Tensor Model Research Articles

Strengthened Local Feature-Based Spatial–Temporal Tensor Model for Infrared Dim and Small Target Detection

Strengthened Local Feature-Based Spatial–Temporal Tensor Model for Infrared Dim and Small Target Detection

A Mutual Information-Based Assessment of Reverse Engineering on Rewards of Reinforcement Learning

Rewards are critical hyperparameters in reinforcement learning (RL), since in most cases different reward values will lead to greatly different performance. Due to their commercial value, RL rewards become the target of reverse engineering by the inverse reinforcement learning (IRL) algorithm family. Existing efforts typically utilize two metrics to measure the IRL performance: the expected value difference and the mean reward loss, which we call them EVD and MRL respectively. Unfortunately, in some cases, EVD and MRL can give completely opposite results, due to MRL focusing on whole state-space rewards while EVD only considering partly sampled rewards. Such situation naturally rises to one fundamental question: whether current metrics and assessment are sufficient and accurate for more general use. Thus, in this paper, based on the metric called normalized mutual information of reward clusters (C-NMI) we propose a novel IRL assessment; we aim to fill this research gap by considering a middle-granularity state space between the entire state space and the specific sampling space. We utilize the agglomerative nesting algorithm (AGNES) to control dynamical C-NMI computing via a 4-order tensor model with injected manipulated trajectories. With such a model, we can uniformly capture different-dimension values of MRL, EVD, and C-NMI, and perform more comprehensive and accurate assessment and analyses. Extensive experiments on several mainstream IRLs are experimented in Object World, hence revealing that the assessing accuracy of our method increases 110.13% and 116.59% respectively when compared with the EVD and MRL. Meanwhile, C-NMI is more robust than EVD and MRL under different demonstrations.

Studying differential cross section for elastic proton scattering by a tensor model

Previous studies have shown the reliability of the Bayesian Gaussian CANDECOMP/PARAFAC tensor decomposition (BGCP) algorithm in predicting the independent fission yields and evaluating global uncertainty of the data. This work proposes to apply the BGCP algorithm for the purpose of predicting and evaluating the differential cross section for elastic proton scattering. The tensor model is developed by training with the experimental data of elastic proton scattering from the EXFOR database. The Root Mean Square Error is used to evaluate the experimental data and search for potential errors and omissions in EXFOR, in order to identify outlying data of 98Mo, 100Mo, 144Sm and 209Bi. After the revision for the outlying data in EXFOR, the reproduced values for 144Sm are compared with the remaining controversial entries. Besides, the predicted data for 9C are compared with the published data not available in EXFOR. The results demonstrate that the tensor model can make reasonable predictions and has a role to play in evaluating the quality of elastic proton scattering data. The tensor model may become a powerful tool for nuclear data evaluation in EXFOR.

Low-rank plus sparse joint smoothing model based on tensor singular value decomposition for dynamic MRI reconstruction

Dynamic magnetic resonance imaging (DMRI) is an important medical imaging modality, but the long imaging time limits its practical applications. This paper proposes a low-rank plus sparse joint smoothing model based on tensor singular value decomposition (T-SVD) to reconstruct DMR images from highly under-sampled k-t space data. The low-rank plus sparse tensor (ℒ+S) model decomposes the DMR data into a low-rank and sparse tensor, which naturally fits the dynamic MR images characteristics and exploits the spatiotemporal correlation of DMRI data to improve reconstruction effect. T-SVD is utilized in the ℒ+S model to maintain the intrinsic structure of the low-rank tensor and further enhance the low-rank property. In addition, considering the global multi-dimensional smoothness of the DMR images, the proposed method joint tensor total variation (TTV) constraints to utilize the smoothness of DMR images to obtain more reconstruction details while protecting the global structure. We conducted experiments on the dynamic cardiac datasets, and the experiment results show that the proposed method has superior performance to several state-of-the-art imaging methods.

