Deciphering Soft Matter Morphology via Small-Angle Scattering with CREASE(-2D) with Arthi Jayaraman

maybe with a short introduction. First of all, welcome everybody to the first webinar of this series. Um, so my name is Fedria Sebastian. I am together with Yansko Ped which I see in the audience and Santos from uh we are putting together this webinar series um in the context of the links smile team which smile means of matter in life. If you're not familiar with it I'll share the link to the team so you can look up and stay informed about the upcoming seminar and activity within the team. Um so this is um the first uh seminar of this series. I'm very happy to have yam to present her work and very interesting approach to analyzing data from smallus scing until now what is published about polymers and my cells and so on but I know that she's working on living nanop particles so it's it's going to be I'm sure very interesting to the audience and to the team that we are interested on so please arty I leave the word to you. >> Excellent. Okay, let me minimize this. I won't be able to see anybody. Um, so just if there's any questions or anything like that, just speak up so I can hear that there's someone online because I'm going to minimize this window if that's okay. >> Yeah, that's fine. >> I can keep an eye on the chat as well if people see either of those. So, just interrupt me as and when. No problem. Okay. Um, thank you very much for the invitation. Uh, good to see you, Yan. uh uh for others who don't know many many many years ago this age is both Yan and myself when I was a posttock in 2006 um I read every single one of Yan's uh review articles and papers on how to do scattering calculations and and almost 20 years later here we are right so um Yan you've had a very positive um impression on my uh past academic career so I'm happy to be here all All right. Um, so I will talk about my former labs work. Uh, I am not working on this topic as of right now, but my former team members are wrapping up uh, many of their ongoing studies. I know some of you in the audience are some of our collaborators. So, nice to see you. I saw the names. Um, and so what I will share today was all work done uh, in the last uh, whatever six to eight years at University of Delaware with a lot of recent work that I'll focus on. Um but currently I have moved to IBM consulting France uh where I get to play with the computing tools for material science and very much like the topic today it involves solving problems uh finding solutions to complex problems that other methods are not able to do and that theme still continues very much but now the problems are more related to what industry is doing it's still soft materials I still continue to do macroolelecules work so hope to interact with you in that context as well all right let me get my laser pointer started. Uh there it is. Okay, great. So um clearly this uh webinar is in the context of folks who work with soft materials who do scattering experiments whether it's small angle X-ray scattering, small angle neutron scattering doesn't matter but that's the audience I understand. uh so I want to get directly to the idea of why small angle scattering X-ray or neutron is very valuable in the context of soft materials and soft materials by that I mean polymers colloids anything that's not purely inorganic but rather organic in the majority and there may be still inorganic particles within uh uh the blend with all these other materials so that's what I mean by soft materials and many of you who are here I will not argue with me I'm sure that's this is a very very powerful technique if you want to understand spatial arrangements in these materials at multiple scales. While I'm not giving you motivation today that I'm sure you know that most soft materials function and application comes from these multiscale structural arrangements. So understanding how the chains are organized, how the monomers organize into the chain RG radius of geration, how the chains organize and then how the chains organized around maybe nanoparticles. All of these different level uh length scales of structural arrangements is what eventually gives you mechanical properties, transport properties, uh electronic uh maybe in some cases thermal conductivity etc. So understanding multi-length scale structure is important and many of us often go to small angle uh x-ray or neutron scattering to understand structural arrangements. Uh while I will not talk about wide angle x-ray scattering or wide angle neutron scattering I've mostly seen wax uh that is another technique that is also useful when you have more precise order at the atomistic scale and I won't be covering that. It's there in the picture. So I thought I should mention it that often people also go towards wide angle X-ray scattering in conjunction with small angle to expand that length scale to go even smaller with wide angle. But the talk today focuses on problems which are relying on small angle X-ray or neutron scattering and the technique uh that we've developed uh to interpret the data. So what does the data look like and what is the traditional analysis? Uh many of you who have used small angle uh scattering um have probably seen this but if some of someone is new in the audience uh usually the the output from a small angle scattering experiment is essentially the materials scattered pattern uh for an incoming either X-ray or neutron. The pattern itself is coming about because of the chemical composition of the material and the structural arrangements of the material as I said the multi-length scale structural arrangement. So usually the pattern is 2D where there's intensity of scattered wave as a function of in this case two wave vectors. But most people don't always look at this 2D. I'm