Matrix Estimation Research Articles

Coherent structures decomposition of internal flow in the double-suction centrifugal pump impeller

Abstract In order to understand the unsteady flow phenomenon of the centrifugal pump, the dynamic mode decomposition method (DMD) is introduced to extract the three-dimensional coherent structure of the rotating flow field in the impeller passage under three different working conditions of the double-suction centrifugal pump. The time series collection of flow field is constructed by CFD numerical simulation, and the approximate matrix characteristic parameters and different modal data are solved. The analysis results show that the position, form and spatial-temporal evolution of the coherent structure can be accurately captured by DMD method corresponding to a single frequency in the double suction pump. For the temporal evolution, the coherent structure corresponding to low frequency is the most stable and dominate the unsteady flow. For the spatial evolution, the coherent structure corresponding to even-fold rotational frequency mostly occurs near the pressure side of the blade at the outlet of the impeller, and the coherent structure corresponding to odd-fold rotational frequency is mostly located in the flow field inside the impeller or near the blade surface.

Evaluating the Effect of Multiple Data Types on a Large Scale Static Origin–Destination Matrix Estimation, Case Study of Tehran, Iran

Evaluating the Effect of Multiple Data Types on a Large Scale Static Origin–Destination Matrix Estimation, Case Study of Tehran, Iran

Interspecific selection in a diverse mycorrhizal symbiosis.

Coevolution describes evolutionary change in which two or more interacting species reciprocally drive each other's evolution, potentially resulting in trait diversification and ecological speciation. Much progress has been made in analysis of its dynamics and consequences, but relatively little is understood about how coevolution works in multispecies interactions, i.e., those with diverse suites of species on one or both sides of an interaction. Interactions among plant hosts and their mutualistic ectomycorrhizal fungi (ECM) may provide an ecologically unique arena to examine the nature of selection in multispecies interactions. Using native genotypes of Monterey pine (Pinus radiata), we performed a common garden experiment at a field site that contains native stands to investigate selection from ECM fungi on pine traits. We planted seedlings from all five native populations, as well as inter-population crosses to represent intermediate phenotypes/genotypes, and measured seedling traits and ECM fungal traits to evaluate the potential for evolution in the symbiosis. We then combined field estimates of selection gradients with estimates of heritability and genetic variance-covariance matrices for multiple traits of the mutualism to determine which fungal traits drive plant fitness variation. We found evidence that certain fungal operational taxonomic units, families and species-level morphological traits by which ECM fungi acquire and transport nutrients exert selection on plant traits related to growth and allocation patterns. This work represents the first field-based, community-level study measuring multispecific coevolutionary selection in nutritional symbioses.

Statistical Inference Using Partially Accelerated Life Test Model for the Weibull Population Mean Unified Hybrid Censored Data

In this paper, estimates of the parameters and the acceleration factor of a new distribution known as the Weibull Population Mean Distribution (WPMD) are explored. We propose the use of the model suggested by Abd-Elrahman [A better alternative to the generalized Bilal distribution: A new model and applications, Int. J. Reliab. Qual. Saf. Eng. 30(6) (2023) 2350027, doi: 10.1142/S0218539323500274] for estimating these parameters. To accomplish this, we employ the maximum likelihood estimation method via a Constant-Stress Partially Accelerated Life Test (CSPALT) model. In this study, we have utilized Unified Hybrid (UH) censored data obtained from the WPMD. Confidence intervals for the model parameters and the acceleration factor are constructed based on the approximate Fisher information matrix. The average and Mean Squared Error (MSE) of estimates are computed to evaluate the performance of the proposed method under the CSPALT model. Additionally, a real data set is provided for illustrative purposes, and a numerical analysis of the UH Censoring Scheme (UHCS) is carried out. Finally, concluding remarks are presented.

