Related papers: Strong factorization and the braid arrangement fan
We factorize three-dimensional terminal flops into a composition of divisorial contractions to points and blowing-up smooth curves.
A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…
We study strong approximation for the intersection of two affine quadrics. As its application, we prove the fibration method for weak approximation over number fields of rank four with nonsplit fibers split by quadratic extensions.
We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and…
Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the…
Jets are extended multipartonic systems and serve as a powerful tool for investigating the dynamics of emergent phenomena driven by many body QCD interactions. In heavy ion collisions, starting from their production during the perturbative…
We show that \emph{efficient Turing computability} at any fixed input/output precision implies the existence of \emph{compositionally sparse} (bounded-fan-in, polynomial-size) DAG representations and of corresponding neural approximants…
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…
We use multi-parton states to examine the leading order collinear factorization of single transverse-spin asymmetries in Drell-Yan processes. Twist-3 operators are involved in the factorization. We find that the so-called soft-gluon-pole…
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be…
We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…
Accurate and efficient amplitude predictions are essential for precision studies of multi-jet processes at the LHC. We introduce a novel neural network architecture that predicts multi-jet amplitudes by leveraging the Catani-Seymour…
Factorizations of monoids are studied. Two necessary and sufficient conditions in terms of so-called descent 1-cocyles for a monoid to be factorized through two submonoids are found. A full classification of those factorizations of a monoid…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…
A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet…
Infrared subtraction algorithms beyond next-to-leading order necessitate the analysis of multiple infrared limits of scattering amplitudes, where several particles sequentially become soft or collinear. In this contribution, we report on…
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…
We summarize the standard factorization theorems for hard processes in QCD, and describe their proofs.
We review the evidence for the presence of a hard singularity in soft forward amplitudes, and give an estimate of its trajectory and couplings.
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…