Related papers: Using Dimensional Reduction for Hadronic Collision…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…
We compute the next-to-leading order QCD corrections to the spin-independent and spin-dependent cross-sections for the production of a single-hadron accompanied by an opposite jet in hadronic collisions. This process is being studied…
In the context of high-energy physics, a reliable description of the parton-level kinematics plays a crucial role for understanding the internal structure of hadrons and improving the precision of the calculations. Here, we study the…
We compare a momentum space implicit regularisation (IR) framework with other renormalisation methods which may be applied to dimension specific theories, namely Differential Renormalisation (DfR) and the BPHZ formalism. In particular, we…
We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed…
We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding…
The matching between Schrodinger Functional renormalization schemes and conventional perturbative schemes is usually done using an intermediate lattice scheme. We propose to do the matching directly. This requires the perturbative…
I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…
We present a technique for implementing in a fast way, and without any approximations, higher-order calculations of partonic cross sections into global analyses of parton distribution functions. The approach, which is set up in…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…
This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…
The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial…
Weak interactions between quarks give rise to hadronic parity violation which can be observed in nuclear and few-nucleon systems. We study the QCD renormalization of the isotensor component of parity violation at next-to-leading order…