Related papers: Tracking discontinuities in parameter space

We present a new computer program, $\texttt{feyntrop}$, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric…

In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion…

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…

This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…

We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine…

We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers. The framework (i) constructs localized first-order…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states [P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10], describing the functional distribution of particle's…

The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…

We study deformations of plane curve singularities from an analytic point of view and obtain some new concrete results. We show some rather unexpected properties of Puiseux coefficients treated as functions on a suitably defined parameter…

We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…

We develop techniques for computing and analyzing multiple unitarity cuts of Feynman integrals, and reconstructing the integral from these cuts. We study the relations among unitarity cuts of a Feynman integral computed via diagrammatic…

The software alignment of planar tracking detectors using samples of charged particle trajectories may lead to global detector distortions that affect vertex and momentum resolution. We present an alignment procedure that constrains such…

In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to…

A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…

We present a subtraction scheme for ultraviolet (UV) divergent, infrared (IR) safe scalar Feynman integrals in dimensional regularization with any number of scales. This is done by the introduction of $u$-variables, which are a suitable…

We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity…

Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…