going to call this 2D profile because in many cases the structure is isotropic. And if the structure is isotropic, you do not have an anisotropic pattern that you need to understand or interpret. So what people do is they'll do a zutal angle averaging. So imagine I average the intensities along this arc that I'm drawing. And so then I'll have high intensity, low intensity, high intensity, low intensity as I go outwards, which then looks like this. Intensity as a function of magnitude of the wave vector. high values here as I go farther. There are ripples and the pattern of these ripples and the shape is really a function of the arrangements in your material. Okay. So when do we care about these 2D patterns? We care about these 2D patterns when there is some information in my structure related to anisotropy. This could be because the structural arrangement is anisotropic or there are anisotropic elements that have local anisotropy but there is overall uh isotropic arrangement. Regardless, some of those signatures show up here and then if we do this aimothal averaging, we will lose that. So there is a need to be able to handle 2D patterns with the anisotropic patterns of uh present in the scattering results because that tells you about anisotropy. Second, if suppose there is no anisotropy and your structure is isotropic, then when you have these 1D profiles in most cases as we all have used many of the Peterson models, many many models exist out there that beautifully fit this data and then once you fit that model, you can get the parameters in the model that you don't know. For this, of course, you have to have expertise in a knowing what the shapes probably are in your material. two, uh, finding the right model for that shape. And so if those two are something you are able to say yes and yes to, then you go fit, you get the answers, problem solved. This is what's been done for decades. But sometimes you access structures either through processing or some really cool polymers formed by like my collaborators. Then you lead to then you cause structures in your system that may not have an analytical model that exists out there. And not all of us are Dr. Peterson and so we can't go and develop our own analytical model for every new system. So what we've come up with is a method here called crease that I'll describe that a either handles this type of problem where you're dealing with 1D scattering profile but you don't have an analogous beautiful analytical model that is applicable for that system or you have 2D and you don't want to do a zuta averaging into 1D and you want to analyze all of this. So this is the expectation that we set out to have for our method. I always say that no method is perfect and the way we can describe a method to be useful is if it satisfies at the very least the expectations we set out to satisfy. So our expectations have to be reasonable. So here are the three expectations that we set out to do. They may be a bit ambitious but we have accomplished these. And I also want you to know what it doesn't do. So first we can handle both X-ray and neutron scattering small nuanced differences in the way you handle the data and also in the way you will do the algorithm as I'll show you very small differences. So we can handle both. For some systems we can have both. The structures that we've handled so far, our collaborators bring us most of this data. So we're not doing the experiments, but they come to us. In many cases, these are unconventional structures. Something does not fit analytical models. So that's what we want to be able to understand and interpret. And then in cases where we get 2D data, as I'll describe to you in the latter half of my talk, we don't want to do a zimaling. We want the method to handle the full 2D profile intensity as a function of wave vector magnitude and azimutal angle full data not as an image necessarily but it should do the whole thing. Second I love polymers. I think I've said this in almost every one of the talks I've given in my entire life since I learned about polymers. Um and the beauty of it or the challenges in it is the fact that there is dispersity. What I mean by that is everything is not precisely one dimension. the chain length. So the molecular weights tend to have distributions. The arrangements in the structure can have distributions even if they're all the same shape. They may have dimensional distributions or they may even have different shapes of arrangements. So we want to be able to give that as an output. So not singular value of certain parameters but rather distribution of parameters that describe our structure. The second part this is also where I'll bring back the idea of wax. If you remember I said that wide angle X-ray scattering tends to work really really well when you have crystallin order or rather is very useful when you have crystallin order and that is not a problem we are trying to understand we're not trying to interpret the crystallin order either in particles or in polymers but rather we are focused on the amorphous or disordered structures now the reason I bring this up is you can imagine this as trying to identify the real space structure for a given scattering profile right so So the math problem is slightly different if you're trying to identify one of the many ordered states the system can access versus the distribution of disordered states that all fit my picture for the scattering profile. So that's the math problem difference. That doesn't mean we cannot handle semi-crystallin polymers or polymers and particles that have some ordered arrangements. It's just it's the type of interpretation that we do that we should keep in mind. Okay, those are the expectations. Let's see how well CRE does. CRE stands for computational reverse engineering