W-representations of the fermionic matrix and Aristotelian 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.

Download Full-text

The full Schwinger-Dyson tower for random tensor models

10.22323/1.318.0147 ◽

2018 ◽

Author(s):

Carlos Ignacio Perez Sanchez

Keyword(s):

Tensor Models ◽

Random Tensor

Download Full-text

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

International Journal of Intelligent Engineering and Systems ◽

10.22266/ijies2021.0228.36 ◽

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.

Download Full-text

Tensor Models

Artificial Intelligence and Creativity - Studies in Cognitive Systems ◽

10.1007/978-94-017-0793-0_10 ◽

1994 ◽

pp. 145-159 ◽

Cited By ~ 3

Author(s):

J. Wiles ◽

G. S. Halford ◽

J. E. M. Stewart ◽

M. S. Humphreys ◽

W. H. Wilson ◽

...

Keyword(s):

Tensor Models

Download Full-text

Next steps

General Relativity ◽

10.1093/oso/9780198822158.003.0013 ◽

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.

Download Full-text

From random matrices to random tensors

Combinatorial Physics ◽

10.1093/oso/9780192895493.003.0011 ◽

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).

Download Full-text