Community detection in hypergraphs, spiked tensor models, and Sum-of-Squares by Kim, Chiheon, Sousa Bandeira, Afonso Jose, Goemans, Michel X

“…Similarly to how the stochastic block model in graphs suggests studying spiked random matrices, our model motivates investigating statistical and computational limits of exact recovery in certain spiked tensor models. In contrast with the matrix case, the spiked model naturally arising from community detection in hypergraphs is different from the one arising in the so-called tensor Principal Component Analysis model. …”
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Exact sequences of tensor categories with respect to a module category by Etingof, Pavel I, Gelaki, Shlomo

“…We generalize the definition of an exact sequence of tensor categories due to Bruguières and Natale, and introduce a new notion of an exact sequence of (finite) tensor categories with respect to a module category. …”
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p-adic dimensions in symmetric tensor categories in characteristic p by Etingof, Pavel I, Harman, Nate, Ostrik, Victor

“…To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. …”
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Capturing transient granular rheology with extended fabric tensor relations by Rojas Parra, Eduardo, Kamrin, Kenneth N

“…The comparison for the modulus and the angle of the principal directions of the fabric tensor showed a very good agreement for all the cases analyzed. …”
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Automatic generation of efficient sparse tensor format conversion routines by Chou, Stephen, Kjolstad, Fredrik, Amarasinghe, Saman

“…This paper shows how to generate code that efficiently converts sparse tensors between disparate storage formats (data layouts) such as CSR, DIA, ELL, and many others. …”
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Automatic generation of efficient sparse tensor format conversion routines by Chou, Stephen, Kjolstad, Fredrik, Amarasinghe, Saman P

“…This paper shows how to generate code that efficiently converts sparse tensors between disparate storage formats (data layouts) such as CSR, DIA, ELL, and many others. …”
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Finite symmetric tensor categories with the Chevalley property in characteristic 2 by Etingof, Pavel, Gelaki, Shlomo

“…<jats:p> We prove an analog of Deligne’s theorem for finite symmetric tensor categories [Formula: see text] with the Chevalley property over an algebraically closed field [Formula: see text] of characteristic [Formula: see text]. …”
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A Tensor Compiler for Simple and EfficientFully Homomorphic Encryption by Krastev, Aleksandar

“…Fhelipe exposes a simple, numpy-style programming interface for working on tensors. Tensors cover key domains that map well to FHE, like machine learning and linear algebra. …”
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Symphony: Orchestrating Sparse and Dense Tensors with Hierarchical Heterogeneous Processing by Pellauer, Michael, Clemons, Jason, Balaji, Vignesh, Crago, Neal, Jaleel, Aamer, Lee, Donghyuk, O'Connor, Mike, Parashar, Angshuman, Treichler, Sean, Tsai, Po-An, Keckler, Stephen, Emer, Joel

“…Sparse tensor algorithms are becoming widespread, particularly in the domains of deep learning, graph and data analytics, and scientific computing. …”
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Tailors: Accelerating Sparse Tensor Algebra by Overbooking Buffer Capacity by Xue, Zi Yu, Wu, Yannan, Emer, Joel, Sze, Vivienne

“…Sparse tensor algebra is a challenging class of workloads to accelerate due to low arithmetic intensity and varying sparsity patterns. …”
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Tailors: Accelerating Sparse Tensor Algebra by Overbooking Buffer Capacity by Xue, Zi Yu

“…Sparse tensor algebra is a challenging class of workloads to accelerate due to few opportunities for data reuse and varying sparsity patterns. …”
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Dual-Phase Cardiac Diffusion Tensor Imaging with Strain Correction by Stoeck, Christian T., Kalinowska, Aleksandra, von Deuster, Constantin, Harmer, Jack, Chan, Rachel W., Niemann, Markus, Manka, Robert, Atkinson, David, Sosnovik, David E., Mekkaoui, Choukri, Kozerke, Sebastian

“…Purpose: In this work we present a dual-phase diffusion tensor imaging (DTI) technique that incorporates a correction scheme for the cardiac material strain, based on 3D myocardial tagging. …”
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Many-body entanglement : topological orders, tensor networks and superconductivity by Liu, Jimmy Fangzhou

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Multi-channel EEG compression based on matrix and tensor decompositions by Srinivasan, K., Dauwels, Justin, Reddy, M. Ramasubba, Cichocki, Andrzej

“…Compression schemes for EEG signals are developed based on matrix and tensor decomposition. Various ways to arrange EEG signals into matrices and tensors are explored, and several matrix and tensor decomposition schemes are applied, including SVD, CUR, PARAFAC, the Tucker decomposition, and recent random fiber selection approaches. …”
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A survey on applications of semi-tensor product method in engineering by Li, Haitao, Zhao, Guodong, Meng, Min, Feng, June

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Berry connection polarizability tensor and third-order Hall effect by Liu, Huiying, Zhao, Jianzhou, Huang, Yue-Xin, Feng, Xiaolong, Xiao, Cong, Wu, Weikang, Lai, Shen, Gao, Weibo, Yang, Shengyuan A.

“…Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. …”
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Taylor's theorem: a new perspective for neural tensor networks by Li, Wei, Zhu, Luyao, Cambria, Erik

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Tensor decomposition based R-dimensional matrix pencil method by Wen, Fuxi, Tay, Wee Peng

“…Furthermore, it is straightforward to extend the proposed R-D tensor MP to other MP type methods, such as R-D unitary tensor MP, R-D beamspace tensor MP.…”
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THEORETICAL STUDY OF SOLVENT EFFECTS AND NMR SHIELDING TENSORS OF DLPC by Perpustakaan UGM, i-lib

“…The 'Gauge Including Atomic Orbital' (GIAO) approach is used to investigate Ab initio GIAO calculations of NMR chemical shielding tensors carried out within SCF-Hartree-Fock approximation are described. …”

COHERENCE ENHANCING DIFFUSION FILTERING BASED ON THE PHASE CONGRUENCY TENSOR by Obara, B, Fricker, M, Grau, V, IEEE

“…This can be accomplished in a natural way by adopting anisotropic diffusion filtering to local texture analysis by means of the structure tensor. Here we propose a contrast independent anisotropic diffusion filtering of curvilinear structures based on a novel concept: the Phase Congruency Tensor (PCT). …”