analysis of scattering experiments. The whole idea is to be able to take as I said either SAXS or SANS data from a system either the 2D full 2D profile before a zenoil averaging or 1D after a zeoil averaging depending on your knowledge of the system. So you should know when there's anotropy when there isn't and you make that decision. The method takes either one or multiple profiles. So when I say multiple, I want to be clear. It's the same system. Maybe it has sachs and then maybe it has some contrast matched s. So then it's two pieces of information for the same system or it might just be one or the other. So that is taken as input. Don't focus on the inside right now. Let's look at the output. Crease's intention is to provide the user distributions of structural features. So this is what this means is quantitative description of structure in real space. This might be domain sizes, domain shapes, extent of orientational order, dispersity in sizes, dispersed in shape. Think of all of these physical parameters that you tend to describe your structures with and think of the corresponding mathematical parameters that describes it in real space. And this is your choice because you know your system. you know what you care about in the structure. So it's these mathematical descriptors whose values I want to identify and it would be great if we also have visuals. So representative three-dimensional structure structures that describe some of these values of structural features. So for some represent representative cases we create these 3D structures. But keep in mind if you leave my talk at the end of this thinking we only generate 3D structures I have failed as a speaker. So please keep in mind that the main output is the distributions of structural features. I also want you to have an expectation very clear in your mind. This is not a onetoone problem. Meaning if I give a scattering profile I have one answer one maybe distribution of values. No, you may have multiple answers where and you almost always have multiple answers all of which give similar scattering profile as the input but then you have to put your physics chemistry hat on to say which of these answers is right. So multiple answers for a given input and distributions of answers and what we do inside is what I'm going to describe in a bit more detail. So basically our idea is we want to reverse engineer all of the relevant values of structural features whose computed scattering matches the experiment. Right? So it's an optimization problem. Keep searching through the values possible values of those mathematical descriptors and identify a family of values which all give computed scattering that match up the experiment. So that's the optimization problem and we use an evolutionary algorithm to do our optimization. You may use something else but the way it begins is we start the first generation and now I'm using words from the world of evolution individuals and technically these structural features are genes of those individuals but if you want to use the mathematical term I'll call these sets sets of structural feature values and in the previous case I gave you just an example as domain shape and size. I would like you to start thinking maybe in the shape of a cylinder for example because my next schematic is a cylinder. So one could be the diameter of a cylinder, length of a cylinder, thickness, maybe some dispersity index or something like that and a few more structural features as you define it. And I know there are analytical models out there for cylinders. I'm just giving this to you as a simple example. You'll see the structures we interpret are way more complex than cylinders. But this helps me illustrate the method. So think of this as diameter, length, thickness and maybe dispersed steam one or more. So I have values of those structural features and these are sets of values that I've started with and they're very diverse sets in the beginning because I know my values could be uh from A to B for each of these structural features where A to B is defined by the scientist. It can't be a 100 nanometer length cylinder. So maximum 100 nanometer it is definitely bigger than 10 nanometer 10 to 100 and so on. So I'd have a diverse initial set where the range of values I'm exploring is defined by my scientist. And so for each of these sets I need to calculate the computed scattering. I'll come to how I do that. I being my former team members who did all of this work. How do we calculate the computed scattering for each of these is something coming up. But we would do this for every set. How many individuals you have in each generation is your choice. How much computing power do you have? How many possible structures do you want to simultaneously evaluate? I will tell you we've come to a point where these can be run on laptops. So this should not be your limiting step. You should be able to explore very generously so you don't miss out on right answers. Anyway, so in the first generation once I have these individuals and their computer scattering, I compare each of these with the input comput in input scattering and those that have a good match are fit individuals or high fitness individuals and those that do not match well are essentially poor fitness but they could still serve a purpose of sharing their genes for the next generation. So basically we start from this initial generation and go generation after generation after generation by basically taking individuals who are fitter and fitter and fitter creating offsprings etc till we go down to a final generation where pretty much all of these individuals computed scattering matches pretty well with experiments and it's not really changing much from the previous generation to this. So fitness has converged quite um uniformly among all