Behavioral Modeling and Digital Predistortion for Power Amplifier Based on the Sparse Smooth Twin Support Vector Regression Method

In this paper, a sparse smooth twin support vector regression (Sparse‐STSVR) model for power amplifier (PA) behavioral modeling is obtained by pruning the kernel matrix based on Cholesky decomposition. Based on the primal smooth twin support vector regression (STSVR) model, the Nystrom approximate matrix of the kernel matrix is found to replace the original kernel matrix, thus simplifying the Newton iterative parameter extraction process of the primal STSVR model and accelerating the convergence of the algorithm. In addition, the new rank approximation kernel matrix has the characteristic of sparse parameters, which further reduces the computational complexity of the feedforward link of the digital predistorter. The 100 MHz 5G New Radio (NR) signal is used for verify the effect of PA modeling and digital predistortion (DPD) experiment. The results show that the proposed method can improve the normalized mean square error (NMSE) by about 2 ~ 3 dB with fewer coefficients compared with the previously proposed machine learning model, and the predistortion linearization effect improves by nearly 3 dB on the adjacent channel power ratio (ACPR), which achieves a good trade‐off between model performance and computational complexity. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Asymptotics of Solutions of Autonomous Singularly Perturbed Equations when the Stability of the Equilibrium Position Changes at Several Points

Considers a system consisting of 2n equations with fast variables and one equation with a slow variable. The first approximation matrix of the system of fast variables has 2n pairwise complex conjugate eigenvalues. The stability of the equilibrium position, a system of fast variables, is influenced by all eigenvalues. Early studies considered cases where the stability of the equilibrium position is affected by only one pair of complex conjugate eigenvalues. The problem of delaying the solution of a system of fast variables near an unstable equilibrium position has been solved. The delay time for the decision is determined.

DFTB Simulation of Charged Clusters Using Machine Learning Charge Inference.

We present a modification to self-consistent charge density functional-based tight binding (SCC-DFTB), which allows computation based on approximate atomic charges. We obtain these charges by means of a machine learning (ML) process that combines a Coulomb model with a neural network. This allows us to avoid the SCC cycles in the SCC-DFTB calculation while maintaining its accuracy. The main input of the model is the atomic positions characterized by a set of atom-centered symmetry functions. The charge inference from our ML algorithm is as close as 10-2 units of charge from the exact SCC solution. Our ML-DFTB approach provides a good approximation of the density matrix and of the energy and forces with only a single diagonalization. This is a significant computational saving with respect to the complete SCC algorithm, which allows us to investigate a bigger ensemble of atoms. We show the quality of our approach in the case of charged silicon carbide (SiC) clusters. The ML-DFTB potential energy surface (PES) mimics the SCC-DFTB PES rather well, despite its simplicity. This allows us to obtain the same geometric structure ordering with respect to energy for small clusters. The dissociation barriers for ion emission are well-reproduced, which opens the way to investigating ion field emission and charged cluster stability. The ML-DFTB approach is obviously not limited to charged clusters or SiC materials. It opens a new route to investigate larger clusters than those investigated by standard SCC-DFTB, as well as surface and solid-state chemistry at the atomic level.

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

AbstractHere, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

Regularizing stock return covariance matrices via multiple testing of correlations

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within multiple testing procedures, controlling either the traditional familywise error rate, a generalized familywise error rate, or the false discovery proportion. Subsequent shrinkage ensures that the final covariance matrix estimate is positive definite and well-conditioned while preserving the achieved sparsity. Compared to alternative estimators, this new regularization method demonstrates strong performance in simulation experiments and real portfolio optimization.

