Related papers: Factorization and subtraction
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We…
We examine the endpoint region of inclusive deep inelastic scattering at next-to-leading power (NLP). Using a soft-collinear effective theory approach with no explicit soft or collinear modes, we discuss the factorization of the cross…
At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order…
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…
We derive a factorization theorem that allows for resummation of small-$x$ logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor $W^{\mu\nu}$ in deep…
In this paper, we firstly varify that the factorization hypothesis is valid for the exclusive process $\rho \gamma^{\star} \to \pi$ at the next-to-leading order (NLO) with the collinear factorization approach, and then extend this proof to…
We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on…
We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the $\Lambda_{\rm QCD}/Q$ and $\sqrt{-t}/Q$ expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case.…
We present a formalism that sums up the soft-virtual (SV) and next-to-SV (NSV) diagonal contributions to inclusive colorless productions in hadron colliders to all orders in perturbative QCD. Using factorisation theorem, renormalisation…
We consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. The logarithmically-enhanced contributions at small transverse momentum are treated to all perturbative orders by a universal…
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the…
We show that both the k_T- and collinear factorization for the DIS structure functions can be obtained by consecutive reductions of the Compton scattering amplitude. Each of these reductions is an approximation valid under certain…
Factorization theorems play a crucial role in our understanding of the strong interaction. For collider processes they are typically formulated at leading power and much less is known about power corrections in the $\lambda\ll 1$ expansion.…
The freedom associated with the definition of parton distribution functions is analyzed and formulae governing the dependence of parton distribution functions and hard scattering cross-sections on unphysical quantities associated with the…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…
Proof of factorization of soft and collinear divergences in non-equilibrium QCD may be necessary to study hadronic signatures of quark-gluon plasma at RHIC and LHC. In this paper we prove factorization of soft and collinear divergences in…