I'm way behind on these, but I'll continue where I left off:
30 June 2017
We're getting more abstracts for our [AMS special session on Applied Category Theory](http://math.ucr.edu/home/baez/ACT2017) on November 4-5! I'm happy to announce that David Spivak has submitted one, because he generally doesn't like to travel.
1) Joseph Moeller submitted one on his work with the Metron project:
* Operads for modeling networks
> **Abstract.** A network is a complex of interacting systems which can often be represented as a graph equipped with extra structure. Networks can be combined in many ways, including by overlaying one on top of the other or sitting one next to another. We introduce network models - which are formally a simple kind of lax symmetric monoidal functor - to encode these ways of combining networks. By applying a general construction to network models, we obtain operads for the design of complex networked systems. (Received June 29, 2017)
> 2) Christina Vasilakopoulou submitted on on her work with David Spivak and Patrick Schultz:
* Abstract dynamical systems
> **Abstract.** We describe a categorical framework of modeling and analyzing systems in a broad sense. The latter can be thought of as ‘machines’ with inputs and outputs, carrying some sort of signal that occurs through some notion of time; special cases include discrete and continuous dynamical systems. Modeling them as algebras for the wiring diagram operad, a central goal is to understand the behavior of composite systems, formed as arbitrary interconnections of component subsystems. This shall be accomplished using lax monoidal functors, which provide a coherent formalization of systems, as well as sheaf theory, which captures the crucial notion of time. (Received June 29, 2017)
3) David Spivak submitted one:
* A higher-order temporal logic for dynamical systems
> **Abstract.** We consider a very general class of dynamical systems—including discrete, continuous, hybrid, deterministic, non- deterministic, etc.—based on sheaves. We call these sheaves behavior types: they tell us the set of possible behaviors over any interval of time. A machine can be construed as a wide span of such sheaves, and these machines can be composed as morphisms in a hypergraph category. The topos of sheaves has an internal language, which we use as a new sort of higher-order internal logic for talking about behaviors. We can use this logic to prove properties about a composite system of systems from properties of the parts and how they are wired together. (Received June 28, 2017)
4) A third-year statistics grad student at Stanford named Evan Patterson submitted an interesting one:
* Knowledge representation in bicategories of relations
> **Abstract.** We introduce the relational ontology log, or relational olog, a categorical framework for knowledge representation based on the category of sets and relations. It is inspired by Spivak and Kent’s olog, a knowledge representation system based on the category of sets and functions. Relational ologs interpolate between ologs and description logic, the dominant formalism for knowledge representation today. On a practical level, we demonstrate that relational ologs have an intuitive yet fully precise graphical syntax, derived from the string diagrams of monoidal categories. We explain several other useful features of relational ologs not possessed by most description logics, such as a type system and a rich, flexible notion of instance data. In a more theoretical vein, we draw on categorical logic to show how relational ologs can be translated to and from logical theories in a fragment of first-order logic. (Received June 29, 2017)
On other news, I got back to Riverside yesterday! I have some big news to report from my visit to Turin, but I'll report that separately. If anyone at UCR wants to talk to me in person, I'll be here until around June 14th - set up an appointment! We've got a lot of projects going that are worth talking about. I'm especially eager to accelerate Kenny's work on coarse-graining Markov processes, and help Brandon finish his increasingly deep and interesting paper on bond graphs, and help Joseph finish a paper on network models, and get him started on a paper on compositional tasking.