Related papers: Method of regions for dual conformal integrals
We apply the method of regions to the evaluation of dual conformal integrals with small off-shellness. In contrast to conventional approach, where the separation of regions is performed via dimensional regularization breaking the dual…
We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…
Noisy, partially overlapping data and the need for real-time processing pose major challenges for rigid registration. Considering that feature-based matching can handle large transformation differences but suffers from limited accuracy,…
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…
We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the…
Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…
We define and study infinite families of all-loop planar, dual conformal invariant (DCI) integrals, which contribute to four-point Coulomb-branch amplitudes and correlators in ${\cal N}=4$ supersymmetric Yang-Mills theory, by solving…
In this pedagogical note I will discuss one-loop integrals, where (i) different regions of the integration region lead to divergences and (ii) where these divergences cancel in the sum over all regions. These integrals cannot be calculated…
A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…
This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit…
High-resolution remote sensing images contain densely distributed objects with pronounced scale variations and complex boundaries, which impose higher demands on both the geometric localization and semantic prediction capabilities of…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
The linear coefficient in a partially linear model with confounding variables can be estimated using double machine learning (DML). However, this DML estimator has a two-stage least squares (TSLS) interpretation and may produce overly wide…
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
Collaborative analysis of decentralized confidential datasets is important, but direct sharing of original datasets is often restricted by privacy and institutional constraints. Data collaboration (DC) analysis transforms each dataset into…