Related papers: A Field Guide to Event-Shape Observables Using Opt…
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels,…
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) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…
The interest in the problem of small asteroids observed shortly before a deep close approach or an impact with the Earth has grown a lot in recent years. Since the observational dataset of such objects is very limited, they deserve…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bears the structure of a shape manifold. A corresponding…
When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to…
Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
Morse complexes and Morse-Smale complexes are topological descriptors popular in topology-based visualization. Comparing these complexes plays an important role in their applications in feature correspondences, feature tracking, symmetry…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
We present precision results for distributions in global event shapes that can be measured at hadron colliders within experimental limitations. These predictions are obtained by combining exact next-to-leading order (NLO) with the all-order…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…
Optimal transport has been used to define bijective nonlinear transforms and different transport-related metrics for discriminating data and signals. Here we briefly describe the advances in this topic with the main applications and…