Calculation Of Covariance Research Articles

Collective nature of phonon energies beyond harmonic oscillators

Phonon quasi-particles have been monumental in microscopically understanding thermodynamics and transport properties in condensed matter for decades. Phonons have one-to-one correspondence with harmonic eigenstates and their energies are often described by simple independent harmonic oscillator models. Higher order terms in the potential energy lead to interactions among them, resulting in finite lifetimes and frequency shifts, even in perfect crystals. However, increasing evidence including constant volume heat capacity violating the Dulong-Petit law suggests the need for re-evaluation of phonons as having independent harmonic energies. In this work, we explicitly examine inter-mode dependence of phonon energies of a prototypical crystal, silicon, through energy covariance calculations and demonstrate the concerted nature of phonon energies even at 300 K, questioning independent harmonic oscillator assumptions commonly used for phonon energy descriptions of thermodynamics and transport.

Scalar spectral functions from the spectral functional renormalization group

We compute spectral functions in a scalar ϕ4-theory in three spacetime dimensions via the spectral functional renormalization group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalization. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation. Published by the American Physical Society 2024

Learning to integrate parts for whole through correlated neural variability.

Neural activity in the cortex exhibits a wide range of firing variability and rich correlation structures. Studies on neural coding indicate that correlated neural variability can influence the quality of neural codes, either beneficially or adversely. However, the mechanisms by which correlated neural variability is transformed and processed across neural populations to achieve meaningful computation remain largely unclear. Here we propose a theory of covariance computation with spiking neurons which offers a unifying perspective on neural representation and computation with correlated noise. We employ a recently proposed computational framework known as the moment neural network to resolve the nonlinear coupling of correlated neural variability with a task-driven approach to constructing neural network models for performing covariance-based perceptual tasks. In particular, we demonstrate how perceptual information initially encoded entirely within the covariance of upstream neurons' spiking activity can be passed, in a near-lossless manner, to the mean firing rate of downstream neurons, which in turn can be used to inform inference. The proposed theory of covariance computation addresses an important question of how the brain extracts perceptual information from noisy sensory stimuli to generate a stable perceptual whole and indicates a more direct role that correlated variability plays in cortical information processing.

Selective cooling and squeezing in a lossy optomechanical closed loop embodying an exceptional surface

A closed-loop, lossy optomechanical system consisting of one optical and two degenerate mechanical resonators is computationally investigated. This system constitutes an elementary synthetic plaquette derived from the loop phase of the intercoupling coefficients. In examining a specific quantum attribute, we delve into the control of quadrature variances within the resonator selected through the plaquette phase. An amplitude modulation is additionally applied to the cavity-pumping laser to incorporate mechanical squeezing. Our numerical analysis relies on the integration-free computation of steady-state covariances for cooling and the Floquet technique for squeezing. We provide physical insights into how non-Hermiticity plays a crucial role in enhancing cooling and squeezing in proximity to exceptional points. This enhancement is associated with the behavior of complex eigenvalue loci as a function of the intermechanical coupling rate. Additionally, we demonstrate that the parameter space embodies an exceptional surface, ensuring the robustness of exceptional point singularities under experimental parameter variations. However, the pump laser detuning breaks away from the exceptional surface unless it resides on the red-sideband by an amount sufficiently close to the mechanical resonance frequency. Finally, we show that this disparate parametric character entitles frequency-dependent cooling and squeezing, which is of technological importance.

Retracted Article: Surface roughness grade evaluation of milling workpiece based on deep transfer learning

ABSTRACT We, the Editors and Publishers of Nondestructive Testing and Evaluation, have retracted the following article: Gaowei Ye, Kaihong Zhou, Qingting Ye & Fucheng Tian (2024). Surface roughness grade evaluation of milling workpiece based on deep transfer learning. Nondestructive Testing and Evaluation. DOI:10.1080/10589759.2024.2321968. After publication, the author, Gaowei Ye, requested the retraction of this article for the following reasons: the use of Figure 9 etc. without the required permissions. the function F (I), which uses captured images to calculate the average definition value, has a serious error in the formula of the algorithm F (I), resulting in data errors in the calculation of covariance, classification loss function, etc. In light of these issues and concerns about the validity of the study, the journal has agreed to retract the article. We have been informed in our decision-making by our editorial policies and the COPE guidelines. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as “Retracted”.

