Applied Category Theory at UCR (Part 2)

21 September, 2017

I’m running a special session on applied category theory, and now the program is available:

Applied category theory, Fall Western Sectional Meeting of the AMS, 4-5 November 2017, U.C. Riverside.

This is going to be fun.

My former student Brendan Fong is now working with David Spivak at MIT, and they’re both coming. My collaborator John Foley at Metron is also coming: we’re working on the CASCADE project for designing networked systems.

Dmitry Vagner is coming from Duke: he wrote a paper with David and Eugene Lerman on operads and open dynamical system. Christina Vaisilakopoulou, who has worked with David and Patrick Schultz on dynamical systems, has just joined our group at UCR, so she will also be here. And the three of them have worked with Ryan Wisnesky on algebraic databases. Ryan will not be here, but his colleague Peter Gates will: together with David they have a startup called Categorical Informatics, which uses category theory to build sophisticated databases.

That’s not everyone—for example, most of my students will be speaking at this special session, and other people too—but that gives you a rough sense of some people involved. The conference is on a weekend, but John Foley and David Spivak and Brendan Fong and Dmitry Vagner are staying on for longer, so we’ll have some long conversations… and Brendan will explain decorated corelations in my Tuesday afternoon network theory seminar.

Here’s the program. Click on talk titles to see abstracts. For a multi-author talk, the person with the asterisk after their name is doing the talking. All the talks will be in Room 268 of the Highlander Union Building or ‘HUB’.

Saturday November 4, 2017, 9:00 a.m.-10:50 a.m.

9:00 a.m.
A higher-order temporal logic for dynamical systems.
David I. Spivak, MIT

10:00 a.m.
Algebras of open dynamical systems on the operad of wiring diagrams.
Dmitry Vagner*, Duke University
David I. Spivak, MIT
Eugene Lerman, University of Illinois at Urbana-Champaign

10:30 a.m.
Abstract dynamical systems.
Christina Vasilakopoulou*, University of California, Riverside
David Spivak, MIT
Patrick Schultz, MIT

Saturday November 4, 2017, 3:00 p.m.-5:50 p.m.

3:00 p.m.
Black boxes and decorated corelations.
Brendan Fong, MIT

4:00 p.m.
Compositional modelling of open reaction networks.
Blake S. Pollard*, University of California, Riverside
John C. Baez, University of California, Riverside

4:30 p.m.
A bicategory of coarse-grained Markov processes.
Kenny Courser, University of California, Riverside

5:00 p.m.
A bicategorical syntax for pure state qubit quantum mechanics.
Daniel M. Cicala, University of California, Riverside

5:30 p.m.
Open systems in classical mechanics.
Adam Yassine, University of California Riverside

Sunday November 5, 2017, 9:00 a.m.-10:50 a.m.

9:00 a.m.
Controllability and observability: diagrams and duality.
Jason Erbele, Victor Valley College

9:30 a.m.
Frobenius monoids, weak bimonoids, and corelations.
Brandon Coya, University of California, Riverside

10:00 a.m.
Compositional design and tasking of networks.
John D. Foley*, Metron, Inc.
John C. Baez, University of California, Riverside
Joseph Moeller, University of California, Riverside
Blake S. Pollard, University of California, Riverside

10:30 a.m.
Operads for modeling networks.
Joseph Moeller*, University of California, Riverside
John Foley, Metron Inc.
John C. Baez, University of California, Riverside
Blake S. Pollard, University of California, Riverside

Sunday November 5, 2017, 2:00 p.m.-4:50 p.m.

2:00 p.m.
Reeb graph smoothing via cosheaves.
Vin de Silva, Department of Mathematics, Pomona College

3:00 p.m.
Knowledge representation in bicategories of relations.
Evan Patterson*, Stanford University, Statistics Department

3:30 p.m.
The multiresolution analysis of flow graphs.
Steve Huntsman*, BAE Systems

4:00 p.m.
Data modeling and integration using the open source tool Algebraic Query Language (AQL).
Peter Y. Gates*, Categorical Informatics
Ryan Wisnesky, Categorical Informatics

Applied Category Theory 2018

12 September, 2017

There will be a conference on applied category theory!

