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I'm Cole Mathis I'm a PhD student at

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Arizona State University I'm a

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theoretical physicist I study the

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original life and I just got back from

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10 days of field work with geochemists

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in Yellowstone I already mentioned the

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title of my talk before I get started I

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want to thank a few people everyone for

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me life is awesome a research lab

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they're great these two smokes a

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constant sounding board for me they're

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both here I appreciate their input on

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all these crazy and half warm thoughts

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that come out of my head some people

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that aren't here vim deck Vito

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peel for introducing me to generative

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models and Niles layman who does auto

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catalytic sets in RNA chemistry has had

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some interesting input my advisor Sarah

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Walker she's spectacular she's super

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awesome oh and the snake river for

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nucleating the idea behind this talk in

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my head somehow also if you're wondering

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what a theoretical physicist ads for

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field work that's that's about it it's

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very theoretical all right here's a

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slightly better name for my talk so I'm

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going to talk about the emergence of

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dynamic community structure and maybe

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autocatalytic network so hopefully I can

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unpack what that means by the end of

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this talk it's a complicated idea but I

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think with excellent introductions from

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Harrison and then it'll be easier for

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you swallow and hopefully I'll

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understand what I'm saying all right so

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if you study the original life

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eventually you ask yourself this

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question right and Tessa touched on this

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earlier what is life we don't have a

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good answer but there's some features

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right it's a one feature of life that

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you might want to try to explain is all

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the diversity we find in the biosphere

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right that's one thing that's like wow

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how do we explain this diversity thats

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everywhere how can we come up with a

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mechanism to really handle that another

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thing you might be curious about is like

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life is actually this very ordered and

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structured sort of set of chemical

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reactions that have a particular

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function and operate in particular way

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so these are two different

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interpretations to this question they're

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both obviously valid answers but

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depending on what you think is more

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interesting more important you might go

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different ways right so if you're

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interested in

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diversity you know our friend Darwin

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told us there's a way to explain this

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diversity it involves things that make

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copies of themselves and a few other

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features you might study things that do

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this in this talk I'm going to focus on

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the kinds of things Ben was talking

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about which are autocatalytic sets which

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are coupled reactions that form networks

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and sometimes these networks have auto

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catalytic features where they can make

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more of themselves and everything in it

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grows exponentially so that's what I'm

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going to focus on today so here's a

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brief outline I'm going to describe my

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model which is very similar to the one

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been described and then I'm going to

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talk about some background in auto

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catalytic sets some results from the

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early 70s and some later refinements I'm

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going to mention networks and in

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particular i'm going to talk about

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stochastic block models as a type of

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generative model then i'm going to talk

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about a little bit of information theory

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describe mutual information it's easy

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don't freak out and then I'm going to

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show how to identify structure in the

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dynamics of these autocatalytic sets and

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maybe some hints that there's a phase

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transition to dynamic order in these

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things which is rampantly speculative

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but I think I can justify all right so

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my model is really similar to Ben's so

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there's this sort of background

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chemistry going on right there's great

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squares and blue squares and they can

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come together they can form these

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sequences grain blue could be one and

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zero they could be a and B whatever you

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like so there's ligation when they come

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together there's Association when they

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fall apart in my model in contrast to

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Ben's it's close mass and i explicitly

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model the degradation so that has some

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interesting feedbacks but it's very

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similar so all of these reactions for

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all possible combinations of sequences

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are possible in mind and then there are

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some catalyzed reactions so this is an

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example of the formation of this gray

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dimer could be catalyzed by the great

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rhymer right there's lots of different

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ones you could do I'm going to spend the

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entire talk talking about this

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particular network of reactions it's

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sort of obvious when you look at it it's

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a mirror image make dimers make trimers

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trimers make these trimers help things

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that go astray right so pretty simple is

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anybody confused by this yet cool all

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right it's a background on our kind of

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like set theory so if you take all of

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these

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reactions and you randomly sprinkle

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catalysts you say this molecule

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catalyzes this reaction you're

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guaranteed to get auto catalytic sets if

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the random you're guaranteed to get auto

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catalytic sets as long as the

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probability is high enough and as long

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as the polymers are long enough this is

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a result from 1970 a lot of chemists got

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really mad about it there's been a lot

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of refinements it's held up for 40 years

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at this point here's a great reference

