Diagrams and incidence structures

Bowtie Structures, Pathway Diagrams, and Topological Explanation

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists migh...

Efficient Data Structures For Decision Diagrams

Algebraic structures on modules of diagrams

There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct characters on Λ and eight distinct families of weight functions on chord diagrams. As a consequence we ...

Cloning Voronoi Diagrams via Retroactive Data Structures

We address the problem of replicating a Voronoi diagram V (S) of a planar point set S by making proximity queries: 1. the exact location of the nearest site(s) in S 2. the distance to and label(s) of the nearest site(s) in S 3. a unique label for every nearest site in S. In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural al...

Carter–Penrose diagrams and differential spaces

In this paper it is argued that a Carter–Penrose diagram can be viewed as a differential space.