Related papers: The simplicial substructure of jets

We present a new model which represents data as a mixture of simplices. Simplices are geometric structures that generalize triangles. We give a simple geometric understanding that allows us to learn a simplicial structure efficiently. Our…

Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the…

The ATLAS Collaboration has developed a method to analyze large-radius jets composed of skinny $R=0.2$ subjets in heavy-ion collisions. We first demonstrate that the measurements pioneered by ATLAS constrain the value of $L_{\rm res}$, the…

The ATLAS collaboration has introduced and implemented a strategy for selecting and analyzing large-radius jets composed of skinny $R=0.2$ subjets in heavy ion collisions at the LHC. We show how measurements of these jets teach us about the…

This Letter applies the concept of `jets', as constructed from calorimeter cell four-vectors, to jets composed (primarily) of photons (or leptons). Thus jets become a superset of both traditional objects such as QCD-jets, photons, and…

Brenti and Welker have shown that for any simplicial complex X, the face vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending only on the dimension of X. We improve and generalize this…

Let $k$ be an algebraically closed field, $S$ a variety over $k$ and m a nonnegative integer. There is a space $S_m$ over $S$ , called the jet scheme of $X$ of order $m$, parameterizing $m$-th jets on $S$. The fiber over the singular locus…

Many practical applications in topological data analysis arise from data in the form of point clouds, which then yield simplicial complexes. The combinatorial structure of simplicial complexes captures the topological relationships between…

This paper develops a complete foundational treatment of simplicial complexes from Euclidean spaces through geometric realizations, emphasizing concrete computations, examples, and practical verification methods. Beginning with finite point…

To each variety $X$ and a nonnegative integer $m$, there is a space $X_m$ over $X$, called the jet scheme of $X$ of order $m$, parametrizing $m$-th jets on $X$. Its fiber over a singular point of $X$ is called a singular fiber. For a…

We present an alternative approach to identifying and characterizing jet substructure. An angular correlation function is introduced that can be used to extract angular and mass scales within a jet without reference to a clustering…

Measurements are presented of the jet invariant mass and substructure in proton-proton collisions at sqrt{s} = 7 TeV with the ATLAS detector using an integrated luminosity of 37 pb-1. These results exercise the tools for distinguishing the…

One of the most common and effective methods of obtaining structural information on simplicial complexes is to use tools from algebraic geometry/commutative algebra (often motivated by properties of toric varieties). However, there is no…

Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…

This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet…

Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…

At the extreme energies of the Large Hadron Collider, massive particles can be produced at such high velocities that their hadronic decays are collimated and the resulting jets overlap. Deducing whether the substructure of an observed jet…

In the 70:th, combinatorialists begun to systematically relate simplicial complexes and polynomial algebras, named Stanley-Reisner rings or face rings. This demanded an algebraization of the simplicial complexes, that turned the empty…

The characterization of the jet substructure can give insight into the microscopic nature of the modification induced on high-momentum partons by the Quark-Gluon Plasma that is formed in ultra-relativistic heavy-ion collisions. Jet shapes…