Related papers: Topology-Informed Jet Tagging using Persistent Hom…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Measurements of jet substructure in ultra-relativistic heavy-ion collisions indicate that interactions with the quark-gluon plasma quench the jet showering process. Modern data-driven methods have shown promise in probing these…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…
Homology is a tool in topological data analysis which measures the shape of the data. In many cases, these measurements translate into new insights which are not available by other means. To compute homology, we rely on mathematical…
We introduce a novel jet substructure method which exploits the variation of observables with respect to a sampling of phase-space boundaries quantified by the variability. We apply this technique to identify boosted W boson and top quark…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Measurements of jet substructure describing the composition of quark- and gluon-initiated jets are presented. Proton-proton (pp) collision data at $\sqrt{s}$ =13 TeV collected with the CMS detector are used, corresponding to an integrated…
Top tagging is a recent approach to identifying boosted hadronic top quarks. It avoids reconstructing individual top decay products and instead uses a jet algorithm to reconstruct the entire top decay. Quite generally, geometrically large…
We initiate the study of the time substructure of jets, motivated by the fact that the next generation of detectors at particle colliders will resolve the time scale over which jet constituents arrive. This effect is directly related to…
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…
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Jet constituents provide a more detailed description of a jet's radiation pattern than global observables. In simulations for ATLAS Run-2 data (2015-2018), transformer-based taggers trained on low-level inputs outperformed traditional…
In the past years significant progress has been made toward achieving a quantitative understanding of jets and their substructure in high-energy proton-proton collisions from first principles in QCD. Precise measurements have become…
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such…
The rejection of forward jets originating from additional proton--proton interactions (pile-up) is crucial for a variety of physics analyses at the LHC, including Standard Model measurements and searches for physics beyond the Standard…