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Paolo Perrone (Apr 29 2020 at 00:00):Hi all! This is the thread of Sophie Libkind's talk.
Title: Unifying open dynamical systems: An algebra of resource sharing machines
When: Thursday 30 April, 12 noon EDT (Boston time)
Zoom Meeting: https://mit.zoom.us/j/280120646
Youtube live: https://youtu.be/egXvGYWyzeU
Paolo Perrone (Apr 30 2020 at 15:55):Hello all. We start in 5 minutes!
Jules Hedges (Apr 30 2020 at 15:57):Are Zoom and Youtube equivalent? Is one preferred on your end, or do we get a free choice?
Paolo Perrone (Apr 30 2020 at 15:57):They are equivalent. Zoom for more "in-person" feeling, Youtube for more privacy.
Paolo Perrone (Apr 30 2020 at 15:58):In both cases, in case of connection problems, we will upload a local HD recording to rewatch anything you might have missed.
Paolo Perrone (Apr 30 2020 at 15:59):However, if you want to take part to the breakout rooms at the end of the talk, use Zoom (you can watch the talk on youtube and join the zoom call at the end).
Paolo Perrone (Apr 30 2020 at 16:00):We start in 30 seconds!
James Fairbanks (Apr 30 2020 at 16:27):I really like this presentation, closest thing I've seen to a chalkboard online.
Brendan Fong (Apr 30 2020 at 16:58):yeah, it's very nicely done!
Brian Pinsky (Apr 30 2020 at 17:06):I remember reading this thing about a graphical notation for lambda calculus at one point, and your talk had pictures that looked very similar. I'm not sure if this is a question or a comment or what, but it may interest you or people who liked your talk to look at it.
James Fairbanks (Apr 30 2020 at 17:48):@David Spivak @Sophie Libkind here is the example of the thing that felt like a hack, in order to model the flow of susceptible people from one city to the next in our multi city SEIR model, you have 4 populations of S people, then when you do the gluing, you end up with 2 populations of S people.
Jules Hedges (Apr 30 2020 at 18:06):@Sophie Libkind Is there a paper coming on this?
Vincent Wang (Apr 30 2020 at 18:12):a half answer to DJMs question as to whether generators exist: maybe, if you're willing to assume the law of mass action. It's a (chemistry) thing that's tantamount to the physical assumption that you're dealing with a large number of well-mixed reactants bumping into each other uniformly randomly, such that the relative rate of any reaction [A + B -> C] as a positive real number is proportional to [amount of A x amount of B]. e.g. if there's only one reaction [A + A -> B], then doubling the amount of A, one expects a fourfold increase in the rate of reaction, because there are four times as many "A meets A" events. The upshot of assuming LMA is then that you can lift directly from the input-output types of the bubbles to polynomials, by mapping the tensor monoid of the inputs into the monoid of polynomials over your state variables with multiplication, and mapping the monoid of outputs to monoid of polynomials over state variables with addition, both maps identity-on-state-variables. Though one only gets out polynomial ordinary differential equations in this way, it's possible to recover things like the Hill equation and the qualitative effects of inhibition and catalysis, so it's "good enough" to do biological modelling.
Vincent Wang (Apr 30 2020 at 18:30):a thought: perhaps LMA can be recovered categorically. In 'biochem' dynamical systems, we want all the bubbles to be freely connected: all typematching inputs and outputs are connected, and all typematching (on state variables) open ports are connected, because each atomic process is concurrent with all the rest. Would be nice if assuming all connections were free in this way forces the kind of semiring (as above) that characterises LMA
Sophie Libkind (Apr 30 2020 at 19:12):Brian Pinsky said:
I remember reading this thing about a graphical notation for lambda calculus at one point, and your talk had pictures that looked very similar. I'm not sure if this is a question or a comment or what, but it may interest you or people who liked your talk to look at it.
Thanks for sharing! I wonder if the overlap is in the underlying operad for this graphical calculus
Sophie Libkind (Apr 30 2020 at 19:13):James Fairbanks said:
David Spivak Sophie Libkind here is the example of the thing that felt like a hack, in order to model the flow of susceptible people from one city to the next in our multi city SEIR model, you have 4 populations of S people, then when you do the gluing, you end up with 2 populations of S people.
Neat! That definitely has the flavor of modeling machines as resource sharers
Sophie Libkind (Apr 30 2020 at 19:13):Jules Hedges said:
Sophie Libkind Is there a paper coming on this?
Nothing started yet ...
Jules Hedges (Apr 30 2020 at 19:34):I hope you do, this is super cool stuff and should be written down
eric brunner (Apr 30 2020 at 23:32):@Brian Pinsky thank you for posting the pointer.
Nathanael Arkor (May 01 2020 at 00:10):James Fairbanks said:
I really like this presentation, closest thing I've seen to a chalkboard online.
Just finished watching the presentation, and wanted to second this: it was very clearly presented, and all the diagrams helped to keep the high-level idea present throughout. I hope to see more talks like this in the future!
James Fairbanks (May 01 2020 at 01:49):It seems like you have the lens approach which is truly oriented, where there is an asymmetric input/output and then resource sharing is truly undirected, and decorated cospans are an artificially directed version of resource sharing. In a cospan algebra you have domains and codomains, which we call input and output, but since you can always exchange a variable from input to output by bending wires, that is just an artifact of shoving an undirected peg into a category shaped hole.
I guess the answer is to build out good tools for operads and lenses so that we don’t have to use cospans to simulate operads
Paolo Perrone (May 01 2020 at 04:06):Hey all! Here's the video. The HD version will be there soon too (same link). https://youtu.be/cjti9KdXLY4
Jules Hedges (May 01 2020 at 10:44):Another thought I had. @Sophie Libkind at some point used the term "lenses" for something extremely general, for bundle morphisms = dependent lenses = container morphisms. I think @David Spivak introduced using the terminology like that in a preprint. But seeing it used in practice has made me think that it's a generalisation too far, I think these things are too general to deserve the name "lens"
Jules Hedges (May 01 2020 at 10:46):At this level, "lens" becomes pretty much a synonym for "morphism in the total category of a fibration", which is a massive level of generality. (To be fair, it's a "concept with an attitude" https://ncatlab.org/nlab/show/concept+with+an+attitude)
Jules Hedges (May 01 2020 at 10:49):Even using the term "lens" for that don't satisfy the 3 lens laws is already questionable and some people don't like it
Gershom (May 01 2020 at 17:44):I had the same feeling watching the video, but I felt like maybe I missed something and there was more structure there? Otherwise, yes, we already have a lot of great terminology about bundles and fibrations and the like, and I'm not sure if using new terminology carries better intuitions than old ones here, or just cuts off off a bit from all the already developed intuitions and technology that accompany the traditional language?
Sophie Libkind (Jul 30 2020 at 20:00):Jules Hedges said:
Sophie Libkind Is there a paper coming on this?