Related papers: E6Tensors: A Mathematica Package for E6 Tensors

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and…

A novel class of electro-magneto-elastic (EME) materials comprise electro-active and magneto-active particles in the polymer matrix that change their elastic behavior with an applied electromagnetic field. The material response for such a…

There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank…

We outline the construction of differential invariants for higher--rank tensors.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations…

We explore the effects of extra neutral gauge boson involved in the supersymmetric E6 model on the spin configuration of the top quark pair produced at the polarized e- e+ collider. Generic mixing terms are considered including kinetic…

Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to $Z$-tensors (which are tensors with…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

In this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear ODEs and PDEs. The main idea here is in…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…

The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…

We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to…

The aim of this work is to find a simple mathematical framework for our established description of particle physics. We demonstrate that the particular gauge structure, group representations and charge assignments of the Standard Model…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Advanced theoretical techniques that combine the linearized coupled-cluster method, configuration interaction method, and perturbation theory are used to calculate energy levels, ionization potentials, electron affinities, field isotope…