Covariance Matrix Method Research Articles

Analysis of statistical uncertainties of non-contact temperature and emissivity measurements in the optical and near infrared ranges

The aim of this report is the analysis of the uncertainties of non-contact measurement of temperature and emissivity determined by the least sum of squares (LSS) method. Analytical expressions are obtained for the uncertainties of the temperature T and the emissivity ε by three methods: (1) linear regression using the Wien approximation, (2) non-linear regression with covariance matrix calculation using the Planck’s equation, and (3) hybrid method that combines linear and non-linear regression methods. It was found that the better the condition for the Wien’s approximation is fulfilled, the worse the accuracy of the emissivity measurement compared to the accuracy of the temperature measurement. The new optimal strategy is proposed to determine the T and the emissivity ε for non-contact measurements. It consists of three steps: (1) the temperature of the radiating body is found by the Wien approximation, TW; (2) the obtained value TW is used as an initial approximation for one-dimensional “hybrid” minimization. Minimization is carried out by one of the numerical methods of one-dimensional minimization. As a result, the values of ε0 and T0 are found at with the sum of the squared residuals, S0, reaches a minimum; (3) Measurement uncertainties are estimated using the covariance matrix method.

Improved Hedge Fund Portfolio Optimization Using 2-Step Covariance Matrix and Fund Transaction Costs

This study focuses on fund portfolio investments in the Chinese market. The application of classic portfolio optimization methods encounters several issues when applied to fund portfolios. For example, issues such as the non-normal distribution of returns on funds or fund portfolios, turnover rate limitations in fund investments, and liquidity constraints of fund assets, which can lead to transaction costs and opportunity costs, are prevalent challenges. The existence of these issues can compromise the effectiveness of classic portfolio optimization methods like Mean-Variance Optimization. This may result in a reduction of accuracy in determining the portfolios optimal weights, a deviation of actual trading results from the models optimal expectation, and may even render the optimal weights impractical in real-world scenarios. To address these challenges, this paper integrates the 2-Step covariance matrix method (2-Step method) and the measurement of fund transaction costs into the portfolio optimization process. The paper finds that the 2-Step method, compared to the baseline, can indeed improve the risk-return indicators of the potimal fund portfolio. The inclusion of the transaction cost can effectively control the turnover frequency of the portfolio. Even after accounting for these costs, the 2-Step method continues to exhibit a significant improvement effect compared to the baseline.

Exploration of Agricultural Product Packaging Design Innovation in the Context of Deep Learning

Abstract Utilizing Internet technology and resources to enhance the packaging design of agricultural products is a critical task for promoting their development in the current era. This study proposes an automatic generation design for agricultural product packaging based on deep learning theory, grounded in the principles of packaging design and market value. To represent the spatial relationship and distribution of color pixels, color moments and color correlation maps are used after obtaining color features of agricultural products through the HSV color space. The grayscale covariance matrix method is employed to get the texture features necessary for the packaging design. Proportion, boundary, pairing, white space, and balance calculations are combined to achieve the layout and typography of feature elements in the agricultural packaging design. The impact of deep learning technology-supported packaging design is analyzed. Data show that in the first group, the average values of the sample group (P001, P002, P004) are 2.98, 3.08, and 2.93, respectively, with an overall average of 2.997, while the overall average of the intelligent group (P003) is 2.96. Overall, deep learning technology-assisted image generation has a positive impact on agricultural product packaging design, contributing to a new level of economic development of farming products.

