Cross-covariance Research Articles

Analyzing asymmetry in brain hierarchies with a linear state-space model of resting-state fMRI data.

This study challenges the traditional focus on zero-lag statistics in resting-state functional magnetic resonance imaging (rsfMRI) research. Instead, it advocates for considering time-lag interactions to unveil the directionality and asymmetries of the brain hierarchy. Effective connectivity (EC), the state matrix in dynamical causal modeling (DCM), is a commonly used metric for studying dynamical properties and causal interactions within a linear state-space system description. Here, we focused on how time-lag statistics are incorporated within the framework of DCM resulting in an asymmetric EC matrix. Our approach involves decomposing the EC matrix, revealing a steady-state differential cross-covariance matrix that is responsible for modeling information flow and introducing time-irreversibility. Specifically, the system's dynamics, influenced by the off-diagonal part of the differential covariance, exhibit a curl steady-state flow component that breaks detailed balance and diverges the dynamics from equilibrium. Our empirical findings indicate that the EC matrix's outgoing strengths correlate with the flow described by the differential cross covariance, while incoming strengths are primarily driven by zero-lag covariance, emphasizing conditional independence over directionality.

Adaptive unscented Kalman filter methods for identifying time‐variant parameters via state covariance re‐updating

AbstractThe conventional parameter identification process generally assumes that parameters remain constant. However, under extreme loading conditions, structures may exhibit nonlinear behavior, and parameters could demonstrate time‐variant characteristics. The unscented Kalman filter (UKF), as an efficient online recursive estimator, is widely used for identifying parameters of nonlinear systems. Nevertheless, it exhibits limitations when attempting to identify time‐variant parameters. To address this issue, this paper proposes a covariance matching technique that produces an array of adaptive UKF algorithms. Firstly, the sensitivity parameter η is defined to identify the instant when the parameter change occurs, and its threshold is calculated based on the sensitivity parameter time history curve. Secondly, an adaptive forgetting factor is introduced to simultaneously update the innovation, cross, and state covariance matrices when the kth‐step sensitive parameter surpasses the threshold. Finally, a secondary correction forgetting factor (SCFF) is employed to further re‐update the state covariance values at the identified damage locations. This creative step enhances the adaptive capability and optimizes the identification accuracy of the proposed algorithms. Both the numerical simulations and shaking table test demonstrate that the proposed adaptive algorithms can efficiently identify the time‐variant stiffness‐type parameters, and accurately capture their time‐variant characteristics.

Testing Conditional Independence Between Latent Variables by Independence Residuals.

Conditional independence (CI) testing is an important problem, especially in causal discovery. Most testing methods assume that all variables are fully observable and then test the CI among the observed data. Such an assumption is often untenable beyond applications dealing with, e.g., psychological analysis about the mental health status and medical diagnosing (researchers need to consider the existence of latent variables in these scenarios); and typically adopted latent CI test schemes mainly suffer from robust or efficient issues. Accordingly, this article investigates the problem of testing CI between latent variables. To this end, we offer an auxiliary regression-based CI (AReCI) test by taking the measured variable as the surrogate variable of the latent variables to conduct the regression over the latent variables under the linear causal models, in which each latent variable has some certain measured variables. Specifically, given a pair of latent variables LX and LY , and a corresponding latent variable set LO , [Formula: see text] holds if and only if [Formula: see text] and [Formula: see text] are statistically independent, where A' and A'' are the two disjoint subset of the measured variable for the corresponding latent variables, A'{LO} ∩A''{LO} = ∅ , and ω1 is a parameter vector characterized from the cross covariance between A{LX} and A'{LO} , and ω2 is a parameter vector characterized from the cross covariance between A{LY} and A''{LO} . We theoretically show that the AReCI test is capable of addressing both Gaussian and non-Gaussian data. In addition, we find that the well-known partial correlation test can be seen as a special case of the AReCI test. Finally, we devise a causal discovery method by using the AReCI test as the CI test. The experimental results on synthetic and real-world data illustrate the effectiveness of our method.

