Related papers: Solving arbitrary one-loop reduction via generatin…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…
Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e+ e- -> 4 fermions. The described methods for 3-point and 4-point integrals…
The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to $\Pep\Pem\to4 $fermions. In particular, the…
It is well known that forward limits of tree-level amplitudes (and those trivalent diagrams they consist of) produce one-loop amplitudes and trivalent diagrams with propagators linear in the loop momentum. They naturally arise from one-loop…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the…
We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of $n$- and $(n-1)$-point scalar integrals that are finite in the limit of vanishing…
In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and…
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…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…