Now this error guys, this is a future. If you're searching for an energy booster without any stimulants, I mean performance lab energy is definitely a product to check. What? Let's find out. Hey, what's up, Rek here, the founder of your reception, welcome to my channel where you can learn top secrets on how you can get hyper-focused every single day. Subscribe below to start your journey. Now here's the thing guys, if you want to get hyper-focused, you need an adequate amount of energy every single day. There is no doubt about it. Now sleep is important, of course, but we all drink caffeine or coffee with caffeine, obviously. We take caffeine pills or, you know, we do any other stuff that helps to improve our energy or boost our energy. But is there a solution on the market without any stimulants that would still work and still improve your energy? Yes, it is. Performance lab energy is definitely a product. It is one of the first products on the market that can help to boost your energy without any stimulants. And how does this work? Well, I'm going to tell you how. But just before I do, let me share my quick experience with performance lab energy. Now, I've been taking performance lab energy for about 10 days. Oh, and by the way, guys, I'm not sponsored by them, so no, just to clarify this. And in these 10 days, I've taken around 30 to, I think, 40 capsules all together. I started with one capsule per day and increased my dose to two capsules. I even tried three, four, and one day I even tried five capsules. I'm not recommend to do that, like to take five capsules per day. But, you know, just I really want to see, like, what happens if I take a very small amount of it and what happens if I take a very, very big amount of it. Now, whenever I took at least two or even three capsules, I felt very, very energized. There was no energy kick like it usually happens if you drink coffee, especially I drink bulletproof coffee, which I definitely recommend. But, you know, there was a kind of a smooth push of energy that came out of nowhere. That's how I felt, at least, you know, and it was there with me and stayed and stayed and stayed. And, you know, I felt, I felt pretty good. There is no doubt about it. Now, but the question is, how is this possible if there are no stimulants in this entropic stack? Now, to answer this, we have to look at the ingredients. So, what do we find in performance lab energy? There is alkanutin inside. There is coinsin, Q10. There is PQQ. And there's black pepper extract and, of course, the lipoic acid. Now, when I look at those ingredients more in details, and if you want to know more about it, you can check it out below, you quickly figure out that, you know, all those ingredients are here to do one thing. They actually attack your main source of energy in your cells. This is your mitochondria. And all those ingredients basically help to recover mitochondria and multiply it. And that's how you kind of get energized as a result of that. So there are no stimulants, but there are a lot of ingredients that work directly on your source of energy from your body or your inner body. Now, how cool is that? I mean, this is, this is next level. There is no doubt about it. By the way, guys, if you want to get in the hyper focus flow every single morning, then check out my special handbook with seven secrets which you can download for free below. So during my 10 day test period, there was no negative side effects, which was great. Now, when it comes to the recommend those, it is between one to two capsules per day. Personally, I recommend two, sometimes in three capsules, but do take them in the morning. There is, you know, this thing, if you take them in the morning on an empty stomach, you should feel better. Now, when I take them on an empty stomach, and then I compare this to taking all the ingredients during my breakfast or even after my breakfast, there was no real difference, nothing that I could actually feel. But again, if you look at the studies, if you look at the recommendations from the brand, you know, that's taking all the ingredients on an empty stomach is kind of the best thing to do. Now, for the maximum effect, I still recommend combine this with coffee, especially bulletproof coffee, which is a great source of energy, or even gerbermatte tea, a great tea that will, you know, elevate your energy.  This will make miracles. There is no doubt about it, but you have to try it out, see how this works for you. So guys, if you want to read my whole review, just check it out below. There's a link below. If you want to order performance lab energy, there's a link below as well. So just check it out. And that's so much about performance lab energy. Thanks for watching this video. Don't forget to subscribe. Don't forget to download my free handbook. And don't forget to follow me, your inception on Facebook and Instagram. Hope to see you soon.


A chyfnodd y byddai'n gofyn o'r ffordd y llwyffydd oedd yn ddiddordebach ymlaen i'r ffordd. Mae'r ffordd yn gydig ar hyn o'r cyfatrwyddol i'r ffordd, ac mae'n baut yn cael ei fod yn cael eu ffordd. Mae hynny'n gallu'n gydig ar hyn o'r cyfatrwyddol, ac mae hynny'n gallu'n gydig ar hyn o'r ffordd. Erich yn ysgrifennu ar gyfer y ffordd, mae'n ddiddordebach ar y ffordd ar gyfer y ffordd, ac mae'n gydig ar hyn o'r cyfatrwyddol. ac wedi gweld wedi'n ymlawef ymygoel sy'n cael eifawr. Fydd ydych chi'n fawr o'r cynodiaeth o storid? A fyddech chi'n amluntol yn fawr oherwydd dechreu fan hyn sydd y storid ei fawr wasio unigol y bydd yn cael ei wneud, felly ddim yn gwbod am fawr. Rwy'n dechrau a'rgynniadau efallai leolethaf yng Nghymru. Rwy'n cymryd yma ar gyfer amddachion gwheiddoeth? nid o wneud o'i weld ysgolwch ar gyferwyr. Felly mae'n gweithio beth o'r hyn yn ei gwybod i'ch meddwl i'ch ffordd. Yn ymgyrchau fysgfaith yw'r tylu yn ymgyrchol, ac mae'n gweithio beth o fe wnaeth yn ymgyrchol. Felly mae'n gweithio beth o fe wnaeth yn ei gweithio'u. Oni'n ddweud o'i gofynu, fe'n gweithio'r hynny, ac mae efallai yn ymgyrchol yn ymgyrchol byddwn i'n gweithio ar gyferwyr. A thysg ar gwaith a'r ffordd o'r ddweud. Mae'n ddweud o'r cwestiynau i'n gwneud ar y ddweud i'n ddweud o'r ddweud, nad yw i'n ddweud i'r ddweud i'r ddweud. Mae'n oed panfod o gwaith o'r ddweud, Eric oedd o'r ddweud o'r ddweud i'r ddweudio yn y ddweud. Mae'n oed i'n gweithio negatifol o'r ddweud o'r ddweud. Rhaid i'n gweithio i'n gweithio. Yn mynd yng Nghaerng honno, rydyn ni. Yn gyfnoddon, edrych yn ffwg o'r ddau'r ddau? Yn byw'r ddau? Yn gyfnodd. Yn gyfnodd, y gallwn am y ddau'r ddau, mae'n