相关论文: The simplicial substructure of jets
Jet substructure observables serve as essential tools for probing the quark-gluon plasma produced in relativistic heavy-ion collisions. Their interpretation, however, is often complicated by edge effects, which arise when correlated…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
Chern number formulas for holomorphic jet bundles are computed for projective curves and for projective surfaces. These formulas are used to show that certain minimal surfaces of general type (generic hypersurfaces of degree at least 5 in…
Herbig-Haro (HH) jets are commonly thought of as homogeneous beams of plasma traveling at hypersonic velocities. Structure within jet beams is often attributed to periodic or ``pulsed'' variations of conditions at the jet source.…
In this paper, we propose a novel method for transforming data into a low-dimensional space optimized for one-class classification. The proposed method iteratively transforms data into a new subspace optimized for ellipsoidal encapsulation…
We report on our investigation in arXiv:2509.08881 of how recent jet substructure measurements constrain the resolution length $L_{\rm res}$ of the quark-gluon plasma formed in heavy-ion collisions. $L_{\rm res}$ is defined such that…
In the realm of large-scale point cloud registration, designing a compact symbolic representation is crucial for efficiently processing vast amounts of data, ensuring registration robustness against significant viewpoint variations and…
We introduce a new class of jet algorithms designed to return conical jets with a variable Delta R radius. A specific example, in which Delta R scales as 1/pT, proves particularly useful in capturing the kinematic features of a wide variety…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent…
We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition on the number of…
The half-open hypersimplex $\Delta'_{n,k}$ consists of those $x = (x_{1}, \ldots, x_{n}) \in[0,1]^n$ with $k-1<x_1+\cdots+x_n\le k$, where $0 < k \leq n$. The $f$-vector of a half-open hypersimplex and related generating functions are…
Embedding symmetries in the architectures of deep neural networks can improve classification and network convergence in the context of jet substructure. These results hint at the existence of symmetries in jet energy depositions, such as…
A filtration over a simplicial complex $K$ is an ordering of the simplices of $K$ such that all prefixes in the ordering are subcomplexes of $K$. Filtrations are at the core of Persistent Homology, a major tool in Topological Data Analysis.…
The Vietoris-Rips complex, denoted $R_\beta(X)$, of a metric space $(X,d)$ at scale $\beta$ is an abstract simplicial complex where each $k$-simplex corresponds to $(k+1)$ points of $X$ within diameter $\beta$. For any abstract simplicial…
We show that recent measurements of substructure-dependent jet suppression constrain the value of the resolution length of the droplets of quark-gluon plasma (QGP) formed in heavy ion collisions. This resolution length, $L_{\rm res}$, is…
Fix a field $k$. When $\Delta$ is a simplicial complex on $n$ vertices with Stanley-Reisner ideal $I_\Delta$, we define and study an invariant called the $\textit{type defect}$ of $\Delta$. Except when $\Delta$ is of a single simplex, the…
The (k,d)-hypersimplex is a (d-1)-dimensional polytope whose vertices are the (0,1)-vectors that sum to k. When k=1, we get a simplex whose graph is the complete graph with d vertices. Here we show how many of the well known graph…
We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…