On one conjugate object in the symmetric tensor C*-category and the statistics of superselection sectors

In this work, a model of a symmetric tensor 𝐶*-category with conjugation is constructed for the dimension of the object 𝑑 = 3. It is proved that the constructed conjugate object of the category satisfies the conjugation equations. The classes of morphisms between objects of the modeled category are considered and studied, and the algebra of observables in the presence of such an conjugate object is introduced. As an application of the model, we consider the theory of quantum information transfer, where it is necessary to take into account the constraints associated with the superselection rules.

Effect of atmospheric stability on the dynamic wake meandering model applied to two 12 MW floating wind turbines

AbstractCurrent global analysis tools for floating wind turbines (FWTs) do not account for the combined effects of atmospheric stability and wakes from neighboring turbines. This work uses the mid‐fidelity dynamic wake meandering model, together with turbulent wind fields generated based on stable, neutral, and unstable atmospheric conditions, to study the low‐frequency content of the global responses of two semisubmersible FWTs separated by eight rotor diameters. Incoming wind fields based on the Kaimal spectrum and exponential coherence model, the Mann spectral tensor model, and a time‐series input‐based turbulence model are used. The respective input parameters for these models are fitted to high‐fidelity large eddy simulation data.In unstable, below‐rated conditions, meandering leads to an increase in the yaw standard deviation of the downwind turbine of almost three times larger than the upwind turbine. Deficit and the upwards wake deflection affect the mean pitch and yaw, especially for the below‐rated wind speed scenario. The mean pitch of the downwind turbine is reduced up to half the mean pitch value of the upwind turbine, whereas the mean yaw changes direction due to the enhanced effect of shear. The effect of meandering on the structural loading is highest on the standard deviation of the tower‐top yaw moment of the downstream turbine, which increases more than 2.2 times compared to the upwind turbine value. Based on these findings, atmospheric stability affects wake deficit and meandering which in turn have a profound effect on the low‐frequency global motions and structural response of floating wind turbines.

High angular diffusion tensor imaging estimation from minimal evenly distributed diffusion gradient directions.

Diffusion-weighted Imaging (DWI) is a non-invasive imaging technique based on Magnetic Resonance Imaging (MRI) principles to measure water diffusivity and reveal details of the underlying brain micro-structure. By fitting a tensor model to quantify the directionality of water diffusion a Diffusion Tensor Image (DTI) can be derived and scalar measures, such as fractional anisotropy (FA), can then be estimated from the DTI to summarise quantitative microstructural information for clinical studies. In particular, FA has been shown to be a useful research metric to identify tissue abnormalities in neurological disease (e.g. decreased anisotropy as a proxy for tissue damage). However, time constraints in clinical practice lead to low angular resolution diffusion imaging (LARDI) acquisitions that can cause inaccurate FA value estimates when compared to those generated from high angular resolution diffusion imaging (HARDI) acquisitions. In this work, we propose High Angular DTI Estimation Network (HADTI-Net) to estimate an enhanced DTI model from LARDI with a set of minimal and evenly distributed diffusion gradient directions. Extensive experiments have been conducted to show the reliability and generalisation of HADTI-Net to generate high angular DTI estimation from any minimal evenly distributed diffusion gradient directions and to explore the feasibility of applying a data-driven method for this task. The code repository of this work and other related works can be found at https://mri-synthesis.github.io/.

Federated generalized scalar-on-tensor regression

Complex systems are generating more and more high-dimensional data for which tensor analysis showed promising results by capturing complex correlation structures of data. Such data is often distributed among various sites creating challenges for developing data-driven models. Specifically, data privacy and security concerns have been exacerbated in recent years and drove the demand to store and analyze data at the edge of networks rather than sharing it with a centralized server. Federated learning frameworks have been introduced as a solution to these concerns. These frameworks allow local clients to learn local models and collaborate with others to develop a more generalizable aggregated model while handling data privacy issues. In this article, we propose a federated generalized scalar-on-tensor regression framework where multiple local tensor models are learned at the edge, and their parameters are shared with and updated by an aggregator. Experiments on synthetic data sets and two real-world data sets from agriculture and manufacturing domains show the superiority of our approach over several benchmarks.

