Chico Camargo Hey man! I hadn't seen the recording, that's cool! I'll send you the slides via email. What diagrams do you want, just to make sure I send you the right thing? Guillermo Valle Pérez 4/22, 12:56pm Guillermo Valle Pérez Well the ones where you show the tree of binary states evolving to other states, and the ones showing the complexity vs frequency for example Chico Camargo 4/22, 12:59pm Chico Camargo Here's the whole thing - https://docs.google.com/presentation/d/1l-IgqXy1ZdBn__aBQX0fUH8Z2y6iuogwt753omsiyAw/edit?usp=sharing

29-06-2015 - Evolution 2015 Guaruja What Darwin didn't know: natural variation is structured Chico Camargo University of Oxford Evolution 2015 Guarujá, Brazil docs.google.com Chico Camargo 4/22, 1:01pm Chico Camargo Just one thing - recently I've changed my definition of phenotype to something more coarse-grained, so the plots for complexity have changed. But they're fine, the new ones say the same as the old ones. The robustness things, however, don't apply so directly to the new phenotype definition I've been exploring, so I would not include that part about robustness. All the rest is fine! Chico Camargo 4/22, 1:03pm Chico Camargo Finally, an interesting paper, in case you haven't seen it: http://rsif.royalsocietypublishing.org/content/royinterface/12/113/20150724.full.pdf Chico Camargo 4/22, 1:03pm Chico Camargo They say some cool stuff there, like "The properties of genotype –phenotype (GP) maps have been studied in great detail for RNA secondary structure. These include a highly biased distribution of genotypes per phenotype, negative correlation of genotypic robustness and evolvability, positive correlation of phenotypic robustness and evolvability, shape-space covering, and a roughly logarithmic scaling of phenotypic robustness with phenotypic frequency. More recently similar properties have been discovered in other GP maps, suggesting that they may be fundamental to biological GP maps, in general, rather than specific to the RNA secondary structure map." Guillermo Valle Pérez 4/22, 2:53pm Guillermo Valle Pérez Yeah i've seen that paper. I've found a way to predict more or less the number of sequences that map to the most frequent sequences, in average over the ensemble of transducers. It's only approximate, but it is about thinking about certain kinds of cycles, and how simpler cycles in the transducer are more probable, so sounds similar to your boolean network cycles thing. It's also related to the idea about constrained and unconstrained parts, which I think is the most fundamental. The idea for transducers is that there are states that give the same output independent of the output (so they are unconstrained). Outputs that admit cycling through these states have most of the input bits unconstrained. Then if one looks at what kinds of cycles there are, one sees that the most probable are the simplest ones, and these correspond to simple outputs Guillermo Valle Pérez 4/22, 2:59pm Guillermo Valle Pérez It's not totally rigorous, but estimating the probabilities of these cycles roughly gives the right frequency of the most probable strings like 11111111.. 011111111, 101010101... etc Chico Camargo 4/22, 3:02pm Chico Camargo That is very interesting! On the boolean networks it turns out that the probability of a cyclic output is an exponential with the cycle length, but the complexity bias exists even for cycles of the same length I still don't understand how the GP map works though, maybe because I don't fully understand what a transducer really is. What is the genotype and the phenotype (and the mapping), in their case? Guillermo Valle Pérez 4/22, 3:04pm Guillermo Valle Pérez grrwhen i said above "same output independent of the output" i meant "same output independent of the input"... Chico Camargo 4/22, 3:04pm Chico Camargo Oh yeah I god that grin emoticon So, I understand that a finite state transducer is like a finite automaton, but with two tapes: an input tape and an output tape reads a tape and writes another Guillermo Valle Pérez 4/22, 3:05pm Guillermo Valle Pérez http://galaxy.eti.pg.gda.pl/katedry/kiw/pracownicy/Jan.Daciuk/personal/thesis/img74.gif

