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Journal articles on the topic 'Higher-order tensor'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Monchiet, Vincent, and Guy Bonnet. "Inversion of higher order isotropic tensors with minor symmetries and solution of higher order heterogeneity problems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (2010): 314–32. http://dx.doi.org/10.1098/rspa.2010.0149.

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In this paper, the derivation of irreducible bases for a class of isotropic 2 n th-order tensors having particular ‘minor symmetries’ is presented. The methodology used for obtaining these bases consists of extending the concept of deviatoric and spherical parts, commonly used for second-order tensors, to the case of an n th-order tensor. It is shown that these bases are useful for effecting the classical tensorial operations and especially the inversion of a 2 n th-order tensor. Finally, the formalism introduced in this study is applied for obtaining the closed-form expression of the strain f

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Hajarian, Masoud. "Solving coupled tensor equations via higher order LSQR methods." Filomat 34, no. 13 (2020): 4419–27. http://dx.doi.org/10.2298/fil2013419h.

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Tensors have a wide application in control theory, data mining, chemistry, information sciences, documents analysis and medical engineering. The material here is motivated by the development of the efficient numerical methods for solving the coupled tensor equations (A1*M X *N B1 + C1 *M Y *N D1 = E1, A2 *M X *N B2 + C2 *M Y *N D2 = E2, with Einstein product. We propose the tensor form of the LSQR methods to find the solutions X and Y of the coupled tensor equations. Finally we give some numerical examples to illustrate that our proposed methods are able to accurately and efficiently find the

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Wimalawarne, Kishan, Makoto Yamada, and Hiroshi Mamitsuka. "Scaled Coupled Norms and Coupled Higher-Order Tensor Completion." Neural Computation 32, no. 2 (2020): 447–84. http://dx.doi.org/10.1162/neco_a_01254.

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Recently, a set of tensor norms known as coupled norms has been proposed as a convex solution to coupled tensor completion. Coupled norms have been designed by combining low-rank inducing tensor norms with the matrix trace norm. Though coupled norms have shown good performances, they have two major limitations: they do not have a method to control the regularization of coupled modes and uncoupled modes, and they are not optimal for couplings among higher-order tensors. In this letter, we propose a method that scales the regularization of coupled components against uncoupled components to prope

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Huang, Zheng-Hai, and Liqun Qi. "Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors." Asia-Pacific Journal of Operational Research 37, no. 04 (2020): 2040019. http://dx.doi.org/10.1142/s0217595920400199.

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In this paper, we investigate stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. We show that there are two special symmetric transition probability tensors of order [Formula: see text] dimension 2, which have and only have two stationary probability vectors; and any other symmetric transition probability tensor of order [Formula: see text] dimension 2 has a unique stationary probability vector. As a byproduct, we obtain that any symmetric transition probability tensor of order [Formula: see text] dimension 2 has a unique positive stationar

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Zheng, Yu-Bang, Ting-Zhu Huang, Xi-Le Zhao, Qibin Zhao, and Tai-Xiang Jiang. "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (2021): 11071–78. http://dx.doi.org/10.1609/aaai.v35i12.17321.

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The popular tensor train (TT) and tensor ring (TR) decompositions have achieved promising results in science and engineering. However, TT and TR decompositions only establish an operation between adjacent two factors and are highly sensitive to the permutation of tensor modes, leading to an inadequate and inflexible representation. In this paper, we propose a generalized tensor decomposition, which decomposes an Nth-order tensor into a set of Nth-order factors and establishes an operation between any two factors. Since it can be graphically interpreted as a fully-connected network, we named it

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Xue, Zhaohui, Sirui Yang, Hongyan Zhang, and Peijun Du. "Coupled Higher-Order Tensor Factorization for Hyperspectral and LiDAR Data Fusion and Classification." Remote Sensing 11, no. 17 (2019): 1959. http://dx.doi.org/10.3390/rs11171959.

