Related papers: Jet Topology
We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers ($\beta_{\rm k},k=1,...,D$), which…
The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles.…
Identifying jets originating from bottom quarks is vital in collider experiments for new physics searches. This paper proposes a novel approach based on Retentive Networks (RetNet) for b-jet tagging using low-level features of jet…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Very long baseline interferometry (VLBI) observations show that some active galactic nuclei (AGN) jets exhibit bending even at parsec scales. The nature of bending is comprehensively analysed only for a small number of individual AGN, and…
Jet taggers provide an ideal testbed for applying explainability techniques to powerful ML tools. For theoretically and experimentally challenging quark-gluon tagging, we first identify the leading latent features that correlate strongly…
We introduce an infinite set of jet substructure observables, derived as projections of $N$-point energy correlators, that are both convenient for experimental studies and maintain remarkable analytic properties derived from their…
Stochastic Structural Stability Theory (S3T) provides analytical methods for understanding the emergence and equilibration of jets from the turbulence in planetary atmospheres based on the dynamics of the statistical mean state of the…
We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that the topological zeta function is a topological invariant for…
Measurements of the substructure of top-quark jets are presented, using 140 fb$^{-1}$ of 13 TeV $pp$ collision data recorded with the ATLAS detector at the LHC. Top-quark jets reconstructed with the anti-$k_{t}$ algorithm with a radius…
Recent observational and theoretical results on blazars are presented and discussed. We are beginning to understand the rich phenomenology of blazars, and we are finding trends which will hopefully lead us to unveil the physics of these…
The study of the substructure of collimated particles from quarks and gluons, or jets, has the promise to reveal the details how color charges interact with the QCD plasma medium created in colliders such as RHIC and the LHC. Traditional…
Cut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions of cut ideals of tree graphs. By employing basic methods from topological combinatorics, we obtain…
The catenary degree is an invariant that measures the distance between factorizations of elements within a numerical semigroup. In general, all possible catenary degrees of the elements of the numerical semigroups occur as the catenary…
These Lectures summarize the relevant material on existent applications of jet manifold techniques to classical and quantum field theory. The following topics are included: 1. Fibre bundles, 2. Jet manifolds, 3. Connections, 4. Lagrangian…
In this paper we study topological invariants of a class of random groups. Namely, we study right angled Artin groups associated to random graphs and investigate their Betti numbers, cohomological dimension and topological complexity. The…
Possibilities for using geometry and topology to analyze statistical problems in biology raise a host of novel questions in geometry, probability, algebra, and combinatorics that demonstrate the power of biology to influence the future of…
Persistent homology encodes the evolution of homological features of a multifiltered cell complex in the form of a multigraded module over a polynomial ring, called a multiparameter persistence module, and quantifies it through invariants…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
Models of intermittent behaviour are usually formulated using a set of multiplicative random weights on a Cayley tree. However, intermittency in particle multiproduction from QCD jets is related to fragmentation of an additive quantum…