相关论文: SINGINT: Automatic numerical integration of singul…
In this note I illustrate the program MINT, a FORTRAN program for Monte Carlo adaptive integration and generation of unweighted distributions.
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
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…
Monte Carlo algorithms have a growing impact on nuclear medicine reconstruction processes. One of the main limitations of myocardial perfusion imaging (MPI) is the effective mitigation of the scattering component, which is particularly…
The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with…
We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…
This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
Stochastic computing (SC) is a high density, low-power computation technique which encodes values as unary bitstreams instead of binary-encoded (BE) values. Practical SC implementations require deterministic or pseudo-random number…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
We give numerical integration results for Feynman loop diagrams such as those covered by Laporta [1] and by Baikov and Chetyrkin [2], and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration…