Related papers: IBIS: Inverse BInomial sum Solver
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to…
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$. In a…
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…
We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
Designing large-scale metasurfaces with nonlocal optical effects remains challenging due to the immense dimensionality and fabrication constraints of conventional optimization methods. We introduce GiBS (Generative Input-side Basis-driven…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of…
In this thesis, a new class of algorithms based on Sums of Squares Programming is developed. These allow to reduce a degree-$d$ homogeneous polynomial $T = \sum_{i = 1}^m \langle a_i, X \rangle^d $ to a quadratic form being close to a…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
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…
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops.…
This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. The paper gives a systematic method for computing the…
Implicit neural representations (INRs) can parameterize continuous beamforming functions in continuous aperture arrays (CAPAs) and thus enable efficient online inference. Existing INR-based beamforming methods for CAPAs, however, typically…
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred from some trigonometric identities.