arXiv research

This article constructs the moduli stack of torsionfree $G$-jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any $\infty$-topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are …

Study moduli spaces of elliptic PDEs using derived $C^{\infty}$-geometry.

Classifies singular foliations of a specific type and studies their extensions.

We introduce jet topics: a framework to identify underlying classes of jets from collider data. Because of a close mathematical relationship between distributions of observables in jets and emergent themes in sets of documents, we can apply recent techniques in "topic modeling" to extract jet topics from data with mini…

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…

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.

Jets from boosted heavy particles have a typical angular scale which can be used to distinguish them from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The angular spectrum allows us to scan energy deposits over the angle between a pair …

The wind is one of the most increasingly used renewable energy resources. Accurate and reliable forecast of wind speed is necessary for efficient power production; however, it is not an easy task because it depends upon meteorological features of the surrounding region. Deep learning is extensively used these days for …

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 $J^1(R,M)$. A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.

Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum $S_{2}(R)$ which is a two-point correlation function of the…

VAE improves anomaly detection for jet tagging at the LHC.

Finite-gap solutions approximate jets of initial data for certain BKM systems.

Paper introduces Modular Jets for diagnosing model decompositions in pipelines.

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.

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…

Recent literature on deep neural networks for tagging of highly energetic jets resulting from top quark decays has focused on image based techniques or multivariate approaches using high-level jet substructure variables. Here, a sequential approach to this task is taken by using an ordered sequence of jet constituents …

Establishes jet transversality for regular maps from flexible manifolds.

Jet bundles as higher-order polarised $k$-contact manifolds

The paper finds two types of metric lines in curve spaces.

In this paper we introduce a natural definition for the affine maps between two Finsler manifolds $(M, F)$ and $(N,\tilde F)$ 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.

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 …

Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.

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 $s_1$-jets of classical connections, on the $s_2$-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…

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 …

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…

Generalizes jet differential bounds and proves asymptotic Serre duality.

Researchers found counterexamples to a 2-jet determination theorem in higher codimension.

Formulates quantum jet bundles over noncommutative algebras with connections and braiding.

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…

Modern machine learning techniques, such as convolutional, recurrent and recursive neural networks, have shown promise for jet substructure at the Large Hadron Collider. For example, they have demonstrated effectiveness at boosted top or W boson identification or for quark/gluon discrimination. We explore these methods…

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…

Characterizes Lie-Backlund vector fields in infinite jet bundles that can be exponentiated.

Recent progress in applying machine learning for jet physics has been built upon an analogy between calorimeters and images. In this work, we present a novel class of recursive neural networks built instead upon an analogy between QCD and natural languages. In the analogy, four-momenta are like words and the clustering…

We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on $\mathbb{R}$ and a vertical hyperplane with first coordinate fixed provides a splitting of a model filiform group, which induces mappings of the group. We prov…

Study of Pascal algebra matrices and their jet bundle map for vector bundles.

We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the $\infty(x)$-Laplace equation in Riemannian vector fields. Due to the differences between Euclidean jets and Riemannian jets, the Euclidean method of proof is not valid in this environm…

Foundation models trained on collider data improve jet generation tasks.

Building on the notion of a particle physics detector as a camera and the collimated streams of high energy particles, or jets, it measures as an image, we investigate the potential of machine learning techniques based on deep learning architectures to identify highly boosted W bosons. Modern deep learning algorithms t…

The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where $T/subset R$, like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atm…

The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.