presented algorithms is the exact sequence for the one-dimensional element, and use of hierarchical shape functions. Consistent with existing results, the presented algorithms for the integration of H 1 {H^{1}} , H ⁢ ( curl ) {H(\operatorname{curl})} , H ⁢ ( div ) {H(\operatorname{div})} , and L 2 {L^{2}} inner products, have the 𝒪 ⁢ ( p 7 ) {\mathcal{O}(p^{7})} computational complexity in contrast to the 𝒪 ⁢ ( p 9 ) {\mathcal{O}(p^{9})} cost of conventional integration routines. Use of Legendre polynomials for shape functions is critical in this implementation. Three boundary value problems under different variational formulations, requiring combinations of H 1 {H^{1}} , H ⁢ ( div ) {H(\operatorname{div})} and H ⁢ ( curl ) {H(\operatorname{curl})} test shape functions, were chosen to experimentally assess the computation time for constructing DPG element matrices, showing good correspondence with the expected rates.

Semi-supervised Power Iteration Clustering

Spectral clustering is of significance for many research areas, but high computation complexity restricted its power obviously. Even though Power Iteration Clustering(PIC) algorithm could speed up its process by random selection of the initial vector, it is still at the cost of accuracy reduction. Aiming at the problems above, we proposed one Semi-supervised Power Iteration Clustering(SPIC) algorithm that is based on semi-supervised learning and power iteration clustering(PIC). Several pairwise constraints could be added to modify the graph adjacency matrix while a new affinity matrix with partial supervision would be built. As opposed to standard spectral methods that largely depends on pairwise distances between points, our algorithm focuses on changing the part of the affinity matrix. At last, various synthetic datasets are collected, then several experiments are performed based on these datasets to validate the superiority of our proposed algorithm over the traditional algorithms.

Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories

Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our methodology is not offered as more accurate than other traditional methods of finding coherent sets, but rather our approach works with alternative kinds of data sets, in the absence of vector field. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, NY, lake effect snow event on Earth, as well as the benchmark test double-gyre system.

Optical Fiber Sensors: Devices and Interrogation Methods

The rise of optical fiber communications in the last three decades has been accompanied with the development of a large number of sensors based on this technology, overcoming in many aspects the characteris-tics of the current electrical sensing systems. Optical fiber sensors pro-vide a wealth of applications in a variety of fields, ranging from struc-tural health monitoring to detection of chemical species. In this article, after enumerating the principal benefits of optical fiber sensors, it is presented a review about the two key aspects of opti-cal fiber sensing system, namely the sensing devices and their interroga-tion methods, respectively. In both parts, the main devices and methods have been included. In the devices section, examples of single-point, multi-point and dis-tributed sensing elements are given. In the same way, a number of inter-rogation methods are briefly described, including standard spectral analysis, interferometry, and time-domain and frequency-domain meth-ods for both point and distributed optical fiber sensing systems.

A spectral element method for meshes with skinny elements

When numerically solving partial differential equations (PDEs), the first step is often to discretize the geometry using a mesh and to solve a corresponding discretization of the PDE. Standard finite and spectral element methods require that the underlying mesh has no skinny elements for numerical stability. Here, we develop a novel spectral element method that is numerically stable on meshes that contain skinny elements, while also allowing for high degree polynomials on each element. Our method is particularly useful for PDEs for which anisotropic mesh elements are beneficial and we demonstrate it with a Navier--Stokes simulation. Code for our method can be found at .

An efficient stochastic dynamic analysis of soil media using radial basis function artificial neural network

Since a lot of engineering problems are along with uncertain parameters, stochastic methods are of great importance for incorporating random nature of a system property or random nature of a system input. In this study, the stochastic dynamic analysis of soil mass is performed by finite element method in the frequency domain. Two methods are used for stochastic analysis of soil media which are spectral decomposition and Monte Carlo methods. Shear modulus of soil is considered as a random field and the seismic excitation is also imposed as a random process. In this research, artificial neural network is proposed and added to Monte Carlo method for sake of reducing computational effort of the random analysis. Then, the effects of the proposed artificial neural network are illustrated on decreasing computational time of Monte Carlo simulations in comparison with standard Monte Carlo and spectral decomposition methods. Numerical verifications are provided to indicate capabilities, accuracy and efficiency of the proposed strategy compared to the other techniques.

Putative HIV and SIV G-Quadruplex Sequences in Coding and Noncoding Regions Can Form G-Quadruplexes.

