相关论文: On the Objectivity and Quasi-Objectivity of TSE an…

Sparse trajectory data consist of a low number of trajectories such that the reconstruction of an underlying velocity field is not possible. Recently, approaches have been introduced to analyze flow behavior based on a single trajectory…

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate…

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore…

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists…

We use transition path sampling to study evaporation in the SPC/E model of liquid water. Based on thousands of evaporation trajectories, we characterize the members of the transition state ensemble (TSE), which exhibit a liquid-vapor…

The identification and visualization of Lagrangian structures in flows plays a crucial role in the study of dynamic systems and fluid dynamics. The Finite Time Lyapunov Exponent (FTLE) has been widely used for this purpose; however, it only…

Accurately estimating spatiotemporal traffic states on freeways is a significant challenge due to limited sensor deployment and potential data corruption. In this study, we propose an efficient and robust low-rank model for precise…

We employ a recently developed single-trajectory Lagrangian diagnostic tool, the trajectory rotation average $ (\mathrm{\overline{TRA}}) $, to visualize oceanic vortices (or eddies) from sparse drifter data. We apply the $…

We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…

Segmental longitudinal strain (SLS) of the left ventricle (LV) is an important prognostic indicator for evaluating regional LV dysfunction, in particular for diagnosing and managing myocardial ischemia. Current techniques for strain…

We develop a maximum likelihood method to infer relevant physical properties of elongated active particles. Using individual trajectories of advected swimmers as input, we are able to accurately determine their rotational diffusion…

Trajectory Representation Learning (TRL) is a powerful tool for spatial-temporal data analysis and management. TRL aims to convert complicated raw trajectories into low-dimensional representation vectors, which can be applied to various…

Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected $l^2$-distance bounds between the LSE and the true regression…

Understanding when and how linguistic knowledge emerges during language model training remains a central challenge for interpretability. Most existing tools are post hoc, rely on scalar metrics, or require nontrivial integration effort,…

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as…

We present a novel self quality evaluation metric SQE for parameters optimization in the challenging yet critical multi-object tracking task. Current evaluation metrics all require annotated ground truth, thus will fail in the test…

Predicting the near-term behavior of a reactive agent is crucial in many robotic scenarios, yet remains challenging when observations of that agent are sparse or intermittent. Vision-Language Models (VLMs) offer a promising avenue by…

Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and…

Trajectory representation learning (TRL) maps trajectories to vectors that can then be used for various downstream tasks, including trajectory similarity computation, trajectory classification, and travel-time estimation. However, existing…