Depth linear discrimination-oriented feature selection method based on adaptive sine cosine algorithm for software defect prediction

Software Defect Prediction (SDP) plays a vital role in the software development life cycle as it helps identify and fix software defects. However, predicting software defects with irrelevant features and overlapping classes is challenging and can lead to lengthy training and low model accuracy. To address these challenges, this research introduces a novel Depth Linear Discrimination-Oriented Feature Selection Method based on Adaptive Sine Cosine Algorithm, named Depth Adaptive Sine Cosine Feature Selection (DASC-FS). DASC-FS integrates the Adaptive Sine Cosine Algorithm (ASCA) as a search algorithm to determine the relevant features and adopts Depth Linear Discriminant Analysis (D-LDA) to identify the discriminative features that maximize class separation. The paper proposes ASCA which is a metaheuristic algorithm meticulously designed to enhance the search capabilities of the standard Sine Cosine Algorithm (SCA). Combining the simplicity of the SCA with the efficiency of multiple mutation operators inspired by Genetic Algorithms (GA), ASCA enhances the diversity of the solutions and imparts remarkable adaptability to various situations. Furthermore, this study introduces a novel linear discriminant method, called Depth Linear Discriminant Analysis (D-LDA) to enhance the robustness of the original LDA. D-LDA systematically integrates the matrix depth concept into LDA, offering a systematic approach to address the challenges associated with scatter matrix estimation. As matrix depth measures how central or deep a particular matrix is within a distribution with respect to different directions, it is an efficient tool for computing a robust scatter matrix estimator that can handle outliers and complex data structures. The experimental results showed that DASC-FS consistently obtains the highest accuracy compared to most existing methods by integrating ASCA and D-LDA, thereby considering both accuracy optimization and class separation. The results also show that the use of multiple mutation operators in ASCA improves the search process capabilities. The results also show that the capacity of D-LDA to reduce data dimensionality and increase class separation yields highly competitive results compared to other LDAs. Finally, features related to code size and complexity have emerged as key factors for SDP because they consistently rank as important features across different classifiers and datasets. DASC-FS offers a valuable solution in domain knowledge for enhancing predictive accuracy and understanding factors contributing to software defects through enhanced search capabilities, robust scatter matrix estimation, and the ability to reduce data dimensionality.

Scattering from time-modulated subwavelength resonators

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We consider the one-dimensional setting. In order to understand the energy of the system, we prove a novel higher-order discrete, capacitance matrix approximation of the subwavelength resonant quasi-frequencies. Further, we perform numerical experiments to support and illustrate our analytical results and show how periodically time-dependent material parameters affect the scattered wave field.

Joint Optimization of Measurement Point Intelligent Selection and End-to-End Network Traffic Calculation in Datacenters

The effective design and management of data centers needs to follow the end-to-end traffic characteristics of data center networks (DCNs). However, directly measuring the end-to-end traffic of the network requires huge software and hardware costs. Since the particularity of the structure of DCNs, the flow estimation method used in the traditional computer network cannot be applied to existing DCNs. In this paper, we study the end-to-end traffic calculation of cloud computing DCNs. We propose <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> , which is an intelligent end-to-end traffic inference algorithm based on network tomography. Only using SNMP (simple network management protocol) data generally supported by switches, end-to-end traffic information can be calculated quickly and accurately. <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> first devices a network traffic measurement point intelligent selection scheme based on node weighting. It first assigns weight to nodes through node criticality, and then uses node weighted incidence matrix approximation algorithm to calculate initial solution. <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> then designs a network tomography method suitable for cloud computing network traffic calculation. It uses the time correlation of data center traffic to model the algorithm problem into a linear state space model, and finally calculates the traffic carried by each path through the improved Kalman filtering algorithm. Our evaluation and analysis demonstrate that <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> can effectively use the extracted coarse-grained traffic characteristics, and greatly improve the accuracy of the calculation on the premise of ensuring the computational efficiency.

Do FDI And Trade Openness Affect Economic Growth Differently Across Income Groups? Case Studies From Asian Countries

This study examines the nexus between foreign direct investment (FDI), trade openness (TRO) and economic growth for selected 11 high-income and 22 middle- and low-income Asian countries within a model using a more recent panel dataset over the period 2000–2021. The cointegration test has been applied in this study, which shows that whether there is a long-term interrelationship between FDI and economic growth, which we focus on in particular, and then the covariance matrix estimators that are developed by Driscoll and Kraay are used. Our findings indicate that there is a positive relationship between FDI and TRO, and economic growth for high-income countries, whereas the relationship between FDI and economic growth is negative for middle- and low-income countries. This study provides insights on why governments and policy makers in developing countries should focus on prioritizing domestic investment and production strategies for sustainable economic growth rather than simply emphasizing the attractiveness of FDI and the indispensability of import-oriented trade liberalization.