Stability Analysis of Super-Large Special-Shaped Deep Excavation in Coastal Water-Rich Region Considering Spatial Variability of Ground Parameters

The excavation of a super-large foundation pit is a greatly risky project in coastal water-rich silt strata, and it is of great significance to establish a numerical model to analyze and predict the stability of the foundation pit retaining its structure for safe construction. Based on a geological investigation report and key node monitoring data, the model parameters have been modified. Subsequently, the random field theory and numerical analysis were employed to proceed with deterministic analysis and uncertainty analysis, respectively. Using the uniform distribution method, Gaussian distribution method and the covariance matrix method to generate a random field model, finite difference software was applied to analyze the impact of spatial variability of cohesion and the internal friction angle on structural deformation. The study shows that the overall distribution of axial force is small on both sides and large in the center, and the axial force is larger near the shaped region. Due to the principle of “lever”, there is a tendency for the horizontal displacement of surrounding piles to partially rebound from the pit when the bearing platform pit is excavated. The spatial variability of the internal friction angle and cohesion has an important influence on the numerical value of the enclosure structure and surface deformation, and the variation pattern is basically unchanged.

Detection of Pancreatic Cancer Using Convolutional Neural Network Classifier

Early-stage pancreatic cancer is highly curable, although it is uncommon to find. This is because symptoms often don’t show up until the disease has spread to other organs. The treatment choices for pancreatic cancer are determined on the extent of the malignancy. Options include surgery, chemotherapy, radiation therapy, or a combination of these. Nevertheless it is are difficult to separate and manually classify because of their small size and hazy boundaries. This study proposes to identify pancreatic cancer by utilizing an optimized convolutional neural network (CNN) classifier. The test image is segmented using the Fuzzy C Means segmentation approach. The Grey Wolf Optimization GWO algorithm is used to optimize the procedure after features are extracted using Gabor based Region Covariance Matrix Method. The result is accurately predicted owing to strong classifier (a GWO-based CNN). The proposed work is implemented using simulation tools from MATLAB.

Comparison of Continuously Recorded Seismic Wavefields in Tectonic and Volcanic Environments Based on the Network Covariance Matrix

AbstractExtended and sufficiently dense seismic networks capture spatiotemporal properties of the continuously recorded wavefields and can be used to compute the level of their coherence at different frequencies via the analysis of the network covariance matrix, which has been successfully used to study volcanic seismicity. Here, we present an application of the covariance matrix method in a subduction zone environment. We show that most coherent signals identified through the covariance matrix analysis are related to regional earthquakes with the wavefield properties affected by the scattering, which depends on the source location. Tectonic tremors, on the other hand, are not characterized by a high level of coherence. We compare real data results with a set of synthetic tests aimed at mimicking the properties of seismic sources and the main features of wave propagation. We conclude that highly coherent volcanic tremor wavefields could be produced in two ways: by a spatially localized group of monochromatic seismic sources or by a single source located in a highly heterogeneous medium. In both cases, the stability of the source position is a necessary condition to reproduce the observations in volcanoes. On the other hand, the low coherence of tectonic tremor wavefields can be explained by a spatially extended distribution of sources, in agreement with large portions of the subduction interface being nearly simultaneously involved in the episodes of slow deformation.

Tracking changes in the co-eruptive seismic tremor associated with magma degassing at Piton de la Fournaise volcano

Volcanic eruptions in basaltic systems represent the most frequent expression of volcanic activity in the World, whose surface manifestations range from effusive lava flows to more explosive events. Their eruptive dynamics and style are largely controlled by the degassing of magma. In this study, we analyze seismic tremors recorded during 23 eruptions that occurred at Piton de la Fournaise volcano (La Réunion, France) during 2014–2021 and show that their properties are strongly linked to the magma degassing. We apply the network covariance matrix method to build a catalog of tremor sources associated with all 23 eruptions, to measure their time-frequency properties, and to locate their sources. We then conduct a multi-disciplinary analysis by comparing the seismic tremor observations with images of the eruptive sites, lava flow rate measurements, impulsive earthquakes, as well as deformation and magma composition data. The tremor depth distribution is found to be well correlated with magma gas content, indicating that the tremor generating mechanism is largely controlled by the shallow magma degassing under the eruptive site. The resulting seismic tremor signals analysis enable to track changes in degassing regimes and associated eruptive styles at the surface, thus improving monitoring and knowledge of the eruptive dynamics of the studied volcano.

