Department of Mathematics
category-theoretic foundation for knowledge representation. Joint with
Robert E. Kent. In this paper we present an application of basic category
theory to the field of knowledge representation. Ontology is the study of
what something is, the intrinsic nature of a subject. Ologs, or ontology
logs, are a framework for recording the results of such a study by breaking
it down into types (objects), aspects (arrows), and facts (commutative
diagrams). Functors between ologs can create translating dictionaries
between various perspectives on a subject, and set-valued functors amount to
instance data or "real world examples" for the system of concepts an olog.
This work was
published in the open-access journal PLoS ONE in January 2012. It is
also available on the
arXiv. An older version,
with a simplified section on communication, may also be useful.
Category-theoretic analysis of hierarchical protein materials and social
networks. Joint with Tristan Giesa, Elizabeth Wood, and Markus Buehler, published
PLoS ONE. In this paper
we use an olog to rigorously compare and contrast the structure of two
proteins and their resulting behaviors under strain. We then compare this
whole setup with that of a social network, contrived to have the same
olog-theoretic description. The examples reviewed here demonstrate that
the intrinsic nature of these complex systems, which in particular
includes a precise relationship between their structure and their
function, can be effectively represented by an olog. This, in turn, allows
for comparative studies between disparate materials or fields of
application, and result in novel approaches to derive functionality in
hierarchical systems. We discuss opportunities and challenges associated
with the description of complex biological materials by using ologs as a
powerful tool for analysis and design in the context of materiomics, and
we present the potential impact of this approach for engineering, life
sciences, and medicine. On the arXiv.
Reoccurring patterns in hierarchical protein materials and music: The power of
analogies. (Joint with Tristan Giesa and Markus Buehler.) In this paper,
we use ologs to display an analogy between hierarchical protein materials and
music. Published (2011) in
Category theory based solution for the building block replacement problem
in materials design. (Joint with Tristan Giesa and Markus Buehler.) In this
paper we show that ologs provide a foundation from which large scale
collaborative efforts in materials science can solve the building block
replacement problem. Published (2012) in
Advanced Engineering Materials.
Materials by design: merging proteins and music. (Joint with Joyce
Wong, John McDonald, Micki Taylor-Pinney, David L. Kaplan, and Markus
J. Buehler.) In this paper we discuss a way to translate musical insight
into engineering insight for building materials. Published (2012)
Implementing a Performant Category-Theory Library in Coq. (Joint with
Jason Gross and Adam Chlipala.) In this paper we discuss some difficulties
and interesting approaches to implementing basic categorical constructions
(e.g. Kan extensions) in the proof assistant Coq. On the arXiv.
Matriarch: A python library for materials architecture"
Joint with Ravi Jagadessan, Tristan Giesa, and Markus Buehler. Published
Biomaterials. The Matriarch software, as well as a user's guide, is
available for free online at the Matriarch website.
This work by David I. Spivak is licensed under a Creative Commons
Attribution-Share Alike 3.0 Unported License.