Guillermo Valle Pérez 4/22, 3:07pm Guillermo Valle Pérez its a finite state machine. You start at a certain state and move to the state according to the symbol you read and following the transition according to the first symbol in "x/y". When you follow that transition you print a "y" oh sorry in that picture i showed you the x and y are swapped relative to my convention that picture isnt ver good wait Guillermo Valle Pérez 4/22, 3:09pm Guillermo Valle Pérez Guillermo Valle Pérez 4/22, 3:09pm Guillermo Valle Pérez thats one of the ones generated by my actual code sideways lol Chico Camargo 4/22, 3:09pm Chico Camargo Beautiful! Ok, it's a finite state machine with two tapes, rather than just traversing (and accepting or rejecting) an input string, it translates an input string to an output string Guillermo Valle Pérez 4/22, 3:09pm Guillermo Valle Pérez so you begin at state 0 and if you see a 0 you go to state 0 printing a 0, and if you see an 1 you go to state 1 also printing a 0 Chico Camargo 4/22, 3:09pm Chico Camargo Cool So you randomly generate a finite state transducer, and see how many input words give you each output word? Guillermo Valle Pérez 4/22, 3:10pm Guillermo Valle Pérez Yep Chico Camargo 4/22, 3:11pm Chico Camargo And the trends are the same even if you generate a lot of those transducers at random? Guillermo Valle Pérez 4/22, 3:11pm Guillermo Valle Pérez yeah the more you generate the more the graph seems to be a linear thing with a given spread in the frequency-vs-complexity, like the one i posted technically you could enumerate all transducers of a given number of states Chico Camargo 4/22, 3:13pm Chico Camargo So the trend is there even if you have a single transducer, but it's more obvious if you plot the results for a lot of them, is that what you're saying? I have more questions: How long are the input strings? How long are the output strings? You said you can enumerate them. How is the transducer represented? I was reading some stuff about formal language theory last night, and it relates so much to that, you have no idea Guillermo Valle Pérez 4/22, 3:14pm Guillermo Valle Pérez Well, the trend is mostly visible if you plot a lot of them. For a single one I tend to find quite some noise. The input strings ive tried are 9-15 bits long, but they can be anything I've made it so that the output strings are the same length as the input. I could make the variable length by adding an "empty" symbol as a possibility but havent tried that The transducers are represented as strings too I think, but I'm using a finite automaton generator, not generating them on my own because it's not that trivial to generate them really uniformly apparently. I think it's because many automatons would be equivalent, and it only generates distinct ones.. Chico Camargo 4/22, 3:17pm Chico Camargo I see Guillermo Valle Pérez 4/22, 3:17pm Guillermo Valle Pérez Tho I'm not sure how it's generating them under the hood tbh, atm Chico Camargo 4/22, 3:17pm Chico Camargo Sure Guillermo Valle Pérez 4/22, 3:18pm Guillermo Valle Pérez and i dont think the answer should be too different if you generated them in a more naive way Chico Camargo 4/22, 3:18pm Chico Camargo I agree with you One thing I'm trying to understand is what space is being mapped to what space But I'm slowly getting it Any string to any string. (well, binary strings in both alphabets, in this case) Guillermo Valle Pérez 4/22, 3:21pm Guillermo Valle Pérez yeah you can choose any alphabet. But i chose binary. and in my case its any binary string to given length to the same set well no there are some strings you can't get in the output so the output space is some subset of {1,0}^* {1,0}^n, n fixed i mean Chico Camargo 4/22, 3:23pm Chico Camargo And there are binary strings that can't be generated by that transducer. Sure Guillermo Valle Pérez 4/22, 3:23pm Guillermo Valle Pérez Yeah quite a few actually which make sense Chico Camargo 4/22, 3:24pm Chico Camargo It does. Guillermo Valle Pérez 4/22, 3:24pm Guillermo Valle Pérez becuase if there is redundancy, the phenotype space must be smaller, for a deterministic map smaller than genotype space Chico Camargo 4/22, 3:25pm Chico Camargo And because each transducer will in fact produce strings of a given shape, like "0 1^n 0 1 0^m 1" And when you choose the number of states in your transducer.. I would imagine I imagine very large transducers would be unnecessarily complex Guillermo Valle Pérez 4/22, 3:27pm Guillermo Valle Pérez well i choose a small number of states, like 5 so that it's simple Chico Camargo 4/22, 3:28pm Chico Camargo Yeap Guillermo Valle Pérez 4/22, 3:28pm Guillermo Valle Pérez I've tried more states and results are not too different, but I worry that I am taking a sample that is much