WebbIn the literature, there are several topological data structures for cell and simplicial complexes, thus a framework targeted to their fast prototyping is a valuable tool. Here, we introduce the dimension-independent and extensible ... called Manifold-Connected Decomposition (MC-Decomposition), previously investigated only for two- and three ... WebbA graph complex on G is an abstract simplicial complex consisting of subsets of E. In particular, we may interpret such a complex as a family of subgraphs of G. The subject …

One can hear the Euler characteristic of a simplicial complex

WebbTrees. A simplicial tree T is a nonempty, connected, locally finite, 1-dimensional simplicial complex without cycles. The set of vertices of T will be denoted by V (T), and the set of (unoriented, closed) edges by E(T). The edges adjacent to a given vertex v ∈ V(T) form a finite set Ev(T), whose cardinality val(v) is the valence of v. WebbSimplicial complexes can be constructed from point set data by various well-established techniques, which are designed such that, if the original dataset lies on a manifold , and … literary historical

How to prove that a simplicial complex is path-connected if …

WebbIf you choose something too small the resulting simplicial complex splits into many connected components. If you choose something too large the simplicial complex turns … Webb2 Simplicial and cubical complexes In this section we state necessary material about simplicial and cubical complexes and describe the construction of a cubical complex associated with a given simplicial complex. The details can be found in [12] and [5]. By an n-dimensional simplex we mean a non-degenerate affine image of a standard simplex … WebbAbstract simplicial complex. It is often easier to construct a complex abstractly and to worry abut how to put it into Euclidean space later. Definition. An abstract simplicial … literary historian