fwyaf yn y ddau sy'n ddau, mae'n ddau o'r ddau, e'n ddau. Yn y ddau, yna. Yn y ddau, mae'n ddau'r ddau. Mae'n amlwg o'r ddau, mae'n ddau'r ddau, mae'n ddau i'n ddau, Felly, all masfer yr adeiladau oedd y bod yn arwag gennym ar yr filoedd ymlwg yw'r adeiladau, ydych chi'n ddiddordeb ddiddordeb perthigai'n ddiddordeb un fyddai ymddwymon i mlyneddau rhai o'r ddiddordeb digwydd. Roedd chi'n dda i ddiddorg o'r gyrdd ac yn fam, gan mynd i ddiddordeb gynhyrchu. Bryd o'r ysgrifennid yn llawer o'r sherf feddwl y pramys. i'w fath o oes oherwydd wrth y llexarniaeth cymuned iddyn nhw. Rydych chi'w meddeithasun oherwydd mae'n meddwl yn meddwl i'n meddwl'r... Rydych chi'n meddwl i'n meddwl i'n meddwl i'n meddwl i'n meddwl i'n meddwl i'n meddwl i'n meddwl iddyn nhw... ..fyrdd eich meddwl wedi bod y Llyfr Tory Mdb sydd ymlaen i'r tyniol a'r ddımıll ar gyfer EID.. Mdb. Mdb, molecule here. Let me check if I already go on. Mdb, and it has Mdb as a score minimisation and it has Mdb as a score dynamics. So it's a stock. It probably doesn't have everything, but it allows you to describe parameters of the simulation. The fact that we're meeting under the sort of biaxel banner tells us something. So the initiative for biaxels is already in place. So that's obviously a very good thing that is helping to develop the field. Mdb analysis is an analysis tool. Mdb tranches is another that is no longer supported, but Mdb analysis is a way forward for future analysis. And all the next time, certainly still very much ahead in that zone. The fact that Eric mentioned this POS white paper that is discussing is that out yet, Eric? No, I think that it hasn't appeared yet, but it should be out in a week or so. I mean that's an essential initiative that has got both key players within the field and also the publications on board as well. And we also wonder whether there should be some sort of benchmarks that POS went forward as well with what can be discussed. In terms of actions, we need to identify what actually are the needs within the community. So that can be something we discuss over the next few days and then come up with our own white paper. There are readers in place, but I think Gromax needs an MMCIF reader. I don't know how to potentially, but obviously you convert back to PDB format before then going into to use Paddock. We need to talk to the various PDBs including the WWE PDB just to get some sort of consensus on this required format. The idea was there also just to comment on that one thing. Eric was saying it would be cool if you could go to a PDB entry and find all the simulations that have been started from that entry. But for that I think it's important that we talk to them. If you were to integrate this data, what kind of format would you like to support? But I don't think that's going into the five formats, right? Provide information to the five formats to make it easier for people to mine everything and start creating these links out for people. But if we come to a format that we have to change all our machinery to be able to use it, that's going to be a huge effort from their side and they're probably not going to do it. But if you tell you or if you provide us JSON, then it's fine, and then see if it's fine, then we know that then we can just integrate it. Yes, I've actually written that as well. So it links directly from the PDBs a sort of simulation information. We need to talk to the journalists as well just to get an idea of the sort of benchmarks or otherwise the sort of integration of all the sort of parameters when it comes to publishing a paper. A couple of key things that Lerwick mentioned as well, reproducibility of the data, and that's serving something that we should act upon. And also looking at other formats such as Yaml and JSON as well. And there's probably a couple of things I missed, but I think that's enough there. Good. Thank you. So you might move on to Team Yellow. Can we elect as both persons to tell us about your things? As we go to the new one, like transfer to the new one, because it's similar to what you've already talked about. Move the board to the front, yeah. Are you sure? Are you sure? See, I've just written an apron on the new set. Yeah, just the apron, yeah. I can use it. I've got to do it. Do you want to? It should be clever. Are you not? No, I'm not. OK, we're going to hold it for a minute or two. Oh, OK. Maybe one of you will see the one of me. The ball of promised it can clip and then it can actually do the same. So let's talk to the what makes it possible. Actually, the boundary between what makes it possible and action is kind of thin. So it needs to be extensible, OK? It needs to be something that we start with a core concept of the five elements. But that is the set of elements. You should be able to add things when you think that it's needed. OK? I don't think it was already... It feels to me more like an initiative rather than something that we already have. Doesn't that really make it easier? More action would be better. It doesn't make it possible. It's something that I need to make it possible. So there's an action. Initiatives is what already exists. Is it correct? So we already have this key value tree format, Jason. They already exist. Something we should build up. I think that's why I thought it was more in an action than more really positive. That Jason exists is a positive thing. Yes, absolutely. It is about positive and not an action. We had existing formats and I'm safe. I can exist in format Jason. So this five format, that's again an action idea, needs to be something that is hard-solid in the software. So you need to come with the idea that you need to come with the idea that you need to come with the idea that you need to come with the idea that you need to come with the idea that you need to come with the five format and be able to use it directly in your core software format. So that goes together with the A-force from the key software. So it kind of comes just from the user point of view. It needs to come also from the software provider. But that would actually, to convince, nice foundation, to convince core software to do this, it needs to be a shared ownership. You cannot just say to someone, just do it and that's it. It needs to find some priorities. It needs to find its own priorities within the initiative. So it needs to be shared ownership between the different partners. We need to have a portable library API as we could find for the item in the format for this Python API. Ultimately, you would have to extend it to see the common knowledge. To