Resolving mode mixing in wheel–rail surface defect detection using EMD based on binary time scale

Due to the mode mixing, empirical mode decomposition (EMD) cannot effectively decompose the vibration signal when the signal is intermittent and pulse interference caused by discontinuous vibration. The methods to solve mode mixing often use noise assistance, such as ensemble EMD (EEMD), complete EEMD (CEEMD), etc. These methods can effectively solve mode mixing, but they also have shortcomings. In EEMD, the added noises not only have residual effects and time-consuming. The drawback of CEEMD is that it is difficult to align during set averaging. In this paper, an improved EMD based on binary time scale (EMD-BTS) is proposed for the fault feature extraction of wheel–rail defect detection. Firstly, the generalized intrinsic mode function (GIMF) is defined based on the time-domain characteristics of non-stationary vibration signals. Then, to tackle the drawbacks of EMD which cannot effectively solve mode mixing caused by signal intermittence and pulse interference, the inherent mode is extracted in the EMD-BTS to decompose the raw signals into GIMFs. Finally, the false components generated by over decomposition are combined based on time-domain cross covariance. A simulation case and a actual case of vehicle bogie are utilized to verify the feasibility of the proposed EMD-BTS. The results indicate that the proposed approach exceeds other typical techniques in extracting intermittent fault features of wheel–rail defect detection.

An Efficient Transformer Model for Synthesizing Dual Energy CT from Single Energy Scanner

Dual-energy CT can be used to optimize radiation treatment. Recently, deep learning has been demonstrated to synthesize high-energy CT images from low-energy ones for dose reduction and lower CT system burden. As the state-of-the-art deep learning architecture, the computation burden of Transformer increases quadratically with the feature size, making the model training resource-demanding or even infeasible. Here, we introduce an efficient transformer for the balance between CT image synthesis quality and computational burden. The model is a U-shape deep neural network with encoders and decoders built by Transformer blocks. The model input is low-energy 100kVp CT image and the output is high-energy 140kVp one. Each block has a Self Channel Correlation Unit (SCCU) and a Self Spatial Attention Unit (SSAU). Local shortcuts are applied for both units. Under-sampling operation achieved by pixel shuffling is used to obtain multi-scale feature maps, and the transformer block is applied on each feature scale. Symmetric skip connection sending features from shallow layers to deep layers, thus an additional 1 × 1 convolution is used for feature fusion in each decoder. In a SCCU, the feature is first mapped to one Query, one Key, and one Value. Then the Query and the Key tensors perform matrix multiplication to compute cross covariance of feature channels. The channel correlation score can be obtained by normalization of the covariance, and it is used to weight the Value tensor. As a result, the model complexity only increases linearly with the feature size. Besides the channel weighting, we enhance spatial information using SSAU, where the feature is mapped to two tensors. One tensor after activation is used to point-wisely calibrate another tensor. Additional Transformer blocks are cascaded to the last decoder for feature refinement. Because of the structure similarity of low- and high-energy CT images, a global shortcut is used to ease model training. Clinical iodine contrast-enhanced dual energy CT image datasets of 19 patients are used in this study. The dual-energy scanning is performed by a SOMATOM Definition Flash DECT scanner. We split the datasets into training dataset of 15 patients, validation dataset of 1 patient, and testing dataset of 3 patients. The image size is 512 × 512 with pixel size 0.5 × 0.5 mm2. The U-Net model with 1.95M parameters and 44.87G FLOPS achieved the averaged PSNR value of 44.55 dB (s.t.d. 1.34) and averaged RMSE value of 0.0060 (s.t.d. 0.001). In comparison, our efficient Transformer with 1.408M parameters and 31.375G FLOPS achieved the averaged PSNR value of 44.78 dB (s.t.d. 1.37) and RMSE value of 0.0059 (s.t.d. 0.001), demonstrating our model has better performance with small model size and less computation. The efficient Transformer model allows high-resolution CT image synthesis with small model scale and computation burden from low-energy CT image.

Dimension of Activity in Random Neural Networks.

Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires knowledge of the structure of this coordinated activity, information contained, for example, in cross covariances between units. Self-consistent dynamical mean field theory (DMFT) has elucidated several features of random neural networks-in particular, that they can generate chaotic activity-however, a calculation of cross covariances using this approach has not been provided. Here, we calculate cross covariances self-consistently via a two-site cavity DMFT. We use this theory to probe spatiotemporal features of activity coordination in a classic random-network model with independent and identically distributed (i.i.d.) couplings, showing an extensive but fractionally low effective dimension of activity and a long population-level timescale. Our formulas apply to a wide range of single-unit dynamics and generalize to non-i.i.d. couplings. As an example of the latter, we analyze the case of partially symmetric couplings.