Faster cosmological analysis with power spectrum without simulations

ABSTRACT Future surveys could obtain tighter constraints on the cosmological parameters with the galaxy power spectrum than with the cosmic microwave background. However, the inclusion of multiple overlapping tracers, redshift bins, and more non-linear scales means that generating the necessary ensemble of simulations for model-fitting presents a computational burden. In this work, we combine full-shape fitting of galaxy power spectra, analytical covariance matrix estimates, the massively optimized parameter estimation and data compression (MOPED) method, and the Taylor expansion interpolation of the power spectrum for the first time to constrain the cosmological parameters directly from a state-of-the-art set of galaxy clustering measurements. We find it takes less than a day to compute the analytical covariance while it takes several months to calculate the simulated ones. Combining MOPED with the Taylor expansion interpolation of the power spectrum, we can constrain the cosmological parameters in just a few hours instead of a few days. We also find that even without a priori knowledge of the best-fitting cosmological or galaxy bias parameters, the analytical covariance matrix with the MOPED compression still gives consistent cosmological constraints to within 0.1σ after two iterations. Therefore, the pipeline we have developed here can significantly speed up the analysis for future surveys.

Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise. We propose a Bayesian approach to obtain a Hessian matrix approximation for stochastic optimization that minimizes the secant equations residue while retaining the extreme eigenvalues between a specified range. Thus, the proposed approach assists stochastic gradient descent to converge to local minima without augmenting gradient noise. We propose maximizing the log posterior using the Newton-CG method. Numerical results on a stochastic quadratic function and an ℓ 2 -regularized logistic regression problem are presented. In all the cases tested, our approach improves the convergence of stochastic gradient descent, compensating for the overhead of solving the log posterior maximization. In particular, pre-conditioning the stochastic gradient with the inverse of our Hessian approximation becomes more advantageous the larger the condition number of the problem is.

Analyzing Geospatial Cost Variability of Hybrid Solar–Gravity Storage System in High-Curtailment Suburban Areas

The increased decentralization of renewable energy has increased curtailment rates in stagnating demand zones, increasing the levelized cost of energy (LCOE). The geographically dynamic nature of gravity energy storage (GES) is emerging in the field of mechanical energy storage, over pumped hydro. However, GES costs vary geospatially, specifically in decentralized suburban areas, due to the impact of urban socioeconomics. This study aims to find a mathematical approximation of a cost-optimized location for suburban Solar–GES hybrid systems in curtailment-prone areas. A multi-parameterization model mathematically programmed land, transmission, supply chain and excavation costs into geospatial matrix approximations for suburban areas of 2500 km2 in Fukuoka and Ibaraki in Japan. It was found that SPV-GES location-dependent costs were mainly affected by distance from the city’s economic center and flat plains in suburbs, and supply chain and transmission costs optimized the location-dependent cost for GES at a specific point. It was also found that flat terrains were more economical than mountainous terrains due to high GES supply chain costs. With GES found to be cost-competitive compared to other storage technologies in Japan, this study reveals that GES introduction benefits the LCOE of suburban, decentralized SPV when curtailment is &gt;50% irrespective of terrain.