allow the users to basically easily write on-read this format. Having a way to define, validate, to find those kind of data with the API that we have for the IHMMC that we have for this teaching area against which to validate the file which we want to delete something. So with a clear metadata of learning of a big problem, software people need to do things. But actually once you have this definition of metadata, it doesn't need to be a software team that doesn't come in the software team. MGS. It needs to be a self-contained file in a song that quantifies one simulation. So we discussed a lot about this format or not concept. So should we have on one side parameters or something like that. On the other side, just the coordinates or should we have everything in one file? The best way to achieve what we want to achieve is to have a file where everything is in there. Okay, it might raise some issues in terms of performance in terms of the size of the file but it shouldn't be the limits we put right now. At first, because of the technology that exists, because we might be able more easily to overcome these limitations where some technology might take other benefits from compute cycles but humans make mistakes. Can I just say that given the actions again quite large, I'm a bit concerned about workload for software. Whether, as was said earlier in the morning, that we need to really refine exactly what are the achievable in the near future rather than just doing that sort of wish list for whatever is possible. Let's take that as an actual item after we've collected everything. It makes it impossible with different priorities for the different... people involved or different needs different priorities. The diversity on the end of data we need to store on share let's do this one. Store space... So I'm here what the MVP is or which will have most impact. The what? So what would be the MVP? I think it's a lot of work. It's a lot of work. On the initiative, I think we already said, so MD analysis on MD training are two examples of that have been made to try to have something generic enough to read and write in different formats. So we can inspire ourselves on this initiative. On the IHM family I can actually... OK. What's the last one? The IHM MMCF initiative. The one that Alex did, right? So let's go with... ... ... I have the next one, you're doing the... ... ... ... ...  So listening to everyone, something that kind of struck me is that actually what you guys are trying to do is build ontologies. So there's actual ontology initiatives that try to interface the quantum mechanics up to the actual mechanics of a car. It's a very complicated thing, a very long-term thing, but just know that these things are out there and people are at least trying them. So it's worth at least seeing what they do. I think the way that these things will eventually work is a very little field to have their own ontologies that will slowly grow together, hopefully over time, over a very long time. So I don't know if this is a positive thing due to the time investment compared to the payoff, but at least it deserves to be upon the boat. And on that, from everything about ontologies, the other kind of neat technology that you start thinking about is the semantic web. So you have things that are not necessarily glued to a single schema, but how do you create a schema that can interoperate? How can they all connect together? And again, I think it's a really negative or positive, simply because it's an extremely complicated idea and not something that I really recommend doing right off the bat, but at least, again, being on the boat and something to be aware of. So on that, a big positive is that there are similar initiatives in other fields. So in quantum materials, there are four or five. In quantum chemistry, we're mostly actually doing one. In things like cryoem, there's tons of spec and schemas coming out. So there's a lot of initiatives that are relatively similar and good ideas that you can pull from there. Most of those are with pink ones, actually. Where's the fact? Oh, that's below. So initiatives we already have exist in other directions. And then ontology we had as a negative, but I guess it's on the boat. Yeah, just about a second. So I think this one's very particular to actual parameters. Like ontology for parameter space. This is like general ontologies that actually stretch the entire spectrum. That there's prior ontologies is very important. We have problems with it. And so another one I have for positive is that there's a clear benefit. Although I have to question mark against this because I think everyone thinks it's a clear benefit because we clearly try this a lot. But why do we try it a lot? What are the actual outcomes we're looking for? Is something I think we should try to answer as well. So I'm going to put this kind of just slightly above the water. Let's see. I think one negative is that in a lot of ways MD programs are fundamentally not interoperable for each other. Like there's a lot of commonalities, but there's still a lot of funshality in each one that's specific to that single program. So I think this is what we should be aware of. And kind of on that kind of vein is that they also have completely different data models. Like how they actually think about their data. How they organize their data is completely different between programs depending if you're GPU or general HBCX86. You know, like it's completely different between programs. Do you have an example of that one? Doesn't nothing come to mind. Sure. So I think this goes back to if you have a 4CAM program and you want a really large, meticulous service you have a C++ program and you usually go for a more hierarchical, you know, kind of like object models. And so fundamentally like they're organized a little bit better than they can go. So how you organize like say your coordinates, for example, is actually different between programs, but if not, it's up. Sure.  