1,268 research outputs found
Energy flow polynomials: A complete linear basis for jet substructure
We introduce the energy flow polynomials: a complete set of jet substructure
observables which form a discrete linear basis for all infrared- and
collinear-safe observables. Energy flow polynomials are multiparticle energy
correlators with specific angular structures that are a direct consequence of
infrared and collinear safety. We establish a powerful graph-theoretic
representation of the energy flow polynomials which allows us to design
efficient algorithms for their computation. Many common jet observables are
exact linear combinations of energy flow polynomials, and we demonstrate the
linear spanning nature of the energy flow basis by performing regression for
several common jet observables. Using linear classification with energy flow
polynomials, we achieve excellent performance on three representative jet
tagging problems: quark/gluon discrimination, boosted W tagging, and boosted
top tagging. The energy flow basis provides a systematic framework for complete
investigations of jet substructure using linear methods.Comment: 41+15 pages, 13 figures, 5 tables; v2: updated to match JHEP versio
Stochastically Stable Quenched Measures
We analyze a class of stochastically stable quenched measures. We prove that
stochastic stability is fully characterized by an infinite family of zero
average polynomials in the covariance matrix entries.Comment: 13 page
Rainbow matchings in properly-coloured multigraphs
Aharoni and Berger conjectured that in any bipartite multigraph that is
properly edge-coloured by colours with at least edges of each
colour there must be a matching that uses each colour exactly once. In this
paper we consider the same question without the bipartiteness assumption. We
show that in any multigraph with edge multiplicities that is properly
edge-coloured by colours with at least edges of each colour
there must be a matching of size that uses each colour at most once.Comment: 7 page
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