相关论文: Planar Linkages and Algebraic Sets

Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…

Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…

We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there…

A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are…

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of…

The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and…

Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…

A linked bar chart is the augmentation of a traditional bar chart where each bar is partitioned into blocks and pairs of blocks are linked using orthogonal lines that pass over intermediate bars. The order of the blocks readily influences…

A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…

An isometry is a geometric transformation that preserves distances between pairs of points. We present methods to classify isometries in the Euclidean plane, and extend these methods to spherical, single elliptical, and hyperbolic geometry.…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there…

New classes of distance-constrained structures are introduced, namely string-node nets and meshes, a mesh being a string-node net for which the nodes are dense in the strings. Various construction schemes are given including the minimal…

Laman graphs naturally arise in structural mechanics and rigidity theory. Specifically, they characterize minimally rigid planar bar-and-joint systems which are frequently needed in robotics, as well as in molecular chemistry and polymer…

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…

For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…

A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on $n$ vertices can have at most $\lfloor 3n - \sqrt{12n -…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…