of the individuals. And so all these sets of values are right answers. And we obviously have to figure out which of these makes physical sense. In many cases they all make physical sense. In some cases some may not. So basically going from the top generation to the bottom we're going from less fitness to more fitness. And now we can look at these final sets of answers to know all possible answers that give a computed scattering that matches experiment. Okay, so now where how do we calculate the computed scattering and where did machine learning come to help us to accelerate this? So originally when we were doing this this goes back to all of the knowledge I learned from the Peterson papers um which is if you have a shape a structure in this case as I said let's take a simple example of a cylinder I can place scatterers in the cylinder and I can do a Dubai uh scattering equation calculation which is very well based in physics and so then I can use that equation on each of these pairs of scatterers and calculate the icon. This is a pretty hefty calculation and this is something that we can do with computers but it takes a little bit of time especially if now I have to do this for each and every one of these individuals and maybe the 100 generations or so that I might have to explore. So this calculation starts to really make it slow. So what we said was we should be able to take the data of the varying values of these structures whatever they are. This could be an amoeba shaped structure. It could be a randomshaped structure. As long as you have some information from another analysis or characterization that says it's amoeba shape. It could be any shape. As long as you've mathematically described it, we should now be able to relate values of those mathematical uh features to the corresponding ifq. We would have this data. So let me go through this a little bit better in more detail so there's no confusion in your mind. This is how we would get started. We would have to decide on the shape of the structure, right? That's what our domain or material science expertise told us. The shapes look like this. Maybe you're thinking amoeba. Feel creative. I'm going to use a simple cylinder as an example. We make using a computing a code static structures. So keep in mind there is no molecular simulation here even though that's one of my favorite tools. Here we're just creating static structures with codes that allow us to vary values of these structural features. And for each structure I place scatterers which is point scatterers delta functions and I can calculate scattering profiles. If I do this repeatedly for various values of dt thickness and length I basically have a database of these values and its corresponding scattering profile. So now with that database I can train a machine learning model to relate values of the DTL directly to icon. This means I don't have to do that hefty Dubai equation in the genetic algorithm loop and instead I can use this machine learning model right there for every set I take the values of that set put it in the machine learning model generate its icon very fast training was done outside of this loop. So if I do this entire genetic algorithm loop, now we went from the slow early version of 1 to two days to less than an hour to a few minutes depending on your laptop. So it's basically allowed us to now create a tool that can be analyzing while you're also making measurements and it's done fast as long as the training has been done before. If you have a clear picture of your shape and um the ranges of values of the structural features for those shapes, the training can be done in one to two days at most. And then this run is very fast on a laptop. Okay. So what have we done so far with crease? I don't have plenty of time. So I've decided to share only two problems with you. Um but I wanted to share the breadth of problems to which we have applied crease and and you can see the variety of shapes and I'll try to highlight specific challenges we had in each of these problems which led us to use crease. So originally we started this problem for a project with Karen Woolly and Darren Pochan. Let me just make sure I'm okay on time. Yeah. And Karen Woolly's lab is incredibly talented in making some exotic polymers. Let me not follow polymer physics Gaussian statistics for their confirmations. So even though the structures they were forming which we could see in microscopy looked my poor shell spherical myels for which we have analytical models because these chains were very um exotic. they were not following Gaussian statistics and the analytical models fits didn't make any sense. So we came up with crease and then we basically analyzed what types of shapes and structures for the shell and the core we could explore and the dispersity etc. This is where it all started and because we don't deal with molecules and we don't leave deal with chains we were not limited in handling only certain number of chain confirmations or certain arrangements. we could explore many more dimensions as long as it was um it was something that we explored within genetic algorithm. Similarly, we also used the very exotic polymers that they made. These are poly glucose carbonate backbone and charged side chains. So, persistence length of two types. The most the the the very exciting polymers. Don't ask me to say the chemistry of these polymers. You'll have to look at the paper. Anyway, so other shapes and sometimes we don't know the shape very well from the microscopy. So then we test multiple shapes with their corresponding structural features. Then we move to something that is close to your team, the lipids team, the smile team at links, which is essentially vesicles. Here it's not lipid vesicles. These were protein peptide based vesicles from