Related papers: The orbit rigidity matrix of a symmetric framework

We build a Shannon orbit equivalence between the universal odometer and a variety of rank-one systems. This is done in a unified manner, using what we call flexible classes of rank-one transformations. Our main result is that every flexible…

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear…

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space ($R^d$ with a metric of indefinite signature). We show that a…

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

A bar framework in R^r, denoted by G(p), is a simple connected graph G whose vertices are points p^1,...,p^n in R^r that affinely span R^r, and whose edges are line segments between pairs of these points. In this paper, we use stress…

A planar framework -- a graph together with a map of its vertices to the plane -- is flexible if it allows a continuous deformation preserving the distances between adjacent vertices. Extending a recent previous result, we prove that a…

A two-dimensional direction-length framework $(G,p)$ consists of a multigraph $G=(V;D,L)$ whose edge set is formed of "direction" edges $D$ and "length" edges $L$, and a realisation $p$ of this graph in the plane. The edges of the framework…

In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…

We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.

Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…

Graph generators learn a model from a source graph in order to generate a new graph that has many of the same properties. The learned models each have implicit and explicit biases built in, and its important to understand the assumptions…

Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…

In this paper, we first introduce the concept of symmetrical symplectic capacity for symmetrical symplectic manifolds, and by using this symmetrical symplectic capacity theory we prove that there exists at least one symmetric closed…

This paper introduces new structures called conic frameworks and their rigidity. They are composed by agents and a set of directed constraints between pairs of agents. When the structure cannot be flexed while preserving the constraints, it…

We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…

Anisotropy of friction force is proved to be an important factor in various contact problems. We study dynamical behavior of thin plates with respect to symmetric and asymmetric orthotropic friction. Terminal motion of plates with circular…

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an…

This paper presents a parametric stiffness analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. First, a compliant modeling of the Orthoglide is conducted based on an existing method. Then stiffness matrix is…