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Objective. Among various deep-network-based sparse-view CT image reconstruction studies, the sinogram upscaling network has been predominantly employed to synthesize additional view information. However, the performance of the sinogram-based network is limited in terms of removing aliasing streak artifacts and recovering low-contrast small structures. In this study, we used a view-by-view back-projection (VVBP) tensor-domain network to overcome such limitations of the sinogram-based approaches. Approach. The proposed method offers advantages of addressing the aliasing artifacts directly in the 3D tensor domain over the 2D sinogram. In the tensor-domain network, the multi-planal anti-aliasing modules were used to remove artifacts within the coronal and sagittal tensor planes. In addition, the data-fidelity-based refinement module was also implemented to successively process output images of the tensor network to recover image sharpness and textures. Main result. The proposed method showed outperformance in terms of removing aliasing artifacts and recovering low-contrast details compared to other state-of-the-art sinogram-based networks. The performance was validated for both numerical and clinical projection data in a circular fan-beam CT configuration. Significance. We observed that view-by-view aliasing artifacts in sparse-view CT exhibit distinct patterns within the tensor planes, making them effectively removable in high-dimensional representations. Additionally, we demonstrated that the co-domain characteristics of tensor space processing offer higher generalization performance for aliasing artifact removal compared to conventional sinogram-domain processing., (Creative Commons Attribution license.)

Background: Cardiac T2 mapping is a valuable tool for diagnosing myocardial edema, inflammation, and infiltration, yet its spatial resolution is limited by the single-shot balanced steady-state free precession acquisition and duration of the cardiac quiescent period, which may reduce sensitivity in detecting focal lesions in the myocardium. To improve spatial resolution without extending the acquisition window, this study examined a novel accelerated Cartesian cardiac T2 mapping technique., Methods: We introduce a novel improved-resolution cardiac T2 mapping approach leveraging a calibrationless space-contrast-coil locally low-rank tensor (SCC-LLRT)-constrained reconstruction algorithm in conjunction with Cartesian undersampling trajectory. The method was validated with phantom imaging and in vivo imaging that involved 13 healthy participants and 20 patients. The SCC-LLRT algorithm was compared with a conventional locally low-rank (LLR)-constrained algorithm and a nonlinear inversion (NLINV) reconstruction algorithm. The improved-resolution T2 mapping (1.4 mm × 1.4 mm) was compared globally and regionally with the regular-resolution T2 mapping (2.3 mm × 1.9 mm) according to the 16-segment model of the American Heart Association. The agreement between the improved-resolution and regular-resolution T2 mappings was evaluated by linear regression and Bland-Altman analyses. Image quality was scored by two experienced reviewers on a five-point scale (1, worst; 5, best)., Results: In healthy participants, SCC-LLRT significantly reduced artifacts (4.50±0.39) compared with LLR (2.31±0.60; P<0.001) and NLINV (3.65±0.56; P<0.01), suppressed noise (4.12±0.35) compared with NLINV (2.65±0.50; P<0.001), and improved the overall image quality (4.38±0.40) compared with LLR (2.54±0.41; P<0.001) and NLINV (3.04±0.50; P<0.001). Compared with the regular-resolution T2 mapping, the proposed method significantly improved the sharpness of myocardial boundaries (4.46±0.60 vs. 3.04±0.50; P<0.001) and the conspicuity of papillary muscles and fine structures (4.46±0.63 vs. 2.65±0.30; P<0.001). Myocardial T2 values obtained with the proposed method correlated significantly with those from regular-resolution T2 mapping in both healthy participants (r=0.79; P<0.01) and patients (r=0.94; P<0.001)., Conclusions: The proposed SCC-LLRT-constrained reconstruction algorithm in conjunction with Cartesian undersampling pattern achieved improved-resolution cardiac T2 mapping of comparable accuracy, precision, and scan-rescan reproducibility compared with the regular-resolution T2 mapping. The higher resolution improved the sharpness of myocardial borders and the conspicuity of image fine details, which may increase diagnostic confidence in cardiac T2 mapping for detecting small lesions., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-24-740/coif). X.T. was a full-time master’s student at Shanghai Jiao Tong University during his participation in this study. After graduating in March 2023, he joined Shanghai United Imaging Healthcare Co. Ltd. as a full-time employee. The other authors have no conflicts of interest to declare., (2024 AME Publishing Company. All rights reserved.)

Background: Soft tissue balance is essential for total knee arthroplasty success. The elastic properties of soft tissues affect knee-joint stability and flexibility. This study proposed a novel methodology for in vivo quantitative analysis of soft tissue elasticity during total knee arthroplasty. In this study, we aimed to (1) establish a mathematical model to depict medial and lateral soft tissue elasticity, (2) report the individual differences and interindividual commonalities in soft tissue elasticity., Methods: A specifically designed knee tensor was used to evaluate soft tissue elasticity by dynamically applying sequential tensions to medial and lateral compartments while measuring knee joint gaps in both compartments. Measurements were performed on ten knees of six cadavers. Bivariate polynomial regression was used for analysis, and the equivalent elastic coefficient (N/mm) was calculated., Findings: Soft-tissue elasticity showed high individual differences. The equivalent elastic coefficient was larger in the medial compartment than in the lateral compartment, and the equivalent elastic coefficient of the lateral compartment gradually decreased while the medial equivalent elastic coefficient remained constant when the knee was flexed. The lateral gaps increased from 0.1 to 3.9 mm, and the medial gaps increased from 0 to 1.5 mm when the tension increased from 60 to 90 N. The shapes and distributions of the silkworm-like lattices in elasticity and balance evaluations are clinically relevant to knee balance., Interpretation: Soft-tissue balance in total knee arthroplasty is significantly affected by soft-tissue elasticity. An intraoperative quantitative analysis of elasticity helps to tail an individualized balancing target for total knee arthroplasty., Competing Interests: Declaration of competing interest Two authors (Hongwei Shi and Yongqiang Zhao) are engineers from the company providing the device, and four authors (Dejing Yang, Yixin Zhou, Hongwei Shi and Yongqiang Zhao) patented the device. The other authors have no conflicts of interest relevant to this study., (Copyright © 2024. Published by Elsevier Ltd.)