Applied Category Theory (ACT 2018). School 23–27 April 2018 and workshop 30 April–4 May 2018 at the Lorentz Center in Leiden, the Netherlands. Organized by Bob Coecke (Oxford), Brendan Fong (MIT), Aleks Kissinger (Nijmegen), Martha Lewis (Amsterdam), and Joshua Tan (Oxford).

The plenary speakers will be:

• Samson Abramsky (Oxford)
• John Baez (UC Riverside)
• Kathryn Hess (EPFL)
• Mehrnoosh Sadrzadeh (Queen Mary)
• David Spivak (MIT)

There will be a lot more to say as this progresses, but for now let me just quote from the conference website:

Applied Category Theory (ACT 2018) is a five-day workshop on applied category theory running from April 30 to May 4 at the Lorentz Center in Leiden, the Netherlands.

Towards an Integrative Science: in this workshop, we want to instigate a multi-disciplinary research program in which concepts, structures, and methods from one scientific discipline can be reused in another. The aim of the workshop is to (1) explore the use of category theory within and across different disciplines, (2) create a more cohesive and collaborative ACT community, especially among early-stage researchers, and (3) accelerate research by outlining common goals and open problems for the field.

While the workshop will host discussions on a wide range of applications of category theory, there will be four special tracks on exciting new developments in the field:

1. Dynamical systems and networks
2. Systems biology
3. Cognition and AI
4. Causality

Accompanying the workshop will be an Adjoint Research School for early-career researchers. This will comprise a 16 week online seminar, followed by a 4 day research meeting at the Lorentz Center in the week prior to ACT 2018. Applications to the school will open prior to October 1, and are due November 1. Admissions will be notified by November 15.

The organizers

Bob Coecke (Oxford), Brendan Fong (MIT), Aleks Kissinger (Nijmegen), Martha Lewis (Amsterdam), and Joshua Tan (Oxford)

We welcome any feedback! Please send comments to this link.

About Applied Category Theory

Category theory is a branch of mathematics originally developed to transport ideas from one branch of mathematics to another, e.g. from topology to algebra. Applied category theory refers to efforts to transport the ideas of category theory from mathematics to other disciplines in science, engineering, and industry.

This site originated from discussions at the Computational Category Theory Workshop at NIST on Sept. 28-29, 2015. It serves to collect and disseminate research, resources, and tools for the development of applied category theory, and hosts a blog for those involved in its study.

The proposal: Towards an Integrative Science

Category theory was developed in the 1940s to translate ideas from one field of mathematics, e.g. topology, to another field of mathematics, e.g. algebra. More recently, category theory has become an unexpectedly useful and economical tool for modeling a range of different disciplines, including programming language theory [10], quantum mechanics [2], systems biology [12], complex networks [5], database theory [7], and dynamical systems [14].

A category consists of a collection of objects together with a collection of maps between those objects, satisfying certain rules. Topologists and geometers use category theory to describe the passage from one mathematical structure to another, while category theorists are also interested in categories for their own sake. In computer science and physics, many types of categories (e.g. topoi or monoidal categories) are used to give a formal semantics of domain-specific phenomena (e.g. automata [3], or regular languages [11], or quantum protocols [2]). In the applied category theory community, a long-articulated vision understands categories as mathematical workspaces for the experimental sciences, similar to how they are used in topology and geometry [13]. This has proved true in certain fields, including computer science and mathematical physics, and we believe that these results can be extended in an exciting direction: we believe that category theory has the potential to bridge specific different fields, and moreover that developments in such fields (e.g. automata) can be transferred successfully into other fields (e.g. systems biology) through category theory. Already, for example, the categorical modeling of quantum processes has helped solve an important open problem in natural language processing [9].

In this workshop, we want to instigate a multi-disciplinary research program in which concepts, structures, and methods from one discipline can be reused in another. Tangibly and in the short-term, we will bring together people from different disciplines in order to write an expository survey paper that grounds the varied research in applied category theory and lays out the parameters of the research program.