smaller than all possible trandsucers of that size With smaller number of states like 2 or 3, maps seem too trivial also Chico Camargo 4/22, 3:30pm Chico Camargo I'd expect that the complexity bias would become too messy if the transducers were too large: you'd be using a very complex algorithm to map input to output, introducing a lot of complexity into the business I find it interesting that when you sample different transducers, you're sampling different GP maps. ...which is something that can evolve, as well. Just like you can change the parameters of an ODE instead of changing its initial conditions, you can change the GP map instead of its I/O Guillermo Valle Pérez 4/22, 3:32pm Guillermo Valle Pérez what i can't quite figure is how to relate these results more directly to other results like that of the boolean network or polyominoes. Yeah, in principles these things should map to a transducer, but how simple a transducer, and do they have some features that simply the {ensemble of all transducers} does not capture. I mean this is precisely the same problems with choosing random network null models in network theory.. Guillermo Valle Pérez 4/22, 3:32pm Guillermo Valle Pérez Yeah i also expect more noise for more states.. Chico Camargo 4/22, 3:33pm Chico Camargo So, normally a boolean network is the genotype, so your input string in this case. Same for an RNA sequence. Your transducer would be the actual map Guillermo Valle Pérez 4/22, 3:35pm Guillermo Valle Pérez "which is something that can evolve". Yeah the whole reason I did was just in the spirit of null models: see if one expects these features just looking at random simple maps, without any other constraint. But I also thought about, why choose the transducers uniformly at random, why not sample them according to the biased output of another transducer, that will produce simpler transducers more often. One can imagine a potentially infinite chain of GP maps determining GP maps, and it'd be interesting to see what one gets.. Guillermo Valle Pérez 4/22, 3:35pm Guillermo Valle Pérez Yeah the whole reason I did -> Yeah the whole reason I did this Chico Camargo 4/22, 3:36pm Chico Camargo I agree with the spirit of null models: that is totally the point Hoho, I know what you mean! In fact I think there is something else to it Guillermo Valle Pérez 4/22, 3:37pm Guillermo Valle Pérez Yeah this looks like whats called hyperparameter optimization in machine learning: when you optimize your machine learning model itself Or genetic programming with evolving GP maps, which has also been tried Another way to do this would be to make a transducer whose output changes the transducer itself, and see how that evolves which tbh sounds like the whole idea of genetic regulatory networks where the phenotype (proteins) in some sense change the GP map (genes->proteins) I guess when one does this one can then still define a meta GP map like what you do in the boolean networks Chico Camargo 4/22, 3:41pm Chico Camargo I think so Coupling GP maps is an interesting idea But you've gotta play with the timescales that that involves For example - also on that potentially infinite chain of GP maps you mentioned: Chico Camargo 4/22, 3:42pm Chico Camargo So, this chain of GP maps determining GP maps is sequential: once, in the history of life, life "chose" a set of basepairs, A-T, C-G. And it's been working pretty much with all that. And by "choosing" I mean that its rate of change slowed down. It could be from reaching a fitness peak, local or not, but the fact is that it slowed down. Then, at some point, life "chose" a genetic code: the way codons map to aminoacids. Once that choice was frozen, life has been working with it ever since. Then it chose some protein families. It chose chromosomes. Yada, yada, yada: (pretty much) frozen choices allowing more complex forms to emerge. And you could argue that the genetic code and these other things are still changing, but they're just changing very slowly, while other things change more quickly Guillermo Valle Pérez 4/22, 3:43pm Guillermo Valle Pérez Hm, I see what you mean Chico Camargo 4/22, 3:43pm Chico Camargo In a similar fashion, I see that with language. We aren't really changing our alphabet, or our grammar structures anymore, it seems like those evolved once and stopped, but they're just changing slowly. On the other hand, new words still appear all the time I think it makes total sense to get the transducer from a set