Background: Cardiac T1 mapping is valuable for evaluating myocardial fibrosis, yet its resolution and acquisition efficiency are limited, potentially obscuring visualization of small pathologies., Purpose: To develop a technique for high-resolution cardiac T1 mapping with a less-than-100-millisecond acquisition window based on radial MOdified Look-Locker Inversion recovery (MOLLI) and a calibrationless space-contrast-coil locally low-rank tensor (SCC-LLRT) constrained reconstruction., Study Type: Prospective., Subjects/phantom: Sixteen healthy subjects (age 25 ± 3 years, 44% females) and 12 patients with suspected cardiomyopathy (age 57 ± 15 years, 42% females), NiCl2-agar phantom., Field Strength/sequence: 3-T, standard MOLLI, radial MOLLI, inversion-recovery spin-echo, late gadolinium enhancement., Assessment: SCC-LLRT was compared to a conventional locally low-rank (LLR) method through simulations using Normalized Root-Mean-Square Error (NRMSE) and Structural Similarity Index Measure (SSIM). Radial MOLLI was compared to standard MOLLI across phantom, healthy subjects, and patients. Three independent readers subjectively evaluated the quality of T1 maps using a 5-point scale (5 = best)., Statistical Tests: Paired t-test, Wilcoxon signed-rank test, intraclass correlation coefficient analysis, linear regression, Bland-Altman analysis. P < 0.05 was considered statistically significant., Results: In simulations, SCC-LLRT demonstrated a significant improvement in NRMSE and SSIM compared to LLR. In phantom, both radial MOLLI and standard MOLLI provided consistent T1 estimates across different heart rates. In healthy subjects, radial MOLLI exhibited a significantly lower mean T1 (1115 ± 39 msec vs. 1155 ± 36 msec), similar T1 SD (74 ± 14 msec vs. 67 ± 23 msec, P = 0.20), and similar T1 reproducibility (28 ± 18 msec vs. 22 ± 15 msec, P = 0.34) compared to standard MOLLI. In patients, the proposed method significantly improved the sharpness of myocardial boundaries (4.50 ± 0.65 vs. 3.25 ± 0.43), the conspicuity of papillary muscles and fine structures (4.33 ± 0.74 vs. 3.33 ± 0.47), and artifacts (4.75 ± 0.43 vs. 3.83 ± 0.55). The reconstruction time for a single slice was 5.2 hours., Data Conclusion: The proposed method enables high-resolution cardiac T1 mapping with a short acquisition window and improved image quality., Evidence Level: 1 TECHNICAL EFFICACY: Stage 1., (© 2024 International Society for Magnetic Resonance in Medicine.)

Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights. However, missing data in the datasets being analyzed can impose challenges. Tensor factorization can be performed with some level of missing data and reconstruct a complete tensor. However, while tensor methods may impute these missing values, the choice of fitting algorithm may influence the fidelity of these imputations. Previous approaches, based on alternating least squares with prefilled values or direct optimization, suffer from introduced bias or slow computational performance. In this study, we propose that censored least squares can better handle missing values with data structured in tensor form. We ran censored least squares on four different biological datasets and compared its performance against alternating least squares with prefilled values and direct optimization. We used the error of imputation and the ability to infer masked values to benchmark their missing data performance. Censored least squares appeared best suited for the analysis of high-dimensional biological data by accuracy and convergence metrics across several studies., Competing Interests: Competing interests: The authors declare that they have no competing interests.

A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation, and represent quantum entanglement. In this sense, a tensor can be viewed as valuable resource whose transformation can lead to an understanding of structure in data, computational complexity, and quantum information. In order to facilitate the understanding of this resource, we propose a family of information-theoretically constructed preorders on tensors, which can be used to compare tensors with each other and to assess the existence of transformations between them. The construction places copies of a given tensor at the edges of a hypergraph and allows transformations at the vertices. A preorder is then induced by the transformations possible in a given growing sequence of hypergraphs. The new family of preorders generalizes the asymptotic restriction preorder which Strassen defined in order to study the computational complexity of matrix multiplication. We derive general properties of the preorders and their associated asymptotic notions of tensor rank and view recent results on tensor rank nonadditivity, tensor networks, and algebraic complexity in this unifying frame. We hope that this work will provide a useful vantage point for exploring tensors in applied mathematics, physics, and computer science but also from a purely mathematical point of view., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

Hyperspectral images (HSIs) possess an inherent three-order structure, prompting increased interest in extracting 3D features. Tensor analysis and low-rank representations, notably truncated higher-order SVD (T-HOSVD), have gained prominence for this purpose. However, determining the optimal order and addressing sensitivity to changes in data distribution remain challenging. To tackle these issues, this paper introduces an unsupervised Superpixelwise Multiscale Adaptive T-HOSVD (SmaT-HOSVD) method. Leveraging superpixel segmentation, the algorithm identifies homogeneous regions, facilitating the extraction of local features to enhance spatial contextual information within the image. Subsequently, T-HOSVD is adaptively applied to the obtained superpixel blocks for feature extraction and fusion across different scales. SmaT-HOSVD harnesses superpixel blocks and low-rank representations to extract 3D features, effectively capturing both spectral and spatial information of HSIs. By integrating optimal-rank estimation and multiscale fusion strategies, it acquires more comprehensive low-rank information and mitigates sensitivity to data variations. Notably, when trained on subsets comprising 2%, 1%, and 1% of the Indian Pines, University of Pavia, and Salinas datasets, respectively, SmaT-HOSVD achieves impressive overall accuracies of 93.31%, 97.21%, and 99.25%, while maintaining excellent efficiency. Future research will explore SmaT-HOSVD's applicability in deep-sea HSI classification and pursue additional avenues for advancing the field., Competing Interests: The authors declare no conflicts of interest.

Molecular dynamics(MD) simulations are essential for molecular structure optimization, drug-drug interactions, and other fields of drug discovery by simulating the motion of microscopic particles to calculate their macroscopic properties (e.g., energy). The main problems of the existing work are as follows: (1) Failure to fully consider the chemical bonding constraints between atoms, (2) Group equivariance can help achieve robust and accurate predictions of MD under arbitrary reference transformations and should be incorporated into the model design, (3) Tensor information such as relative position, velocity, and torsion angle can be used to enhance the prediction of molecular dynamics. And the existing methods are mainly limited to the scalar domain. In this paper, we propose a new model-tensor improve equivariant graph neural network for molecular dynamics prediction (TEGNN): (1) The model materialization of chemical bond constraints between atoms into geometric constraints. The molecule's forward kinematic information (position and velocity) is represented by generalized coordinates. In this way, the interatomic chemical bonding constraints are implicitly and naturally encoded in the forward kinematics, (2) The equivariant information transfer is allowed in TEGNN, which significantly improves the accuracy and computational efficiency of the final prediction, (3) TEGNN introduces equivariant locally complete frames into scalar-only equivariant graph neural networks, thus allowing the projection of tensor information of a given order onto the frame. On the N-body dataset of simulated molecular systems consisting of particles, sticks, and hinges, as well as on the real dataset MD17 for molecular dynamics prediction, multiple experiments support that TEGNN is ahead of the current state-of-the-art GNN in terms of prediction accuracy, constraint satisfaction, and data efficiency. We extend the current state-of-the-art equivariant neural network model. The proposed TEGNN accommodates more tensor information and considers the chemical bonding constraints between atoms during motion, ultimately improving the performance of predicting the kinematic states of molecules., Competing Interests: Declaration of competing interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Partially impaired sensor arrays pose a significant challenge in accurately estimating signal parameters. The occurrence of bad data is highly probable, resulting in random loss of source information and substantial performance degradation in parameter estimation. In this paper, a tensor variational sparse Bayesian learning (TVSBL) method is proposed for the estimate of direction of arrival (DOA) and polarization parameters jointly based on a conformal polarization sensitive array (CPSA), taking into account scenarios with the partially impaired sensor array. First, a sparse tensor-based received data model is developed for CPSAs that incorporates bad data. Then, a column vector detection method is proposed to diagnose the positions of the impaired sensors. In scenarios involving partially impaired sensor arrays, a low-rank matrix completion method is employed to recover the random loss of signal information. Finally, variational sparse Bayesian learning (VSBL) and minimum eigenvector methods are utilized sequentially to obtain the DOA and polarization parameters estimation, successively. Furthermore, the Cramér-Rao bound is given for the proposed method. Simulation results validated the effectiveness of the proposed method., Competing Interests: Author Lai Jiang was employed by the company State-Owned Changhong Machine Factory. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Lorentz-Dirac equation is formulated and studied in flat Minkowski spacetime. A concise, novel derivation of the equation is presented. The problem is then enlarged to study radiation damping of an electron moving through a gravitational field. The equation of motion is obtained for this case as well. It is suggested the study of the problem might motivate experiments which could shed light on the recent work related to the emergence of space-time and its structure by means of quantum effects such as quantum entanglement., (© 2024. The Author(s).)

