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okay hello my name is a benin toy and

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today i would like to present the

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effects of a spatial diffusion on a

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model of peopie iike revolution worked

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i'm doing with my postdoctoral advisor

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professor Halle and collaborator iron

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wine being all at the university of

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minnesota-twin cities so some are quick

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motivation a protein first origin of

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life model can resolve against paradox

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which is the low probability of

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generating a randomly constructing a

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starter naked gene and we assume an

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initiative enters the formation of a

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network of interacting molecules assumed

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to be polymers but not necessarily

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proteins we have a no genome and we

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assume that it comes much later and

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unlike previous similar models we assume

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here that a necessary condition for a

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pre biochemical system is it is that it

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may be that it be a stationary state out

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of equilibrium so real quickly would

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like to go over a caufman like binary

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polymer model so my reactions are

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ligation and our ligation incision of

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binary polymers so here I have just an

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example reaction so 0 10 plus 10

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catalyzed by polymer 11 gets ligated in

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2010 10 and then the opposite direction

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is a season and so to make our network

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give it a maximum polymer length value

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which we call L max which is a parameter

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in era and our model we go through each

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possible reaction of the form a plus B

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goes to a be catalyzed by C and included

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in the network with probability P which

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is another primary model and the

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chemical species in the network form an

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autocatalytic set which will be

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elaborated on in coal Matthysse's talk

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preceding mine and so for dynamics we

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come with our chemical network that we

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just made we combine it with reaction

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rates to generate an artificial

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chemistry then so classically simulate

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the following a master differential

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equation so NL is basically the number

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of polymers of species L and all these

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terms represent the reaction rate self

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in a ligation incision and the

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parameters in our model are p l max the

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number of food particles and the maximum

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number of particles that we can have in

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our system now i'd like to just give a

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brief general structure of what we did

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so for

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different p values we generate multiple

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networks typically 10,000 and that check

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if they're viable and all viable means

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is that it's possible to go from the

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food set all the way to a molecule

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amount of length l max given the

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reactions in the network and then we do

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then we do multiple dynamical

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simulations with the random with random

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dish with random initial conditions

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using a given by little Network combined

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with reaction rates until a steady state

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is reached so here you know these have

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them the viable networks labeled in blue

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and then the non viable my clitoris

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labeled in red and so for each viable

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network we didn't actually assist

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dynamic we do dynamic runs and depending

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on whether or not they're in a 0 and

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then we count basically after we run

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into steady stages reach we count the

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number of life like steady States by

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checking if the systems out of

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equilibrium so basically with these runs

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we just check if they're out of

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equilibrium or not and with this we now

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have a measurement for the public of a

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forming of life-like state for a given

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value of P so I would like to go over

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where Kaufman in our group differ

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someone Kaufman simulated these models

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he saw population growth with increasing

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p so here i have a little example or red

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is the population as a function of time

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simulation time we see that increases

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over the system might be growing but it

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might be chemical in chemical

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equilibrium so here I have these two

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runs with the same pic p value in

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artificial chemistry and also the same

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chemical network and this one although

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it's growing which is a chemical

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equilibrium and here in the green line I

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have a measure what we mean by a

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chemical equilibrium or one is where the

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system is chemical equilibrated in 0 as

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the system is not chemically

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equilibrated we see that this one

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reaches chemical equilibrium whereas

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this one grows to a maximum what stays

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out of a chemical equilibrium and is

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trapped in kinetically trapped in the

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nonequilibrium steady state which we

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postulate be a necessary condition for

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life and that this non-equilibrium

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constraint reduces the probability of

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life like systems at large p given the

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maxim giving a maximum value at a small

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value p so here i have a figure from a

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previously published paper where i have

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the

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value or p 0.005 so now I'd like to

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explain you know how do we how close the

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system is that chemical equilibrium we

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use a entropy so a core screen by Palmer

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length so NL basic NL is the number of

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followers of length l and we have a

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distribution of these for all the

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different lengths and i given maximum

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state the number of possible

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configurations is given as w given as

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this formula and we say the entropy is

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defined as s which is equal to KB log W

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and this is a thermodynamic more of a

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thermodynamic entropy rather than from

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information and should be we say

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chemical equilibrium is reached when any

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this entropy is maximized which we call

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seq with the constraint that there in

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total molecules of the system and we

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simulate until steady state and

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concerted life like if the entropy is

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less than alpha times seq where alpha is

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a parameter in our model that's between

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0 and 1 so now like to go into why we

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want to extend this to diffusion through

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space and motivations so wondering how

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my spatial structure effect prebiotic

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evolution and so from force of

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motivations wondering if the non

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equilibrium states of the model without

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diffusion survive interaction with the

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environment through diffusion so this

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gets into the cup arm

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compartmentalization that the test was

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going over earlier and we're also

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wondering if their collective effects

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which might suggest the beginnings of

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multicellularity so this sort of goes

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into complexity so now I'd like to go

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over our Spacely extended model we study

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64 sites arranged as an eight-by-eight

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to the periodic lattice and you have a

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little sketch where these squares

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represent sites and insight an inside

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each site there's the same our official

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chemistry and our molecules are allowed

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to diffuse from site to site at a at a

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rate parameterize by ADA and due to

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computational limitations we sell it we

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set a l max equal to 6 so now that we

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have a space under model not only can be