Angle resolved x-ray photoelectron spectroscopy assessment of the structure and composition of nanofilms—including uncertainties—through the multilayer model

The multilayer model (MLM) for assessing the structural and composition parameters of multilayered nanofilms from angle-resolved x-ray photoelectric spectroscopy is described in detail. It is compared with regularized back-transform (RBT) approaches such as the maximum entropy method (MEM) with Tikhonov-type regularizations. The advantages of MLM over MEM, such as the possibility of assessing confidence ranges, modeling structures beyond conformal multilayered nanofilms, and modeling abrupt interfaces, are discussed and exemplified. In contrast with MLM, the RBT methods have shortcomings such as the violation of the conservation of information and the inability to adequately address the dependence of the effective attenuation length on the material. Examples of the application of MLM to conformal films and systems with protrusions are shown. The covariance matrix method (CMM) is described and applied to assess uncertainties in structural parameters and composition under the MLM. The CMM constitutes the canonical method for assessing confidence ranges and adequately accounts for the covariance among structural (e.g., layer thicknesses) and composition parameters.

Evolution of circuit complexity in a harmonic chain under multiple quenches

We study Nielsen’s circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. This simple system is amenable to analytical computations and yet offers considerable insight into the dynamics of quantum information. For a single quench scenario, we highlight some important differences between our results that explicitly use the wavefunction, as compared to the recently proposed covariance matrix method and point out the consequences. In a multiple quench scenario, the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy and the out of time ordered correlator. In particular, the latter is known to show signs of chaos in this integrable system, but our results indicate the contrary. We further show the presence of a ‘residual complexity,’ i.e. after two successive quenches, when the frequency returns to its initial value, the complexity has a non-zero lower limit. Further, applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. Finally, we show that this simplistic model exhibits the interesting phenomenon of ‘complexity crossover’ between two successive quenches performed at different times.

Detailed peak fitting analysis of the Ni 2p photoemission spectrum for metallic nickel and an initial oxidation

A quantitative study of the surface composition of clean metallic and partially oxidized nickel exposed to oxygen was carried out employing X-ray photoelectron spectroscopy (XPS). By fitting both branches of the metallic Ni 2p spectrum, it was possible to resolve two previously unreported satellite peaks in the Ni 2p1/2 portion of the spectrum. For the partial oxidation of the nickel surface, we analyzed the Ni 2p, O 1s, and C 1s angle-resolved XPS spectra. Using state-of-the-art peak-fitting (including the block approach) and background modeling methods (including the active approach) it was possible to discriminate the peaks of Ni2O3 from those of metallic nickel for both branches of the Ni 2p spectra from partially oxidized nickel. The oxidation of metallic nickel is through the formation of a Ni+3 oxide layer together with deep protrusions. The uncertainties are calculated with the covariance matrix method. The strong overlap and shape similarity of the Ni0 L3M45M45 Auger structure with that of the Ni+3 strongly suggests that the modified Auger Parameter does not provide direct additional insight about the chemical state to that provided by the photoemission spectra.

The study of geomagnetic jerk from 2010 to 2021 based on hourly mean data from global geomagnetic observatories