my colleague late Christy kick. uh her lab was interested in understanding vesicle dimensions and they had a lot of poly dispersity. So here the poly dispersity is what made this problem hard to fit with analytical models. If you removed poly dispersity and you had mono disperse vesicles there are great analytical models out there but here she was having lots of dispersity in the dimensions of the vesicles. We also looked at a system from Tim Lodge and Frank Bates which are metal cellulose fibrals. a metal cellulose or cellulose derivatives that form twisted fibrals and a lot of the science that they got by fitting analytical models were fascinating and the results were just surprising. So one of the things we wanted to do was challenge and say is it because of the choice of the analytical model or is this the same result we would get if we did crease. The answer in this case was we got the same result. Um and it's okay because here we were just testing if this was a limitation. The answer was a limitation of the analytical model. It was not. Those were systems where molecules formed forms and that form factor was what we cared about. But the structural arrangement because dilute it didn't matter. Now we looked at systems where the form the example I'll show you is where the form is pretty straightforward. Spherical particles which has dispersity but the structural arrangement is what we want to go after. So I'll highlight that. I won't go more into it right now. We also looked at work with Bhnesh Parati where we focused on both changing form changing structure as we changed conditions. So we didn't assume did not assume a form and then interpret structure. Instead we were interpreting both simultaneously which is the holy grail with an at least isotropic um soft material systems. The last part will be an example. So there'll be two examples today. One from the previous slide and one from this slide where we've expanded to uh apply crease to systems that have anisotropy. The anisotropy could be in the particles, could be in the arrangements, could be in the self assembled system upon shearing. It doesn't matter what gave rise to the anisotropy, but crease can handle 2D scattering profiles that are relevant when you're doing anotropic structures. So, I will highlight one example from here and I saw Simona in the audience. So Simona will find this very very familiar. Okay. So first let's get started with a system where my form so my particles are soft particles uh and they have a form which is spherical and I'll show you proof that it is spherical and uh what we want to go after is the arrangement. So it's a mixture of nanoparticles and I want to understand degree of mixing and also mixture composition. just because of the way the part the the assembled state is made. You cannot guess the mixture of the composition. You may know the mixture of the initial uh solution but not the self assembled particle. So this is what we want to find out. These are both related to structural arrangements. So a little bit more about this project. This is uh this was supported by air force when I was in the US and our collaborators who worked very very closely in so many publications with us and created this gathering data. Ali noa's lab, Nathan's lab did the synthesis and so we were a collaborative team. Okay. So what is the system? It is a bio inpired system and I know that's something of interest to the smile lab soft matter in life. Um and here the motivation was to mimic melanin. All of us have seen how we react to very sunny days how our skin changes color. So this project was all about mimicking what organisms of every form do to create color in their skin and create synthetic materials that did the same. So one of the ways we were accomplishing that and this the whole phenomena is called structural color. So achieving that is through controlling structure and the chemistry of the particles. So we had two types of particles silica and polydopamine which is the melanin mimic and we created mixtures of those we being Ali Dinojala's lab and an unveil um where they basically started with a certain composition of the particles h in one solvent and then they blended in another solvent. So in this case octanol was already there water was added that led to this reverse emulsion formation and then basically the droplets lost the water outside and as the water left the droplet you form these self assembled superbles and so what we wanted to know was what is the arrangement within the super bowl so the degree of mixing and the mixture composition in the super bowls so for this uh Ali's lab did sachs and sands when you have mixtures it's nice to contrast match one against the other the solvent. So you get one of the particles highlighted and then SAX gave the idea of the whole particle especially when you have a pure silica or pure polyopamine particle. So both profiles were used. I also want to motivate as I said why we care about the structural aspects like mixing and silica composition because that's what gives me color and at the end of the day this was what the project was about is to create color in synthetic materials by mimicking melon. So let's now go directly to scattering results. Just very briefly before I say that before we apply crease to any experimental data my team members had always created insilico replicas for which they knew the answers and when they put the scattering profile from that incilico system and ran it through crease they could compare the output to the answers they knew were correct. This is the way we knew crease worked well on pretty much perfect systems before we applied it to the experimental data. So that we know the method works well and now let's see how it works on experimental data. Like I said if you have sands and you