of transducers - but if you're picking a simple transducer, you're probably already doing that Guillermo Valle Pérez 4/22, 3:44pm Guillermo Valle Pérez well im picking simple ones in the sens of small number of states Chico Camargo 4/22, 3:45pm Chico Camargo If the transducer can really be represented as a string, then I'd be sure of that Guillermo Valle Pérez 4/22, 3:45pm Guillermo Valle Pérez but i haven tried generating transducers from a transducer yet but in your example above it seems like it would like generating random transducers and then fixing to one. Then using that fixed transducers as maybe a building block out of which new meta transducers can be built... tho im not sure i understand where GP maps fit in all the biological examples you mention above Chico Camargo 4/22, 3:49pm Chico Camargo a GP map is a translation, an I/O machine, a transducer. Something that converts information of a kind into information of another kind Guillermo Valle Pérez 4/22, 3:50pm Guillermo Valle Pérez first the atcg is an alphabet, not a GP map right? Then it evolved the codon-aminoacid, which i see its a GP map. What is the protein family, and what do the chromosomes have to do with a GP map? i mean I would understand that gene-> protein is a GP map. Then protein->some cellular phenotype is another one.. Chico Camargo 4/22, 3:52pm Chico Camargo Ok, point taken, the ATCG is not a GP map. It is an alphabet. Let me put it this way: Chico Camargo 4/22, 3:59pm Chico Camargo Nature chooses a way store information, then it pretty much settles for that one according to some criteria like thermodynamical stability and to how much information you can store with that system - for instance, ATCG basepairs. Or, another way to store information, aminoacids. So now we have two alphabets, one with four letters, one with ~20. Then, once those had been pretty much chosen, eventually nature chose/found a way to translate between them. Or maybe it found the latter alphabet as an outcome of finding the GP map that converts information stored in DNA sequences to information stored in aminoacid sequences. But anyway, it chose the alphabets, then it chose the GP map. Focusing on the GP maps: DNA-> Proteins, Protein shape-> Protein function in the cell, gene networks -> cellular phenotype, cell type composition -> tissue structure/function/identity, whatever mapping from one kind of information to another (but just mappings, so nothing about the chromosomes I had mentioned). My point is that I think often nature tries many "transducers", many I/O machines, and eventually it chooses some of them, and builds on top of them. So the I/O alphabets and GP maps are conserved along evolution. In this sense, humans probably use the same cell types as other apes. And we all use the same body plans as other mammals. And the same embryonic development genes as worms. Etc etc downards, ad infinitum. Chico Camargo 4/22, 4:01pm Chico Camargo I'm saying this because some structures evolve quickly and others don't: in the hierarchy of which genes regulate which other ones, the further up a gene is placed, the less it changes over time: the more conserved it is. And I think that makes total sense, considering that it is part of a GP map that was "chosen" long ago Guillermo Valle Pérez 4/22, 4:02pm Guillermo Valle Pérez and because many things depend on it, it's hard to change right? Chico Camargo 4/22, 4:02pm Chico Camargo that too in theory you could change it, but today that'd mean a drastic reduction on fitness it'd be like trying to reinvent the genetic code: it won't work, life relies too much on that Guillermo Valle Pérez 4/22, 4:03pm Guillermo Valle Pérez that's what I mean, unless you change many things along with it, in just the right ways.. which is highly unlikely Chico Camargo 4/22, 4:03pm Chico Camargo Exactly That'd be like changing the English grammar, or semantics On the other hand, if the evolutionary innovation is pretty fresh, there's probably not much relying on it, so it's ok to break it Guillermo Valle Pérez 4/22, 4:06pm Guillermo Valle Pérez This is just why it's so hard to say switch from qwerty to dvorak keyboards, it's changing your whole word-hand movement GP map, on which your whole internet life depends Chico Camargo 4/22, 4:06pm Chico Camargo haha yeah! So, I think the easiest story you can tell is that a transducer is a very simple a GP map, without all the biological details. Which features did you say are not captured