Background: Gene expression may be regulated by the DNA methylation of regulatory elements in cis, distal, and trans regions. One method to evaluate the relationship between DNA methylation and gene expression is the mapping of expression quantitative trait methylation (eQTM) loci (also called expression associated CpG loci, eCpG). However, no open-source tools are available to provide eQTM mapping. In addition, eQTM mapping can involve a large number of comparisons which may prevent the analyses due to limitations of computational resources. Here, we describe Torch-eCpG, an open-source tool to perform eQTM mapping that includes an optimized implementation that can use the graphical processing unit (GPU) to reduce runtime., Results: We demonstrate the analyses using the tool are reproducible, up to 18 × faster using the GPU, and scale linearly with increasing methylation loci., Conclusions: Torch-eCpG is a fast, reliable, and scalable tool to perform eQTM mapping. Source code for Torch-eCpG is available at https://github.com/kordk/torch-ecpg ., (© 2024. The Author(s).)

Microscopic hyperspectral images has the advantage of containing rich spatial and spectral information. However, the large number of spectral bands provides a significant amount of spectral features, but also leads to data redundancy and noise, which seriously affect the recognition and classification performance of the images, as well as increasing the requirements for computation and storage. To address this issue, we propose a dimensionality reduction algorithm named enhanced discriminant local constraint preserving projection (EDLCPP). Specifically, the global spectral attention mechanism focuses on important bands, the high discriminability sample selection module measures the discriminability of samples using a modified average neighborhood margin, the graph construction module preserves the local geometric relationship and discriminant information, and the graph embedding module embeds the constructed graphs into a low-dimensional space to obtain the projection matrices. Experimental results on eight cholangiocarcinoma (CCA) hyperspectral images, Bloodcell1-3, and Bloodcell2-2 datasets have demonstrated the effectiveness of the proposed method., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Objective. In this paper, we propose a new tensor decomposition to extract event-related potentials (ERP) by adding a physiologically meaningful constraint to the Tucker decomposition. Approach. We analyze the performance of the proposed model and compare it with Tucker decomposition by synthesizing a dataset. The simulated dataset is generated using a 12th-order autoregressive model in combination with independent component analysis (ICA) on real no-task electroencephalogram (EEG) recordings. The dataset is manipulated to contain the P300 ERP component and to cover different SNR conditions, ranging from 0 to -30 dB, to simulate the presence of the P300 component in extremely noisy recordings. Furthermore, in order to assess the practicality of the proposed methodology in real-world scenarios, we utilized the brain-computer interface (BCI) competition III-dataset II. Main results. Our primary results demonstrate the superior performance of our approach compared to conventional methods commonly employed for single-trial estimation. Additionally, our method outperformed both Tucker decomposition and non-negative Tucker decomposition in the synthesized dataset. Furthermore, the results obtained from real-world data exhibited meaningful performance and provided insightful interpretations for the extracted P300 component. Significance. The findings suggest that the proposed decomposition is eminently capable of extracting the target P300 component's waveform, including latency and amplitude as well as its spatial location, using single-trial EEG recordings., (Creative Commons Attribution license.)

Graph-based change-point detection methods are often applied due to their advantages for using high-dimensional data. Most applications focus on extracting effective information of objects while ignoring their main features. However, in some applications, one may be interested in detecting objects with different features, such as color. Therefore, we propose a general graph-based change-point detection method under the multi-way tensor framework, aimed at detecting objects with different features that change in the distribution of one or more slices. Furthermore, considering that recorded tensor sequences may be vulnerable to natural disturbances, such as lighting in images or videos, we propose an improved method incorporating histogram equalization techniques to improve detection efficiency. Finally, through simulations and real data analysis, we show that the proposed methods achieve higher efficiency in detecting change-points.

TensorView for MATLAB is a GUI-based visualization tool for depicting second-rank Cartesian tensors as surfaces on three-dimensional molecular models. Both ellipsoid and ovaloid tensor display formats are supported, and the software allows for easy conversion of Euler angles from common rotation schemes (active, passive, ZXZ, and ZYZ conventions) with visual feedback. In addition, the software displays all four orientation-equivalent Euler angle solutions for the placement of a single tensor in the molecular frame and can report relative orientations of two tensors with all 16 orientation-equivalent Euler angle sets that relate them. The salient relations are derived and illustrated through several examples. TensorView for MATLAB expands and complements the earlier implementation of TensorView within the Mathematica programming environment and can be run without a MATLAB license. TensorView for MATLAB is available through github at https://github.com/LeoSvenningsson/TensorViewforMatlab, and can also be accessed directly via the NMRbox resource., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper, (Copyright © 2022 Elsevier Inc. All rights reserved.)

Background: Bats harbor various viruses without severe symptoms and act as their natural reservoirs. The tolerance of bats against viral infections is assumed to originate from the uniqueness of their immune system. However, how immune responses vary between primates and bats remains unclear. Here, we characterized differences in the immune responses by peripheral blood mononuclear cells to various pathogenic stimuli between primates (humans, chimpanzees, and macaques) and bats (Egyptian fruit bats) using single-cell RNA sequencing., Results: We show that the induction patterns of key cytosolic DNA/RNA sensors and antiviral genes differed between primates and bats. A novel subset of monocytes induced by pathogenic stimuli specifically in bats was identified. Furthermore, bats robustly respond to DNA virus infection even though major DNA sensors are dampened in bats., Conclusions: Overall, our data suggest that immune responses are substantially different between primates and bats, presumably underlying the difference in viral pathogenicity among the mammalian species tested., (© The Author(s) 2023. Published by Oxford University Press GigaScience.)

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus, the utility of such tensors is low, in terms of the amount of interpretable and exploitable structure that one can extract from them. In this paper, we introduce the problem of finding a tensor of adaptive aggregated granularity that can be decomposed to reveal meaningful latent concepts (structures) from datasets that, in their original form, are not amenable to tensor analysis. Such datasets fall under the broad category of sparse point processes that evolve over space and/or time. To the best of our knowledge, this is the first work that explores adaptive granularity aggregation in tensors. Furthermore, we formally define the problem and discuss different definitions of "good structure" that are in practice and show that the optimal solution is of prohibitive combinatorial complexity. Subsequently, we propose an efficient and effective greedy algorithm called ICEBREAKER, which follows a number of intuitive decision criteria that locally maximize the "goodness of structure," resulting in high-quality tensors. We evaluate our method on synthetic, semi-synthetic, and real datasets. In all the cases, our proposed method constructs tensors that have a very high structure quality., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Pasricha, Gujral and Papalexakis.)