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Hyperspectral and light detection and ranging (LiDAR) data fusion and classification has been an active research topic, and intensive studies have been made based on mathematical morphology. However, matrix-based concatenation of morphological features may not be so distinctive, compact, and optimal for classification. In this work, we propose a novel Coupled Higher-Order Tensor Factorization (CHOTF) model for hyperspectral and LiDAR data classification. The innovative contributions of our work are that we model different features as multiple third-order tensors, and we formulate a CHOTF model

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7

Stepanov, S., and I. Tsyganok. "Vanishing theorems for higher-order Killing and Codazzi." Differential Geometry of Manifolds of Figures, no. 50 (2019): 141–47. http://dx.doi.org/10.5922/0321-4796-2019-50-16.

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A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonpositive (resp. non-negative) sectional curvature. In the first case we prove that an arbitrary symmetric traceless Killing p-tensor is parallel on M if its norm is a Lq -function for some q > 0. If in addition the volume of this manifold is infinite, then this tensor is equal to zero. In the second

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8

Morita, Satoshi, and Naoki Kawashima. "Calculation of higher-order moments by higher-order tensor renormalization group." Computer Physics Communications 236 (March 2019): 65–71. http://dx.doi.org/10.1016/j.cpc.2018.10.014.

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9

Xiao, B., and J. Feng. "Higher order elastic tensors of crystal structure under non-linear deformation." Journal of Micromechanics and Molecular Physics 04, no. 04 (2019): 1950007. http://dx.doi.org/10.1142/s2424913019500073.

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The higher-order elastic tensors can be used to characterize the linear and non-linear mechanical properties of crystals at ultra-high pressures. Besides the widely studied second-order elastic constants, the third- and fourth-order elastic constants are sixth and eighth tensors, respectively. The independent tensor components of them are completely determined by the symmetry of the crystal. Using the relations between elastic constants and sound velocity in solid, the independent elastic constants can be measured experimentally. The anisotropy in elasticity of crystal structures is directly d

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10

Surana, Karan S., and Stephen W. Long. "Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality." Entropy 22, no. 4 (2020): 443. http://dx.doi.org/10.3390/e22040443.

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This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders n

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11

Al-Qashbari, Adel Mohammed Ali, and Aminah Omar Awadh Mubark. "A study of recurrent Finsler spaces of higher order with Cartan’s Curvature Tensor." University of Aden Journal of Natural and Applied Sciences 27, no. 2 (2023): 291–300. http://dx.doi.org/10.47372/uajnas.2023.n2.a10.

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In the present communication, we have derived Bianchi and Veblen identities along with a few more related results in a recurrent and generalized nth-recurrent Finsler space with Cartan’s curvature tensor field. A Finsler space \(F_n\) whose Cartan's third curvature tensor \(R_{jkh}^i\) satisfies the condition \(R_{jkh|m_1|m_2|…|m_n}^{i} = λ_{m_1m_2…m_n} R_{jkh}^{i} + μ_{m_1m_2…m_n} (δ_{h}^{i} g_{jk} - δ_{k}^{i} g_{jh})\), where \(R_{jkh}^i\)≠0 and \(|m_1 |m_2 |…|m_n\) are h-covariant differentiation (Cartan's second kind covariant differential operator) with respect to x^m to nth order, \(λ_{m

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12

Schultz, T., and G. Kindlmann. "A Maximum Enhancing Higher-Order Tensor Glyph." Computer Graphics Forum 29, no. 3 (2010): 1143–52. http://dx.doi.org/10.1111/j.1467-8659.2009.01675.x.

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13

Qi, Liqun, Gaohang Yu, and Ed X. Wu. "Higher Order Positive Semidefinite Diffusion Tensor Imaging." SIAM Journal on Imaging Sciences 3, no. 3 (2010): 416–33. http://dx.doi.org/10.1137/090755138.

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14

Yuan, Ming, and Cun-Hui Zhang. "Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion." IEEE Transactions on Information Theory 63, no. 10 (2017): 6753–66. http://dx.doi.org/10.1109/tit.2017.2724549.

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15

Zhang, Lipeng, Peng Zhang, Xindian Ma, Shuqin Gu, Zhan Su, and Dawei Song. "A Generalized Language Model in Tensor Space." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7450–58. http://dx.doi.org/10.1609/aaai.v33i01.33017450.

