12 citations · 23 across the 5 of their papers we have counts for
8 papers
Formal composition of hybrid systems
Jared Culbertson, Paul Gustafson, Daniel E. Koditschek +1
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hiera…
Extendable shellability for -dimensional complexes on vertices
Jared Culbertson, Anton Dochtermann, Dan P. Guralnik +1
We prove that for all a shellable -dimensional simplicial complex with at most vertices is extendably shellable. The proof involves considering the structure of…
Edge Erasures and Chordal Graphs
Jared Culbertson, Dan P. Guralnik, Peter F. Stiller
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete sub…
Functorial Hierarchical Clustering with Overlaps
Jared Culbertson, Dan P. Guralnik, Peter F. Stiller
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial t…
Consistency constraints for overlapping data clustering
Jared Culbertson, Dan P. Guralnik, Jakob Hansen +1
We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based m…
Injective metrizability and the duality theory of cubings
Jared Culbertson, Dan P. Guralnik, Peter F. Stiller
Following his discovery that finite metric spaces have injective envelopes naturally admitting a polyhedral structure, Isbell, in his pioneering work on injective metric spaces, at…
Torsion Sections of Elliptic Surfaces
Rick Miranda, Peter F. Stiller
Given a torsion section of a semistable elliptic surface, we prove equidistribution results for the components of singular fibers which are hit by the section, and for the root of…
The Geometry and Arithmetic of Elliptic Surfaces
Peter F. Stiller
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be…