In formulating this research program, we are motivated by recent successes where category theory was used to model a wide range of phenomena across many disciplines, e.g. open dynamical systems (including open Markov processes and open chemical reaction networks), entropy and relative entropy [6], and descriptions of computer hardware [8]. Several talks will address some of these new developments. But we are also motivated by an open problem in applied category theory, one which was observed at the most recent workshop in applied category theory (Dagstuhl, Germany, in 2015): “a weakness of semantics/CT is that the definitions play a key role. Having the right definitions makes the theorems trivial, which is the opposite of hard subjects where they have combinatorial proofs of theorems (and simple definitions). […] In general, the audience agrees that people see category theorists only as reconstructing the things they knew already, and that is a disadvantage, because we do not give them a good reason to care enough” [1, pg. 61].

In this workshop, we wish to articulate a natural response to the above: instead of treating the reconstruction as a weakness, we should treat the use of categorical concepts as a natural part of transferring and integrating knowledge across disciplines. The restructuring employed in applied category theory cuts through jargon, helping to elucidate common themes across disciplines. Indeed, the drive for a common language and comparison of similar structures in algebra and topology is what led to the development category theory in the first place, and recent hints show that this approach is not only useful between mathematical disciplines, but between scientific ones as well. For example, the ‘Rosetta Stone’ of Baez and Stay demonstrates how symmetric monoidal closed categories capture the common structure between logic, computation, and physics [4].

[1] Samson Abramsky, John C. Baez, Fabio Gadducci, and Viktor Winschel. Categorical methods at the crossroads. Report from Dagstuhl Perspectives Workshop 14182, 2014.

[2] Samson Abramsky and Bob Coecke. A categorical semantics of quantum protocols. In Handbook of Quantum Logic and Quantum Structures. Elsevier, Amsterdam, 2009.

[3] Michael A. Arbib and Ernest G. Manes. A categorist’s view of automata and systems. In Ernest G. Manes, editor, Category Theory Applied to Computation and Control. Springer, Berlin, 2005.

[4] John C. Baez and Mike STay. Physics, topology, logic and computation: a Rosetta stone. In Bob Coecke, editor, New Structures for Physics. Springer, Berlin, 2011.

[5] John C. Baez and Brendan Fong. A compositional framework for passive linear networks. arXiv e-prints, 2015.

[6] John C. Baez, Tobias Fritz, and Tom Leinster. A characterization of entropy in terms of information loss. Entropy, 13(11):1945–1957, 2011.

[7] Michael Fleming, Ryan Gunther, and Robert Rosebrugh. A database of categories. Journal of Symbolic Computing, 35(2):127–135, 2003.

[8] Dan R. Ghica and Achim Jung. Categorical semantics of digital circuits. In Ruzica Piskac and Muralidhar Talupur, editors, Proceedings of the 16th Conference on Formal Methods in Computer-Aided Design. Springer, Berlin, 2016.

[9] Dimitri Kartsaklis, Mehrnoosh Sadrzadeh, Stephen Pulman, and Bob Coecke. Reasoning about meaning in natural language with compact closed categories and Frobenius algebras. In Logic and Algebraic Structures in Quantum Computing and Information. Cambridge University Press, Cambridge, 2013.

[10] Eugenio Moggi. Notions of computation and monads. Information and Computation, 93(1):55–92, 1991.

[11] Nicholas Pippenger. Regular languages and Stone duality. Theory of Computing Systems 30(2):121–134, 1997.

[12] Robert Rosen. The representation of biological systems from the standpoint of the theory of categories. Bulletin of Mathematical Biophysics, 20(4):317–341, 1958.

[13] David I. Spivak. Category Theory for Scientists. MIT Press, Cambridge MA, 2014.

[14] David I. Spivak, Christina Vasilakopoulou, and Patrick Schultz. Dynamical systems and sheaves. arXiv e-prints, 2016.

Entropy 2018

6 July, 2017

The editors of the journal Entropy are organizing this conference:

Entropy 2018 — From Physics to Information Sciences and Geometry, 14–16 May 2018, Auditorium Enric Casassas, Faculty of Chemistry, University of Barcelona, Barcelona, Spain.

