Related papers: Numerical evaluation of two-loop integrals with py…
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…
In this paper, we present a novel approach to synthesize invariant clusters for polynomial programs. An invariant cluster is a set of program invariants that share a common structure, which could, for example, be used to save the needs for…
In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…
Three programs are presented for automatically generating and calculating Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the LoopTools package. The…
Probabilistic programs are key to deal with uncertainty in e.g. controller synthesis. They are typically small but intricate. Their development is complex and error prone requiring quantitative reasoning over a myriad of alternative…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
A set of programs is presented for automatically generating and calculating Feynman diagrams. Diagrams are generated with FeynArts, then algebraically simplified using a combination of Mathematica and FORM implemented in the package…
We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…
Focused optical fields are key to a multitude of applications involving light-matter interactions, such as optical microscopy, single-molecule spectroscopy, optical tweezers, lithography, or quantum coherent control. A detailed vectorial…
Recent years have witnessed substantial progress on monocular depth estimation, particularly as measured by the success of large models on standard benchmarks. However, performance on standard benchmarks does not offer a complete…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by…
Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators,…
In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…