Related papers: Using Dimensional Reduction for Hadronic Collision…
Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \R^N that best explains the data \F increases dramatically with the dimension of \R^N. In this article, we study a class of…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…
An explicit example is presented (a one-loop triangle graph) where dimensional regularization fails to regulate the infra-red singularities that emerge at intermediate steps of studying large-$Q^2$ Sudakov factorization. The mathematical…
We consider the longitudinal momentum distribution of hadrons inside jets in proton-proton collisions. At partonic threshold large double logarithmic corrections arise which need to be resummed to all orders. We develop a factorization…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…
Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of…
We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard…
This paper applies the quadtree structure for image coding. The goal is to adapt the block size and thus to increase the compression ratio (without reducing SNR). Also, the computational time is not significatively increased. It has been…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…
A simple parametrization of the QCD running coupling at low scales is introduced and used to illustrate various schemes for the estimation of non-perturbative power corrections. The `infrared matching' scheme proposed earlier gives…
Spin asymmetries in collisions of spin-polarized hadrons probe polarized parton distributions, which encode the spin structure of the colliding hadrons. To perform precision physics studies with spin asymmetries, higher order QCD…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a…
Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability…
Having access to the parton-level kinematics is important for understanding the internal dynamics of particle collisions. Here, we present new results aiming to an efficient reconstruction of parton collisions using machine-learning…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
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…
This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and…
Proof of transverse-momentum-dependent(TMD) factorization for hadron-hadron collision is given in this paper. We focus on processes without detected soft final hadrons or detected final hadrons that are collinear to initial hadrons. This…