The HIV virus is one of the most studied viruses in the world. This is especially true in terms of gene sequencing, and to date more than 9 thousand genomic sequences of HIV isolates have been sequenced and analyzed. In this study, a series of DNA sequences, which have the potential to form G-quadruplex structures, is analyzed. Several such sequences were found in various coding and noncoding virus domains, including the U3 LTR, tat, rev, env, and vpx regions. Interestingly, a homological sequence to the already well-known HIV integrase aptamer was identified in the minus-strand. The sequences derived from original isolates were analyzed using standard spectral and electrophoretic methods. In addition, a recently developed methodology is applied which uses induced circular dichroism spectral profiles of G-quadruplex-ligand (Thiazole Orange) complexes to determine if G-rich sequences can adopt G-quadruplex structure. Targeting the G-quadruplexes or peptide domains corresponding to the G-rich coding sequence in HIV offers researchers attractive therapeutic targets which would be of particular use in the development of novel antiviral therapies. The analysis of G-rich regions can provide researchers with a path to find specific targets which could be of interest for specific types of virus.

Ebola virus derived G-quadruplexes: Thiazole orange interaction.

The Ebola and Marburg viruses are some of the deadliest viruses in the world. In this study a series of G-rich DNA sequences derived from these types of viruses which possess the potential to form G-quadruplex structures are analyzed. A set of DNA oligonucleotides derived from original viral isolates was used as a representative modeling sequence with which to demonstrate the influence of thiazole orange on circular dichroism (CD) spectral profiles. The results show the unique profile of the induced CD (ICD) signal in the visible region caused by interactions between the ligand and G-quadruplexes. This ligand was found to stabilize the G-quadruplex structure and can also induce topological changes and facilitate G-quadruplex multimerization. Thus, the ICD signatures can be used to determine whether specific unknown sequences can form G-quadruplex motifs. The viral sequences were analyzed using standard spectral and electrophoretic methods. In addition, the ability to target G-quadruplexes located in filoviruses offers researchers attractive therapeutic targets which would be of particular use in the development of novel antiviral therapies. This article is part of a Special Issue entitled "G-quadruplex" Guest Editor: Dr. Concetta Giancola and Dr. Daniela Montesarchio.

Beta oscillations in the parkinsonian primate: Similar oscillations across different populations

Parkinson's disease (PD) is characterized by excessive beta band oscillations (BBO) in neuronal spiking activity across basal ganglia (BG) nuclei. High frequency stimulation of the subthalamic nucleus, an effective treatment for PD, suppresses these oscillations. There is still a heated debate on the origin and propagation of BBO and their association to clinical symptoms. The key prerequisite in addressing these issues is to obtain an accurate estimation of the subpopulation of oscillatory neurons and the magnitude of their oscillations. Studies have shown that neurons in different BG nuclei vary dramatically in the magnitude of their oscillations. However, the stochastic nature of neuronal activity subsamples the oscillatory neuronal rate functions, thus causing standard spectral analysis methods to be dramatically biased by biological and experimental factors such as variations in the neuronal firing rate across BG nuclei. In order to overcome these biases, and directly analyze the expression of BBO within BG nuclei, we used a novel objective method, the modulation index. This method reveals that unlike previous spectral results, individual neurons in the different nuclei display similar magnitudes of oscillations, whereas only the size of the oscillatory subpopulation varies between nuclei. During stimulation, the magnitude of the BBO does not change but the fraction of oscillatory neurons decreases in the globus pallidus internus, leading to a significant change in BG output. This non-biased oscillation quantification thus enables the reconstruction of oscillations at the single neuron and nuclei population levels, and calls for a reassessment of the role of BBO during PD.

Limitations and improvements of standard spectral methods for pricing standard options

We discuss the issue of how to improve the efficiency of standard spectral methods for pricing options. As a prototype example, we consider American options which are frequently used in the market as they enjoyed the early exercise opportunities. Such options are often modeled by nonlinear partial differential equations, solutions of which are not obtainable in a closed form and thus necessitates robust numerical techniques. For the discretisation in space (asset) direction, we use a rational spectral methods. For time integration involved in the process, we looked at comparing the efficiency of the method by using contour integral method based on the inversion of the Laplace transform, and the Exponential Time Differencing Runge–Kutta method of order 4. It is known that when these spectral methods are applied to option pricing problems, they no longer retain their higher order convergence. This order reduction is attributed due to the non-smooth initial conditions. To overcome this, we propose a domain decomposition method based on our rational spectral method. For the problem under consideration, we divide the domain into two sub-domains, with the transition point as the strike price. To represent the solution in each sub-domains, we choose to approximate the solution by linear rational interpolants due to their improved stability properties as compared to the polynomial interpolant. Comparative results are also presented.