It should go away, but people very much care that they can read it directly into their program. I'm not sure why, but it's something that we see across the board that people are extremely concerned with. They're internal representations being the same as external representations. I mean a good example is, for example, with a lot of the ways that people have coordinate files, they're all the X's then all the Y's then all the Z's because that's what's coming from the program. Whereas we take the PDB, it's Atom, X, Y, Z, Atom, X, Y, Z, Atom, X, Y, Z. So what you, essentially what you're talking about here is a data model. So the PDB data model is that we have frames and inside frames we have atoms and het atoms inside an atom, we have an atom name a residue name, an X, Y, Z, coordinate blah blah blah. But that data model can be represented on disk in many different formats. And actually the format that the data model is actually represented on disk really doesn't matter because it's the data model of how bits of data are interrelated with one another. That's what we're saying in the PDB. What happens is that when I search it into a program a program will extract the bits of that data model that support the program and then arrange it in memory in a way that the program needs to most efficiently run. Now the issue we have in the field is that we tend to write programs that go directly from the disk representation straight to the application representation and we don't actually think about the data models that are actually held that are represented in that file format. What we really need to be doing is rather than saying should it be in JSON or should it be in XML or should it be in SCDF or should it be in the final format actually saying what is the data that we need to actually represent how does that data relate what type of data is it arranged or flowed to the arrays or doubles how does that data get packaged up with other data so we have a data for a molecule but then there's also data for parameters then we have data for running simulations blah blah blah again what are those bits of data how do they get interrelated and once you've built a data model that says one of the bits of data are now interrelated how you've blacked that data model to disk who cares really if it's one file, a hundred files, a thousand files who cares because ultimately it's that bits model which is the thing you then want to go and take into application space to run applications if you say actually if everyone is working from a common data model then we can support lots of formats underneath and for the application speaker data model they can actually get intermedically with that as well and I am quite biased in this my sayings because this is what the biasing space project is is we basically have an extremely flexible data model that relates parameters force fields, molecules molecular systems how do you run simulations blah blah blah and we deliberately do not write this data model to disk what we have are interconverters that effectively enable you to read and write any type of molecular data any file format into the data model and then the data model invites the input files for the individual program to run them effectively empty analysis does that for trajectory cool I'll look forward to reading more about that so we can get the tools in place sure that actually covers a lot of state news that internal external representation should very much differ underneath the initiatives we have again think models and not formats like I think a lot of people are thinking that for JSON or something like that and I would argue that this is kind of the wrong way thinking all these things and instead of what you should really be thinking about again is what kind of key value array sort of thing do you have what kind of fundamental structure do you have how do you collect various objects that are in these kinds of ideas and a lot of people say like you know what let's do JSON because JSON is great and that's true but JSON in a lot of ways is actually a really good format for as you see it's extraordinarily slow the numbers are not serialized in any kind of way you know instead there's all kinds of things which are like message pack or parquet and these things can actually represent arrays and the thing is you can convert them between JSON and the animal and whatever you want extremely easily so I wouldn't think about JSON I think JSON as in like key value array structure that's what you should think about but not JSON and as was pointed out is that people are doing this data model idea that is actually pretty common so I think in the analysis and detrage has mostly kind of had a project for aeroporting different kinds of trajectory formats that has internal data models as well so I think you can find a lot of people trying to send for representation so we're thinking about them taking ideas and then the final action that we really want to say is that you know all of this topic that we talked about what we're really trying to do is figure out like where the data model split is like so what's the trajectory, what is metadata I think that isn't very clear because like a lot of people have what you would think of as metadata but trajectory is vice versa so the question is more like how do we conceptually organize this data and so I think thinking about that will actually dictate a lot of what we think about in terms of file formats and how we actually write these things and help them I actually had to think about and is that going to be the work? Identification of needs Yes The nice thing with data models is it's not up to the software programs it's up to the field to say this is the data this is how we need to arrange it but once you've got the data model that's actually quite simple for a software program that's a data model I've already seen for that something that tried to counter software programmers go and work so it's a problem for us We don't have that much and we had a little bit of a challenge because at our table there was nobody who was actually developing file formats or just these kind of programs so we were a little bit more thinking about what we as users would like to have in these kind of ways so like first of all what we want to have is that it's storage efficient we don't know how to really do this they are already trying out different kind of file formats we also have like actually the we actually did not Yeah So we have like storage space Yes We also agree that so for us different existing file formats is not really that much of a problem so we don't like aim for having just one file format because there are so many tools which easily just convert it but we rather would like to have that all the formats have some standard input which is actually in them so that every file format from these things have the same kind of input of what can extract from them so in the end that when you took the conversion tools like you said before these backing up go ahead things So we have competing data models that are currently expressing file formats is that one of the idea? Yeah Okay Yeah The meta data like the