by the transducers? Guillermo Valle Pérez 4/22, 4:09pm Guillermo Valle Pérez Well in theory all GP maps should potentially be expressed as transducers, though probably of many more states. Having 5 states is like considering the set of sufficiently coarse-grained biological models I suppose.. Chico Camargo 4/22, 4:11pm Chico Camargo Hm, there is one thing I still don't see What you said resonates very well with the ideas in that paper I sent you: that all these properties come from the sequence nature of genotypes and phenotypes or genotypes at least. and sequences = I/O strings, great Guillermo Valle Pérez 4/22, 4:13pm Guillermo Valle Pérez If you consider any number of states, transducers pretty much include everything else.. But I'm only considering simple ones. A simple transducer can either be justified as some process during the earliest stages of evolution of some form of life (natural or artificial) where the system itself is actually simple. Say a few dots in game of life, or a few molecules. Then the justification to apply to more complex life is probably the same as why we use coarse-grained models: yeah life is full of intricate details, but it is organized in such a way that is approximately simple. I think this would like saying complex life is really behainv as a transducer with many many states, but this transducer is coarse-grainable to a transducer of few states. This actually agrees nicely with the idea that life current GP maps were in some way determined by previous GP maps, and thus are expected to be simpler than just a random GP map from ATCG to tissue... Chico Camargo 4/22, 4:14pm Chico Camargo Yeah I'm happy with that there is only one thing that I still fail to agree/understand A transducer translates input to output by treating the input as an (ordered) string: it first reads the first character, then the second, then the third And even though the map in the end is from string A to string B, it's calculated from this step-by-step reading Guillermo Valle Pérez 4/22, 4:15pm Guillermo Valle Pérez that's how it "mechanically" works yeah Chico Camargo 4/22, 4:16pm Chico Camargo Yeah But for example, a gene network. The network, really. It can be written as a string, but you can also do any permutations on the gene order, and that'd give you a different string. The GP map for gene networks is also from string to string, but it doesn't rely on reading anything step by step and it's harder for me to talk about "what parts of the string are unconstrained", for instance Guillermo Valle Pérez 4/22, 4:17pm Guillermo Valle Pérez "written as a string, but you can also do any permutations on the gene order, and that'd give you a different string." but it'd give you the same network, you mean? Chico Camargo 4/22, 4:17pm Chico Camargo It'd give you a network that is isomorphic to it (like, B->A instead of A->B). That could possibly give you the same phenotype or an isomorphic phenotype. Hm Guillermo Valle Pérez 4/22, 4:18pm Guillermo Valle Pérez but i mean, if you have some map from finite strings to finite strings, it is always in principle writeable as a finite transducer Chico Camargo 4/22, 4:18pm Chico Camargo Oh. That's true. Guillermo Valle Pérez 4/22, 4:18pm Guillermo Valle Pérez the transducer may be quite large though Chico Camargo 4/22, 4:18pm Chico Camargo There's a theorem that does that, right? that says that shit. That's awesome. Guillermo Valle Pérez 4/22, 4:19pm Guillermo Valle Pérez yeah... I mean it's kind of floating around the results of turing and church and co. I think A Turing machin is just a kind of finite transducer with infinite memory so like infinite number of states.. Chico Camargo 4/22, 4:20pm Chico Camargo yeah yeah Guillermo Valle Pérez 4/22, 4:20pm Guillermo Valle Pérez But the thing is that a map between two finite sets can always be expressible with finite memory Chico Camargo 4/22, 4:20pm Chico Camargo no, there is, I'm sure I read this theorem yesterday, it's all coming back Guillermo Valle Pérez 4/22, 4:20pm Guillermo Valle Pérez ah cool Chico Camargo 4/22, 4:21pm Chico Camargo What I actually read: Guillermo Valle Pérez 4/22, 4:21pm Guillermo Valle Pérez You can make your own! Map any finite set of inputs to any output: http://examples.mikemccandless.com/fst.py?terms=pepe%2F33%0D%0Amoth%2F1%0D%0Apop%2F2%0D%0Astar%2F3%0D%0Astop%2F4%0D%0Atop%2F5%0D%0A&cmd=Build+it! examples.mikemccandless.com examples.mikemccandless.com Chico Camargo 4/22, 4:23pm