They write:

One of the most frequently used scientific words is the word “entropy”. The reason is that it is related to two main scientific domains: physics and information theory. Its origin goes back to the start of physics (thermodynamics), but since Shannon, it has become related to information theory. This conference is an opportunity to bring researchers of these two communities together and create a synergy. The main topics and sessions of the conference cover:

• Physics: classical and quantum thermodynamics
• Statistical physics and Bayesian computation
• Geometrical science of information, topology and metrics
• Maximum entropy principle and inference
• Kullback and Bayes or information theory and Bayesian inference
• Entropy in action (applications)

The inter-disciplinary nature of contributions from both theoretical and applied perspectives are very welcome, including papers addressing conceptual and methodological developments, as well as new applications of entropy and information theory.

All accepted papers will be published in the proceedings of the conference. A selection of invited and contributed talks presented during the conference will be invited to submit an extended version of their paper for a special issue of the open access journal Entropy.

Information Processing in Chemical Networks (Part 2)

13 June, 2017

I’m in Luxembourg, and I’ll be blogging a bit about this workshop:

Dynamics, Thermodynamics and Information Processing in Chemical Networks, 13-16 June 2017, Complex Systems and Statistical Mechanics Group, University of Luxembourg. Organized by Massimiliano Esposito and Matteo Polettini.

I’ll do it in the comments!

I explained the idea of this workshop here:

Information processing in chemical networks.

and now you can see the program here.

Applied Category Theory at UCR

6 April, 2017

The American Mathematical Society is having a meeting here at U. C. Riverside during the weekend of November 4th and 5th, 2017. I’m organizing a session on Applied Category Theory, and I’m looking for people to give talks.

The goal is to start a conversation about applications of category theory, not within pure math or fundamental physics, but to other branches of science and engineering—especially those where the use of category theory is not already well-established! For example, my students and I have been applying category theory to chemistry, electrical engineering, control theory and Markov processes.

Alas, we have no funds for travel and lodging. If you’re interested in giving a talk, please submit an abstract here:

General information about abstracts, American Mathematical Society.

More precisely, please read the information there and then click on the link on that page to submit an abstract. It should then magically fly through cyberspace to me! Abstracts are due September 12th, but the sooner you submit one, the greater the chance that we’ll have space.

For the program of the whole conference, go here:

Fall Western Sectional Meeting, U. C. Riverside, Riverside, California, 4–5 November 2017.

We’ll be having some interesting plenary talks:

• Paul Balmer, UCLA, An invitation to tensor-triangular geometry.

• Pavel Etingof, MIT, Double affine Hecke algebras and their applications.

• Monica Vazirani, U.C. Davis, Combinatorics, categorification, and crystals.

Quantifying Biological Complexity

23 January, 2017

Next week I’m going to this workshop:

Biological Complexity: Can It Be Quantified?, 1-3 February 2017, Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe Arizona. Organized by Paul Davies.

I haven’t heard that any of it will be made publicly available, but I’ll see if there’s something I can show you. Here’s the schedule:

Wednesday February 1st

9:00 – 9:30 am Paul Davies

Brief welcome address, outline of the subject and aims of the meeting

Session 1. Life: do we know it when we see it?

9:30 – 10:15 am: Chris McKay, “Mission to Enceladus”

10:15 – 10:45 am: Discussion

10:45– 11:15 am: Tea/coffee break

11:15 – 12:00 pm: Kate Adamala, “Alive but not life”

12:00 – 12:30 pm: Discussion

12:30 – 2:00 pm: Lunch

Session 2. Quantifying life

2:00 – 2:45 pm: Lee Cronin, “The living and the dead: molecular signatures of life”

2:45 – 3:30 pm: Sara Walker, “Can we build a life meter?”

3:30 – 4:00 pm: Discussion

4:00 – 4:30 pm: Tea/coffee break

4:30 – 5:15 pm: Manfred Laubichler, “Complexity is smaller than you think”

5:15 – 5:30 pm: Discussion

The Beyond Annual Lecture

7:00 – 8:30 pm: Sean Carroll, “Our place in the universe”

Thursday February 2nd

Session 3: Life, information and the second law of thermodynamics

9:00 – 9:45 am: James Crutchfield, “Vital bits: the fuel of life”

9:45 – 10:00 am: Discussion

10:00 – 10:45 pm: John Baez, “Information and entropy in biology”

10:45 – 11:00 am: Discussion

11:00 – 11:30 pm: Tea/coffee break

11:30 – 12:15 pm: Chris Adami, “What is biological information?”