Super-sample covariance of the power spectrum, bispectrum, halos, voids, and their cross covariances

Super-sample covariance of the power spectrum, bispectrum, halos, voids, and their cross covariances

Scalable recursive state estimation for nonlinear two‐dimensional complex networks with switching topology

SummaryThis paper investigates a scalable recursive state estimation method for nonlinear two‐dimensional (2‐D) stochastic complex networks. In these networks, the switching topology is modelled by random variables generated by the Bernoulli distribution. Considering the Extended Kalman Filter structure, we employ the Taylor series expansion to handle the nonlinear functions in the model. Hence, high‐order terms emerging in the linearization process are modelled by norm‐bounded parameter uncertainties. Due to the uncertainty of such a system, we obtain an upper bound for the estimation error covariance. Furthermore, we obtain an upper bound for the cross covariance to reduce the proposed filter's computational complexity and improve scalability. Within the established setting, next, the proposed filter is designed in such a way that the presented upper bounds are minimized. Finally, a numerical example is provided to illustrate the effectiveness of the proposed state estimation algorithm.

Direct Assimilation of All-Sky GOES-R ABI Radiances in GSI EnKF for the Analysis and Forecasting of a Mesoscale Convective System

Abstract In this study, all-sky GOES-R ABI infrared radiances at their native resolution are assimilated using an enhanced GSI ensemble Kalman filter (EnKF) data assimilation (DA) system, and the impacts of the data on the analysis and forecast of a mesoscale convective system (MCS) are explored. Results show that all-sky ABI BT data can correctly build up observed storms within the model and effectively remove spurious storms in model background through frequent DA cycles. Both bias and root-mean-squared innovation of the background and analysis are significantly reduced during the DA cycles, and free forecasts are improved when verified subjectively and objectively against observed ABI BTs and independent radar reflectivity observations. A horizontal localization radius of 30 km is found to produce the best results while 5-min DA cycles improve the storm analyses over 15-min cycles, but the differences in forecasts are small. Further analyses show that the clearing of spurious clouds by ABI radiance is correctly accompanied by reduction in moisture through background error cross covariance, but overdrying often occurs, which can cause spurious storm decay in the forecast. The problem is reduced when the ensemble mean of observation prior instead of observation prior of the ensemble mean state is used in the ensemble mean state update equation of EnKF. The significant difference between the two ways that the ensemble mean of observation prior is calculated when the observational operator is very nonlinear has not been recognized in earlier cloudy radiance DA studies. Significance Statement Satellite observations in cloudy regions are not used in most current operational weather prediction systems due to complex nonlinear relations between satellite-observed quantities, the radiances, and model state in such regions. The models also must predict clouds reasonably well for cloudy observations to be effectively assimilated. The latest NOAA geostationary satellites can provide radiance observations at high spatial and temporal resolutions and such data in both cloudy- and clear-air regions are assimilated using an advanced data assimilation method into a model that explicitly represents convection. Forecasts up to 4 h are improved by the assimilation while several issues associated with the assimilation are discussed. The study contributes to the eventual use of all-sky satellite radiance data in operational models.

Closely spaced modes of bridges estimated by a hybrid time–frequency method using a multi-sensor scanning vehicle: Theory and practice

A hybrid time–frequency method is proposed for accurately estimating the modal parameters of bridges, including the closely spaced modes, by a single-axle scanning vehicle fitted with multi sensors. The novelty of the method is the combined use of the wavelet transform (WT) and singular value decomposition (SVD) for processing the cross covariances of the multi-sensor responses generated by the scanning vehicle, which allows closely spaced modes to be accurately identified. The procedure of modal parameters identification is first given in detail, including the key issues related to the treatment of closely spaced modes. Then, the feasibility of the proposed method is verified for a numerical case, with its advantage over the fast Fourier transform (FFT) clearly shown. Also, a parametric study is presented for various factors including the vehicle damping, vehicle speed, signal-to-noise ratio (SNR) and pavement roughness, by which the robustness of the method was confirmed. Finally, the method is successfully applied to the field test of a three-span girder bridge in Xiamen, China. By the numerical and field-test results, the proposed method is demonstrated to be of high accuracy in identification of modal parameters of bridges, including the closely spaced modes.

Application of the extended bias factor method for highly reliable benchmark suite

It was tried to get useful information feedback on cross section and covariance by application of extended bias factor method with experimental benchmarks’ C/E, sensitivity coefficient and covariance data. As a result, it was succeeded to distinguish “the case unrecommended by specialists” as outlier case. And it was succeeded to get the hints that there is room for improvement in cross section or covariance of some nuclides by investigating outlier cases judged as recommended case by specialists.

