5 papers
A Parameterized Algorithm for Testing whether the Limit of a Diagram is Empty
Ernst Althaus, Benjamin Merlin Bumpus, James Fairbanks +2
A limit of a (small) diagram in a complete category can be thought of as specifying a set of equations involving the objects of . To motivate this intuitively,…
Algorithmic and Extremal Obstructions Through the Language of Cohomology
Anny Beatriz Azevedo, Benjamin Merlin Bumpus, Matteo Capucci +2
We model problems as presheaves that assign sets of certificates to input instances, and we show how to use presheaf Äech cohomology to capture the precise ways in which local sol…
Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid
Luke Morris, George Rauta, Kevin Carlson +1
The discrete exterior calculus (DEC) defines a family of discretized differential operators which preserve certain desirable properties from the exterior calculus. We formulate and…
Lassos: Pushing Tree Decompositions Forward Along Homomorphisms
Benjamin Merlin Bumpus, James Fairbanks, Will J. Turner
It is folklore that tree-width is monotone under taking subgraphs (i.e. injective graph homomorphisms) and contractions (certain kinds of surjective graph homomorphisms). However,…
Towards a Unified Theory of Time-Varying Data
Benjamin Merlin Bumpus, James Fairbanks, Martti Karvonen +2
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a gene…