Objective. We introduce extended Block-Term Tensor Regression (eBTTR), a novel regression method designed to account for the multilinear nature of human intracranial finger movement recordings. Approach. The proposed method relies on recursive Tucker decomposition combined with automatic component extraction. Main results. eBTTR outperforms state-of-the-art regression approaches, including multilinear and deep learning ones, in accurately predicting finger trajectories as well as unintentional finger coactivations. Significance. eBTTR rivals state-of-the-art approaches while being less computationally expensive which is an advantage when intracranial electrodes are implanted acutely, as part of the patient's presurgical workup, limiting time for decoder development and testing., (© 2022 IOP Publishing Ltd.)

The assessment of Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI) associated with brain changes remains a challenging task. Recent studies have demonstrated that combination of multi-modality imaging techniques can better reflect pathological characteristics and contribute to more accurate diagnosis of AD and MCI. In this paper, we propose a novel tensor-based multi-modality feature selection and regression method for diagnosis and biomarker identification of AD and MCI from normal controls. Specifically, we leverage the tensor structure to exploit high-level correlation information inherent in the multi-modality data, and investigate tensor-level sparsity in the multilinear regression model. We present the practical advantages of our method for the analysis of ADNI data using three imaging modalities (VBM-MRI, FDG-PET and AV45-PET) with clinical parameters of disease severity and cognitive scores. The experimental results demonstrate the superior performance of our proposed method against the state-of-the-art for the disease diagnosis and the identification of disease-specific regions and modality-related differences. The code for this work is publicly available at https://github.com/junfish/BIOS22.

Recently, the joint estimation for time delay (TD) and direction of arrival (DOA) has suffered from the high complexity of processing multi-dimensional signal models and the ineffectiveness of correlated/coherent signals. In order to improve this situation, a joint estimation method using orthogonal frequency division multiplexing (OFDM) and a uniform planar array composed of reconfigurable intelligent surface (RIS) is proposed. First, the time-domain coding function of the RIS is combined with the multi-carrier characteristic of the OFDM signal to construct the coded channel frequency response in tensor form. Then, the coded channel frequency response covariance matrix is decomposed by CANDECOMP/PARAFAC (CPD) to separate the signal subspaces of TD and DOA. Finally, we perform a one-dimensional (1D) spectral search for TD values and a two-dimensional (2D) spectral search for DOA values. Compared to previous efforts, this algorithm not only enhances the adaptability of coherent signals, but also greatly decreases the complexity. Simulation results indicate the robustness and effectiveness for the proposed algorithm in independent, coherent, and mixed multipath environments and low signal-to-noise ratio (SNR) conditions.

Introduction: The relationship between gap balancing and clinical outcome of total knee arthroplasty (TKA) has been researched. Tourniquet is widely used by most surgeons; however, there are little quantitative data about the gap depending on the tourniquet usage. We aimed to investigate whether the knee position at tourniquet inflation affected the gap measurement intra-operatively., Methods: TKA was performed for 104 knees and the tourniquet was inflated with the knee at full flexion and extension. The gap was measured in each static knee flexion status (0°, 30°, 45°, 60°, 90°, 120°, and in full flexion) using a tensor. We measured the gap twice; under the tourniquet inflation and release. The gap difference at each static knee flexion status was calculated by subtracting the gap under release from that under inflation., Results: When the tourniquet was inflated with the knee at full flexion, the mean gap differences were < 1 mm and < 1° in each static knee flexion status. When the tourniquet was inflated with the knee at full extension, the mean gap differences were < 1 mm and < 1°, respectively. All values of the gap difference were minimum, and were not affected by the tourniquet, whether the knee position at the tourniquet inflation was flexed or extended., Conclusions: We postulated that the knee position at tourniquet inflation would affect the gap, which was refuted by our results. This shows that we can measure the gap without considering the knee position at tourniquet inflation., (© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Background: The accurate characterization of protein functions is critical to understanding life at the molecular level and has a huge impact on biomedicine and pharmaceuticals. Computationally predicting protein function has been studied in the past decades. Plagued by noise and errors in protein-protein interaction (PPI) networks, researchers have undertaken to focus on the fusion of multi-omics data in recent years. A data model that appropriately integrates network topologies with biological data and preserves their intrinsic characteristics is still a bottleneck and an aspirational goal for protein function prediction., Results: In this paper, we propose the RWRT (Random Walks with Restart on Tensor) method to accomplish protein function prediction by applying bi-random walks on the tensor. RWRT firstly constructs a functional similarity tensor by combining protein interaction networks with multi-omics data derived from domain annotation and protein complex information. After this, RWRT extends the bi-random walks algorithm from a two-dimensional matrix to the tensor for scoring functional similarity between proteins. Finally, RWRT filters out possible pretenders based on the concept of cohesiveness coefficient and annotates target proteins with functions of the remaining functional partners. Experimental results indicate that RWRT performs significantly better than the state-of-the-art methods and improves the area under the receiver-operating curve (AUROC) by no less than 18%., Conclusions: The functional similarity tensor offers us an alternative, in that it is a collection of networks sharing the same nodes; however, the edges belong to different categories or represent interactions of different nature. We demonstrate that the tensor-based random walk model can not only discover more partners with similar functions but also free from the constraints of errors in protein interaction networks effectively. We believe that the performance of function prediction depends greatly on whether we can extract and exploit proper functional similarity information on protein correlations., (© 2022. The Author(s).)

Objective: To determine the efficacy of diffusion-weighted MRI (DWI) and diffusion tensor imaging (DTI) in the characterization of mediastinal lymphadenopathy and the differentiation between malignant and benign lymph nodes (LNs)., Methods: a retrospective evaluation of 58 patients with mediastinal lymphadenopathy that underwent DWI and DTI with calculation of apparent diffusion coefficient (ADC), fractional anisotropy (FA), and mean diffusivity (MD) values of LNs. Final diagnosis was made by the histopathology and proved metastatic (n = 21), lymphomatous (n = 14), granulomatous (n = 11) and reactive (n = 12) LNs., Results: Malignant mediastinal LNs had remarkably lower ADC and MD; (p = 0.001) and higher FA; (p = 0.001) than in benign LNs. The threshold of ADC, MD, and FA at (1.48, 1.32 × 10 -3 mm 2 /s), (1.31, 1.33 × 10 -3 mm 2 /s), (0.62, 0.52) to differentiate malignant from benign LNs has AUC of (0.89, 0.94), (0.96, 0.95), (0.72, 0.82), accuracy of (87%, 86%), (89%, 86%), (70%, 72%) by both observers respectively. The threshold of ADC, MD, and FA at (1.47, 1.32 × 10 -3 mm 2 /s), (1.31, 1.3 × 10 -3 mm 2 /s), (0.62, 0.67) used to differentiate metastatic from reactive LNs revealed AUC of (0.90, 0.94), (0.96, 0.96), (0.73, 0.77), accuracy of (87%, 81%), (87%, 81%), (72%, 66%) by both observers respectively. The mean ADC and MD values of metastatic LNs were statistically significant (p = 0.001) and (p = 0.002, 0.02) respectively when compared with that of lymphoma. The threshold of ADC, and MD (0.94, 0.97 × 10 -3 mm 2 /s) and (0.87, 0.91 × 10 -3 mm 2 /s) used to differentiates metastatic from lymphomatous nodes revealed AUC of (0.90, 0.91), (0.81, 0.74), an accuracy of (85%, 91%), (71%, 71%), by both observers respectively. The inter-class correlation between two observers for all nodes for ADC, MD and FA was r= 0.931, 0.956 and 0.885 respectively., Conclusion: Using ADC, MD, and FA can help in the characterization of mediastinal lymphadenopathy noninvasively., (Copyright © 2021 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.)