Comparison of the imaginary parts of the atmospheric refractive index structure parameter and aerosol flux based on different measurement methods

Abstract. The complexity of aerosol particle properties and the diversity of characterizations make aerosol vertical transport flux measurements and analysis difficult. Although there are different methods, such as aerosol particle number concentration flux and aerosol mass flux based on the eddy covariance principle as well as aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle, there is a lack of mutual validation among the different methods. In this paper, a comparison of aerosol mass flux measurements based on the eddy covariance principle and aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle is carried out. The key idea of aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle is the determination of the imaginary part of the atmospheric equivalent refractive index structure parameter (AERISP). In this paper, we first compare the AERISPs measured by two different methods and then compare the aerosol mass vertical transport fluxes obtained by different methods. The experiments were conducted on the campus of the University of Science and Technology of China (USTC). A light propagation experiment was carried out between two tall buildings to obtain the imaginary and real parts of the AERISPs for the whole path, which in turn can be used to obtain the aerosol vertical transport flux. An updated visibility meter is installed on the meteorological tower in the middle of the light path, which is utilized to obtain the single-point visibility, which is then converted to the imaginary part of the atmospheric equivalent refractive index (AERI). The imaginary parts of the AERISP were obtained via spectral analysis with visibility data. The results show that the imaginary parts of the AERISPs obtained by different methods are in good agreement. The imaginary part of the AERI measured by the visibility meter and the vertical wind speed obtained by the ultrasonic anemometer were used for covariance calculations to obtain the aerosol vertical transport flux. The trends in aerosol vertical transport fluxes obtained by the different methods are consistent, and there are differences in some details, which may be caused by the inhomogeneity in the vertical transport of aerosol fluxes. The experimental results also showed that urban green land is a sink area for aerosol particles.

Systemic risk monitoring model from the perspective of public information arrival

We introduce a new technique called the market correlation deviation test, which aims to detect systemic anomalies and facilitate market monitoring by using high-frequency price data from the Chinese stock market. Our method achieves a significant reduction in calculation time (to one N of the traditional method, where N represents the number of stocks) while maintaining the accuracy of calculations. This reduction is achieved by converting the covariance calculation into a difference calculation. By comparing our approach with the conventional Barndorff-Nielson-Shephard (BNS) and Corsi-Pirino-Reno (CPR) models, we demonstrate superior accuracy in identifying anomalies and efficiency in monitoring. Notably, our method can measure local price synchronization behavior, often associated with the arrival of public information, and we also observe the impact of public information on pricing. To the best of our knowledge, this study is the first to directly observe and quantify the effect of public information on pricing.

A Time-Local Weighted Transformation Recognition Framework for Steady State Visual Evoked Potentials Based Brain-Computer Interfaces.

Canonical correlation analysis (CCA), Multivariate synchronization index (MSI), and their extended methods have been widely used for target recognition in Brain-computer interfaces (BCIs) based on Steady State Visual Evoked Potentials (SSVEP), and covariance calculation is an important process for these algorithms. Some studies have proved that embedding time-local information into the covariance can optimize the recognition effect of the above algorithms. However, the optimization effect can only be observed from the recognition results and the improvement principle of time-local information cannot be explained. Therefore, we propose a time-local weighted transformation (TT) recognition framework that directly embeds the time-local information into the electroencephalography signal through weighted transformation. The influence mechanism of time-local information on the SSVEP signal can then be observed in the frequency domain. Low-frequency noise is suppressed on the premise of sacrificing part of the SSVEP fundamental frequency energy, the harmonic energy of SSVEP is enhanced at the cost of introducing a small amount of high-frequency noise. The experimental results show that the TT recognition framework can significantly improve the recognition ability of the algorithms and the separability of extracted features. Its enhancement effect is significantly better than the traditional time-local covariance extraction method, which has enormous application potential.

Reply to: Analysis of covariance and sample size calculation for comparing means in randomized controlled trials.

Reply to: Analysis of covariance and sample size calculation for comparing means in randomized controlled trials.

Quantifying the impact of climate smart agricultural practices on soil carbon storage relative to conventional management

Climate smart agricultural practices have received considerable attention recently for their potential for climate change mitigation through sequestering atmospheric carbon. Despite the enthusiasm for climate smart practices, there is limited evidence they are more effective at removing carbon from the atmosphere and storing it in the soil than current practices. We hypothesized that a field with aspirational (ASP) practices (i.e., no-till corn-soybean-wheat-hay rotation with cover crops) would accumulate more soil organic carbon (SOC) versus a business-as-usual (BAU) field (i.e., conventional-tillage, corn-soybean-soybean rotation). We used deep soil cores (1 m) to assess changes in soil organic carbon (ΔSOC) between 2016 and 2022 for the two fields and compare with estimates based on eddy covariance calculation of ΔSOC. We found that the ASP field had ΔSOC that was positive, and larger than the BAU field. Both the soil sample method (ΔSOCSS) and the eddy covariance method (ΔSOCEC) agreed on this point, but the magnitude of ΔSOC was much larger when estimated with soil samples (ΔSOCSS was 1.9 ± 1.7 % yr−1 and -0.7 ± 1.3 % yr−1 at ASP and BAU, respectively) than with eddy covariance (ΔSOCEC was 0.80 ± 0.09 % yr−1 and 0.12 ± 0.06 % yr−1 at ASP and BAU, respectively). Finally, we used the continuous measurements of carbon fluxes from the eddy covariance towers to examine how conservation practices (cover crops, no-till, or expanded crop rotation) led to increased carbon storage. We found that unharvested cover crops add carbon to the soil that offsets net carbon losses that otherwise reduce soil carbon storage when the field is fallow. No-till and expanded crop rotations also affect the carbon budget of the agro-ecosystems. Results from this study illustrate the value of conservation practices in a changing climate and the value of eddy covariance measurements for assessing climate smart practices.