Overview of Tensor-Based Cooperative MIMO Communication Systems-Part 1: Tensor Modeling.

Due to increasingly strong and varied performance requirements, cooperative wireless communication systems today occupy a prominent place in both academic research and industrial development. The technological and economic challenges for future sixth-generation (6G) wireless systems are considerable, with the objectives of improving coverage, data rate, latency, reliability, mobile connectivity and energy efficiency. Over the past decade, new technologies have emerged, such as massive multiple-input multiple-output (MIMO) relay systems, intelligent reflecting surfaces (IRS), unmanned aerial vehicular (UAV)-assisted communications, dual-polarized (DP) antenna arrays, three dimensional (3D) polarized channel modeling, and millimeter-wave (mmW) communication. The objective of this paper is to provide an overview of tensor-based MIMO cooperative communication systems. Indeed, during the last two decades, tensors have been the subject of many applications in signal processing, especially for digital communications, and more broadly for big data processing. After a brief reminder of basic tensor operations and decompositions, we present the main characteristics allowing to classify cooperative systems, illustrated by means of different architectures. A review of main codings used for cooperative systems is provided before a didactic and comprehensive presentation of two-hop systems, highlighting different tensor models. In a companion paper currently in preparation, we will show how these tensor models can be exploited to develop semi-blind receivers to jointly estimate transmitted information symbols and communication channels.

Tensor completion with noisy side information

We develop a new model for tensor completion which incorporates noisy side information available on the rows and columns of a 3-dimensional tensor. This method learns a low rank representation of the data along with regression coefficients for the observed noisy features. Given this model, we propose an efficient alternating minimization algorithm to find high-quality solutions that scales to large data sets. Through extensive computational experiments, we demonstrate that this method leads to significant gains in out-of-sample accuracy filling in missing values in both simulated and real-world data. We consider the problem of imputing drug response in three large-scale anti-cancer drug screening data sets: the Genomics of Drug Sensitivity in Cancer (GDSC), the Cancer Cell Line Encyclopedia (CCLE), and the Genentech Cell Line Screening Initiative (GCSI). On imputation tasks with 20% to 80% missing data, we show that the proposed method TensorGenomic matches or outperforms state-of-the-art methods including the original tensor model and a multilevel mixed effects model. With 80% missing data, TensorGenomic improves the R^2 from 0.404 to 0.552 in the GDSC data set, 0.407 to 0.524 in the CCLE data set, and 0.331 to 0.453 in the GCSI data set compared to the tensor model which does not take into account genomic side information.

Computing of Permeability Tensor and Seepage Flow Model of Intact Malan Loess by X-ray Computed Tomography

Malan loess is an eolian sediment in arid and semi-arid areas. It is of great significance to study the pore structure of Malan loess for its evolution, strength, and mechanical properties. In order to quantitatively characterize the absolute permeability tensor of Malan loess and to simulate the seepage process of Malan loess, this study calculated the specific yield of intact Malan loess with a homemade seepage experimental device and recorded the water flow process on the surface of Malan loess during the seepage process. Modern computed tomography was used to scan the intact Malan loess samples from Jiuzhoutai, Lanzhou (western part of the Loess Plateau, China); the specific yield of the intact loess was used as the parameter value for the threshold segmentation of the scanned image for the 3D reconstruction of the connected pore space, the solver program in AVIZO software was used to solve the absolute permeability tensor of Malan loess using the volume averaging method combined with the CT scan to reconstruct the 3D pore space, and the simulation of the seepage process was carried out. The simulation results showed that Malan loess is a highly anisotropic loess; the absolute permeability in the vertical direction is 9.02 times and 3.86 times higher than the permeability in the horizontal direction. The pore spaces are well connected in the vertical direction (forming a near-vertical arrangement of pipes) and weakly connected in the horizontal direction. In the seepage simulation, it was found that the water flows first along the vertically oriented channels and then fills the horizontally oriented pores; the absolute permeability coefficient was calculated to be 0.3482 μm2. The indoor seepage experiment was consistent with the simulation experiment, which verifies the reliability of the calculated model.

