New method identifies quark and gluon jets from collider data.
problem Determine quark and gluon jet distributions from collider data.
method Apply topic modeling to jet distributions, using parton shower and theoretical predictions.
result Determined separate quark and gluon jet distributions and spectra.
Interpretable deep learning classifies two-prong jets using jet spectra.
problem Lack of interpretability in deep learning for jet classification.
method Truncated Taylor series jet spectrum for interpretability.
result Interpretable network performs similarly to CNN but is simpler.
Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliate manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introd…
Machine learning identifies jet substructure from boosted Higgs decays.
problem Distinguishing jets from boosted heavy particles from QCD jets.
method Spectral analysis using neural networks on angular scale.
result ANN of angular spectrum input performs similarly to existing taggers.
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. W…
A Jet groupoid R_q over a manifold X is a special Lie groupoid consisting of q-jets of local diffeomorphisms from X to X. As a subbundle of the q-th order jet bundle of the trivial bundle X times X, a jet groupoid can be considered as a nonlinear system of partial differential equations (PDE). This leads to the concept…
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…
Jet spaces on Carnot groups have a canonical Lie group structure.
problem Understanding jet spaces on Carnot groups.
method Constructing jet spaces over stratified Lie groups and showing they are stratified Lie groups.
result Every stratified Lie group of step s+1 can be embedded in a jet space over a stratified Lie group of step s. Wind speed prediction improved using a novel deep ensemble learning model inspired by jet aerodynamics.
problem Accurate wind speed forecasting for renewable energy production.
method Proposes a novel Deep Ensemble Learning using Jet-like Architecture (DEL-Jet) to enhance robustness and generalization of a learning system.
result The DEL-Jet technique improves the robustness and generalization of the learning system, as shown by performance evaluations.
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space J1(R,M). A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.
A new jet constituent-based method for top quark tagging achieves high background rejection.
problem Tagging highly energetic jets resulting from top quark decays.
method Sequential approach using ordered jet constituents as inputs, avoiding loss of information.
result Achieves a background rejection of 45 at a 50% efficiency operating point.
The study examines projections in jet space Carnot groups and their Hausdorff dimensions.
problem Understanding projections and dimensions in jet space Carnot groups.
method Defined analogues of projections for jet space Carnot groups and proved Marstrand-type theorems.
result Determined possible Hausdorff dimensions of images of sets under these mappings.
VAE improves anomaly detection for jet tagging at the LHC.
problem Anomaly detection in jet tagging at the LHC.
method Variational Autoencoder (VAE) trained on background QCD jets, with latent space learning for anomaly detection.
result Outlier Exposed VAE (OE-VAE) achieves excellent results in both sensitivity and decorrelation of jet mass.
Machine learning improves jet charge classification.
problem Classifying jets according to their electric charge.
method Convolutional, recurrent, and recursive neural networks, including distance within the jet and clustering history.
result Significant improvement in jet charge extraction over traditional methods.
Finite-gap solutions approximate jets of initial data for certain BKM systems.
problem Approximating jets of initial data for specific PDE systems.
method Using finite-reduction map to finite-gap solutions of Stäckel systems.
result Full jet-surjectivity for KdV and Kaup--Boussinesq, partial for Camassa--Holm.
Paper introduces Modular Jets for diagnosing model decompositions in pipelines.
problem Evaluating model decompositions in pipelines for unique identification.
method Estimates empirical jets from module-level representations to diagnose mirage vs identifiable decompositions.
result Proves jet-identifiability theorem for two-module linear regression pipelines.
Recursive neural networks mimic QCD for jet physics.
problem Improving jet physics predictions using machine learning.
method Analogies between QCD and natural languages for jet clustering.
result Recursive architectures are more accurate and data efficient than previous methods.
In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geome…
Study jets of flat partial connections in foliations.
problem Characterize and understand flat partial connections in foliations.
method Define and apply jets to flat partial connections in smooth foliations and locally free sheaves, focusing on codimension one and arbitrary codimension foliations.
result Define and apply jets to characterize transversely affine and projective structures in foliations.
We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in parti…
Study curvature estimates for metrics on jet bundles over projective varieties.
problem Curvature estimates for metrics on jet bundles.
method Analogue of Demailly's holomorphic Morse inequalities for invariant jets.
result Analogue of Demailly's results for invariant jets.
Jet bundles as higher-order polarised k-contact manifolds
problem Recognizing finite-order jet bundles as polarised Nπr-contact manifolds method Introducing new classes of polarisations for k-contact distributions result Main recognition theorem
Establishes jet transversality for regular maps from flexible manifolds.
problem Transversality for regular maps in algebraic geometry.
method Algebraic version of Forstnerič's theorem for holomorphic maps.
result Genericity theorems for regular maps of maximal ranks.
