Abstract. A new methodology that structures the semantics of a collection of documents into the geometry of a simplicial complex is developed. A simplicial complex is topologically...
We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the inde...
Barycentric coordinates are a fundamental concept in computer graphics and geometric modeling. We extend the geometric construction of Floater’s mean value coordinates [8,11] to...
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.
In [Spi], we developed a category of databases in which the schema of a database is represented as a simplicial set. Each simplex corresponds to a table in the database. There, our...