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if you're curious about these kind of

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things didn't port act studies I'm

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extensively and he's really good at at

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handling them so now let's take a step

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back so keep this in your head keep this

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in your head here's another thing to

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keep in your head all right what are

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networks Harrison did a good job

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describing these things here's some

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example of networks right nodes and

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edges an entity and a link between

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entities right how do we describe them

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one way to describe networks is with

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what's called an adjacency matrix right

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so like this network you have one two

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three and four here right we could label

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1234 1234 we could put a zero if there's

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a no link and one if there is a link

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right simple description and then you

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could get different combinations of

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these to form different different

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matrices right so these these are two

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representations of the same thing

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similarly we could wait the edges right

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so this is a slightly different kind of

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network but all we've done is instead of

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ones and zeros on this adjacency matrix

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we've put real value numbers right the

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slight generalization ok so now that's

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in your head how do we describe networks

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one way to describe networks is with a

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thing called a generative model there's

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lots of different kinds of generative

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models and the idea here is you have a

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statistical representation of the

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network you define a set of parameters

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that you can use to generate networks

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which are statistically similar to the

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one you're interested in so for example

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here we've got three different networks

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they all have four nodes and they all

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have what four edges yeah maybe boy I

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can't count so the idea here is these

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are all equivalent they all have the

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same number of nodes at the same number

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of edges so I could make a generative

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model that says I'm going to describe my

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network by the number of nodes and the

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number of edges you can refine that a

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lot further right so generative models

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described structure

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in a statistical sense it's key point

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all right I stole these slides from a

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professor here at cu-boulder Erin closet

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he's pretty rad he put them online for

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free I don't think he'll mind they're

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great right a particular class of

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generative models for networks that have

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become very very popular are called

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stochastic block models stochastic block

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models look for community structure in

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networks so computer scientists mostly

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worried about these kinds of things and

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computer scientists like well-formed

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problems right so here's a well-formed

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problem I'm gonna give you guys a social

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network for everyone in this room right

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and then you're going to tell me if

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there's community structure in it and

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what that is right and so we know

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there's community structure in here

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right there's like a bunch of us from

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ASU there's all these see you people

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right so this might be our social

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network lots of us know each other but

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these might be the communities within it

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right this might be a su this might be

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bolder this might be somewhere else this

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might be everybody else right so you

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want to break you want to break the

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network into structures where within the

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community their links are their

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properties are similar and without the

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community their properties are different

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right it's a simple idea there's a lot

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of different ways to do with it do it

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this is a associative network right so

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where things that are similar associate

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with each other starts to look like this

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this is the inverse of that dissociative

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you don't hang out with anybody that's

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like you right this is what you should

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do at a conference right don't hang out

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with the people from your lab go meet

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other people there's ordered ones where

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it's kind of in between and then there's

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these core periphery ones which are a

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particular interest to metabolisms all

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right so what have I told you I told you

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about my model I've told you about a

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generative model for networks right I we

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can describe the structure of networks

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and statistical sense by creating a

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model that makes things like it right

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all right everybody got all this in

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their head I'm gonna add another piece

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here's information theory this is like

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page 2 of an information theory textbook

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it's not stare it's called mutual

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information if you have two variables x

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and y the mutual information between x

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and y is how much do I learn about why

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given that I know X or how much do I

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learn about x given that I know why it's

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symmetric it's totally correlation

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there's no causal anything

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you can think of it like a linear

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correlation except super generalized

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right so it's kind of like a nard

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squared value for things that are like

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so far away from linear you couldn't

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even couldn't even fathom all right so

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remember my model this is why my model

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looks right like right so what are my

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variables I've got lots of the different

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concentrations of these different

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polymers floating around right so I

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could look at a time series of these

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concentrations which is what these are

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right darker colors means there was more

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at a given time lighter colors means

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there was fewer time goes that way that

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direction okay and I could say all right

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this is one sequence and this is another

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sequence how correlated are they what's

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the mutual information between these two

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sequences I get a number right great

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simple number throat in this equation

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comes out the other end I can do this

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for all possible pairs of sequences in

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my system right up to length 6 because I

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don't want to do it forever all right

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and I can build something like this

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right so this is all these numbers where

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I've calculated what would happen what

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the mutual information between them

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would be right so now I've got a