The paper finds two types of metric lines in curve spaces.
problem Classifying metric lines in jet spaces of curves.
method Established the existence of two families of metric lines in the 2-jet space of plane curves.
result Found precise criteria for identifying metric lines in sub-Riemannian geodesics.
Extends classical jets theory to algebraic ideals of smooth functions.
problem Extend classical jets theory to algebraic ideals of smooth functions.
method Introduce algebraic notions and differentiable structures on jets spaces.
result Nice functorial properties in the extended jets theory.
Improved jet tagging reduces systematic uncertainties and enhances signal purity.
problem Boosted resonance decay signals from jets are difficult to distinguish from background.
method Adversarial neural networks to decorrelate jet substructure tagger.
result Adversarial trained tagger outperforms conventional methods in discovery significance.
In this paper we introduce a natural definition for the affine maps between two Finsler manifolds (M,F) and (N,F~) and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;…
Study shows no periodic geodesics in jet space.
problem Existence of periodic geodesics in jet space.
method Characterization and classification of subRiemannian geodesics.
result No periodic geodesics found in the space of k-jets.
Deep learning improves jet discrimination in particle physics.
problem Automating quark/gluon jet discrimination in collider physics.
method Convolutional neural networks trained on color-enhanced jet images.
result Deep networks outperform traditional jet variables in discrimination.
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet electromagnetic Yang-Mills energies, starting from some given nonlinear evolution OD…
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension …
The paper studies geometrical objects in time-dependent Hamiltonian systems.
problem Understanding time-dependent Hamiltonian systems through geometrical objects.
method Analyzes distinguished tensors, time-dependent semisprays, and nonlinear connections on the dual jet space.
result Mathematical connections between these geometrical objects in time-dependent Hamiltonian systems.
Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.
problem Optimal holomorphic extensions of jets along submanifolds for high tensor powers.
method Careful study of Schwartz kernels and Bergman projectors for asymptotic analysis.
result Explicit asymptotic formula for the extension operator as tensor power tends to infinity.
Reviews connections in fiber and jet bundles, linking to PDEs and multivector fields.
problem Exploring different interpretations of connections in fiber and jet bundles.
method Analyzes connections in fiber and jet bundles, relating them to PDEs and multivector fields.
result Relates connections in fiber and jet bundles to PDEs and multivector fields.
Generative model simulates jet radiation patterns with high accuracy.
problem Simulating jet radiation patterns accurately and efficiently.
method Generative adversarial network with cycle-consistent architecture.
result Model retrieves jet radiation patterns within a few percent accuracy.
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems model…
The reduction theorems for general linear and classical connections are generalized for operators with values in higher order gauge-natural bundles. We prove that natural operators depending on the s1-jets of classical connections, on the s2-jets of general linear connections and on the r-jets of tensor fields …
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Itô SDEs. We show how jets can be used…
Study interprets deep learning for LHC jet tagging.
problem Understanding deep learning models in LHC jet tagging.
method Recursive neural networks, comparative study of jet tagging tasks.
result Interesting observations on the latent space of jet tagging models.
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this …
Generalizes jet differential bounds and proves asymptotic Serre duality.
problem Bounding the number of linearly independent holomorphic sections of jet bundles.
method Generalizes existing results for invariant jet differentials, proving asymptotic duality.
result Establishes an asymptotic lower bound on the number of sections of jet bundles.
We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are affine bundles; as a by-product we obtain a new expression for the associated vector bundles. We use Green-Vinogradov formul…
Researchers found counterexamples to a 2-jet determination theorem in higher codimension.
problem Counterexample construction to the 2-jet determination Chern-Moser Theorem in higher codimension.
method Constructed counterexamples of quadratic submanifolds with specific properties.
result Generated counterexamples to the 2-jet determination Chern-Moser Theorem in higher codimension.
Formulates quantum jet bundles over noncommutative algebras with connections and braiding.
problem Defining jet bundles over noncommutative algebras with connections and braiding.
method Formalizes jet bundles over noncommutative algebras with flat connections and braiding tensor obeying Yang-Baxter equation.
result Examples include permutation groups, matrix algebras, and quantum spacetime models.
In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…
Characterizes Lie-Backlund vector fields in infinite jet bundles that can be exponentiated.
problem Characterizing Lie-Backlund vector fields in infinite dimensional jet bundles that can be exponentiated.
method Characterization through conditions for exponentiation and providing non-trivial examples.
result Conditions for exponentiation of Lie-Backlund vector fields in J∞(Rn,Rm), with different results for m=1 and m>1. Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions of the theory with applications to the calculus of variations and mechanics are…
Study of Pascal algebra matrices and their jet bundle map for vector bundles.
problem Defining and studying Pascal algebra matrices and their map on jet bundles.
method Identifying Pascal algebra matrices, showing generator well defines Pascal map, using it for intrinsic contact definition.
result Intrinsic definition of point-wise contact between Hermitian vector bundles using unitary equivalence of Pascal maps.