5 papers · 1 filter
Decomposing time-varying data into simple pieces: structured decompositions of narratives
Benjamin Merlin Bumpus, Jana K. Nickel
Graphs that change over time arise throughout applications, but there is no single standard way to decompose them into smaller pieces. In this paper, we propose a systematic catego…
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,…
Additive Invariants of Open Petri Nets
Benjamin Merlin Bumpus, Sophie Libkind, Jordy Lopez Garcia +2
We classify all additive invariants of open Petri nets: these are -valued invariants which are additive with respect to sequential and parallel composition of open Petr…
Structured Decompositions: Structural and Algorithmic Compositionality
Benjamin Merlin Bumpus, Zoltan A. Kocsis, Jade Edenstar Master +1
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidt…
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…