Related papers: Multivariate Residues and Maximal Unitarity
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
We show that certain determinantal functions of multiple matrices, when summed over the symmetries of the cube, decompose into functions of the original matrices. These are shown to be true in complete generality; that is, no properties of…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
Relations between multiple unitarity cuts and coproducts of Feynman integrals are extended to allow for internal masses. These masses introduce new branch cuts, whose discontinuities can be derived by placing single propagators on shell and…
We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values.…
In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
This article discusses the geometric application of the method of multiplier ideal sheaves. It first briefly describes its application to effective problems in algebraic geometry and then presents and explains its application to the…
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results we give an algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root…
It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle content, and a same propagator…
We apply the theory of Bruhat-Tits trees to the study of optimal embeddings of two and three dimensional commutative orders into quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in a…