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weighted network right this is an

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adjacency matrix for a weighted network

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where the weights on the edges are the

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mutual information shared between those

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two sequences and the nodes are the

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sequences this is capturing the dynamic

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correlations in this complicated model

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right so this is what this model looks

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like this is what the correlations look

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like now I've got the stochastic block

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model so i can ask is this structured is

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their structure there is there a

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rigorous way to characterize it and the

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answer is yes sometimes so depending on

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how effective my catalysts are structure

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emerges or a dozen in this system right

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so this is I used a different color

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scheme I'm sorry I made all these slides

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yesterday so these are the same networks

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that I just showed you this is when the

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catalyst is increases the reaction rate

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by a factor of 10 and this is when the

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catalyst increases the reaction rate by

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a factor of 1.1 it's a zero but that's

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type of right so in this case if i use a

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bayesian inference method i can be

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confident my belief can be almost unity

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that there is structure here and it's

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the algorithm kind of breaks it up into

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this core periphery structure here which

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is nice the same thing for the low

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calluses rate my belief is like barely

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better than then fifty-fifty chance I'm

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like now this is just it's probably a

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mistake like there might not be

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structure there at all it's 5050 who

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knows right so these are two limits okay

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so now what I can do is swing between

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these different catalysis rates and

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figure out what the likelihood of

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structure being seen there is which is

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what you see here man that came out

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really bad okay all right so this is is

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basically relative belief how much

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stronger do I think how much more should

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I believe that there is structure there

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then I shouldn't believe so 5050 means

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like thats toss toss of a coin you can't

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really be sure here is the catalysis

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rate so i started at 0.1 here and then

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all the way to 10 you know dislike it

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stays pretty constant all the way till

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about five five and a half and then you

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get this sharp upswing here this is

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actually very well known in a very

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different context so people have seen

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phase transitions like this in icing

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models they've seen this in the

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community detection literature in

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network science so I can't be sure yet

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because I made this yesterday but I'm

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pretty sure this is a proper phase

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transition so what do I even mean by

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that what is this phase transition

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represent running out of time so I'll

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try it out quick what do I mean all

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right do you guys know what Bernard

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cells are like if you take a thin layer

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of fluid and you heat it on the bottom

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and like for a while nothing happens but

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you turn it way up and you start to make

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these like cycles right here right can

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it the onset of convection instead of

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just conduction that's what's happening

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here this is order on the scale of the

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dynamics in the system right this is

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disordered this is ordered this is the

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transition from disordered to ordered in

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the dynamics so it's an ordered phase

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transition in the dynamics and

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all right we got time for like one

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question if it's awesome anyone anyone

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nothing so I confuse that everyone got

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one oh man I just kind of noticed that

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this catalytic increasing factor that's

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something in this very abstract model

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that you could actually relate to the

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real world is so could you perhaps go

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through and say like you know this

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catalyst this enzyme is really efficient

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so that would be more likely to cause

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more order in the system right so so

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that's what's interesting right so even

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if you have catalysts if they're not

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very effective if you're in this regime

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you're not going to see this global

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scale change hmm but they don't have to

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be that effective right so the average

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effect of the catalyst is to speed up

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the like uncatalyzed reaction by a

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factor of five right here which like we

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00:14:12,100 --> 00:14:10,010
care to the bios yeah that's not much

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for right and here where it was

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completely ordered it was only a factor

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of 10 Wow so yeah so Troy factor of a

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thousand right yeah million i did i did

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00:14:27,220 --> 00:14:23,240
this asymptotes it goes yeah yeah yeah

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um so yeah it's a good question yeah

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that's awesome all right thank you very

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much oh I'm gonna plug one more thing if

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00:14:34,420 --> 00:14:32,750
you think that scientific publishing can

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00:14:35,950 --> 00:14:34,430
be done better and you think

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00:14:37,510 --> 00:14:35,960
astrobiology can help do it you should

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00:14:39,940 --> 00:14:37,520
talk to me before we leave because I'm

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00:14:42,850 --> 00:14:39,950
really passionate about that are you

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00:14:44,200 --> 00:14:42,860
starting your own journal I I'm open to

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00:14:45,730 --> 00:14:44,210
anything I'm gonna try to get everybody

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00:14:47,470 --> 00:14:45,740
on free prints first and then we could