Oral History Interview: Warren Brown

This interview is one of a series conducted concerning West Virginia business history. Warren Brown was an employee of BML Lighting, a theatrical lighting company. He discusses: company history; business practices; different jobs they were hired for; their education; bookkeeping; and how technology has affected their business.https://mds.marshall.edu/oral_history/1287/thumbnail.jp

Towards a directed homotopy type theory

In this paper, we present a directed homotopy type theory for reasoning synthetically about (higher) categories, directed homotopy theory, and its applications to concurrency. We specify a new `homomorphism' type former for Martin-L\"of type theory which is roughly analogous to the identity type former originally introduced by Martin-L\"of. The homomorphism type former is meant to capture the notions of morphism (from the theory of categories) and directed path (from directed homotopy theory) just as the identity type former is known to capture the notions of isomorphism (from the theory of groupoids) and path (from homotopy theory). Our main result is an interpretation of these homomorphism types into Cat, the category of small categories. There, the interpretation of each homomorphism type hom(a,b) is indeed the set of morphisms between the objects a and b of a category C. We end the paper with an analysis of the interpretation in Cat with which we argue that our homomorphism types are indeed the directed version of Martin-L\"of's identity types

Plate tectonics: When ancient continents collide

The geological record preserves scant evidence for early plate tectonics. Analysis of eclogites — metamorphic rocks formed in subduction zones — in the Trans-Hudson mountain belt suggests modern-style subduction may have operated 1,800 million years ago