Related papers: A recursive reduction of tensor Feynman integrals
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Computation of spin-resummed observables in post-Minkowskian dynamics typically involve evaluation of Feynman integrals deformed by an exponential factor, where the exponent is a linear sum of the momenta being integrated. Such integrals…
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…
The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…
This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to…
We determine the number of functionally independent components of tensors involving higher-order derivatives of a Riemannian metric.
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…
Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle,…
The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor completion. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based…
Low-rank tensor approximation error bounds are proposed for the case of noisy input data that depend on low-rank representation type, rank and the dimensionality of the tensor. The bounds show that high-dimensional low-rank structured…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
We consider conformal four-point Feynman integrals to investigate how much of their mathematical structure in two spacetime dimensions carries over to higher dimensions. In particular, we discuss recursions in the loop order and spacetime…
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…
Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from…
In this thesis, we study the three-loop QCD form factors. After an introduction and a discussion of the physics motivation, we generate the quark form factor using Qgraf. We then show how to bring the Feynman integrals into a unique form by…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…