Related papers: A Lecture on Integration by Parts
A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times.…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
Executing a control sequence requires computation. While this is a simple observation, developing a framework that relates a controller's required computation to its ability to successfully control a system (e.g. lower control cost) is…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
In this paper, we show how a resource allocation problem can be solved through Integer Linear Programming (ILP). A detailed illustrative example is presented, together with an exhaustive overview of the mathematical model. The size of the…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching…
Tabular data learning has extensive applications in deep learning but its existing embedding techniques are limited in numerical and categorical features such as the inability to capture complex relationships and engineering. This paper…