Evidence map›Paper›PMID 40458229›Full record

ArticleSIAM journal on matrix analysis and applications : a publication of the Society for Industrial and Applied Mathematics2024

KRONECKER PRODUCT OF TENSORS AND HYPERGRAPHS: STRUCTURE AND DYNAMICS.

Joshua Pickard, Can Chen, Cooper Stansbury, Amit Surana, Anthony Bloch, Indika Rajapakse

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Article in SIAM journal on matrix analysis and applications : a publication of the Society for Industrial and Applied Mathematics, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.

0numbers the graph read from it
0cells of the map it votes in
2citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

2 citing papers in PubMed.

  1. Review
  2. Article
4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

6 authors.

Joshua PickardDepartment of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA.
Can ChenSchool of Data Science and Society and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
Cooper StansburyDepartment of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA.
Amit SuranaRaytheon Technologies Research Center, East Hartford, CT 06108.
Anthony BlochDepartment of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.
Indika RajapakseDepartment of Computational Medicine & Bioinformatics, Medical School and Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.

Funding

Systems and Integrative Biology Training ProgramT32GM150581 · NIGMS · UNIVERSITY OF MICHIGAN AT ANN ARBOR · PI DANIEL A BEARD · 2023 to 2026
$1.2M
NIGMS NIH HHS T32 GM150581
6 · The paper itself

Abstract

Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in graph or matrix contexts, its utility in studying multiway interactions, such as those represented by tensors and hypergraphs, remains elusive. In this article, we present a comprehensive exploration of algebraic, structural, and spectral properties of the tensor Kronecker product. We express Tucker and tensor train decompositions and various tensor eigenvalues in terms of the tensor Kronecker product. Additionally, we utilize the tensor Kronecker product to form Kronecker hypergraphs, a tensor-based hypergraph product, and investigate the structure and stability of polynomial dynamics on Kronecker hypergraphs. Finally, we provide numerical examples to demonstrate the utility of the tensor Kronecker product in computing Z-eigenvalues, various tensor decompositions, and determining the stability of polynomial systems.

Indexed as

05C6515A69block tensorshypergraph productsmultilinear systemtensor decompositiontensor eigenvaluestensor Kronecker product

Identifiers

PMID40458229
PMCPMC12128617

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.