Related papers: A Systematic and Efficient Method to Compute Multi…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
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…
We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no…
An efficient method is described to handle mesh indexes in multidimensional problems like numerical integration of partial differential equations, lattice model simulations, and determination of atomic neighbor lists. By creating an…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
Planning in hybrid systems with both discrete and continuous control variables is important for dealing with real-world applications such as extra-planetary exploration and multi-vehicle transportation systems. Meanwhile, generating…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
In this paper we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane. This algorithm can be used for counting and…
I give an efficient algorithm for the reduction of multi-leg one-loop integrals of rank one. The method combines the basic ideas of the spinor algebra approach with the dual vector approach and is applicable to box integrals or higher point…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the…
In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of…
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes representations arising from massive loop integrals, by modifying the contours of integration. We implement an exact solution to the differential equation determining…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…