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chemically equilibrating diffuse if you

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leak will rate so i just wanted to go

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over how we can parse out the system to

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be partially and completely

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equilibria so now that we have space in

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the model or a purple our polymer length

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distribution also depends on a space

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which we coli and we call it and we call

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we label that point P in this macro

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macro state space with them with the 384

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dimensions and like i said before can be

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diffusible equilibrated which we call

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the diffusive lee did and locally live

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that just means all the particles of

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length L are evenly distributed across

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lettuce and has a different distribution

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is so and we label at PD on this macro

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space and the system can also be

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chemically equilibrated at each site

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which we call diffusive lee live locally

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dead and that just we label that as pc

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on this macro space the system could

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also be chemically and diffusive lee

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equilibrated and which we call total

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equilibrated and we just called dead and

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if it is not diffusive lee or chemically

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collaborated we call it the diffusive

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lee live in locally life and so how to

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how the check how far the system is away

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from these different partial equilibria

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we basically take the Euclidean distance

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between the distributions so we have the

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distributions of the system point and

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the what it should be if it's partially

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that in this case partially the

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partially diffusely equilibrated and we

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just basically take your Clayton

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distance we call that rd the distance

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between the system point and the point

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out which is diffusive lee equilibrated

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in our see the distance between the

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system point and the point on which it's

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chemically calibrated at each site so

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now i just want to show an example of

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results for these two distances in a

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simulated non-equilibrium steady States

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so here's a really to look at this so

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this is a scatterplot with to about

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20,000 runs or the color of the point

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denotes the HP ratio and and note that

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we already require that the entry ratio

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to be less than 0.6 and these to

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normalize distances that I defined

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earlier so now with the scatter plot we

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can start labeling these steady states

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depending on how far they are from

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either being diffusive Lee or chemically

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equilibrated so if the system is

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diffusive Lee equilibrated so it's close

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to this too it's a diffusive

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equilibrated point of far away from its

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chemical equilibrated point we call it

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diffusely dead locally alive so the

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points in here are considered dee dee la

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if it is system is chemically

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collaborated but far away from its

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diffusive the equilibrated point we call

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the system diffusely a live locally did

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and in which in which you will encompass

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all the points in this compartment and

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then if the system is both far away from

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being chemically Enda feasibly

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equilibrated we say it's the fuse of the

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alive and locally alive and it will end

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would be all the points in this part now

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with this we can start forming

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probabilities so here i have the

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probabilities of forming these three

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states which are the high taxes on all

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these plots as a function of P data so p

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is that width axis and the ada is the

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depth axis on all these plots and some

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things the note is the probability of

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finding these da LD tald states is

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fairly low compared to the others and

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that we get the similar results with the

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single site model for the DD la states

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or starting from p equal to 0 and

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increasing key we see that the

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probability formula flights state goes

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up and comes back down well that's not

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the case when we look at these diffusely

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and locally alive states or the

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probability formula lifelike state seems

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to taper off even at the seams that

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there seems to be still life like states

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even at a high p value so looking at

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these states we see that they display

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these cancer like explosions so here i

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have the entropy ratio as a then this is

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for a single run i have the entropy

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ratio as a function of time and we see

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that in the it starts off in some metal

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stable state where we don't consider it

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live because it's HP ratio is greater

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than 0.6 but after some time and all sun

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the system goes down into another stable

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into another metastable state where it

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is now considered a life since it's it

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is its entropy ratios less than 0.6 so

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looking at a screen shot before and

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after this jump we see that before the

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jump that they're rough they're less

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than 100 non food particles per site but

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after the jump with it at this bread

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eggs we see that all of a sudden

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the number of food particles on one and

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one side goes up to 900 so this would be

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considered the pulley diffusely out of

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equilibrium since all the particles are

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mostly on one side and no pep this is

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for a very very low value for ADA so if

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we increase say that we see that we see

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in a collective effect where within were

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these this explosion spreads so here i

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have the same the ratio of the entropies

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as a function of time and we see like

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before it starts off in some type of

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metastable state and then right before

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this is a cliff it we see one side

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explode and then in that explosion will

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spread to other sites before it reaches

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a minimum and then we see the entropy

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ratio go up to one since the system is

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starting to be totally equilibrated so

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just serve some conclusions I've stated

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most of this before there were you know

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we started we kind of likelihood it as a

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function of PA de these lifelike States

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cataract characterized as da la da LD

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and DD LA and we see that these DD LA so

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you see that the dvla States closely

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reproduced the states in earlier single

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site model these da LD life likes states

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are rare the ala exhibit he's explosive

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like growth and then for some future

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work we'd like to explore some other

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forms of spatial I'm homogeneity which I

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have listed here thank you we have time

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for some questions hi very interesting

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talk I am wondering about the polymers

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which polymer stating are possible on

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earth like since you would it be well

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that's the thing we'd yeah we didn't

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have that much yeah because we wanted to

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be as abstract as possible so we didn't

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we didn't want to have any like

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terrestrial life like bias in our models

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so that's why we have a you know very

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simple simple model but we don't there

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are couple applications but I can't

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as a no to that question there are at

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least a couple laps where people have

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looked at these types of systems and RNA

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chemistry as well as like peptide

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chemistry so it's except the RNA I was

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wondering is there other possible

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palmers any other question okay next we