Related papers: Tensor Reduction of Sunset by Generating Function
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
Remarkable penetration of renewable energy in electric networks, despite its valuable opportunities, such as power loss reduction and loadability improvements, has raised concerns for system operators. Such huge penetration can lead to a…
A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the…
Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…
Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate…
We develop a new approach to calculate the obtainable limit of photoconversion efficiency of tandem solar cells (SCs) and applied it to SCs with both vertical and lateral designs at AM0 and AM1.5 conditions. To get the maximum efficiency,…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…
We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Computational challenges associated with the use of Wigner functions to identify non-classical properties of states are addressed with the aid of generating functions. It allows the computation of the Wigner functions of photon-subtracted…
Tensor numerical methods, based on the rank-structured tensor representation of $d$-variate functions and operators, are designed to provide $O(dn)$ complexity of numerical calculations on $n^{\otimes d }$ grids contrary to $O(n^d)$ scaling…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
In this paper we present new optimization strategies for the reconstruction of X-ray images of solar flares by means of the data collected by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The imaging concept of the…