scholarly journals Tensor models, Kronecker coefficients and permutation centralizer algebras

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Joseph Ben Geloun ◽  
Sanjaye Ramgoolam
Keyword(s):  
Centralizer Algebras ◽  
Tensor Models ◽  
Kronecker Coefficients

scholarly journals Gauge invariants, correlators and holography in bosonic and fermionic tensor models

2017 ◽  
Vol 2017 (9) ◽  
Author(s):  
Robert de Mello Koch ◽  
David Gossman ◽  
Laila Tribelhorn
Keyword(s):  
Tensor Models

scholarly journals Nonzero Kronecker Coefficients and What They Tell us about Spectra

2007 ◽  
Vol 270 (3) ◽  
pp. 575-585 ◽  
Author(s):  
Matthias Christandl ◽  
Aram W. Harrow ◽  
Graeme Mitchison
Keyword(s):  
Kronecker Coefficients

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

scholarly journals A New Weighted-learning Approach for Exploiting Data Sparsity in Tag-based Item Recommendation Systems

2021 ◽  
Vol 14 (1) ◽  
pp. 387-399
Author(s):  
Noor Ifada ◽  
◽  
Richi Nayak ◽  
Keyword(s):  
Recommendation System ◽  
Recommendation Systems ◽  
Learning Approach ◽  
Tensor Model ◽  
Learning Approaches ◽  
Data Sparsity ◽  
Tensor Models ◽  
Sparsity Problem ◽  
Weighted Rank

The tag-based recommendation systems that are built based on tensor models commonly suffer from the data sparsity problem. In recent years, various weighted-learning approaches have been proposed to tackle such a problem. The approaches can be categorized by how a weighting scheme is used for exploiting the data sparsity – like employing it to construct a weighted tensor used for weighing the tensor model during the learning process. In this paper, we propose a new weighted-learning approach for exploiting data sparsity in tag-based item recommendation system. We introduce a technique to represent the users’ tag preferences for leveraging the weighted-learning approach. The key idea of the proposed technique comes from the fact that users use different choices of tags to annotate the same item while the same tag may be used to annotate various items in tag-based systems. This points out that users’ tag usage likeliness is different and therefore their tag preferences are also different. We then present three novel weighting schemes that are varied in manners by how the ordinal weighting values are used for labelling the users’ tag preferences. As a result, three weighted tensors are generated based on each scheme. To implement the proposed schemes for generating item recommendations, we develop a novel weighted-learning method called as WRank (Weighted Rank). Our experiments show that considering the users' tag preferences in the tensor-based weightinglearning approach can solve the data sparsity problem as well as improve the quality of recommendation.

Tensor Models

1994 ◽  
pp. 145-159 ◽  
Author(s):  
J. Wiles ◽  
G. S. Halford ◽  
J. E. M. Stewart ◽  
M. S. Humphreys ◽  
W. H. Wilson ◽  
...  
Keyword(s):  
Tensor Models

Next steps

2019 ◽  
pp. 109-116
Author(s):  
Steven Carlip
Keyword(s):  
Approximate Solutions ◽  
Cosmic Censorship ◽  
Field Equations ◽  
Singularity Theorems ◽  
Open Questions ◽  
Tensor Models ◽  
General Relativity And Gravitation ◽  
Active Research ◽  
Experimental Gravity

This final chapter consists of a brief discussion of where the reader can go from here: active research topics in general relativity and gravitation, open questions, and ideas for further study. Topics include exact and approximate solutions of the field equations, including numerical methods and perturbation theory; problems in mathematical relativity, including global geometric methods, singularity theorems, cosmic censorship, and asymptotic conditions; alternative models such as scalar-tensor models; approaches to quantum gravity; and experimental gravity. These topics are not discussed in any depth; rather, the chapter is meant as a “teaser” to encourage readers to look further.

From random matrices to random tensors

2021 ◽  
pp. 166-177
Author(s):  
Adrian Tanasa
Keyword(s):  
Matrix Models ◽  
Random Matrices ◽  
Mathematical Physics ◽  
Natural Generalization ◽  
Random Surface ◽  
The Third ◽  
Planar Surfaces ◽  
Tensor Models ◽  
Feynman Graphs ◽  
The Matrix

After a brief presentation of random matrices as a random surface QFT approach to 2D quantum gravity, we focus on two crucial mathematical physics results: the implementation of the large N limit (N being here the size of the matrix) and of the double-scaling mechanism for matrix models. It is worth emphasizing that, in the large N limit, it is the planar surfaces which dominate. In the third section of the chapter we introduce tensor models, seen as a natural generalization, in dimension higher than two, of matrix models. The last section of the chapter presents a potential generalisation of the Bollobás–Riordan polynomial for tensor graphs (which are the Feynman graphs of the perturbative expansion of QFT tensor models).

Operator Algebras with Contractive Approximate Identities

1994 ◽  
Vol 46 (2) ◽  
pp. 397-414 ◽  
Author(s):  
Yiu-Tung Poon ◽  
Zhong-Jin Ruan
Keyword(s):  
Operator Algebra ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Approximate Identity ◽  
The Other ◽  
Double Centralizer ◽  
Approximate Identities ◽  
Centralizer Algebras ◽  
Matrix Norms ◽  
Centralizer Algebra

AbstractWe study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

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