The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function by Chuanqing Gu, Yong Liu

“…As an application, the TPTA for computing the tensor exponential function is presented. Numerical examples are given to demonstrate the efficiency of the proposed algorithm.…”
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Learning tensor networks with tensor cross interpolation: New algorithms and libraries by Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal

“…In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. …”
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Tensor z-Transform by Shih Yu Chang, Hsiao-Chun Wu

“…Finally, numerical evaluations are presented to demonstrate certain interesting phenomena of the new tensor z-transform.…”
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Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization by Kuang-dai Leng, Qiang Yang

“…One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.…”
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Sum and Tensor of Quantitative Effects by Giorgio Bacci, Radu Mardare, Prakash Panangaden, Gordon Plotkin

“…As our main result, we show that the sum and tensor of two quantitative equational theories correspond to the categorical sum (i.e., coproduct) and tensor, respectively, of their effects qua monads. …”
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Thermal Radiation Transport with Tensor Trains by Alex A. Gorodetsky, Patrick D. Mullen, Aditya Deshpande, Joshua C. Dolence, Chad D. Meyer, Jonah M. Miller, Luke F. Roberts

“…We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. …”
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Tensor nested ring embedding used for domain adaptation of cross-source heterogeneous remote sensing feature tensors by Tong Gao, Min Liu, Wei Hu, Hao Chen

“…Although domain adaptation methods can reduce cross-source feature differences, they can only handle vector or homogeneous tensors and fail to process multisource data represented as heterogeneous tensors. …”
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Brouwer degree, equivariant maps and tensor powers by Z. Balanov, W. Krawcewicz, A. Kushkuley

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Fermionic tensor network contraction for arbitrary geometries by Yang Gao, Huanchen Zhai, Johnnie Gray, Ruojing Peng, Gunhee Park, Wen-Yuan Liu, Eirik F. Kjønstad, Garnet Kin-Lic Chan

“…We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and a locally ordered formalism. …”
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Low-temperature Gibbs states with tensor networks by Denise Cocchiarella, Mari Carmen Bañuls

“…We demonstrate the performance of our approach with a tree tensor network ansatz, although it can be extended to other tensor networks, and present results illustrating its effectiveness in capturing the finite-temperature properties in one- and two-dimensional scenarios. …”
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Survey on Computational Applications of Tensor-Network Simulations by Marcos Diez Garcia, Antonio Marquez Romero

“…This paper presents a broad but not exhaustive literature review of state-of-the-art applications of tensor networks and related topics across many research domains, including: machine learning, mathematical optimization, materials science, quantum chemistry and quantum circuit simulation. …”
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Tensor Network Enhanced Dynamic Multiproduct Formulas by Niall F. Robertson, Bibek Pokharel, Bryce Fuller, Eric Switzer, Oles Shtanko, Mirko Amico, Adam Byrne, Andrea D’Urbano, Salome Hayes-Shuptar, Albert Akhriev, Nathan Keenan, Sergey Bravyi, Sergiy Zhuk

“…Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. …”
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AN ORDER-P TENSOR MULTIPLICATION WITH CIRCULANT STRUCTURE by Itsar Mangngiri, Qonita Qurrota A’yun, Wasono Wasono

“…First, we present a theorem of the -product of tensors involving circulant matrices. …”
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Diffusion tensor metrics as biomarkers in Alzheimer's disease. by Julio Acosta-Cabronero, Stephanie Alley, Guy B Williams, George Pengas, Peter J Nestor

“…To date, frequently inconsistent results have been reported, though lack of standardisation in acquisition and analysis make such discrepancies difficult to interpret. There is also, at present, little knowledge of how the biometric properties of diffusion tensor imaging might evolve in the course of Alzheimer's disease.…”
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Process tensor approaches to modeling two-dimensional spectroscopy by Roosmarijn de Wit, Jonathan Keeling, Brendon W. Lovett, Alex W. Chin

“…The method employs a process tensor framework to efficiently compute multitime correlations in a numerically exact way. …”
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On the stability of electrovacuum space-times in scalar–tensor gravity by Kirill A. Bronnikov, Sergei V. Bolokhov, Milena V. Skvortsova, Rustam Ibadov, Feruza Y. Shaymanova

“…Abstract We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. …”
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Functional Connectome Fingerprinting Through Tucker Tensor Decomposition by Vitor Carvalho, Mintao Liu, Jaroslaw Harezlak, Ana María Estrada Gómez, Joaquín Goñi

“…Relative to FC matrices as well as to Principal Components Analysis (PCA), tensor decomposition significantly increases the functional connectome’s fingerprint. …”
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Deep Circuit Compression for Quantum Dynamics via Tensor Networks by Joe Gibbs, Lukasz Cincio

“…By the efficient use of environment tensors, the algorithm is scalable in depth far beyond prior work, and we present circuit compilations of up to 64 layers of $SU(4)$ gates. …”
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Relativistic Symmetries of Hulthén Potential Incorporated with Generalized Tensor Interactions by A. N. Ikot, H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar

“…The bound-state energy spectra and the radial wave functions are approximately obtained in the case of spin and pseudospin symmetries. The tensor interactions and the degeneracy-removing role are presented in details.…”
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Geršhgorin-type theorems for Z1-eigenvalues of tensors with applications by Shen Xiaowei, Hao Qian, He Jun, Wang Guangbin

“…In this article, we present several Geršhgorin-type theorems for Z1{Z}_{1}-eigenvalues of tensors, which improve the results provided by Wang et al. …”
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