Tensor-Train-Based Multiuser Multivariate Multiorder Physical Markov Process Informed Multimodal Prediction for Industrial Trajectory Applications

By combining data driven approaches and physical laws for industrial trajectory prediction can improve the performance of industrial applications, such as path planning of robots, routing selection of vehicles in transportation system. In the era of industrial big data, the application of industrial trajectory prediction based on physical Markov process and tensor model has attracted much attention. To synchronously improve the prediction accuracy and computational efficiency, this paper proposes a tensor-train (TT) based multiuser multivariate multiorder (3M) physical Markov prediction approach for multimodal industrial trajectory pattern mining. First, we propose a TT-based unified product calculation rule with its scalable computation approach based on decomposed TT cores to speed up the execution efficiency. Then, a TT-based 3M (TT-3M) Markov transition approach is presented. Furthermore, we put forward a TT-based power method to calculate the stationary joint eigentensor (SJE) and an SJE-based multimodal prediction algorithm to mine concealed trajectory patterns. Experimental results based on real GPS trajectory dataset show that compared with the original tensor-based 3M approach, the TT-3M approach can improve the computational efficiency up to 3 times and reduce the memory space proportion to a minimum of 1‰ while ensuring basically consistent prediction accuracy.

Electromagnetism of one-component plasmas of massless fermions

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Aether scalar tensor theory confronted with weak lensing data at small accelerations

Context.The recently proposed aether scalar tensor (AeST) model reproduces both the successes of particle dark matter on cosmological scales and those of modified Newtonian dynamics (MOND) on galactic scales. But the AeST model reproduces MOND only up to a certain maximum galactocentric radius. Since MOND is known to fit very well to observations at these scales, this raises the question of whether the AeST model comes into tension with data.Aims.We tested whether or not the AeST model is in conflict with observations using a recent analysis of data for weak gravitational lensing.Methods.We solved the equations of motion of the AeST model, analyzed the solutions’ behavior, and compared the results to observational data.Results.The AeST model shows some deviations from MOND at the radii probed by weak gravitational lensing. The data show no clear indication of these predicted deviations.

Tensor Robust Principal Component Analysis With Side Information: Models and Applications

As a domain-dependent prior knowledge, side information has been introduced into Robust Principal Component Analysis (RPCA) to alleviate its degenerate or suboptimal performance in some real applications. It has recently realized that the natural structural information can be better retained if the observed data is kept in the original tensor form rather than matricizing it or other order reduction means. Hence, studies on RPCA of tensor version have attracted more and more attentions. To share the merits from both direct tensor modeling and side information, we propose three models to deal with the problem of Tensor RPCA with side information based on tensor Singular Value Decomposition (t-SVD). To solve these models, we develop an efficient algorithm with convergence guarantee using the well-known alternating direction method of multiplier. Extensive experimental studies on both synthetic and real-world tensor data have been carried out to demonstrate the superiority of the proposed models over several other state-of-the-arts. Our code is released at https://github.com/zsj9509/TPCPSF.

Accelerating Magnetic Resonance T1ρ Mapping Using Simultaneously Spatial Patch-Based and Parametric Group-Based Low-Rank Tensors (SMART).