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In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling language. Developing a higher-order tensor representation is challenging, in terms of deriving an effective solution and showing its generality. In this paper, we propose a language model named Tensor Space Language Model (TSLM), by utilizing tensor networks and tensor decomposition. In TSLM, we build a high-dimensional semantic space constructed by the tensor pro

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16

Li, Dazhou, Chuan Lin, Wei Gao, Zihui Meng, and Qi Song. "Short-Term Rental Forecast of Urban Public Bicycle Based on the HOSVD-LSTM Model in Smart City." Sensors 20, no. 11 (2020): 3072. http://dx.doi.org/10.3390/s20113072.

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As a kind of transportation in a smart city, urban public bicycles have been adopted by major cities and bear the heavy responsibility of the “last mile” of urban public transportation. At present, the main problem of the urban public bicycle system is that it is difficult for users to rent a bike during peak h, and real-time monitoring cannot be solved adequately. Therefore, predicting the demand for bicycles in a certain period and performing redistribution in advance is of great significance for solving the lag of bicycle system scheduling with the help of IoT. Based on the HOSVD-LSTM predi

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17

Liu, Chunlei, Sarah C. Mang, and Michael E. Moseley. "In vivo generalized diffusion tensor imaging (GDTI) using higher-order tensors (HOT)." Magnetic Resonance in Medicine 63, no. 1 (2009): 243–52. http://dx.doi.org/10.1002/mrm.22192.

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18

Zare, Ali, Alp Ozdemir, Mark A. Iwen, and Selin Aviyente. "Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA." Proceedings of the IEEE 106, no. 8 (2018): 1341–58. http://dx.doi.org/10.1109/jproc.2018.2848209.

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19

Capozziello, Salvatore, Maurizio Capriolo, and Gaetano Lambiase. "Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity." Particles 5, no. 3 (2022): 298–330. http://dx.doi.org/10.3390/particles5030026.

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An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1p

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20

Capozziello, Salvatore, and Maurizio Capriolo. "The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity." Filomat 37, no. 25 (2023): 8617–34. http://dx.doi.org/10.2298/fil2325617c.

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The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pse

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21

Langlois, David, Michele Mancarella, Karim Noui, and Filippo Vernizzi. "Effective description of higher-order scalar-tensor theories." Journal of Cosmology and Astroparticle Physics 2017, no. 05 (2017): 033. http://dx.doi.org/10.1088/1475-7516/2017/05/033.

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22

Flanagan, Éanna É. "Higher-order gravity theories and scalar–tensor theories." Classical and Quantum Gravity 21, no. 2 (2003): 417–26. http://dx.doi.org/10.1088/0264-9381/21/2/006.

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23

Qiao, Ya-nan, Qi Yong, and Hou Di. "Tensor Field Model for higher-order information retrieval." Journal of Systems and Software 84, no. 12 (2011): 2303–13. http://dx.doi.org/10.1016/j.jss.2011.06.057.

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24

Sherman, Samantha, and Tamara G. Kolda. "Estimating Higher-Order Moments Using Symmetric Tensor Decomposition." SIAM Journal on Matrix Analysis and Applications 41, no. 3 (2020): 1369–87. http://dx.doi.org/10.1137/19m1299633.

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25

Chen, Yanyan, Liyun Lu, and Ping Zhong. "One-class support higher order tensor machine classifier." Applied Intelligence 47, no. 4 (2017): 1022–30. http://dx.doi.org/10.1007/s10489-017-0945-9.

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26

Papenfuss, Christina. "Maximum Entropy Closure Relation for Higher Order Alignment and Orientation Tensors Compared to Quadratic and Hybrid Closure." Journal of Modeling and Simulation of Materials 5, no. 1 (2022): 39–52. http://dx.doi.org/10.21467/jmsm.5.1.39-52.

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A closure relation expresses the fourth order orientation tensor as a function of the second order one. Two well-known closure relations, the hybrid closure and the maximum entropy closure, are compared in the case of a rotation symmetric orientation distribution function. The maximum entropy closure predicts a positive fourth order parameter in the whole range of the second order parameter, whereas the hybrid closure results in negative fourth order parameters for small values of the second order one. For the maximum entropy closure quadratic fit polynomials are presented. For a general distr

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27

Deitmar, Anton, and Ivan Horozov. "Iterated Integrals and Higher Order Invariants." Canadian Journal of Mathematics 65, no. 3 (2013): 544–52. http://dx.doi.org/10.4153/cjm-2012-020-8.

