David Spivak

Research Scientist
Department of Mathematics

Email: dspivak--math/mit/edu

Ologs: a 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 (2011) in 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 BioNanoScience.

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) in Nano Today.

Experience 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 in ACS Biomaterials. The Matriarch software, as well as a user's guide, is available for free online at the Matriarch website.

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This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.