Assessing the Accuracy of 3D-VAR in Supercell Thunderstorm Forecasting: A Regional Background Error Covariance Study

Data assimilation (DA) integrates observational data with numerical weather predictions to enhance weather forecast accuracy. This study evaluates three regional background error (BE) covariance statistics for numerical weather prediction (NWP) via a variational data assimilation (VAR) scheme. The best practices in DA are highlighted, as well as the impact of BE covariance calculation in DA procedures by employing the Weather Research and Forecasting (WRF) model. Forecasts initialized at different intervals were used to compute distinct regional background error statistics utilizing three control variable (CV) methodologies over a span of 20 days. These statistics are used by the three-dimensional VAR DA process of WRF DA software, producing analysis fields that lead to forecasts for a distinct convective supercell event during the summer of 2019 over northern Greece. This high-impact convective event underscores the importance of selecting appropriate BE over complex terrain areas. The results emphasize the significance of BE usage in DA, proposing the optimal DA approach for simulations of convective systems.

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.

Bayesian adaptive beamformer for robust electromagnetic brain imaging of correlated sources in high spatial resolution.

Reconstructing complex brain source activity at a high spatiotemporal resolution from magnetoencephalography (MEG) or electroencephalography (EEG) remains a challenging problem. Adaptive beamformers are routinely deployed for this imaging domain using the sample data covariance. However adaptive beamformers have long been hindered by 1) high degree of correlation between multiple brain sources, and 2) interference and noise embedded in sensor measurements. This study develops a novel framework for minimum variance adaptive beamformers that uses a model data covariance learned from data using a sparse Bayesian learning algorithm (SBL-BF). The learned model data covariance effectively removes influence from correlated brain sources and is robust to noise and interference without the need for baseline measurements. A multiresolution framework for model data covariance computation and parallelization of the beamformer implementation enables efficient high-resolution reconstruction images. Results with both simulations and real datasets indicate that multiple highly correlated sources can be accurately reconstructed, and that interference and noise can be sufficiently suppressed. Reconstructions at 2-2.5mm resolution (~150K voxels) are possible with efficient run times of 1-3 minutes. This novel adaptive beamforming algorithm significantly outperforms the state-of-the-art benchmarks. Therefore, SBL-BF provides an effective framework for efficiently reconstructing multiple correlated brain sources with high resolution and robustness to interference and noise.

A 3D Drizzle Algorithm for JWST and Practical Application to the MIRI Medium Resolution Spectrometer

We describe an algorithm for application of the classic “drizzle” technique to produce 3D spectral cubes using data obtained from the slicer-type integral field unit (IFU) spectrometers on board the James Webb Space Telescope. This algorithm relies upon the computation of overlapping volume elements (composed of two spatial dimensions and one spectral dimension) between the 2D detector pixels and the 3D data cube voxels, and is greatly simplified by treating the spatial and spectral overlaps separately at the cost of just 0.03% in spectrophotometric fidelity. We provide a matrix-based formalism for the computation of spectral radiance, variance, and covariance from arbitrarily dithered data and comment on the performance of this algorithm for the Mid-Infrared Instrument’s Medium Resolution IFU Spectrometer. We derive a series of simplified scaling relations to account for covariance between cube spaxels in spectra extracted from such cubes, finding multiplicative factors ranging from 1.5–3 depending on the wavelength range and kind of data cubes produced. Finally, we discuss how undersampling produces periodic amplitude modulations in the extracted spectra in addition to those naturally produced by fringing within the instrument; reducing such undersampling artifacts below 1% requires a four-point dithering strategy and spectral extraction radii of 1.5 times the point-spread function FWHM or greater.

Design, Synthesis, Antimicrobial Evaluation of Novel 2-Oxo-4-Substituted Aryl-Azetidine Benzotriazole Derivatives.