have smearing you have to bring in you can do that in the computed scattering calculation. Okay. So these particles sacks on them shows they are spherical particles both in microscopy and the form factor fit is perfect. you get the diameter and distribution. So it is poly disperse. And then when you look at the super balls in the microscopy, you see that there's arrangement of the particles that is not ordered. So amorphous arrangements. And now this is the sax data from pure melanin and pure silica. So think of the composition as 100% silica. Here 0% here. As I said, we had a whole series of intermediate compositions that were handled with sands. Um and what you see here is if I try to fit this with a sticky hard sphere model which is uh quite often used in such scenarios I do not get a good fit. Same here did not get a good fit. But if we did the final generations computed scattering on top of the experiment you see there's no difference which means they're perfect match. Just because it's a match doesn't mean the answers are right. So the only way we will know that the final answers that come out of crease are correct is if they also computationally predict the same color as we see in experiments because in this case color is coming from the structural features. So if you have other properties that are coming because of structure, you could use that property measurement, compare that to the calculated property from the 3D representations and that can be a way to know if your answers are right or if something is numerically right in the genetic algorithm but physically not right. So here we collected color sorry computed color on the representative 3D structures we got out of crease. So the synthesis of the materials happened. They went for experimental color response measurement. These materials went for scattering X-ray and neutron depending on mixtures and pure. Uh the scattering profiles like I showed you came to crease. priest did the calculations gave the structural features distributions as well as representative 3D structures that when used in you know optical color calculations essentially gives a computed color response you can compare the two together if the answers are physically correct then these two should match and it's not one color response versus one experimental prof response as you can see multiple samples from the same materials were tested here. Multiple right answers color calculation together gave the error bar. So error bar sources are different but within error they have exactly the same shape and exactly the same spot in the color map. This means that the final answers are correct because they produce the same color as an experiments that comes from structure. Like I said that was just for structure. Now imagine if my particles were changing form as I changed concentration or temperature. That's what we did in the paper with Bubesh Bari where basically um silica coated with surfactants was changing form as you changed pH and temperature. So you couldn't just assume oh it's a sphere sphere. Let's just focus on structure. We had to do both together. Okay. So moving from isotropic systems to now anisotropic. uh I want to show you our capability that we have so far with crease 2D and I want to highlight again that before the experimental systems I'll talk about today we had to do all of this in silico where we had structures whose answers we knew we created these structures the machine learning model did not see it so when we input that known structure scattering profile to the crease algorithm it produces mathematical values and distributions and that can then be compared with the right answer. So this is how we first demonstrated we can handle entire 2D scattering patterns and get right answers. So once we had that capability then we were lucky enough to collaborate with Dave Adams at University of Glasgow. His group has been focused for many years on very creative assembly of deptide systems in variety of solvents and salts because peptides have charges on them. They can respond to salt. They have interactions that are very unique with water and other solvents, hydrophobicity, hydrophilicity. So with a combination of deptides and their isomers and salt and solvent, they were able to form variety of assembled structures. For some systems, these assembled structures are very easy to understand from microscopy, cryotm, etc. But for certain uh deptides, it was not so straightforward as you will see that this their their um their scattering data didn't fit analytical models for tubes or cylinders. And so they came to us with we have some anisotropy we think and even in the isotropic systems we're not able to understand why the analytical models don't give a good fit. I also want to highlight how the data looks. Um I usually emphasize that this data is ugly but I know Dave student is here in former students here in the audience. So when I say ugly data I want to be clear. I'm not saying that the data is bad. The data is beautiful. But that is not perfect. And so when we do the computed scattering calculations, we have to impose such imperfections on the computed scattering so that you can fairly compare it with experiments. So here are just four of many many many um profiles that they have um gathered from various synretron sources. And so I'll highlight two systems uh today. But before I highlight that, I have to tell you that our interactions with Dave's lab as well as ourselves, we were first trying to find what were the right night right types of structural features that describes the system. And after much back and forth, we came to a point where we realized what was really happening was these dieptide tubes that were forming were very floppy. This is our um interpretation. And these floppy tubes have