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AbstractWe show that higher order invariants of smooth functions can be written as linear combinations of full invariants times iterated integrals. The non-uniqueness of such a presentation is captured in the kernel of the ensuing map from the tensor product. This kernel is computed explicitly. As a consequence, higher order invariants form a free module of the algebra of full invariants.

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Ishida, Akio, Takumi Noda, Jun Murakami, Naoki Yamamoto, and Chiharu Okuma. "Calculation of Fourth-Order Tensor Product Expansion by Power Method and Comparison of it with Higher-Order Singular Value Decomposition." Applied Mechanics and Materials 444-445 (October 2013): 703–11. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.703.

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Higher-order singular value decomposition (HOSVD) is known as an effective technique to reduce the dimension of multidimensional data. We have proposed a method to perform third-order tensor product expansion (3OTPE) by using the power method for the same purpose as HOSVD, and showed that our method had a better accuracy property than HOSVD, and furthermore, required fewer computation time than that. Since our method could not be applied to the tensors of fourth-order (or more) in spite of having those useful properties, we extend our algorithm of 3OTPE calculation to forth-order tensors in th

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Luo, Yuan, and Chengsheng Mao. "PANTHER: Pathway Augmented Nonnegative Tensor Factorization for HighER-order Feature Learning." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 1 (2021): 371–80. http://dx.doi.org/10.1609/aaai.v35i1.16113.

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Genetic pathways usually encode molecular mechanisms that can inform targeted interventions. It is often challenging for existing machine learning approaches to jointly model genetic pathways (higher-order features) and variants (atomic features), and present to clinicians interpretable models. In order to build more accurate and better interpretable machine learning models for genetic medicine, we introduce Pathway Augmented Nonnegative Tensor factorization for HighER-order feature learning (PANTHER). PANTHER selects informative genetic pathways that directly encode molecular mechanisms. We a

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30

Li, Keren, and Sergey Utyuzhnikov. "Tensor Train-Based Higher-Order Dynamic Mode Decomposition for Dynamical Systems." Mathematics 11, no. 8 (2023): 1809. http://dx.doi.org/10.3390/math11081809.

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Higher-order dynamic mode decomposition (HODMD) has proved to be an efficient tool for the analysis and prediction of complex dynamical systems described by data-driven models. In the present paper, we propose a realization of HODMD that is based on the low-rank tensor decomposition of potentially high-dimensional datasets. It is used to compute the HODMD modes and eigenvalues to effectively reduce the computational complexity of the problem. The proposed extension also provides a more efficient realization of the ordinary dynamic mode decomposition with the use of the tensor-train decompositi

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Saleh, Salem, and A. M. A. Al-Qashbari. "On Generalized Recurrent Finsler Spaces of Higher Order with Berwald’s Curvature Tensor." Cihan University-Erbil Scientific Journal 7, no. 2 (2023): 35–41. http://dx.doi.org/10.24086/cuesj.v7n2y2023.pp35-41.

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In this present paper, we introduced a Finsler space Fn which projective curvature tensor K^i_ijkh satisfies the generalized five recurrence property with respect to Berwald’s connection parameters G^i_kh, we have derived some theorems and some identities along with few more related results in a recurrent and generalized 5-recurrent Finsler space with Berwald’s curvature tensor field.

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32

Schultz, T. "Topological Features in 2D Symmetric Higher-Order Tensor Fields." Computer Graphics Forum 30, no. 3 (2011): 841–50. http://dx.doi.org/10.1111/j.1467-8659.2011.01933.x.

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33

Qun Li and Dan Schonfeld. "Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification." IEEE Transactions on Pattern Analysis and Machine Intelligence 36, no. 12 (2014): 2524–37. http://dx.doi.org/10.1109/tpami.2014.2342214.

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34

Boyer, Rmy, Lieven De Lathauwer, and Karim Abed-Meraim. "Higher Order Tensor-Based Method for Delayed Exponential Fitting." IEEE Transactions on Signal Processing 55, no. 6 (2007): 2795–809. http://dx.doi.org/10.1109/tsp.2007.893981.

