Related papers: Conic Frameworks Infinitesimal Rigidity
We show that a generic framework $(G,p)$ on the cylinder is globally rigid if and only if $G$ is a complete graph on at most four vertices or $G$ is both redundantly rigid and $2$-connected. To prove the theorem we also derive a new…
Collective organization in physical, biophysical, and biological systems often emerges from many weak, local interactions, yet the resulting global structures display striking regularities and apparent limits in diversity. Existing…
Labourie and the author independently showed that a convex real projective structure on an oriented surface of genus at least 2 is equivalent to a conformal structure plus a holomorphic cubic differential U. We analyze the behavior of the…
Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework $\C$ in $\bR^d$. These equations are used to derive symmetry-adapted…
Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance…
We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of…
We define cone structures and asymptotic invariants for multigraded systems of ideals, and show that essentially the only restrictions on such structures is convexity, which is imposed formally.
The method of alternating projections (MAP) is a common method for solving feasibility problems. While employed traditionally to subspaces or to convex sets, little was known about the behavior of the MAP in the nonconvex case until 2009,…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
This work introduces a distributed formation control strategy for multi-agent systems based solely on rotation symmetry constraints. We propose a potential function that enforces inter-agent \textbf{rotational} symmetries, whose gradient…
The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry…
This paper addresses the problem of position- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in a $3$D workspace with obstacles. More specifically, we design a decentralized control protocol…
This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…
This article considers the problem of conflict-free distribution of point-sized agents on a circular periphery encompassing all agents. The two key elements of the proposed policy include the construction of a set of convex layers (nested…
The concept of the 'agent' has profoundly shaped Artificial Intelligence (AI) research, guiding development from foundational theories to contemporary applications like Large Language Model (LLM)-based systems. This paper critically…
Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
Iterative LLM systems(self-refinement, chain-of-thought, autonomous agents) are increasingly deployed, yet their temporal dynamics remain uncharacterized. Prior work evaluates task performance at convergence but ignores the trajectory: how…