Chico Camargo There is a correspondence between formal grammars (sets of strings) and automata (that might accept or reject a string, saying that it does or doesn't belong in that grammar). Finite grammars map to finite automata, Context-free grammars to push-down automata, and so on, Until phrase structure grammars that map to Turing machines. Grammars and finite automata are slightly different from FST, but I'm sure there must be a version of that theorem that talks about FST. Chico Camargo 4/22, 4:24pm Chico Camargo Ah brilliant! That's really interesting, since any finite set is enumerable (and more specifically enumerable in binary), any finite set can be translated to strings. But that alone doesn't mean that you would have any bias of any sort Now it's clear to me that it isn't about the sequence order, as in which part comes first, but simply from the hypercube nature of the space of sequences Guillermo Valle Pérez 4/22, 4:31pm Guillermo Valle Pérez See page 20 of http://web.cs.ucdavis.edu/~rogaway/classes/120/spring13/eric-transducers.pdf there it effectively says what we want, that they can encode any map between finite sets web.cs.ucdavis.edu web.cs.ucdavis.edu Guillermo Valle Pérez 4/22, 4:32pm Guillermo Valle Pérez what is comes "from the hypercube nature of the space of sequences"? Chico Camargo 4/22, 4:32pm Chico Camargo yup! I see it Guillermo Valle Pérez 4/22, 4:33pm Guillermo Valle Pérez Also the bias comes from constraining the maps to be simple in the sense of few states in the fst, I think. Clearly if you considered all possible maps between two sets there wouldn't be bias in average i meant: what comes "from the hypercube nature of the space of sequences"? my internal fst is making so many mistakes.. Chico Camargo 4/22, 4:34pm Chico Camargo I agree that if you considered all the possible FST you wouldn't get any nice average, you need simple FSTs haha have you switched to dvorak? Chico Camargo 4/22, 4:34pm Chico Camargo What I mean is that the paper I sent you they say: "The Fibonacci GP map therefore offers strong evidence that the sequential nature of biological information determines the fundamental structure of GP maps, which in turn has a profound impact on the course of biological evolution." Guillermo Valle Pérez 4/22, 4:35pm Guillermo Valle Pérez no i meant internal as in in the brain. I wanted to swithc to dvorak but havent had time tongue emoticon Yeah I didn't get that part Chico Camargo 4/22, 4:35pm Chico Camargo And when they say "the sequential nature", I think it suggests that the fact that information is stored in ordered sequences. But I think it isn't so much about that Guillermo Valle Pérez 4/22, 4:35pm Guillermo Valle Pérez Yeah I thought it was more about it having constrained and unconstrained parts which doesnt say anything about how the information is stored/read Chico Camargo 4/22, 4:36pm Chico Camargo Yeah. I think the order doesn't really matter. exactly. and the unconstrained parts could be in the beginning, middle, end, or just have no order Guillermo Valle Pérez 4/22, 4:37pm Guillermo Valle Pérez yeah, in fact in the fsts unconstrained parts are not a fixed portion of the input string, but depend on the previous portions of the input string Chico Camargo 4/22, 4:37pm Chico Camargo as long as you have an unconstrained part whose contribution to the designability of your phenotype size grows exponentially (or just a lot) with the size of the unconstrained part: like 4^L, in the case of RNA, or 2^L in the binary case Guillermo Valle Pérez 4/22, 4:38pm Guillermo Valle Pérez "An unconstrained part" should more correctly be a property of the FST mechanism than a part of the input string. In the FSTs, an unconstrained part is a state whose outputs are the same irresepective of input. Chico Camargo 4/22, 4:39pm Chico Camargo indeed unconstrained means ignored by the GP map Guillermo Valle Pérez 4/22, 4:40pm Guillermo Valle Pérez In the case of the FSTs as you grow the length of the input, the input has more chances of looping through these states and everytime you go through it the number of possibilities multiplies by 2, so it grows almost exponentially Chico Camargo 4/22, 4:40pm Chico Camargo so if the GP map doesn't care about sequence/string order, the unconstrained parts of the genotype won't be ordered, won't be "after a stop codon" yeah Guillermo Valle Pérez 4/22, 4:41pm Guillermo Valle Pérez well there may be some order to them, but may be more