A series of compounds was synthesized and characterized to explore new antimicrobial agents. These compounds were evaluated by using the agar cup plate method. The most active compound exhibited a zone of inhibition 18±0.09 mm and 19±0.09 mm against E. Coli and S. aureus, respectively. To gain insights into the intermolecular interactions, molecular docking studies were performed at the active site of the glucosamine fructose 6 phosphate synthase (GlcN 6 p) enzyme (PDB Id: 1XFF). The results of the molecular docking studies are in agreement with the pharmacological evaluation with potent compounds, exhibiting docking scores of -11.2. However, deformability, B-factor and covariance computations showed a result that the most active compound favored molecular connections with the protein. Therefore, our research is important for the development of antimicrobial agents.

Adaptive Transfer Kernel Learning for Transfer Gaussian Process Regression

Transfer regression is a practical and challenging problem with important applications in various domains, such as engineering design and localization. Capturing the relatedness of different domains is the key of adaptive knowledge transfer. In this paper, we investigate an effective way of explicitly modelling domain relatedness through transfer kernel, a transfer-specified kernel that considers domain information in the covariance calculation. Specifically, we first give the formal definition of transfer kernel, and introduce three basic general forms that well cover existing related works. To cope with the limitations of the basic forms in handling complex real-world data, we further propose two advanced forms. Corresponding instantiations of the two forms are developed, namely Trkαβ and Trkω based on multiple kernel learning and neural networks, respectively. For each instantiation, we present a condition with which the positive semi-definiteness is guaranteed and a semantic meaning is interpreted to the learned domain relatedness. Moreover, the condition can be easily used in the learning of TrGP αβ and TrGP ω that are the Gaussian process models with the transfer kernels Trkαβ and Trkω respectively. Extensive empirical studies show the effectiveness of TrGP αβ and TrGP ω on domain relatedness modelling and transfer adaptiveness.

Functional principal component analysis for partially observed elliptical process

The robust principal component estimators for partially observed functional data with heavy-tail behaviors are presented, where sample trajectories are collected over individual-specific subintervals. The method considers partially sampled trajectories as the elliptical process filtered by the missing indicator process and implements robust functional principal component analysis under this framework. The proposed method is computationally efficient and straightforward by estimating the robust correlation function through pairwise covariance computation combined with M-estimation. The asymptotic consistency of the estimators is established under general conditions. The simulation studies demonstrate the superior performance of the method in the approximation of the subspace of data and reconstruction of full trajectories. The proposed method is then applied to hourly monitored air pollutant data containing anomaly trajectories with random missing segments.

The BRICS in the sustainable agenda: Performance analysis of ESG indices in the financial markets in Brazil, China, India and South Africa

The term ESG emerged in the report of the Global Compact (UN) in partnership with the World Bank, entitled Who Cares Wins: Connecting Financial Markets to a Changing World. However, the concept and measurement associated with ESG is not a fixed concept and there is no consensus on the exact list of issues and their materiality, but it is certain that it affects the value creation of a company. In 2006, a grouping was created, incorporating the foreign policy of Brazil, Russia, India and China, the bloc focuses on solving socioeconomic problems and using its competitive advantages, the BRICS has a proposal for sustainable development and consequently ESG. This study is justified by the fact that several empirical evidences show the benefits of the ESG agenda in the market, however, there is a gap when considering developing countries. In this article, a comparison was made between returns and performances through the average return, then the risk measurement measures are presented, namely variance, standard deviation, volatility and value at risk, in addition to the calculation of covariance, correlation, beta and drawdown, with data from the MSCI ESG Leaders index. We confirm the theory of long-term gains since in the period studied the average profitability of the ESG indices were higher in all countries compared to the broad index. As for volatility risk measures, our study confirmed the hypothesis that the risks of larger companies are greater than those of ESG companies.

Efficient computation of the super-sample covariance for stage IV galaxy surveys

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the ∼15% level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3×2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30%.

UbiNN: A Communication Efficient Framework for Distributed Machine Learning in Edge Computing

Deployment of distributed machine learning at the edge is conducive to reducing latency and protecting privacy associated with transmitting data back to the cloud. Nonetheless, as machine learning models scale, bandwidth resources are limited and heterogeneity in data collection from heterogeneous edge devices is visible, resulting in low model accuracy and high communication overhead. In this paper, a novel distributed deep learning framework called ubiquitous neural network (UbiNN) is proposed to improve communication efficiency without affecting the accuracy of the local neural network model at the edge or the global neural network model in the cloud. As for the accuracy of the neural network model, a common dataset with a small portion of insensitive data is constructed for training the neural network model, and its accuracy is enhanced by a new algorithm based on knowledge distillation and covariance computation (KDCC). Experimental results demonstrate that the test accuracy of UbiNN is extremely close to the centralized machine learning and non-federated learning scheme DDNN and up to 18.74% better than that of other classic federated learning schemes when using public datasets such as MNIST, CIFAR-10, and REUTERS-21578. Meanwhile, communication overheads are substantially reduced in terms of data transmission volume and latency.