N-jettiness beam functions at N3LO

We present the first complete calculation for the quark and gluon N-jettiness ($$ {\mathcal{T}}_N $$ T N ) beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the $$ {\mathcal{T}}_N $$ T N subtraction methods to N3LO, and to resum $$ {\mathcal{T}}_N $$ T N distributions at N3LL′ accuracy both for quark as well as for gluon initiated processes.

A DUAL COORDINATE DESCENT ALGORITHM FOR SVMs COMBINED WITH RATIONAL KERNELS

This paper presents a novel application of automata algorithms to machine learning. It introduces the first optimization solution for support vector machines used with sequence kernels that is purely based on weighted automata and transducer algorithms, without requiring any specific solver. The algorithms presented apply to a family of kernels covering all those commonly used in text and speech processing or computational biology. We show that these algorithms have significantly better computational complexity than previous ones and report the results of large-scale experiments demonstrating a dramatic reduction of the training time, typically by several orders of magnitude.