The secular variation in the global geomagnetic field was analyzed in terms of the annual differences in monthly means by using the hourly mean data from 18 foreign (outside China) observatories of the World Data Center (WDC) for Geomagnetism from January 2010 to January 2020 as well as 9 observatories in the Geomagnetic Network of China from January 2015 to April 2021. In addition, according to the correlation of noisy components from the observatories, a covariance matrix was constructed based on residuals between observations and the CHAOS-7.4 model to remove external contamination. Through a comparison before and after denoising, we found that the overall average standard deviations were reduced by 29.97% in China and by 41.4% outside China. Results showed the correlation coefficient between external noise (mainly the magnetosphere ring current) and the <italic>Dst</italic> index was 0.82, and the correlation coefficient between external noise and the Ring Current (RC) index reached 0.94. A geomagnetic jerk was globally discovered around 2018.0 on the geomagnetic eastward component <italic>Y</italic>. The jerk timing in China was around 2020.0, and the earliest one was in 2018.75, whereas the timing outside China was around 2018.0, and the earliest one was in 2017.67. This 2-year lag may have been caused by the higher electrical conductivity of the deep mantle. After more data were added, this jerk event was found to occur in an orderly manner in the northern hemisphere as the longitude increased and the intensity gradually increased as well. The variations in location of the jerk center were analyzed according to the CHAOS-7.4 model. Results revealed six extreme points distributed nearby the equator. The strongest was near the equator, at 170°E, and the strength gradually decreased as it extended to the northern and southern hemispheres. Another extreme point with the opposite sign was located at the equator, at 20°W, in the south-central part of the Atlantic, and the strength gradually decreased as it extended into Europe. The covariance matrix method can be used to analyze data from the Macau Science Satellite-1 mission in the future, and this method is expected to play a positive role in modeling and separating the large-scale external field.

A novel online BCI system using speech imagery and ear-EEG for home appliances control

Background and ObjectiveThis paper investigates a novel way to interact with home appliances via a brain-computer interface (BCI), using electroencephalograph (EEG) signals acquired from around the user's ears with a custom-made wearable BCI headphone. MethodsThe users engage in speech imagery (SI), a type of mental task where they imagine speaking out a specific word without producing any sound, to control an interactive simulated home appliance. In this work, multiple models are employed to improve the performance of the system. Temporally-stacked multi-band covariance matrix (TSMBC) method is used to represent the neural activities during SI tasks with spatial, temporal, and spectral information included. To further increase the usability of our proposed system in daily life, a calibration session, where the pre-trained models are fine-tuned, is added to maintain performance over time with minimal training. Eleven participants were recruited to evaluate our method over three different sessions: a training session, a calibration session, and an online session where users were given the freedom to achieve a given goal on their own. ResultsIn the offline experiment, all participants were able to achieve a classification accuracy significantly higher than the chance level. In the online experiments, a few participants were able to use the proposed system to freely control the home appliance with high accuracy and relatively fast command delivery speed. The best participant achieved an average true positive rate and command delivery time of 0.85 and 3.79 s/command, respectively. ConclusionBased on the positive experimental results and user surveys, the novel ear-EEG-SI-based BCI paradigm is a promising approach for the wearable BCI system for daily life.

Direction-of-Arrival Estimation Under Coexistence of both Circular and Strictly Non-Circular Signals in Coprime Linear Array

Direction-of-arrival (DOA) in coprime linear array involves the problem that existing algorithms have less taken signal features into consideration. Considering that there is coexistence of multiple both circular and strictly non-circular signals in communication systems, an approach to DOA estimation of high accuracy and degree of freedom is proposed in this letter. We first use the ellipse covariance matrix and matrix completion method to reconstruct the covariance matrix of a virtual linear array. This virtual matrix only concludes the components of noncircular signals. Then, we similarly use the covariance matrix and matrix completion method to reconstruct a new covariance matrix including all signals of another virtual linear array. We use the virtual non-circular covariance matrix to eliminate the non-circular components in another virtual matrix. Finally, this matrix only concludes the circular signals. And we apply multiple signals classification to obtain the DOAs of two kinds of signals separately. Simulation results show that the proposed algorithm can obtain a highest degree of freedom than existing algorithms and hold on a preferable accuracy.

An Eigenvalues-Based Covariance Matrix Bootstrap Model Integrated With Support Vector Machines for Multichannel EEG Signals Analysis.