A visual servo reinforcement learning control of uncalibrated manipulators with multi-channel gain decision

A technology based on Kalman filtering method combined with multi-channel gain training reinforcement learning for uncalibrated camera visual servo tasks is proposed in this paper. First, a dynamic system with state variables formed from the elements of the image Jacobian matrix is constructed to describe the mapping relationship between two-dimensional images and three-dimensional poses. Kalman filter is used to estimate the state variables of the constructed system online. Next, the Jacobian matrix estimation and depth determination strategy gradient (DDPG) methods are combined to jointly train multi-channel gains by setting a reasonable segmented reward and punishment mechanism. Through training, a more effective gain decision can be obtained. The robustness of Kalman filtering to interference to a certain extent reduces the precise dependence of reinforcement learning models, thereby achieving higher robustness in intelligent visual servo control. Finally, the effectiveness and advantages of the Kalman-DDPG method have been demonstrated through simulation comparison and six-degree-of-freedom (DOF) uncalibrated manipulator physical experiments.

Improvements on Gaussian mixture model and its application in identifying aerosol types in two major cities in the Yangtze River Delta, China

Accurately identifying the authentic local aerosol types is one of the fundamental tasks in studying aerosol radiative effects and model assessment. In this paper, improvements were made to the traditional Gaussian Mixture Model, leading to the following results: 1) This study introduces several improvements to the traditional Gaussian Mixture Model (GMM), referred to as M-GMMs. These improvements include the incorporation of multivariate kurtosis coefficients, Mahalanobis distance instead of Euclidean distance, and weights of variables. The M-GMMs overcome the issues related to dimensional units and correlations among multiple parameters, thereby enhancing the estimation of the covariance matrix. 2) The proposed M-GMMs model was evaluated for its clustering performance using machine-generated data with known classifications and real iris flower data. The results demonstrated that the classification performance of M-GMMs was superior to other models. Furthermore, compared to the slightly less effective K-means algorithm (which requires manual definition of the number of aerosol types), the M-GMMs model was able to automatically iterate and produce consistent classification results based on similar characteristics. 3) There is still a significant disparity between the characteristics of real stations and typical aerosols. Directly evaluating local aerosols using the characteristics of typical aerosols results in substantial errors. However, the M-GMMs model can effectively reflect the authentic aerosol characteristics at the local level. 4) The M-GMMs model was utilized to perform cluster analysis on the Xuzhou and Nanjing stations of AERONET. This analysis yielded quantitative proportions, temporal distribution characteristics, and spectral distribution features of aerosol types in the two regions. The improved M-GMMs model presented in this paper enables more accurate and continuous characterization of aerosol type variations. Its findings hold significant theoretical and practical value in reassessing aerosol radiative effects.

Inverse matrix estimations by iterative methods with weight functions and their stability analysis

In this paper, we construct a parametric family of iterative methods to compute the inverse of a nonsingular matrix. This class is free of inverse operators. We prove the third-order of convergence under some conditions involving the parameter of the family. Moreover, a dynamical analysis is made for the first time to a matrix iterative method, finding intervals of stability, that include but are wider than those found in the convergence analysis. Numerical tests on large random matrices confirm the results found.

High-Dimensional Multivariate Linear Regression with Weighted Nuclear Norm Regularization

We consider a low-rank matrix estimation problem when the data is assumed to be generated from the multivariate linear regression model. To induce the low-rank coefficient matrix, we employ the weighted nuclear norm (WNN) penalty defined as the weighted sum of the singular values of the matrix. The weights are set in a nondecreasing order, which yields the non-convexity of the WNN objective function in the parameter space. Although the objective function has been widely applied, studies on the estimation properties of its resulting estimator are limited. We propose an efficient algorithm under the framework of the alternative directional method of multipliers (ADMM) to estimate the coefficient matrix. The estimator from the suggested algorithm converges to a stationary point of an augmented Lagrangian function. Under the orthogonal design setting, the effects of the weights for estimating the singular values of the ground-truth coefficient matrix are derived. Under the Gaussian design setting, a minimax convergence rate on the estimation error is derived. We also propose a generalized cross-validation (GCV) criterion for selecting the tuning parameter and an iterative algorithm for updating the weights. Simulations and a real data analysis demonstrate the competitive performance of our new method. Supplementary materials for this article are available online.