Related papers: Jet Topology
Jet identification tools are crucial for new physics searches at the LHC and at future colliders. We introduce the concept of Mass Unspecific Supervised Tagging (MUST) which relies on considering both jet mass and transverse momentum…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
The phenomenology of dark sector is complicated if dark sector is charged under a confined hidden gauge group. In such kind of model, a dark parton produced at a high energy collider showers and hadronize to a cluster of dark mesons. Dark…
Discriminating quark-like from gluon-like jets is, in many ways, a key challenge for many LHC analyses. First, we use a known difference in Pythia and Herwig simulations to show how decorrelated taggers would break down when the most…
Jet tagging has become an essential tool for new physics searches at the high-energy frontier. For jets that contain energetic charged leptons we introduce Feature Extended Supervised Tagging (FEST) which, in addition to jet substructure,…
Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information…
The substructure of jets produced in an exclusive and a charm-induced dijet sample in photoproduction and in charged and neutral current interactions has been studied with the ZEUS detector at HERA. Jets were identified using the…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
In this paper we discuss open problems concerning L^2-invariants focusing on approximation by towers of finite coverings.
We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…
Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…
In this survey article we describe the geometry of toric hyperk\"ahler varieties, which are hyperk\"ahler quotients of the quaternionic vector spaces by tori. In particular, we discuss the Betti numbers, the cohomology ring, and variation…
To each link $L$ in $S^3$ we associate a collection of certain labelled directed trees, called width trees. We interpret some classical and new topological link invariants in terms of these width trees and show how the geometric structure…
In this paper we give a complete description of the irreducible components of the jet schemes (with origin in the singular locus) of a two-dimensional quasi-ordinary hypersurface singularity. We associate with these components and with…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
This note quantifies, via a sharp inequality, an interplay between (a) the characteristic rank of a vector bundle over a topological space X, (b) the Z/2Z-Betti numbers of X, and (c) sums of the numbers of certain partitions of integers. In…