12:15 – 12:30 pm: Discussion

12:30 – 2:00 pm: Lunch

Session 4: The emergence of agency

2:00 – 2:45 pm: Olaf Khang Witkowski, “When do autonomous agents act collectively?”

2:45 – 3:00 pm: Discussion

3:00 – 3:45 pm: William Marshall, “When macro beats micro”

3:45 – 4:00 pm: Discussion

4:00 – 4:30 am: Tea/coffee break

4:30 – 5:15pm: Alexander Boyd, “Biology’s demons”

5:15 – 5:30 pm: Discussion

Friday February 3rd

Session 5: New physics?

9:00 – 9:45 am: Sean Carroll, “Laws of complexity, laws of life?”

9:45 – 10:00 am: Discussion

10:00 – 10:45 am: Andreas Wagner, “The arrival of the fittest”

10:45 – 11:00 am: Discussion

11:00 – 11:30 am: Tea/coffee break

11:30 – 12:30 pm: George Ellis, “Top-down causation demands new laws”

12:30 – 2:00 pm: Lunch

Information Processing in Chemical Networks (Part 1)

4 January, 2017

There’s a workshop this summer:

Dynamics, Thermodynamics and Information Processing in Chemical Networks, 13-16 June 2017, Complex Systems and Statistical Mechanics Group, University of Luxembourg. Organized by Massimiliano Esposito and Matteo Polettini.

They write, “The idea of the workshop is to bring in contact a small number of high-profile research groups working at the frontier between physics and biochemistry, with particular emphasis on the role of Chemical Networks.”

The speakers may include John Baez, Sophie de Buyl, Massimiliano Esposito, Arren Bar-Even, Christoff Flamm, Ronan Fleming, Christian Gaspard, Daniel Merkle, Philippe Nge, Thomas Ouldridge, Luca Peliti, Matteo Polettini, Hong Qian, Stefan Schuster, Alexander Skupin, Pieter Rein ten Wolde. I believe attendance is by invitation only, so I’ll endeavor to make some of the ideas presented available here at this blog.

Some of the people involved

I’m looking forward to this, in part because there will be a mix of speakers I’ve met, speakers I know but haven’t met, and speakers I don’t know yet. I feel like reminiscing a bit, and I hope you’ll forgive me these reminiscences, since if you try the links you’ll get an introduction to the interface between computation and chemical reaction networks.

In part 25 of the network theory series here, I imagined an arbitrary chemical reaction network and said:

We could try to use these reactions to build a ‘chemical computer’. But how powerful can such a computer be? I don’t know the answer.

Luca Cardelli answered my question in part 26. This was just my first introduction to the wonderful world of chemical computing. Erik Winfree has a DNA and Natural Algorithms Group at Caltech, practically next door to Riverside, and the people there do a lot of great work on this subject. David Soloveichik, now at U. T. Austin, is an alumnus of this group.

In 2014 I met all three of these folks, and many other cool people working on these theme, at a workshop I tried to summarize here:

Programming with chemical reaction networks, Azimuth, 23 March 2014.

The computational power of chemical reaction networks, 10 June 2014.

Chemical reaction network talks, 26 June 2014.

I met Matteo Polettini about a year later, at a really big workshop on chemical reaction networks run by Elisenda Feliu and Carsten Wiuf:

Trends in reaction network theory (part 1), Azimuth, 27 January 2015.

Trends in reaction network theory (part 2), Azimuth, 1 July 2015.

Polettini has his own blog, very much worth visiting. For example, you can see his view of the same workshop here:

• Matteo Polettini, Mathematical trends in reaction network theory: part 1 and part 2, Out of Equilibrium, 1 July 2015.

Finally, I met Massimiliano Esposito and Christoph Flamm recently at the Santa Fe Institute, at a workshop summarized here:

Information processing and biology, Azimuth, 7 November 2016.

So, I’ve gradually become educated in this area, and I hope that by June I’ll be ready to say something interesting about the semantics of chemical reaction networks. Blake Pollard and I are writing a paper about this now.