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In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Lower limbs exoskeletons provide assistance during standing, squatting, and walking. Gait dynamics, in particular, implies a change in the configuration of the device in terms of contact points, actuation, and system dynamics in general. In…
Systems whose movement is highly dissipative provide an opportunity to both identify models easily and quickly optimize motions. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the…
High frequency pedestrian motion forecasting when interacting with autonomous vehicles (AVs) can be enhanced through the use of behavioural frameworks, such as discrete choice models, that can explicitly account for correlation among…
Serially connected robots are promising candidates for performing tasks in confined spaces such as search-and-rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
Skeleton-based gait emotion recognition has received significant attention due to its wide-ranging applications. However, existing methods primarily focus on extracting spatial and local temporal motion information, failing to capture…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
Human movements are physical processes combining the classical mechanics of the human body moving in space and the biomechanics of the muscles generating the forces acting on the body under sophisticated sensory-motor control. One way to…
A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a…
Learning world models from their sensory inputs enables agents to plan for actions by imagining their future outcomes. World models have previously been shown to improve sample-efficiency in simulated environments with few objects, but have…
Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…
A vast number of applications for legged robots entail tasks in complex, dynamic environments. But these environments put legged robots at high risk for limb damage. This paper presents an empirical study of fault tolerant dynamic gaits…
We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter…
We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…