Related papers: Advances towards the systematization of calculatio…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
In higher order calculations a number of new technical problems arise: one needs diagrams in arbitrary dimension in order to obtain their needed $\epsilon$-expansion, zero Gram determinants appear, renormalization produces diagrams with…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
This paper is a continuation of our earlier work \cite{NRxx} in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave…
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
Ultra-fast, precise, and controlled amplitude surrogates are essential for future LHC event generation. First, we investigate the noise reduction and biases of network ensembles and outline a new method to learn well-calibrated systematic…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
In this work, we present an algorithm for the diagonalization of the Integration-by-Parts (IBP) equations. Diagonalized IBP equations are indispensable for reducing loop integrals with high numerator powers to master integrals and for…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
In recent years it has been shown that for many linear algebra operations it is possible to create families of algorithms following a very systematic procedure. We do not refer to the fine tuning of a known algorithm, but to a methodology…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$.…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…