Related papers: Tensor Reduction of Sunset by Generating Function

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…

As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…

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…

Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…

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…

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

Light trapping for solar cells can reduce production cost and improve energy conversion efficiency. Understanding some of the basic theoretical constraints on light trapping is therefore of fundamental importance. Here, we develop a general…

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

We present a method for converting tensors into tensor train format based on actions of the tensor as a vector-valued multilinear function. Existing methods for constructing tensor trains require access to "array entries" of the tensor and…

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…

Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…

In this paper, we introduce the applications of third-order reduced biquaternion tensors in color video processing. We first develop algorithms for computing the singular value decomposition (SVD) of a third-order reduced biquaternion…

With increasing concerns of climate change, renewable resources such as photovoltaic (PV) have gained popularity as a means of energy generation. The smooth integration of such resources in power system operations is enabled by accurate…

We calculate one--loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh propagator…

Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…

In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of…

The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified…

Photosynthesis is nature's route to convert intermittent solar irradiation into storable energy, while its use for an industrial energy supply is impaired by low efficiency. Artificial photosynthesis provides a promising alternative for…