Quantitative magnetic resonance (MR) [Formula: see text] mapping is a promising approach for characterizing intrinsic tissue-dependent information. However, long scan time significantly hinders its widespread applications. Recently, low-rank tensor models have been employed and demonstrated exemplary performance in accelerating MR [Formula: see text] mapping. This study proposes a novel method that uses spatial patch-based and parametric group-based low-rank tensors simultaneously (SMART) to reconstruct images from highly undersampled k-space data. The spatial patch-based low-rank tensor exploits the high local and nonlocal redundancies and similarities between the contrast images in [Formula: see text] mapping. The parametric group-based low-rank tensor, which integrates similar exponential behavior of the image signals, is jointly used to enforce multidimensional low-rankness in the reconstruction process. In vivo brain datasets were used to demonstrate the validity of the proposed method. Experimental results demonstrated that the proposed method achieves 11.7-fold and 13.21-fold accelerations in two-dimensional and three-dimensional acquisitions, respectively, with more accurate reconstructed images and maps than several state-of-the-art methods. Prospective reconstruction results further demonstrate the capability of the SMART method in accelerating MR [Formula: see text] imaging.

Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models

Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models

Efficient tensor model‐Toeplitz matrix iterative reconstruction for angle estimation with nested array

AbstractThis letter proposes an efficient tensor model for Direction of Departure (DOD) and Direction of Arrival (DOA) estimation based on bistatic nested Multiple‐Input Multiple‐Output (MIMO) radar. Tensor offers a robust solution in characterizing multi‐dimensional data structures, ensuring data integrity, and has demonstrated remarkable effectiveness in the realm of multi‐dimensional parameter estimation. However, the complexity of traditional methods for constructing tensors is a major obstacle to practical applications. In response, this research introduces a novel approach that utilizes an iterative two‐dimensional Toeplitz matrix reconstruction method to rapidly derive expanded virtual covariance matrices prior to tensor construction. This streamlines the algorithm and improves efficiency. Numerical simulations have verified the superiority of this algorithm.

An efficient peridynamics-based statistical multiscale method for fracture in composite structures

This paper proposes a peridynamics-based statistical multiscale (PSM) framework to simulate the macroscopic structure fracture with high efficiency. The heterogeneities of composites, including the shape, spatial distribution and volume fraction of particles, are characterized within the representative volume elements (RVEs), and their impact on structure failure are extracted as two types of peridynamic parameters, namely, statistical critical stretch and equivalent micromodulus. At the microscale level, a bond-based peridynamic (BPD) model with energy-based micromodulus correction technique is introduced to simulate the fracture in RVEs, and then the computational model of statistical critical stretch is established through micromechanical analysis. Moreover, based on the statistical homogenization approach, the computational model of effective elastic tensor is also established. Then, the equivalent micromodulus can be derived from the effective elastic tensor, according to the energy density equivalence between classical continuum mechanics (CCM) and BPD models. At the macroscale level, a macroscale BPD model with the statistical critical stretch and the equivalent micromodulus is constructed to simulate the fracture in the macroscopic homogenized structures. The algorithm framework of the PSM method is also described. Two- and three-dimensional numerical examples illustrate the validity, accuracy and efficiency of the proposed method.

Differentiate tensor low rank soft decomposition in thermography defect detection

Composites are prone to defects in manufacture，which are to be evaluated for safety through non-destructive testing (NDT) techniques. Thermal images are acquired for NDT by using Optical pulsed thermography. Defect detection can be performed by proposing defect detection algorithms. However, due to the low resolution of defect contrast, the detection performance of the existing algorithm is still sub-optimal. In this work, a decomposition algorithm by differentiating low-rank tensors is proposed to extract weak defect information from complex thermal pattern disturbances for surface and sub-surface defect detection. The algorithm mines deep insight into the information on the differentiation of different ranks between structures from the results of Tucker decomposition to extract defect features. In particular, a probabilistic tensor model is introduced to correct potential mismatch patterns enhance defect contrast, and suppress noise and light spot interference. To verify the effectiveness and robustness of the proposed algorithm, a variety of complex composite specimens have been used for validation. The experimental results show that the proposed algorithm achieves better performance compared to the state-of-the-art algorithms especially in enhancing the defect contrast and suppressing the light spot in seven common samples. In overall, it can provide on average of approximately 15% F-score and 3 dB SNR improvement for validation.