Resonant Ultrasound Spectroscopy estimates the stiffness coefficients of a material from the free resonant frequencies of a single specimen. It is particularly suitable for complete stiffness characterization of anisotropic materials available only as small samples (typically a few mm), and it does not suffer from some limitations associated to quasi-static mechanical test and ultrasound wave velocity measurements. RUS has been used for decades on geological samples and single crystals, but was until recently not applied to mineralized tissues such as bone. The reason is the significant mechanical damping presents in these materials, which causes the resonant peaks to overlap and prevent a direct measurement of the resonant frequencies. This chapter describes the use of RUS for the elastic characterization of mineralized tissues, cortical bone in particular. All steps are described, from sample preparation and measurement setup to signal processing and data analysis, including the developments and adaptions necessary to overcome the difficulties linked to damping. Viscoelastic characterization, from the width of the resonant peaks, is also presented. Mostly technical aspects are developed in this chapter, while the data obtained from RUS on several collections of mineralized tissues specimens are presented and discussed in Chap. 13., (© 2022. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Background: Femoral intramedullary canal referencing is used by most knee arthroplasty systems for distal femoral cut; to avoid the opening of the femoral canal different solutions have been presented such as navigation, patient-specific instruments (PSI) or the use of an extramedullary device. The FuZion ® system is a tensor device, created to merge the two main techniques for performing a total knee arthroplasty: the ligament balancing and measured resection techniques. Our idea was to use the tensor as an extramedullary cutting guide for the distal femoral cut, based on a 90° tibial resection., Methods: A total of 110 patients were operated on with this technique. Patients were evaluated with weight-bearing long-standing X-rays, knee a-p and lateral views, validated PROMs (Oxford Knee Score, EQ-5D and EQ-VAS), the Knee Society Scoring System (KSS) and the Forgotten Joint Score (FJS). Minimum follow up was 3 years (range 38-50 months)., Results: Complete results were available for 104 patients (5 were lost in follow up and 1 died). Significant improvements were registered for all the evaluated scores from pre-op to the final follow up. Pre-op long-standing X-rays showed 21 valgus knees (20%) with a mean HKA of 187.6° (± 3.2°), 70 varus knees (62%) with a mean 172.2° (± 3.7°) HKA and 19 neutrally aligned knees, with a mean HKA of 179.5° (0 ± 2°). The radiographic evaluation at 3 months post-op showed 20 valgus knees (mean HKA 183.7° ± 1.5°), 67 varus knees (mean HKA 176.1° ± 1.8°) and 23 neutrally aligned knees with a mean HKA of 179.3° (0 ± 2°). At final follow up the survival rate was 100% for revision of the implant as the endpoint. With any reoperation as the endpoint Kaplan-Meier survival estimate showed a survival rate of 95.1% at 3 years., Conclusions: This technique for performing a ligament driven alignment in total knee arthroplasty showed encouraging clinical outcomes at mid-term follow up leaving a residual deformity on the coronal plane., (© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Multi-modal image fusion integrates different images of the same scene collected by different sensors into one image, making the fused image recognizable by the computer and perceived by human vision easily. The traditional tensor decomposition is an approximate decomposition method and has been applied to image fusion. In this way, the image details may be lost in the process of fusion image reconstruction. To preserve the fine information of the images, an image fusion method based on tensor matrix product decomposition is proposed to fuse multi-modal images in this article. First, each source image is initialized into a separate third-order tensor. Then, the tensor is decomposed into a matrix product form by using singular value decomposition (SVD), and the Sigmoid function is used to fuse the features extracted in the decomposition process. Finally, the fused image is reconstructed by multiplying all the fused tensor components. Since the algorithm is based on a series of singular value decomposition, a stable closed solution can be obtained and the calculation is also simple. The experimental results show that the fusion image quality obtained by this algorithm is superior to other algorithms in both objective evaluation metrics and subjective evaluation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Lu, Wang, Gao, Sun and Zhu.)

This article discusses new diffusion-weighted imaging (DWI) sequences, diffusion tensor imaging (DTI), and fiber tractography (FT), as well as more advanced diffusion imaging in pediatric brain and spine. Underlying disorder and pathophysiology causing diffusion abnormalities are discussed. Multishot echo planar imaging (EPI) DWI and non-EPI DWI provide higher spatial resolution with less susceptibility artifact and distortion, which are replacing conventional single-shot EPI DWI. DTI and FT have established clinical significance in pediatric brain and spine. This article discusses advanced diffusion imaging, including diffusion kurtosis imaging, neurite orientation dispersion and density imaging, diffusion spectrum imaging, intravoxel incoherent motion, and oscillating-gradient spin-echo., (Copyright © 2021 Elsevier Inc. All rights reserved.)

Purpose: To evaluate the diagnostic value of diffusion tensor imaging (DTI) of renal cortex in assessment of lupus nephritis (LN) and prediction of its pathological subtypes., Methods: Prospective study was performed upon 39 female patients with pathologically proven LN and 16 sex- and age-matched healthy controls. Patients and controls underwent DTI of kidney. Mean diffusivity (MD) and fractional anisotropy (FA) of renal cortex were calculated by two radiologists. LN patients were pathologically classified into either non-proliferative (n = 15) or proliferative (n = 24)., Results: Mean MD of renal cortex in LN was significantly lower (p = 0.001) than that of controls with cut-off (2.16 and 2.2 X10 -3 mm 2 /s), area under curve (AUC) of (0.92, 0.94) and accuracy of (91%, 89%) for both observers. Mean FA of renal cortex in LN was significantly higher (p = 0.001) than that of controls with cut-off (0.20, 0.21), AUC of (0.86, 0.82) and accuracy of (86%, 84%) for both observers. Renal cortex MD and FA in non-proliferative LN were significantly different (p = 0.001) from that of proliferative LN for both observers. There was excellent inter-observer agreement of MD and FA (ICC = 0.96 and 0.81)., Conclusion: MD and FA of renal cortex may help to assess renal affection in LN patients and predict its pathological subtypes., (© 2021. Japan Radiological Society.)

Multi-modal fusion can achieve better predictions through the amalgamation of information from different modalities. To improve the performance of accuracy, a method based on Higher-order Orthogonal Iteration Decomposition and Projection (HOIDP) is proposed, in the fusion process, higher-order orthogonal iteration decomposition algorithm and factor matrix projection are used to remove redundant information duplicated inter-modal and produce fewer parameters with minimal information loss. The performance of the proposed method is verified by three different multi-modal datasets. The numerical results validate the accuracy of the performance of the proposed method having 0.4% to 4% improvement in sentiment analysis, 0.3% to 8% improvement in personality trait recognition, and 0.2% to 25% improvement in emotion recognition at three different multi-modal datasets compared with other 5 methods.

