Related papers: Symmetry adapted Assur decompositions
Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…
A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an…
With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Amortized optimization accelerates the solution of related optimization problems by learning mappings that exploit shared structure across problem instances. We explore the use of Scale Equivariant Graph Metanetworks (ScaleGMNs) for this…
The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…