Related papers: Algorithmic derivation of Dyson-Schwinger Equation…
Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
We present bipartiteSUSY, a Mathematica package designed to perform calculations for physical theories based on bipartite graphs. In particular, the package can employ the recently developed arsenal of techniques surrounding on-shell…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of…
Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in…
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
We describe how to apply adjoint sensitivity methods to backward Monte-Carlo schemes arising from simulations of particles passing through matter. Relying on this, we demonstrate derivative based techniques for solving inverse problems for…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…
Automated searches for strong gravitational lensing in optical imaging survey datasets often employ machine learning and deep learning approaches. These techniques require more example systems to train the algorithms than have presently…
We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
Dynamic symbolic execution (DSE) is an effective method for automated program testing and bug detection. It is increasing the code coverage by the complex branches exploration during hybrid fuzzing. DSE tools invert the branches along some…