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i.e., multiway arrays) and compressed via tensor-SVDs under the tensor-tensor product constructs and its generalizations. We begin by proving Eckart-Young optimality results for families of tensor-SVDs under two different truncation strategies. Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tensor construct subsume the matrix construct in terms of representation efficiency? The answer is positive, as proven by showing that a tensor-tensor representation of an equal dimensional spanning space can be superior to its matrix counterpart. We then use these optimality results to investigate how the compressed representation provided by the truncated tensor SVD is related both theoretically and empirically to its two closest tensor-based analogs, the truncated high-order SVD and the truncated tensor-train SVD., Competing Interests: The authors declare no competing interest.

Human activity recognition (HAR) by wearable sensor devices embedded in the Internet of things (IOT) can play a significant role in remote health monitoring and emergency notification to provide healthcare of higher standards. The purpose of this study is to investigate a human activity recognition method of accrued decision accuracy and speed of execution to be applicable in healthcare. This method classifies wearable sensor acceleration time series data of human movement using an efficient classifier combination of feature engineering-based and feature learning-based data representation. Leave-one-subject-out cross-validation of the method with data acquired from 44 subjects wearing a single waist-worn accelerometer on a smart textile, and engaged in a variety of 10 activities, yielded an average recognition rate of 90%, performing significantly better than individual classifiers. The method easily accommodates functional and computational parallelization to bring execution time significantly down.

Aging is associated with widespread alterations in cerebral white matter (WM). Most prior studies of age differences in WM have used diffusion tensor imaging (DTI), but typical DTI metrics (e.g., fractional anisotropy; FA) can reflect multiple neurobiological features, making interpretation challenging. Here, we used fixel-based analysis (FBA) to investigate age-related WM differences observed using DTI in a sample of 45 older and 25 younger healthy adults. Age-related FA differences were widespread but were strongly associated with differences in multi-fiber complexity (CX), suggesting that they reflected differences in crossing fibers in addition to structural differences in individual fiber segments. FBA also revealed a frontolimbic locus of age-related effects and provided insights into distinct microstructural changes underlying them. Specifically, age differences in fiber density were prominent in fornix, bilateral anterior internal capsule, forceps minor, body of the corpus callosum, and corticospinal tract, while age differences in fiber cross section were largest in cingulum bundle and forceps minor. These results provide novel insights into specific structural differences underlying major WM differences associated with aging., (© The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.)

How can we detect fraudulent lockstep behavior in large-scale multi-aspect data (i.e., tensors)? Can we detect it when data are too large to fit in memory or even on a disk? Past studies have shown that dense subtensors in real-world tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or fraudulent behavior such as retweet boosting, bot activities, and network attacks. Thus, various approaches, including tensor decomposition and search, have been proposed for detecting dense subtensors rapidly and accurately. However, existing methods suffer from low accuracy, or they assume that tensors are small enough to fit in main memory, which is unrealistic in many real-world applications such as social media and web. To overcome these limitations, we propose D-Cube, a disk-based dense-subtensor detection method, which also can run in a distributed manner across multiple machines. Compared to state-of-the-art methods, D-Cube is (1) Memory Efficient: requires up to 1,561× less memory and handles 1,000× larger data ( 2.6TB ), (2) Fast: up to 7× faster due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on the densities of the detected subtensors, and (4) Effective: spotted network attacks from TCP dumps and synchronized behavior in rating data most accurately., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Shin, Hooi, Kim and Faloutsos.)

Great attention is paid to detecting video forgeries nowadays, especially with the widespread sharing of videos over social media and websites. Many video editing software programs are available and perform well in tampering with video contents or even creating fake videos. Forgery affects video integrity and authenticity and has serious implications. For example, digital videos for security and surveillance purposes are used as evidence in courts. In this paper, a newly developed passive video forgery scheme is introduced and discussed. The developed scheme is based on representing highly correlated video data with a low computational complexity third-order tensor tube-fiber mode. An arbitrary number of core tensors is selected to detect and locate two serious types of forgeries which are: insertion and deletion. These tensor data are orthogonally transformed to achieve more data reductions and to provide good features to trace forgery along the whole video. Experimental results and comparisons show the superiority of the proposed scheme with a precision value of up to 99% in detecting and locating both types of attacks for static as well as dynamic videos, quick-moving foreground items (single or multiple), zooming in and zooming out datasets which are rarely tested by previous works. Moreover, the proposed scheme offers a reduction in time and a linear computational complexity. Based on the used computer's configurations, an average time of 35 s. is needed to detect and locate 40 forged frames out of 300 frames.

Aims: Pulmonary arterial hypertension (PAH) is a progressive condition with high mortality. Quantitative cardiovascular magnetic resonance (CMR) imaging metrics in PAH target individual cardiac structures and have diagnostic and prognostic utility but are challenging to acquire. The primary aim of this study was to develop and test a tensor-based machine learning approach to holistically identify diagnostic features in PAH using CMR, and secondarily, visualize and interpret key discriminative features associated with PAH., Methods and Results: Consecutive treatment naive patients with PAH or no evidence of pulmonary hypertension (PH), undergoing CMR and right heart catheterization within 48 h, were identified from the ASPIRE registry. A tensor-based machine learning approach, multilinear subspace learning, was developed and the diagnostic accuracy of this approach was compared with standard CMR measurements. Two hundred and twenty patients were identified: 150 with PAH and 70 with no PH. The diagnostic accuracy of the approach was high as assessed by area under the curve at receiver operating characteristic analysis (P < 0.001): 0.92 for PAH, slightly higher than standard CMR metrics. Moreover, establishing the diagnosis using the approach was less time-consuming, being achieved within 10 s. Learnt features were visualized in feature maps with correspondence to cardiac phases, confirming known and also identifying potentially new diagnostic features in PAH., Conclusion: A tensor-based machine learning approach has been developed and applied to CMR. High diagnostic accuracy has been shown for PAH diagnosis and new learnt features were visualized with diagnostic potential., (© The Author(s) 2020. Published by Oxford University Press on behalf of the European Society of Cardiology.)

Many demographic and ecological processes generate seasonal and other periodicities. Seasonality in infectious disease transmission can result from climatic forces such as temperature and humidity; variation in contact rates as a result of migration or school calendar; or temporary surges in birth rates. Seasonal drivers of acute immunizing infections can also drive longer-term fluctuations.Tensor decomposition has been used in many disciplines to uncover dominant trends in multi-dimensional data. We introduce tensors as a novel method for decomposing oscillatory infectious disease time series.We illustrate the reliability of the method by applying it to simulated data. We then present decompositions of measles data from England and Wales. This paper leverages simulations as well as much-studied data to illustrate the power of tensor decomposition to uncover dominant epidemic signals as well as variation in space and time. We then use tensor decomposition to uncover new findings and demonstrate the potential power of the method for disease incidence data. In particular, we are able to distinguish between annual and biennial signals across locations and shifts in these signals over time.Tensor decomposition is able to isolate variation in disease seasonality as a result of variation in demographic rates. The method allows us to discern variation in the strength of such signals by space and population size. Tensors provide an opportunity for a concise approach to uncovering heterogeneity in disease transmission across space and time in large datasets., (© 2020 The Authors. Methods in Ecology and Evolution published by John Wiley & Sons Ltd on behalf of British Ecological Society.)