JSON file which is more or less where is So you have my existing file Yes, exactly it was mentioned in the talks something like this which includes which includes the information what everyone had so where are exactly these our structures coming in the end it would be like to be started from the PDB file then have information code was processed and absolutely there wish list but it would already be great when you could have some files the information where where you got these information from how long are your trajectory files and these kind of things Also the thing which we would like to have is something like a streaming feature so that you don't have to load the complete trajectory in a stream information like for example like in a YouTube you can just jump to a certain frame and look from that on and something like this that you don't have to actually load everything in there so that's something which we actually would like and I think so far all the tools only so we have to load it at least once per day So there's a net CDF that's why you use net CDF because you could just jump to any frame Okay I guess it's a container file There is progress in this field obviously everybody has made one for this but yeah I guess that's actually something useful So what makes it complex like we have to agree on all the information which should go into these files I guess that's sort of a brilliant point Yeah or like to make it complex to get that So that's sort of there's models and formats and types of information that's a point At the point what about post analysis so do we also want to have a file format which gives us something out of the amounts which is the same for everything Yeah I think it was a one point that is something that's hard to distinguish it's not always what is just the opportunity that when we define a state it might have something to do with analysis running during the simulation upon which the simulation decides when we're ready to go over it to stop and all these like stop conditions for example they can be they can be in the state crystal ideas of Donald they can be hard to write the thing because I don't think about it like in a system I don't think about the simulation I don't think about the scientific workflow there's another other level in there and you need to have a process result There's actually NASA's done a lot of work on this and what they've done is actually come to a three level model I think it's generally applicable and the top level is simulation so the data is actually running for the simulation the middle level is what they call campaign and campaign and all the simulations all the things which revolve but actually the complete campaign is a complete experiment and then they have archive and archive is now the campaign that's finished it's now gone on to cold storage and they have different formats and different things for a running live running the campaign and then going to archive there's actually different uses and needs for those three levels Who is this? NASA So that's a good... Chris, can you make a push to the left? Yes Because they have a weird good paper actually where they describe this because they run a wide range of simulations Yeah Like it was mentioned in the talk something like the Jason file format or something like that and like we already discussed that it has pros and cons and yeah it was like sure I don't like it's already existing and in general tools for readability so those which are human readable and machine readable if you think you could also think like what you don't actually need to have all the file formats being readable readable by the human if you have good tools who give you the output in a good way that everybody can read it so you had it? Action Action Alright so thank you everybody for that large question and ideas we have about half an hour no less, 15 minutes left where we didn't talk about how we moved forward from this set of ideas we didn't really reflect there's a lot of other things that need to be done by software people but we as a large community need to be involved in setting up the boundary conditions for those some of them My impression is that there are a little bit tool opinions which direction we should go with there is roughly one direction is that we have a standard file format in all the programs that we are using and then these programs give up on their own formats so then everybody would be using same formats and there would not be these specific formats for each program anymore the other direction is that programs gives their formats and then we have converters and my feeling is that I have a little bit third arguments for both direction but sometimes it's alright, you can have a program that can read both performance and I think that's by far it's unlikely that all programs will give up the ability to read their native formats right away but I think being able to read this format too provides an easy solution and you don't have to convert Ultimately if the new formats deliver value to funders or PIs or students or users then they will get adopted the software that has not yet adapted to be able to read them right so that's I think the path to getting things done that I was wrong trying to come up with some software that says you can't put a mail unless you do this for them Can I go back to data models and look at what needs to be done but I think for data models there's also a lot of work that has been done so far it's just largely neglected because nobody really cares right so there are people who have to develop data models but nobody really can for example from it's actually a pretty good model I think it needs to start with so you don't have to start from scratch you can already parcel data from older major and the software packages Conrad Hinson has developed several data models and there are also general data models that are sitting out there and now how you would call each field I think it doesn't really matter because the structure exists out there so I don't think there is so much effort about actually building the software but it's more about reaching the consensus about what kind of code can you be able to put in and how do you want to hold these what are the variable names and I think that's where the code begins and then it starts right there Is this the same as ontology you were mentioning? Yes, essentially it's connected because ontologies and what kind of semantic work do you kind of know which word means what and we need to agree that this word actually means that particular thing so