Toward the Discrimination of Oil Spills in Newly Formed Sea Ice Using C-Band Radar Polarimetric Parameters

Climate-driven sea ice loss has exposed the Arctic to increased human activity, which comes along with a higher risk of oil spills. As a result, we investigated the ability of C-band polarimetric parameters in a controlled mesocosm to accurately identify and discriminate between oil-contaminated and uncontaminated newly formed sea ice (NI). Parameters, such as total power, copolarization ratio, copolarization correlation coefficient, and others, were derived from the normalized radar cross section and covariance matrix to characterize the temporal evolution of NI before and after oil spill events. For separation purposes, entropy ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> ) and mean-alpha ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula> ) were extracted from eigen decomposition of the coherency matrix. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> versus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> scatterplot revealed that a threshold classifier of 0.3- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> and 18°- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> could distinguish oil-contaminated NI from its oil-free surroundings. From the temporal evolution of the polarimetric parameters, the results demonstrate that the copolarization correlation coefficient is the most reliable polarimetric parameter for oil spill detection, as it provides information on a variety of oil spill scenarios, including oil encapsulated within ice and oil spreading on top of ice. Overall, these findings will be used to support existing and future C-band polarimetric radar satellites for resolving ambiguities associated with Arctic oil spill events, particularly during freeze-up seasons.

XSUN-2022/SUSD3D n/γ sensitivity-uncertainty code package with recent JEFF-3.3 and ENDF/B-VIII.0 covariance data

A new version of the XSUN-2022 computer code package is under preparation to be released through NEA Data Bank which includes the latest updates of the SUSD3D sensitivity/uncertainty (S/U) code and the corresponding cross section and covariance matrix libraries based on the JEFF-3.3, ENDF/B-VIII.0 and FENDL-3.2 evaluations. The XSUN code package is a user–computer interface environment, written in Xbase++ ® and using Compiler 1.90.331 and Alaska 32-Bit Linker, for user-friendly pre- and post-processing of the input and output data for a complete and self-consistent set of deterministic codes. The flowchart integrates the codes TRANSX, PARTISN, and SUSD3D, all available from the OECD/NEA Data Bank and RSICC. The codes are used for the preparation of multigroup nuclear cross-section, neutron and gamma transport calculations for criticality and shielding calculations and nuclear data sensitivity and uncertainty calculations, respectively. XSUN-2022 is the 3rdreleased version, after XSUN-2013 and -2017.

Resilient Unscented Kalman Filtering Fusion With Dynamic Event-Triggered Scheme: Applications to Multiple Unmanned Aerial Vehicles

In this article, the resilient unscented Kalman filtering fusion issue is investigated for a class of nonlinear systems under the dynamic event-triggered mechanism where each sensor node transmits the measurement information to its corresponding local filter in an intermittent way. Compared with its static counterpart, the dynamic event-triggered scheme is capable of scheduling the frequency of data transmission in a more efficient way, thereby better reducing communication burden and energy consumption. In addition, for each local filter, the variation of the filter gain is characterized by a multiplicative noise term. To cope with the intractable problem of computing the cross covariance between local filters, the sequential covariance intersection fusion strategy is introduced into the proposed distributed fusion framework. Finally, the proposed algorithm is applied to a maneuvering target tracking scenario with multiple unmanned aerial vehicles, and both numerical simulations and hardware experiments are provided to elucidate the effectiveness and practicality of the proposed filtering scheme.

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

Investigation of the Differences in Onset Times for Magnetically Conjugate Magnetometers

We have identified nearly 1,000 onsets using two pairs of hemispheric conjugate ground magnetometers where the onset is defined based on a sharp decline in the H component of the magnetic field at a ground magnetometer station. Specifically, we used the pair of stations at West Antarctica Ice Sheet Divide and Sanikiluaq, Canada; Syowa, Antarctica; and Tjörnes, Iceland. While the onset time in the southern hemisphere is identified by eye, the value of the differences in the onset time between the northern and southern hemispheres is determined using cross covariance. We observe differences in the onset time between the two hemispheres as large as several minutes, but 53% of the events show no difference in the onset time. Using statistics, we show that the largest differences in onset time are associated with the summer and winter seasons and when the IMF By value is limited between 0.5 and 2.5 nT, which is the IMF By range when the local time difference between the northern and southern hemisphere foot points is the smallest. The results indicate that ionospheric conductivity associated with solar illumination plays a role in the differences in onset time between the northern and southern hemisphere when only non-zero differences in onset time are considered. We validate these results with two other less robust methods. The median value of the differences in onset time indicates that the onsets occur ∼23 s earlier in the winter hemisphere than that in the summer hemisphere. It has been reported that the time difference between the start of the substorm in the magnetotail and the observed auroral break up (substorm auroral onset) in the ionosphere is 30 s to 2 min in the current disruption model and the near earth neutral line model, respectively. Our results may be of interest to those two models.