Recently, machine learning methods have gained lots of attention from researchers seeking to analyze brain images such as Resting-State Functional Magnetic Resonance Imaging (rs-fMRI) to obtain a deeper understanding of the brain and such related diseases, for example, Alzheimer's disease. Finding the common patterns caused by a brain disorder through analysis of the functional connectivity (FC) network along with discriminating brain diseases from normal controls have long been the two principal goals in studying rs-fMRI data. The majority of FC extraction methods calculate the FC matrix for each subject and then use simple techniques to combine them and obtain a general FC matrix. In addition, the state-of-the-art classification techniques for finding subjects with brain disorders also rely on calculating an FC for each subject, vectorizing, and feeding them to the classifier. Considering these problems and based on multi-dimensional nature of the data, we have come up with a novel tensor framework in which a general FC matrix is obtained without the need to construct an FC matrix for each sample. This framework also allows us to reduce the dimensionality and create a novel discriminant function that rather than using FCs works directly with each sample, avoids vectorization in any step, and uses the test data in the training process without forcing any prior knowledge of its label into the classifier. Extensive experiments using the ADNI dataset demonstrate that our proposed framework effectively boosts the fMRI classification performance and reveals novel connectivity patterns in Alzheimer's disease at its early stages., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2020 Noroozi and Rezghi.)

Biclustering is an important exploratory analysis tool that simultaneously clusters rows (e.g., samples) and columns (e.g., variables) of a data matrix. Checkerboard-like biclusters reveal intrinsic associations between rows and columns. However, most existing methods rely on Gaussian assumptions and only apply to matrix data. In practice, non-Gaussian and/or multi-way tensor data are frequently encountered. A new CO-clustering method via Regularized Alternating Least Squares (CORALS) is proposed, which generalizes biclustering to non-Gaussian data and multi-way tensor arrays. Non-Gaussian data are modeled with single-parameter exponential family distributions and co-clusters are identified in the natural parameter space via sparse CANDECOMP/PARAFAC tensor decomposition. A regularized alternating (iteratively reweighted) least squares algorithm is devised for model fitting and a deflation procedure is exploited to automatically determine the number of co-clusters. Comprehensive simulation studies and three real data examples demonstrate the efficacy of the proposed method. The data and code are publicly available.

Background: Differences in measurement outcomes using different tensors in total knee arthroplasty (TKA) remain unknown. This study aimed to compare intraoperative soft tissue balance between two measurement systems in TKA., Methods: This study included 24 cruciate-retaining (CR) and 27 posterior-stabilized (PS) TKAs for varus-type osteoarthritis. All TKAs were performed with the measured resection technique. Intraoperative soft tissue balance was assessed with femoral component placement and patellofemoral joint reduction throughout the range of motion. Measurements were performed using the Offset Repo-Tensor (Zimmer) and Ligament Sensor Tensor (Depuy). Joint component gaps and varus/valgus ligament balance were compared statistically in CR and PS TKAs., Results: Joint component gaps with the Offset Repo-Tensor were significantly larger at 0°, 10°, 30°, and 60° of knee flexion in CR TKA and at all knee flexion angles, except 0° and 135°, in PS TKA than those with the Ligament Sensor Tensor (P < .05). Varus balance with the Offset Repo-Tensor was significantly larger at 0°, 10°, and 30° of knee flexion in CR TKA and at 10°, 30°, 60°, 90°, and 120° of knee flexion in PS TKA than that with the Ligament Sensor Tensor (P < .05)., Conclusion: Surgeons should consider the discrepancy in assessing intraoperative soft tissue balance depending on the tensor used. The Ligament Sensor Tensor tended to underestimate soft tissue balance in CR and PS TKAs compared with the Offset Repo-Tensor, especially in PS TKA. Thus, surgeons should know the difference in values between the offset-type tensor with consistent distraction force and a spring-loaded tensor., Competing Interests: Declaration of competing interest The authors declare that there are no conflicts of interest. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors., (Copyright © 2020. Published by Elsevier B.V.)

The identification of essential proteins can help in understanding the minimum requirements for cell survival and development. Ever-increasing amounts of high-throughput data provide us with opportunities to detect essential proteins from protein interaction networks (PINs). Existing network-based approaches are limited by the poor quality of the underlying PIN data, which exhibits high rates of false positive and false negative results. To overcome this problem, researchers have focused on the prediction of essential proteins by combining PINs with other biological data, which has led to the emergence of various interactions between proteins. It remains challenging, however, to use aggregated multiplex interactions within a single analysis framework to identify essential proteins. In this study, we created a multiplex biological network (MON) by initially integrating PINs, protein domains, and gene expression profiles. Next, we proposed a new approach to discover essential proteins by extending the random walk with restart algorithm to the tensor, which provides a data model representation of the MON. In contrast to existing approaches, the proposed MON approach considers for the importance of nodes and the different types of interactions between proteins during the iteration. MON was implemented to identify essential proteins within two yeast PINs. Our comprehensive experimental results demonstrated that MON outperformed 11 other state-of-the-art approaches in terms of precision-recall curve, jackknife curve, and other criteria., (Copyright © 2020 Zhao, Hu, Liu, Xiong, Han, Zhang, Li and Wang.)

Magnetoencephalography (MEG) and electroencephalography (EEG) are contemporary methods to investigate the function and organization of the brain. Simultaneously acquired MEG-EEG data are inherently multi-dimensional and exhibit coupling. This study uses a coupled tensor decomposition to extract the signal sources from MEG-EEG during intermittent photic stimulation (IPS). We employ the Coupled Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization (C-SECSI). After comparing its performance with alternative methods using simulated benchmark data, we apply it to MEG-EEG recordings of 12 participants during IPS with fractions of the individual alpha frequency between 0.4 and 1.3. In the benchmark tests, C-SECSI is more accurate than SECSI and alternative methods, especially in ill-conditioned scenarios, e.g., involving collinear factors or noise sources with different variances. The component field-maps allow us to separate physiologically meaningful oscillations of visually evoked brain activity from background signals. The frequency signatures of the components identify either an entrainment to the respective stimulation frequency or its first harmonic, or an oscillation in the individual alpha band or theta band. In the group analysis of both, MEG and EEG data, we observe a reciprocal relationship between alpha and theta band oscillations. The coupled tensor decomposition using C-SECSI is a robust, powerful method for the extraction of physiologically meaningful sources from multidimensional biomedical data. Unsupervised signal source extraction is an essential solution for rendering advanced multi-modal signal acquisition technology accessible to clinical diagnostics, pre-surgical planning, and brain computer interface applications., (Copyright © 2020 Naskovska, Lau, Korobkov, Haueisen and Haardt.)

We propose and analyse a general tensor-based framework for incorporating second-order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods and recently proposed cases from the literature, but we also identify many interesting extensions. In particular, we define a mutually reinforcing (spectral) version of the classical clustering coefficient. The underlying object of study is a constrained nonlinear eigenvalue problem associated with a cubic tensor. Using recent results from nonlinear Perron-Frobenius theory, we establish existence and uniqueness under appropriate conditions, and show that the new spectral measures can be computed efficiently with a nonlinear power method. To illustrate the added value of the new formulation, we analyse the measures on a class of synthetic networks. We also give computational results on centrality and link prediction for real-world networks., Competing Interests: The authors declare that they have no competing interests., (© 2020 The Author(s).)