cross-sections that have variability with along the tube. So think of it like a straw that you would never drink out of because it's so floppy, right? And so the parameters that describe these are obviously dimensions. But in particular, I want you to look at this parameter called eccentricity that says a cross-section is circular eccentricity one. If it's tapelike, eccentricity, sorry, eccentricity zero. Tapeelike is eccentricity one. and anything in between tells you that it's not circular and not tape like and some. Um the left column here describes all that we wanted to have represented in our structural features but these are written out in English in physics chemistry language and these are all the mathematical parameters that allow us to interpret these aspects of orientational order tortuosity stuffies. So when I describe the answers to you, they'll be in this format. But I'll do the interpretation to the physical interpretation with my explanations. I also want to highlight uh two things. One is the choice of the machine learning model is really yours. It's how much data you collect from those static structural variations that you create. 3,00 2,000 is a reasonable data set. XG boost model does well. I also want to highlight that we do not deal with 2D scattering patterns as images. Instead, we deal with this as a 2D vector of intensity as a function of ray vector magnitude and a zig line. And you can work with polar coordinates or cartisian coordinates. It's totally up to you. It's back and forth. Conversion is straightforward. Okay. So, this is the data. And now we go towards looking at the analysis. Okay. So when we give this input we see there's no anisotropy. So my values of kappa which describe the orientational order and in this case it's in log scale should be very very small and it is the plot here is a violin plot of all possible structural features and the values that crease says the final generation has. It doesn't tell you sets. There is a set could be a value d here, omega here, alpha here, maybe epsilon over there, kappa here. So it just has a collection of all the sets, but it doesn't look at the sets individually. But we can look at the sets individually. And so here you can see three families of answers. You can do clustering of the final answers into families. And you can see the different parameters and their values. So like I said, I'll do the conversion to physical language. Diameter 100 anstroms, which I believe Dave's lab has seen many times with their tubes or whatever they see in the microscopy. These are tapes because the eccentricity is one. There is some variability in the eccentricity. We do not pay attention to these values because they do not the eccentricity dispersity does not have a unique effect on the scattering profile. So it can give you many but the presence of dispersity is there. This we can trust the mean value of eccentricity as we've shown in the past with our incilical structures. Kappa and the log scale is very small. Now let's look at the three representative structures. They have some tortuosity. There's no anisotropic order. Orientational order is missing. These are just floppy tubes. Sorry, floppy tapes. Now let's look at this other input scattering profile. again family of answers. You can see now the kappa has moved up and it's in log scale which means that there is anisotropy and you see it and so now these are the reconstructed computed scattering before we impose this this flaws that we find in the experimental profile. Now we have two sets of families of answers which differ in their story. One says it's 100 angstroms circular cross-section. So these are tubes high anisotropic order. So orientational order is high tortuosity is not very high. One is now 300 angstroms tapes and yes there's some anisotropy slightly less some torch. Okay. So how can this be two sets of answers? Is one wrong? When we proposed this to Dave, he suggested that actually there is merit to both because there can be tubes that are 100 anstroms. But salt interaction, salt induced aggregation or solvent induced aggregation can lead to tubes aggregating next to each other looking like tapes that can have larger diameters. So we believe that there is merit to this picture of 100 angstrom tubes or 300 angstrom tape like structures existing simultaneously. So how do we ever know that the crease interpretation is right? One is exactly what I showed you before by property calculation. One would be molecular dynamic simulations if you have force fields but you'll never get to all the length scales. It's going to be very very very hefty calculations. You only do that for the select few for which you have a good force field. The other is microscopy images and this is the knowledge that Dave had that enabled us to say that this what we observed with these two families of answers is not wrong. All right. So I'm going to stop there. I have one more slide and I'll come back to the acknowledgement slide. I know this team here smiles team is very interested in the lipid uh vesicle crease story and yes we do have a story that my former postto Rohan has completed with folks in illoba Leonel Porsar and Ursula Perez this is manuscript that'll be submitted very soon uh and then there's one more manuscript that my former postto Andrea Finley is wrapping up this is with Dave and Simona on using crease 2D to analyze realology and SAS happening simultaneously. Okay, so thanks to the members who did all the work. Uh thanks to the experimentalist who gave us a ton of different forms of data and trusted us to to to use crease in a in in a way to give them interpretation. All the codes are in the crease GitHub page on my lab. So if you look at RTJ Ram on GitHub, you'll find it past financial support and thank you for your attention.