Security weakness of dynamic watermarking-based detection for generalised replay attacks

Dynamic watermarking (DW)-based detection methods can effectively detect replay attacks, however these detection methods cannot achieve the desired effectiveness for generalised replay attacks (GRAs). The objectiveness of this paper is to investigate security weakness of DW-based detection for GRAs. Firstly, unlike replaying history data from replay attacks, data accuracy compromised by GRAs is analysed, where their characteristics are similar to that compromised by replay attacks, and the current data are distorted by typical GRAs such as injection, replacement and scaling attacks. Secondly, considering the corresponding hidden Markov models of different types of GRAs, the stealthiness is quantified by auto covariance of residuals and cross covariance between residuals and watermarking signals. It is found that if both auto and cross covariance keep unchanged or increase along with watermarking intensity increasing, GRAs cannot be detected effectively. Thirdly, after DW-based detection is invalid for GRAs, it is proved that the stability of closed-loop systems for open-loop unstable dynamics will be destroyed, or the admissible system state bounds can be crossed within a finite time. Finally, experiments are operated on a networked inverted pendulum platform, and experimental results confirm security weakness of DW-based detection for GRAs.

On underwater acoustic particle velocity channels: Some experimental results

Studies have shown that acoustic particle velocity channels, in addition to the acoustic pressure channel, can be beneficial for underwater acoustic communication [A. Abdi and H. Guo, “A new compact multichannel receiver for underwater wireless communication networks,” IEEE Trans. Wireless Commun. 8, 3326–3329 (2009); A. Abdi, et al., “An overview of underwater acoustic communication via particle velocity channels: Channel modeling and transceiver design,” Proc. Meetings Acoust. 9, 070002 (2010)]. In this paper, we use experimentally measured acoustic particle velocity and acoustic pressure channels, using transmitted linearly frequency modulated (LFM) signals, to investigate and compare various signal and noise characteristics of these channels. Examples include signal and noise powers and ratios, delay spreads of the channels, temporal and spatial auto and cross covariance functions for the particle velocity and acoustic pressure noise components, and frequency responses of the acoustic particle velocity and acoustic pressure channels. Understanding these signal and noise characteristics allows a system designer to design and implement reliable and efficient underwater acoustic communication systems that employ multiple acoustic particle velocity channels, together with the acoustic pressure channel. [The work is supported in part by the National Science Foundation (NSF), Grant IIP-1500123.]

Genomic mating in outbred species: predicting cross usefulness with additive and total genetic covariance matrices.

Diverse crops are both outbred and clonally propagated. Breeders typically use truncation selection of parents and invest significant time, land, and money evaluating the progeny of crosses to find exceptional genotypes. We developed and tested genomic mate selection criteria suitable for organisms of arbitrary homozygosity level where the full-sibling progeny are of direct interest as future parents and/or cultivars. We extended cross variance and covariance variance prediction to include dominance effects and predicted the multivariate selection index genetic variance of crosses based on haplotypes of proposed parents, marker effects, and recombination frequencies. We combined the predicted mean and variance into usefulness criteria for parent and variety development. We present an empirical study of cassava (Manihot esculenta), a staple tropical root crop. We assessed the potential to predict the multivariate genetic distribution (means, variances, and trait covariances) of 462 cassava families in terms of additive and total value using cross-validation. Most variance (89%) and covariance (70%) prediction accuracy estimates were greater than zero. The usefulness of crosses was accurately predicted with good correspondence between the predicted and the actual mean performance of family members breeders selected for advancement as new parents and candidate varieties. We also used a directional dominance model to quantify significant inbreeding depression for most traits. We predicted 47,083 possible crosses of 306 parents and contrasted them to those previously tested to show how mate selection can reveal the new potential within the germplasm. We enable breeders to consider the potential of crosses to produce future parents (progeny with top breeding values) and varieties (progeny with top own performance).

Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition

AbstractWe present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the Lagrangian Submesoscale Experiment (LASER) dataset. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.