Blood vessel segmentation plays a fundamental role in many computer-aided diagnosis (CAD) systems, such as coronary artery stenosis quantification, cerebral aneurysm quantification, and retinal vascular tree analysis. Fine blood vessel segmentation can help build a more accurate computer-aided diagnosis system and help physicians gain a better understanding of vascular structures. The purpose of this article is to develop a blood vessel segmentation method that can improve segmentation accuracy in tiny blood vessels. In this work, we propose a tensor-based graph-cut method for blood vessel segmentation. With our method, each voxel can be modeled by a second-order tensor, allowing the capture of the intensity information and the geometric information for building a more accurate model for blood vessel segmentation. We compared our proposed method's accuracy to several state-of-the-art blood vessel segmentation algorithms and performed experiments on both simulated and clinical CT datasets. Both experiments showed that our method achieved better state-of-the-art results than the competing techniques. The mean centerline overlap ratio of our proposed method is 84% on clinical CT data. Our proposed blood vessel segmentation method outperformed other state-of-the-art methods by 10% on clinical CT data. Tiny blood vessels in clinical CT data with a 1-mm radius can be extracted using the proposed technique. The experiments on a clinical dataset showed that the proposed method significantly improved the segmentation accuracy in tiny blood vessels., (Copyright © 2019. Published by Elsevier B.V.)

Purpose: To study diagnostic accuracy of diffusion tensor imaging (DTI) in differentiating malignant from benign compressed vertebrae., Methods: This study was done on 43 patients with compressed vertebrae on conventional magnetic resonance study that underwent DTI. The mean diffusivity (MD) and fractional anisotropy (FA) of malignant (n = 24) and benign (n = 19) compressed vertebrae were calculated by two readers., Results: There was a significantly lower (P = 0.001) MD of both readers between malignant (0.74 ± 0.2 and 0.78 ± 0.2 × 10 -3  mm 2 /s) and benign (1.67 + 0.3 and 1.63 ± 0.3 × 10 -3  mm 2 /s) compressed vertebrae. The FA of malignant compressed vertebrae of both readers (0.55 ± 0.2 and 0.52 ± 0.1) was significantly higher (P = 0.001) than that of benign (0.26 ± 0.1 and 0.28 ± 0.1) compressed vertebrae. There was excellent inter-reader agreement between both readers using MD (K = 0.91) and FA (K = 0.86). The thresholds of MD and FA used for differentiating malignant from benign compressed vertebrae of both readers were 1.15 and 1.16 × 10 -3  mm 2 /s and 0.37 and 0.34 with area under the curve (AUC) of 0.98, 0.96, 0.93, and 0.92 and diagnostic accuracy of 95.3%, 88.4%, 90.1%, and 86.0% respectively. Combined MD and FA revealed AUC of 0.99 and 0.97 and diagnostic accuracy of 95.3% and 93.0% by both readers respectively., Conclusion: DTI is a non-invasive technique providing accurate imaging parameters that can be used for differentiating malignant from benign compressed vertebrae.

The representation of nuclear magnetic resonance (NMR) tensors as surfaces on three-dimensional molecular models is an information-rich presentation that highlights the geometric relationship between tensor principal components and the underlying molecular and electronic structure. Here, we describe a new computational tool, TensorView, for depicting NMR tensors on the molecular framework. This package makes use of the graphical interface and built-in molecular display functionality present within the Mathematica programming environment and is robust for displaying tensor properties from a broad range of commercial and user-specific computational chemistry packages. Two mathematical forms for representing tensor interaction surfaces are presented, the popular ellipsoidal construct and the more technically correct "ovaloid" form. Examples are provided for chemical shielding and shift tensors, dipole-dipole and quadrupolar couplings, and atomic anisotropic displacement parameters (thermal ellipsoids) derived from NMR crystallography., (© 2018 John Wiley & Sons, Ltd.)

Since most of the previous video watermark algorithms regard a video as a series of consecutive images, the embedding and extraction of watermark are performed on these images, and the correlation and redundancy among frames of a video are not considered. Such algorithms are weak in protecting against frame attacks. In order to improve the robustness, we take into consideration the correlation and redundancy among the frames of a video to propose a blind video watermark algorithm based on tensor decomposition. First, a grayscale video is represented as a 3-order tensor, and the core tensor is obtained by tensor decomposition. Second, the watermark embedding position is selected based on the stability of the maximum value in the core tensor because the core tensor represents the main energy of a video. Then, the watermark is embedded by quantifying the maximum value in the core tensor. Finally, the watermark is uniformly distributed across frames of a video by inverse tensor decomposition. The experiments show that our algorithm based on tensor decomposition has better imperceptibility and robustness against common video attacks.

T2-weighted (T2W) imaging is the most important sequence for detection of acute traumatic spinal cord pathology in clinical practice. Intramedullary hemorrhage on T2W imaging is associated with some component of irreversible injury and arguably the most robust MR imaging predictor of injury severity. The MR imaging appearance of the injured spinal cord in the early stages of injury is highly dynamic, and the time delay from injury to imaging must be considered in image interpretation. Diffusion imaging offers promise as specific tool for interrogating spinal cord integrity, although well-designed, prospective clinical studies validating its application remain limited., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Background: Differentiation between residual head and neck squamous cell carcinoma and post-radiation changes is difficult with routine computed tomography and magnetic resonance imaging., Purpose: To assess the reliability and reproducibility of mean diffusivity (MD) and fractional anisotropy (FA) parameters of diffusion tensor imaging in differentiation residual head and neck squamous cell carcinoma from post-radiation changes., Material and Methods: A retrospective analysis of diffusion tensor imaging of 43 patients with head and neck squamous cell carcinoma cancer after radiotherapy. The MD and FA of the lesion were calculated by the same reader at two-time points., Results: There was a significantly lower difference (P = 0.001) in MD of both readings between residual head and neck squamous cell carcinoma (1.48 ± 0.06 and 1.47 ± 0.07 × 10 -3  mm 2 /s) and post-radiation changes (1.72 ± 0.08 and 1.71 ± 0.11 × 10 -3  mm 2 /s). The FA of residual head and neck squamous cell carcinoma of both readings (0.41 ± 0.09 and 0.42 ± 0.09) shows a significantly higher difference (P = 0.001) than post-radiation changes (0.17 ± 0.04 and 0.16 ± 0.03). There was excellent intra-reader agreement between both readings using MD (K = 0.958) and FA (K = 0.987). The threshold MD and FA used for differentiating the residual from post-radiation changes of both readings was 1.61, 1.65 × 10 -3  mm 2 /s and 0.27, 0.25 with an area under the curve of 0.991, 0.934, 0.993 and 0.990 respectively., Conclusion: MD and FA of diffusion tensor imaging are non-invasive reliable and reproducible parameters that can help in differentiation residual head and neck squamous cell carcinoma from post-radiation changes., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Alzheimer's disease (AD) is a degenerative brain disease that affects millions of people around the world. As populations in the United States and worldwide age, the prevalence of Alzheimer's disease will only increase. In turn, the social and financial costs of AD will create a difficult environment for many families and caregivers across the globe. By combining genetic information, brain scans, and clinical data, gathered over time through the Alzheimer's Disease Neuroimaging Initiative (ADNI), we propose a new Joint High-Order Multi-Modal Multi-Task Feature Learning method to predict the cognitive performance and diagnosis of patients with and without AD.