Related papers: Distributed Transformations of Hamiltonian Shapes …
This paper considers a formation shape control problem for point agents in a two-dimensional ambient space, where the control is distributed, is based on achieving desired distances between nominated agent pairs, and avoids the possibility…
This is the second in a series of papers where we construct an invariant of a four-dimensional piecewise linear manifold $M$ with a given middle cohomology class $h\in H^2(M,\mathbb C)$. This invariant is the square root of the torsion of…
By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…
The Multi-Agent Path Finding (MAPF) problem aims to determine the shortest and collision-free paths for multiple agents in a known, potentially obstacle-ridden environment. It is the core challenge for robotic deployments in large-scale…
This paper proposes a port-Hamiltonian framework for angle-based formation stabilization and maneuvers using bearing and velocity measurements with an underlying triangulated Laman graph. The corresponding port-Hamiltonian controller is…
Contact Hamiltonian systems extend symplectic Hamiltonian mechanics to dissipative settings while retaining geometric structure. We develop a structure-preserving splitting framework for contact Hamiltonian systems on $J^1(\mathbb{R}^n)$…
We propose a model to show the self-assembling of network-like structures between a set of nodes without using preexisting positional information or long-range attraction of the nodes. The model is based on Brownian agents that are capable…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
We consider a Su-Schrieffer-Heeger chain to which we attach a semi-infinite undimerized chain (lead) to both ends. We study the effect of the openness of the SSH model on its properties. A representation of the infinite system using an…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, and nonlinear geometry of model representations. We apply…
In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of $n\in\mathbb{N}$ robots in the $\mathcal{OBLOT}$ model and analyze their collective $\mathcal{F}$sync dynamics using of…
This paper addresses the problem of distributed detection in multi-agent networks. Agents receive private signals about an unknown state of the world. The underlying state is globally identifiable, yet informative signals may be dispersed…
We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature,…
Shape manipulation is a central research topic in computer graphics. Topology editing, such as breaking apart connections, joining disconnected ends, and filling/opening a topological hole, is generally more challenging than geometry…
For contact manifolds, it is well-known that the map which assigns to an infinitesimal contact transformation its contact Hamiltonian function is a linear isomorphism, and an explicit local formula for its inverse can be given. In contrast,…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information…
This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and…
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…