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Biharmonic distance (\bd) is a powerful graph distance metric with many applications, including identifying critical links in road networks and mitigating over-squashing problem in \gnn. However, computing \bd\ is extremely difficult,…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…
In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…
3D Scene Graphs integrate both metric and semantic information, yet their structure remains underutilized for improving path planning efficiency and interpretability. In this work, we present S-Path, a situationally-aware path planner that…
We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph…
X-ray phase-contrast imaging offers enhanced sensitivity for weakly-attenuating materials, such as breast and brain tissue, but has yet to be widely implemented clinically due to high coherence requirements and expensive x-ray optics.…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
In this paper, we present an iterative method to quickly traverse multi-dimensional paths considering jerk constraints. As a first step, we analyze the traversal of each individual path dimension. We derive a range of feasible target…
In the Disjoint Paths problem, one is given a graph with a set of $k$ vertex pairs $(s_i,t_i)$ and the task is to connect each $s_i$ to $t_i$ with a path, so that the $k$ paths are pairwise disjoint. In the optimization variant, Max…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
In this paper, we propose a new algorithm based on radial symmetry center method to track colloidal particles close to contact, where the optical images of the particles start to overlap in digital video microscopy. This overlapping effect…
In situations where humans and robots are moving in the same space whilst performing their own tasks, predictable paths taken by mobile robots can not only make the environment feel safer, but humans can also help with the navigation in the…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
Cyclists face a disproportionate risk of injury, yet conventional crash records are too sparse to identify risk factors at fine spatial and temporal scales. Recently, naturalistic studies have used video data to capture the complex…
This paper presents a robust tracking controller for tracking curvature-constrained paths by vehicles/robots with uncertain Dubins dynamics. Although Dubins paths have been widely used in vehicular and robotic applications, robust and…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
Particle tracking is a key to single-particle-level confocal microscopy observation of colloidal suspensions, emulsions, and granular matter. The conventional tracking method has not been able to provide accurate information on the size of…
This paper presents a novel approach to pedestrian trajectory prediction for on-board camera systems, which utilizes behavioral features of pedestrians that can be inferred from visual observations. Our proposed method, called…
The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the pseudospectral boundary? The present study of the mathematical properties of the boundary of the pseudospectrum is the…
The finely tuned structures of membrane channels allow selective passage of ions through the available aqueous pores. In order to understand channel function, it is crucial to locate the pore and study its physical and chemical properties.…