Identification of alcoholism is clinically important because of the way it affects the operation of the brain. Alcoholics are more vulnerable to health issues, such as immune disorders, high blood pressure, brain anomalies, and heart problems. These health issues are also a significant cost to national health systems. To help health professionals to diagnose the disease with a high rate of accuracy, there is an urgent need to create accurate and automated diagnosis systems capable of classifying human bio-signals. In this study, an automatic system, denoted as (CT-BS- Cov-Eig based FOA-F-SVM), has been proposed to detect the prevalence and health effects of alcoholism from multichannel electroencephalogram (EEG) signals. The EEG signals are segmented into small intervals, with each segment passed to a clustering technique-based bootstrap (CT-BS) for the selection of modeling samples. A covariance matrix method with its eigenvalues (Cov-Eig) is integrated with the CT-BS system and applied for useful feature extraction related to alcoholism. To select the most relevant features, a nonparametric approach is adopted, and to classify the extracted features, a radius-margin-based support vector machine (F-SVM) with a fruit fly optimization algorithm (FOA), (i.e., FOA-F-SVM) is utilized. To assess the performance of the proposed CT-BS model, different types of evaluation methods are employed, and the proposed model is compared with the state-of-the-art models to benchmark the overall effectiveness of the newly designed system for EEG signals. The results in this study show that the proposed CT-BS model is more effective than the other commonly used methods and yields a high accuracy rate of 99%. In comparison with the state-of-the-art algorithms tested on identical databases describing the capability of the newly proposed FOA-F-SVM method, the study ascertains the proposed model as a promising medical diagnostic tool with potential implementation in automated alcoholism detection systems used by clinicians and other health practitioners. The proposed model, adopted as an expert system where EEG data could be classified through advanced pattern recognition techniques, can assist neurologists and other health professionals in the accurate and reliable diagnosis and treatment decisions related to alcoholism.

Fast and Accurate Spectrum Estimation via Virtual Coarray Interpolation Based on Truncated Nuclear Norm Regularization

Compared with the Nyquist sampling scheme, the coprime sampling scheme reduces the requirement of sampling rate significantly and simultaneously shows high degrees of freedom. Actually, the information received by the sampler is not fully utilized due to the non-uniformity of derived second-order virtual coarray. In addition, the virtual signals corresponding to the non-uniform virtual coarray may be contaminated by noise, which could affect the accuracy of spectrum estimation. In this letter, we propose a novel virtual coarray interpolation method for the inexact Toeplitz covariance matrix based on truncated nuclear norm regularization. The missing elements and exact covariance matrix can be obtained simultaneously by solving the covariance matrix completion problem that contains the error term and non-Toeplitz errors propagation control term. Simulation results demonstrate the superiorities of the proposed spectrum estimation method in terms of accuracy and computational complexity.

A generalised eigenvalue reweighting covariance matrix estimation algorithm for airborne STAP radar in complex environment

To improve the space-time adaptive processing (STAP) performance of airborne radar in complex environment, a generalised eigenvalue reweighting covariance matrix estimation algorithm called GERCM is proposed here. First, the interference plus noise (IPN) covariance matrix of cell under test (CUT) data is estimated by the selected target-free training samples around the CUT with the sample covariance matrix method. Then, with the component decompositions of the selected training samples and the assumption of approximately equal subspace, the IPN covariance matrix of CUT data is reformulated by the eigenvector matrix, eigenvalue matrix, and the eigenvalue reweighting vector. Subsequently, based on the modified covariance matching estimation criterion, the eigenvalue reweighting vector is estimated by solving the redesigned convex optimisation problem with the Lagrange dual method. Finally, the STAP weight vector is calculated to process the CUT data. The proposed algorithm can obtain a relatively accurate IPN covariance matrix of CUT data by sufficiently utilising the non-homogeneous training samples and can effectively protect the moving targets in CUT data, which can be applied to airborne radar with arbitrary array structure and antenna configuration. Simulation results and performance analyses based on the multi-channel airborne radar measurement data demonstrate the effectiveness of the proposed GERCM algorithm.