we don't have different definition of I don't know what's thermostat I mean you can think that in Central Georgia I don't know or something like it so we need to make sure that we know that every word is like one to one I think essentially because there's no space for ambiguity it all gets to a point where they think that resisting far formats are too slow to evolve because there's a burden of some committee period to get new keywords accepted that tend to go with aren't key value stores are really wonderful and then they throw away the existing far forward they jump onto key value stores and then over time they produce they have different meanings for the keys and different data types of the values and then they suddenly realise they need to create a committee that standardises the key names and standardises the data types that's the thing so ontology is what a community can do as a community in the final ontology and actually agree the meanings of things and what how they're going to relate the solution is not generic key value stores because generic key value stores is just everybody coming up with their own names and everybody coming up with their own values and as soon as different groups start inviting those to this then we've got chaos because we want to meet different things I think one of the things that came out and some of it we've really struggled with with Biosyn's face is there's this naive view that all of our tools are interoperable when they're not you know, if I take the same input from my MND package it will not run in another MND package there isn't a standard definition of what we need about the terms, the integrators or any of those things and this is why these initiatives fail as soon as you get past kind of the coordinates the velocities, the force field parameters and even with the force field parameters there's a disagreement actually what they mean, what is tip 3p water or actually it's different from packages so what I'd like to see is not so much just a community bubble I would like the community to begin to evolve what is the ontology for this area what do we mean by tip 3p water what is a tip 3p water in terms of the force field parameters how it works, how interactory shake what is a protein how do we define them in those kind of things what is the ontology of formats and how is it all discussed so trivial I think everybody agrees that's the good thing to aim for but we need to start somewhere where there's enough common ground and probably something where there's enough incentive to work together that you could do something cool that you couldn't do before and I don't know if that's like taking the MND or something like that and be able to export in this common data model format that would then be usable in all of our simulation codes right out of the back that would be useful for example but there might be something else that would be a minimal subset of things we could do and then some cool thing we could do with it immediately the thing I'd love to see is basically more take up I mean I have nothing to do with the MND analysis project or the MND tragic project because they recognise that it doesn't matter what the trajectory format is it's what we're doing with the trajectory that's the interesting thing it doesn't matter what you know you'll just load up whatever trajectory format you've got and as a community we can actually support and develop a tragic darling is that but if we can support and develop MND analysis we really begin throwing stuff into that through our own individual analysis tools that would be great but that doesn't help with debugging and running things from one software to the other and that sort of thing I'd say that too very different part right coordinates and all these analysis that's a very simple problem farce it's like two or three orders of magnitude that's specifying all the parameters that should be run and in that case in point there is not a single packet that provides an ability to cross reference parameters and start simulations in different packages simply because it has to be exact it's not I can't interpret it I use exactly the same words exactly the same sentence on the other hand I think the good thing is that it is well defined because all of these programmes they have implementations that implementations are exact this is the issue sure but the implementation is accurate and over them and Rolex and then we might have to realise that they differ and then we have to use different words for it to fix the implementation so I suggest we finish off by reflecting on what things we individually might be able to contribute to these in future in order to contribute to running some words for all my paper optimists in order to in fact can I contribute to the evolution of these ontologies can I recognise existing efforts such as I've owned can we build those into data models that are suitable for some minimum viable product of things relative to binolecular simulations or binolecular calculations more generally thinking broader than indeed can we then set up some boundary conditions so that the people who are implementing analysis suites and simulation packages and docking programmes and web servers and all these kinds of things have the ability to refer to a community document and say ok, these are the things I want my users need now I can make sure that I get that done and that it's consistent and it's going to be scalable and detailed Can I also add one more thing? So how do those ensure that whatever we do doesn't follow the same list name between the credits so it lives for two years and the guys and it's on and we can say it's so nice What happened to it? It's no longer supported and we're responsible for being the caretakers and stewards of useful, interoperable software tools for our community No, but I would say no that's also been right, because none of them are funding for more than the next four or five years and then they might be gone and that's because back then if we're going to do this you can't think that there is funding available we will have to take this on as a long-term engagement even if we don't have money a short term we might be able to fund it but if we want this we can't think of securing funding for it which is a scary part But we still need people to do it, right? Yes, but it will have to be an engagement that we prioritize in our groups even when we don't have dedicated funding for it Otherwise, good funding fluctuates No matter what funding we find for this there will be a point in time where there