Related papers: Harmonic factorization and reconstruction of the e…
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
We consider diagrams with up to four t-channel gluons in order to specify gluonic twist-four contributions to deep inelastic structure functions. This enables us to extend the method developed by R.K.Ellis, W.Furmanski, and R.Petronzio…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
In this paper, we compute the H- and Z-eigenvalues of even order symmetric tensors by using the adaptive cubic regularization algorithm.
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd…
Using effective theories for jets and heavy quarks it is possible to prove that the double differential top-antitop invariant mass distribution for the process $e^+e^-\to t\bar t$ in the resonance region for c.m. energies $Q$ much larger…
Cartesian harmonic tensors are completely symmetric traceless tensors in three dimensional space constructed from the direct product of unit vectors. They are useful in generating expressions for the angular coupling of spherical harmonics…
This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much…
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…