Related papers: A Spectral Metric for Collider Geometry
Continuously monitored quantum systems are emerging as promising platforms for quantum metrology, where a central challenge is to identify measurement strategies that optimally extract information about unknown parameters encoded in the…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
A measurement of novel event shapes quantifying the isotropy of collider events is performed in 140 fb$^{-1}$ of proton-proton collisions with $\sqrt s=13$ TeV centre-of-mass energy recorded with the ATLAS detector at CERN's Large Hadron…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
From a combinatorial point of view, we consider the Earth Mover's Distance (EMD) associated with a metric measure space. The specific case considered is deceptively simple: Let the finite set [n] = {1,...,n} be regarded as a metric space by…
The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of…
In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by…
As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free…
The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
The phase space of hadron collider events spans hundreds of dimensions, generating an intricate geometry that we are just starting to explore. The number of possible new physics signals is exponential in the number of dimensions and…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
Very little attention has been paid to the comparison of efficiency between high accuracy statistical parsers. This paper proposes one machine-independent metric that is general enough to allow comparisons across very different parsing…
Numerical wave models can output partitioned wave parameters at each grid point using a spectral partitioning technique. Because these wave partitions are usually organized according to the magnitude of their wave energy without considering…
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…