is that funding specific funding is no longer available and then it will die if we focus entirely on funding in time but equally if we one of the problems in the field is we tend to produce new tools from scratch we get rewarded for producing new normal tools from scratch as to how grants work and we tend to produce a new tool from scratch and actually when it comes to writing a new analysis thing for MD if we just throw it into tools like MD Analysis you would then begin to build a pop-rock and source community which makes it more immune to having individual funding fluctuating and then in terms of sustainability we're very good at producing tools and producing tests Grants is a very good example of sustained piece of software but most software that we've got tends to be written in a way where it's not able to be picked up and put down because it doesn't have tests and very much are on proper documentation and a proper community management model and we need to add those things onto the software project we made so that then with the original group with us away another group can come in and immediately keep building in the same framework and that's how all open source projects basically became successful they didn't have continual funding from the government they did bend up and down because they put the community layers for sustainable suffering in place I think for people where I think about this tool not just what tools do we need but how it can be sustained and how to build so yeah we need people to contribute words to this we need people to think about ontologies we need people to then think about how to convert those into software so those are going to be challenges for us all there are those of us with time and funding right now to the primary work in here I'm happy to contribute to those efforts I hope some of you are able to as well in the different areas where you have different kinds of expertise I'm not the right person to be specifying what the data model is because I don't run simulations I don't want to see empty packages it's no good just looking at oh you're the software guy I'm not going to do it all for you I don't have the time or the amount of funding as do you want It's true for funding so here we are mostly we are bio exteriors some European organisation we think that at least this consortium can give something to start with a bit of money to try to do something to start something or I don't know or can we identify at least some sources that can be conducted to try to find that by some specs which I think is the British equivalents they still are both like how old person we can personally first of all try to basically write a couple of lines there because obviously everything we focus around is defining data models and the importance of building data models and how you build them in a simple way so did that really contribute time for people to write in bits and things like that the same thing on bio itself we can certainly find people time to help them to find things and do better implementations but it's also the danger there right is that if you have two or three places with funding for it it easily becomes a site for it that those groups are involved in and that's we need to take a sustainability how do we feel that this is a shared ownership that we all do together at some point in the shorter near time there might be some funding for it too but I think we need to start by things on how do we involve all the community and it's unlikely it's not fun here but it's unlikely that we will find the grants that will be able to support everybody because those grants they don't exist collaborations 2, 3, 4 groups yes but 25 groups no does there also have to be something we see many benefits of having this common data model but does there have to be something particularly interesting here different codes or things together yeah that's what we have to put into the buy some space grant so specifically building it so you could run different workflows with different underlying packages and do you force build on that comparisons so this comparison could be the explicit yeah we're looking towards this big energy and accuracy comparison or performance comparison or the accuracy what's the best method to apply a prediction of binding I find accuracy far more interesting than the performance yes because again we can start a comparison of free and de-calculations right there are a ton of small settings so are there things that we know that tend to improve accuracy that's essentially what you get so whoever is you going to shell get a little bit of a trick essentially there is kind of a question what is the right book what does this department actually mean anything much more concrete level that is side tracking a little bit for the code like the grammar so I think one very useful thing is to separate the internal data representation and the external data representation that means splitting off like XCC file reading more into libraries than having this seen as being part of a grammar mix as already has happened with the TNG but I think there is lots of like file dialogue going on that is so much intertwined what the program does internally that might be a smaller input package we could immediately benefit actually we already have the XTR files that are regular it will be implemented all the time though for a package so it's great one thing I would like to see is actually for the packages to document their data models so I mean Gromax is very good for that I think it is because I work with auto-MD packages that Gromax is by far the best because actually in the manual it does define 90% of what's in the file not in terms of the data model but in terms of what the line should be most of the time it's correct there are times where it's not correct 51% but I think it is too much for me Amber is terrible in terms of defining what their data format is they have nothing to say what the data model is except for the NCDF trajectory spec which is brilliant everything else is terrible Charm PSF multi file format oh my god but there's the thing for the individual software package we can actually define a document that says this is the schema this is the grammar for this format this is the data model and it says those documents might be so much easier for us to build these tools and actually we need to look at the file formats in terms of their ontologies so that then you can find commonalities we want several things though we want both the low level, serialized format and there again could be multiple