Related papers: Towards a mathematical theory of trajectory infere…

We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of…

This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel…

We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…

Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent…

Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

We systematically develop beneficial and practical velocity measures for accurate and efficient statistical simulations of the Langevin equation with direct applications to computational statistical mechanics and molecular dynamics…

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…

In this paper, we present a novel optimization-based framework for autonomous excavator trajectory generation under various objectives, including minimum joint displacement and minimum time. Traditional methods on excavation trajectory…

This paper considers a trajectory planning problem for a robot navigating complex terrains, which arises in applications ranging from autonomous mining vehicles to planetary rovers. The problem seeks to find a low-cost dynamically feasible…

This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer…

We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We…

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…

Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…

The ability to generate artificial human movement patterns while meeting location and time constraints is an important problem in the security community, particularly as it enables the study of the analog problem of detecting such patterns…

Trajectory generation has recently drawn growing interest in privacy-preserving urban mobility studies and location-based service applications. Although many studies have used deep learning or generative AI methods to model trajectories and…