complicated and subtle, and not-apparent Chico Camargo 4/22, 4:43pm Chico Camargo but see, a gene network isn't ordered per se. When you decide to represent it as a string, sure, you've ordered it. For the same GP map, different orderings will produce different transducers, and therefore different orderings of the unconstrained parts, but there is no inherent order on a gene network Chico Camargo 4/22, 4:44pm Chico Camargo There is, though, an exponential contribution to designability: 3^X, where X is the number of "unconstrained" interactions Guillermo Valle Pérez 4/22, 4:44pm Guillermo Valle Pérez And you can actually construct GP maps where the bias is towards some designed complex sequence instead of towards simple ones. However these require very special kinds of structures with the sequence coded into it, while a bias towards a simple output requires a simple structure, and thus appears often in FSTs Chico Camargo 4/22, 4:45pm Chico Camargo precisely. Guillermo Valle Pérez 4/22, 4:46pm Guillermo Valle Pérez yeah i agree that for the network the output shouldnt depend on the ordering. However, maybe due to the nature of the FST different ordering conventions may need different FSTs Chico Camargo 4/22, 4:46pm Chico Camargo Yeah Guillermo Valle Pérez 4/22, 4:47pm Guillermo Valle Pérez "3^X, where X is the number of "unconstrained" interactions". what are the uncstrained interactions? Chico Camargo 4/22, 4:47pm Chico Camargo the genotype for a gene network is the network's directed graph each link between nodes A and B can be +, -, or non-existent (0). That's what I called 'interactions': these links Guillermo Valle Pérez 4/22, 4:49pm Guillermo Valle Pérez and it is unconstrained if it doesnt affect the phenotype you define? Chico Camargo 4/22, 4:50pm Chico Camargo Exactly. When I said "There is, though, an exponential contribution to designability: 3^X, where X is the number of "unconstrained" interactions", I meant that if there are X interactions that can be a +, a - or an 0 and that won't make a difference for the resulting phenotype, they'll be increasing the designability of that phenotype by 3^X. Guillermo Valle Pérez 4/22, 4:53pm Guillermo Valle Pérez It'd be interesting to find the actual FST for the network description to cycle/phenotype and see if those unconstrained parts can be seen as unconstrained states in the fst Chico Camargo 4/22, 4:54pm Chico Camargo I mean, if for every GP map there is a FST, it should be I'm still pondering This sequence story: The cause for all these properties would not be "sequential nature of biological information", but the fact that in nature you often have unconstrained parts whose contribution to the designability of your phenotype size grows exponentially. Guillermo Valle Pérez 4/22, 4:58pm Guillermo Valle Pérez Yeah Chico Camargo 4/22, 4:58pm Chico Camargo Well, it's from the same principles behind PCA, that most things need a short description that's sloppiness, essentially Guillermo Valle Pérez 4/22, 4:58pm Guillermo Valle Pérez PCA? Chico Camargo 4/22, 4:59pm Chico Camargo Principal Component Analysis. It's a technique that effectively reduces the dimensionality of a dataset by finding a set of axes (the base, in linear algebra terms) where most of the variation in your dataset can be described by the first axes Guillermo Valle Pérez 4/22, 5:00pm Guillermo Valle Pérez Ah yeah. Yeah I mean, we are trying to find (at least part) of the explanation of the simplicity in the word smile emoticon Chico Camargo 4/22, 5:01pm Chico Camargo in the word and in the world? wink emoticon Guillermo Valle Pérez 4/22, 5:02pm Guillermo Valle Pérez haha yeah lucky mistake Chico Camargo 4/22, 5:02pm Chico Camargo Man, I'm really hungry, I gotta get some lunch But let's keep talking about this! This is really exciting, and it's awesome to talk to you about that grin emoticon Also, would you send me your code so I play with it as well? Guillermo Valle Pérez 4/22, 5:04pm Guillermo Valle Pérez Sure, i'll put it on github and share! And yeah we'should talk again Chico Camargo 4/22, 5:04pm Chico Camargo Sweet! See you later then! Guillermo Valle Pérez 4/22, 5:04pm Guillermo Valle Pérez like emoticon Guillermo Valle Pérez 4/22, 5:18pm Guillermo Valle Pérez https://github.com/guillefix/fst-bias

guillefix/fst-bias fst-bias - Code for the exploration of bias for simplicity in the output of random finite state transducers github.com Chico Camargo 4/22, 5:52pm Chico Camargo Cheers!