Related papers: Reduction formalism for dimensionally regulated on…

We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…

We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the…

Recently there is an alternative reduction method proposed by Chen in [1,2]. In this paper, using the one-loop scalar integrals with propagators having higher power, we show the power of the improved version of Chen's new method in which we…

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate…

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

We report on the progress in constructing contracted one-loop tensors. Analytic results for rank R=4 tensors, cross-checked numerically, are presented for the first time.

We develop a notion of {\em inner rank} as a tool for obtaining lower bounds on the rank of matrix multiplication tensors. We use it to give a short proof that the border rank (and therefore rank) of the tensor associated with $n\times n$…

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…

As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the…

We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis…

Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…

In this paper, we address the open problem (stated in Pennisi and Trovato, 1987. Int. J. Engng Sci., 25(8), 1059-1065) associated with the irreducibility of representations for isotropic functions. In particular, we prove that for isotropic…

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…

We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_\beta \times \mathbb{S}^3$. This is done by evaluating a class of integrals over the…

We obtain an explicit formula for the total number of descents and levels in tensor words and cyclic tensor words of arbitrary dimension. We also establish the exact maximal number of descents in words and use it to obtain an upper bound on…

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…