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35

Chatzichristos, Christos, Eleftherios Kofidis, Manuel Morante, and Sergios Theodoridis. "Blind fMRI source unmixing via higher-order tensor decompositions." Journal of Neuroscience Methods 315 (March 2019): 17–47. http://dx.doi.org/10.1016/j.jneumeth.2018.12.007.

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36

Biglari, Fahimeh, Malik Abu Hassan, and Wah June Leong. "New quasi-Newton methods via higher order tensor models." Journal of Computational and Applied Mathematics 235, no. 8 (2011): 2412–22. http://dx.doi.org/10.1016/j.cam.2010.10.041.

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37

Zhifeng Hao, Lifang He, Bingqian Chen, and Xiaowei Yang. "A Linear Support Higher-Order Tensor Machine for Classification." IEEE Transactions on Image Processing 22, no. 7 (2013): 2911–20. http://dx.doi.org/10.1109/tip.2013.2253485.

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38

Beaupère, Matthias, David Frenkiel, and Laura Grigori. "Higher-Order QR with Tournament Pivoting for Tensor Compression." SIAM Journal on Matrix Analysis and Applications 44, no. 1 (2023): 106–27. http://dx.doi.org/10.1137/20m1387663.

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39

Fossati, Caroline, Salah Bourennane, Romuald Sabatier, and Antonio Di Giacomo. "Tensorial Model for Photolithography Aerial Image Simulation." Advances in OptoElectronics 2009 (December 6, 2009): 1–9. http://dx.doi.org/10.1155/2009/457549.

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In this paper, we propose to adapt the multilinear algebra tools to the tensor of Transmission Cross-Coefficients (TCC) values for aerial image simulation in order to keep the data tensor as a whole entity. This new approach implicitly extends the singular value decomposition (SVD) to tensors, that is, Higher Order SVD or TUCKER3 tensor decomposition which is used to obtain lower rank- tensor approximation (LRTA ). This model requires an Alternating Least Square (ALS) process known as TUCKALS3 algorithm. The needed number of kernels is estimated using two adapted criteria, well known in signal

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Al-Qashbari, Adel Mohammed Ali, and Fahmi Ahmed Mothana AL-ssallal. "GENERALIZATION OF WELY'S PROJECTIVE CURVATURE TENSOR IN FINSLER SPACES: A STUDY ON GENERALIZED W-RECURRENT, BIRECURRENT, AND RICCI TENSORS." Electronic Journal of University of Aden for Basic and Applied Sciences 6, no. 1 (2025): 9–18. https://doi.org/10.47372/ejua-ba.2025.1.419.

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In this study, we explore the generalization of Wely’s projective curvature tensor \(W_{jkh}^i\) satisfying a specific recurrence relation (3.1), which defines a generalized W-recurrent space, denoted as G2nd W|h - BRFn . By investigating the conditions under which this tensor satisfies the generalized recurrence relations, we define and analyze the properties of generalized W-recurrent, birecurrent, and Ricci tensors in the context of second-order covariant derivatives. We derive a series of equations that describe the behavior of these tensors, including the covariant derivative expressions

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41

Adel, M. Al-Qashbari, A. Abdallah Alaa, and S. Nasr Kamal. "Generalization of h-Torsion and Curvature Structures in Generalized Recurrent Space of Third Order by Cartan Covariant Derivatives." GPH - International Journal of Mathematics 8, no. 02 (2025): 01–09. https://doi.org/10.5281/zenodo.14916640.

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In this research, we explore the generalized <em>h</em>-Torsion and curvature structures in Finsler spaces, specifically within the framework of the generalized <strong>Uₕ-TRFₙ</strong> tensor field. By deriving various expressions for these tensors, we reveal the relationships between the generalized <em>h</em>-Torsion tensor and Cartan’s curvature tensor. This paper extends the generalized <strong>Uₕ-Trirecurrent</strong> Finsler space. Furthermore, we obtain some relationships among different curvature tensors by using Cartan’s connection parameter <strong>Γⁱₖₕ</strong>. T

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42

Akkerman, Erik M. "The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging." Journal of Magnetic Resonance 206, no. 1 (2010): 9–19. http://dx.doi.org/10.1016/j.jmr.2010.05.016.