An adaptive method for tuning process noise covariance matrix in EKF-based three-phase distribution system state estimation

This paper proposes a new adaptive method for online tuning of process noise covariance matrix in the Extended Kalman Filter based three-phase distribution system state estimator. Specifically, a new form of exponential function is proposed for tuning the process noise covariance matrix, adapting it to the level of state changes. A new indicator derived from normalized innovations of the available real-time and virtual measurements is developed for tracking the level of state changes. The proposed method relies on measurements of the existing distribution networks, and therefore can be easily implemented in the advanced distribution management system. The method efficiently adapts process noise to system state variations and can deal with both quasi steady-state and unexpected sudden state changes caused by changes in the system topology, generation or demand. Comparison results with other state-of-the-art adaptive methods on the modified IEEE 37-bus and IEEE 123-bus distribution systems show that the proposed method achieves better accuracy under quasi steady-state condition while being more robust to unexpected sudden state changes.

Using Optimum Index Factor and Determinant Covariance Methods and Compare to PCA on Satellite Images to Determine The Earth’s Landmarks ( Part of Tar- An Najaf and Its Neighbours)

The research focuses on mixing of Landsat8 ETM+ images for sector of Tar An- Najaf Phenomenon for the sake of gaining the optimum description showing the ground guidelines of the studied area. The optimum Index Factor (OIF) method has ensured that RGB567 represents the preferred mixed bands, where vegetated areas, water and rocks and deposits more obviously distributed. The determinant covariance matrix method stated that RGB457 considered the optimum for spectral resolution. For comparison with Principal Component Analysis, the latter involves PC1,2,3 and shows clear variations that serve the interpreter as a detailed study. Through the study, the best method is the second one.

Constraining the orientation of the spin axes of extrasolar minor bodies 1I/2017 U1 (‘Oumuamua) and 2I/Borisov

Context.The orientation of the spin axis of a comet is defined by the values of its equatorial obliquity and its cometocentric longitude of the Sun at perihelion. These parameters can be computed from the components of the nongravitational force caused by outgassing if the cometary activity is well characterized. The trajectories of known interstellar bodies passing through the Solar System show nongravitational accelerations.Aims.The spin-axis orientation of 1I/2017 U1 (‘Oumuamua) remains to be determined; for 2I/Borisov, the already released results are mutually exclusive. In both cases, the values of the components of the nongravitational force are relatively well constrained. Here, we investigate – within the framework of the forced precession model of a nonspherical cometary nucleus – the orientation of the spin axes of ‘Oumuamua and 2I/Borisov using public orbit determinations that consider outgassing.Methods.We applied a Monte Carlo simulation using the covariance matrix method together with Monte Carlo random search techniques to compute the distributions of equatorial obliquities and cometocentric longitudes of the Sun at perihelion of ‘Oumuamua and 2I/Borisov from the values of the nongravitational parameters.Results.We find that the equatorial obliquity of ‘Oumuamua could be about 93°, if it has a very prolate (fusiform) shape, or close to 16°, if it is very oblate (disk-like). Different orbit determinations of 2I/Borisov gave obliquity values of 59° and 90°. The distributions of cometocentric longitudes were in general multimodal.Conclusions.Our calculations suggest that the most probable spin-axis direction of ‘Oumuamua in equatorial coordinates is (280°, +46°) if very prolate or (312°, −50°) if very oblate. Our analysis favors a prolate shape. For the orbit determinations of 2I/Borisov used here, we find most probable poles pointing near (275°, +65°) and (231°, +30°), respectively. Although our analysis favors an oblate shape for 2I/Borisov, a prolate one cannot be ruled out.

Extracting the Meaning Order of Alley [Case Study: Historical Context of Sari City Center

The present study is an attempt to find out conceptual and fondumental aspects of alley meaning in the context of Sari historical city center. In this research the considered environment is the allies of historical center context of Sari city. This research tries to discover the hidden meaning system behind the current behaviors and activities in the alleys of this area. This research is based on Exploratory factor analysis research method which is one of the branches of correlation research method and is calculated by using covariance matrix method of analysis. The results of this study showed that there is a collection of meaning components which are working as a network in the final model. The study identified 17 components that were categorized into four main systems: individual social position, individual internal feelings, cultural relationships, and tradition. This paper concludes that the proposed model carefully shows the meanings regulation of the historical fabric of alleys.