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43

Baker, Mark Robert, and Julia Bruce-Robertson. "Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities." Canadian Journal of Physics 99, no. 9 (2021): 764–71. http://dx.doi.org/10.1139/cjp-2020-0623.

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Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-n field for each spin-n). For this reason they are sometimes referred to as the generalized “Riemann” tensors. In this article, a method for deriving these curvature tensors from first principles is presented; the derivation is completed without any a priori knowledge of the existence of the Riemann tensors or the curvature tensors of higher-spin gauge theories. To

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Roy, Anubhav, Darren W. Branch, Daniel S. Jensen, and Christopher M. Kube. "propSym: a tool to establish relationships between property constants for material property tensors of any order." Journal of Applied Crystallography 54, no. 6 (2021): 1894–901. http://dx.doi.org/10.1107/s160057672101058x.

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The properties of crystalline materials can be described mathematically by tensors whose components are generally known as property constants. Tabulations of these constants in terms of the independent components are well known for common material properties (e.g. elasticity, piezoelectricity etc.) aptly described by tensors of lower rank (e.g. ranks 2–4). General relationships between constants of higher rank are often unknown and sometimes reported incorrectly. A computer program is developed here to calculate the property constant relationships of a property of any order, represented by a t

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45

Jiang, Shan, and Pengfei Zhang. "Comprehensive and quantitative study of rank-4 order diffusion tensor imaging and positive definite rank-4 order diffusion tensor imaging: A higher order tensor imaging study." International Journal of Imaging Systems and Technology 24, no. 1 (2014): 83–93. http://dx.doi.org/10.1002/ima.22082.

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46

SEGAL, ARKADY Y. "POINT PARTICLE–SYMMETRIC TENSORS INTERACTION AND GENERALIZED GAUGE PRINCIPLE." International Journal of Modern Physics A 18, no. 27 (2003): 5021–38. http://dx.doi.org/10.1142/s0217751x03015842.

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The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of ex

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Kulikov, Leonid, Natalia Inkova, Daria Cherniuk, Anton Teslyuk, and Zorigto Namsaraev. "TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on Higher-Order Tensor Decompositions." Water 13, no. 18 (2021): 2578. http://dx.doi.org/10.3390/w13182578.

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Satellite research methods are frequently used in observations of water bodies. One of the most important problems in satellite observations is the presence of missing data due to internal malfunction of satellite sensors and poor atmospheric conditions. We proceeded on the assumption that the use of data recovery methods based on spatial relationships in data can increase the recovery accuracy. In this paper, we present a method for missing data reconstruction from remote sensors. We refer our method to as Tensor Interpolating Empirical Orthogonal Functions (TIEOF). The method relies on the t

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Khoromskij, B. N. "Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D." Computational Methods in Applied Mathematics 6, no. 2 (2006): 194–220. http://dx.doi.org/10.2478/cmam-2006-0010.

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AbstractThe structured tensor-product approximation of multidimensional nonlocal operators by a two-level rank-(r1, . . . , rd) decomposition of related higher-order tensors is proposed and analysed. In this approach, the construction of the desired approximant to a target tensor is a reminiscence of the Tucker-type model, where the canonical components are represented in a fixed (uniform) basis, while the core tensor is given in the canonical format. As an alternative, the multilevel nested canonical decomposition is presented. The complexity analysis of the corresponding multilinear algebra

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Tretyakov, Petr V. "Dynamical stability of Minkowski space in higher order gravity." International Journal of Geometric Methods in Modern Physics 12, no. 09 (2015): 1550094. http://dx.doi.org/10.1142/s0219887815500942.

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We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space is proposed. This method was applied for some modified gravity theories, such as f(R) gravity, f(R)+αR□R gravity and scalar–tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of f(R) gravity Minkowski solution is asymptotically stable in ghost-free (f′ > 0) and tachyon-free (f″ > 0) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of h

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Bailey, Quentin G. "Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory." Symmetry 13, no. 5 (2021): 834. http://dx.doi.org/10.3390/sym13050834.

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We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot d

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