things multiple realizations of the same data model which is what we want people to use but if we want them to use it we also need a common implementation that's well documented and that is easy to link against and that's maybe easy to stand alone somewhere Python API as well to easily manipulate from that so that's the great thing about things like NCDF is that the NCDF for Python implementation is very easy to use or you can grab it into your Fortran or C but there's so much support for developers to easily use it that it's easier to do that than to roll your own reader or writer which I presume is what happens with these XTC funds just one of the packages wrote up in the windiness it was like all of themselves there's an NCDF basically as pandas which is some people have heard of pandas it's just so easy to use Python buys a single install line and then you have things like pandas which is a generic data analysis platform which you can interface with an ump and a map which you can then do analysis of any type of NCDF up because it's already in that data frame format I would love to see Tyfil I would say yes, we're just all going to put all of our array data just put straight on to NCDF everyone's life is so much easier and again that's a data format they've built we really doesn't matter exactly what the format is if we can at least all agree on that data model and I think that would be phenomenal we have a bunch of priorities in the development of the TNG library that worked out these couple of different levels that should be able to be generalized to wider community needs so is it then Voyager or a TS9 ha ha ha ha should I turn next time Rachael ha ha ha ha ha


Two logistic things, we looked at the legacy of landmines. We looked at what it means when landmines are planted and then left behind. And what it means to leave landmines amongst a civilian population once a conflict ends.  It's just the menace that never goes away. You know, Paul Pottaway said that a landmine was the perfect soldier. You know, you don't have to feed it, you don't have to pay it. It just lies in wait. There was one thing I didn't realize until then, is that landmines is like, intoxicate all your daily life. And these people, like, they are surrounded by landmine fields. But they have no choice because they live there, to go through them. I traveled to Laos in early March of 2014 to learn the amount of cluster bombs that were dropped. It was approximately 270 million, and a lot of them never got exploded because there might be a hundred in one casing that's being dropped. So a certain percentage of those has exploded. The rest are unexploded, or it's still found today.  Sajad was in the field attending his family ship with his three brothers. They stepped on an exploded cluster munition. Sajad lost both of his leg. Two of his brother got killed. His younger brother suffered from stomatial aceratization. He couldn't play with his fellow kids.  He couldn't go anywhere. He couldn't do anything. And that is the face that I've seen for most of the nights that I wasn't able to sleep after the assignments. And I think that ECRC will be able to give him back that dignity with prosthetics. And this is one of the reasons why projects in Iraq are very important to those people. It was interesting to see how important the processes are for them and how they can transform their lives. What's impressive most, they're working in everything. You know, they are suit repairs. They are working in the field, you know, agricultural stuff, coffee plantations. The last big thing I met was Hon Ramon Lopez. And he was a combatant during the Nicaraguan Revolution. He started a new business looking for gold in the rivers, near the mountains. He was making a living for the last seven years and supporting all the world family, a big family. And this is what amazed me. Keep working and keep developing ideas to survive, you know. When you have that level of poverty, landmines aren't your most pressing issue. AIDS is your most pressing issue. Education, agriculture, there's so many other things that are higher up on the totem pole than landmines. Yet they remain an ever-present issue that has to be addressed at some point.  And one thing that I really respected amongst these people who work in this profession is the incredible patience. They move one meter by one meter on their knees. It does that for about 10 hours a day every day with incredible dedication and incredible efforts. I couldn't do that job. I'd have too much attention deficit disorder and I'd get blown up. So I think it takes a very specific person to work in this profession. What I learned from this experience in Iraq is that education is key. Mine awareness education programs spread around the country that will definitely prevent at least children playing around with cluster ammunition and explosive ordinance and landmines.   It blends in with the dead leaves and comes more to the soil, especially during rainy season. Three mothers all agreed to be photographed. I had to say, you know, is it okay? It's so important that I photograph you because we have to tell the story. You lost your son and I wanted to take them back to where it happened. I think considering that they never had anybody that showed this amount of attention after their sons were killed, I think it was it made them quite emotional. I think they realized that someone actually really cares. One of the landmine victims we met, Zoran, told us that he founded a volleyball league for landmine victims. Once they get their outfit and they go into the court, you feel like they are just themselves again, I guess. Like everybody is equal. Having things and playing is a big message of hope for the country because during the time lapse of the match, they all play together. Doesn't matter which faction they're from.  It's a lifeless and, yeah. All these things, like maybe, you know, reflect about your own life, like, okay, you are always complaining about these things or these things. And but when you meet these people, you say, you have two legs, you have two hands, stop complaining and just do it, you know. The people who got injured in the last decade, they need rehabilitation, they need social support constantly until, you know, for the rest of their lives. Having covered so many other war zones and conflict areas to me, it's like you keep on seeing the same things over and over again. What happens after the fact? You know, how many generations? If you laid them, you should be responsible for unlaying them once the conflict is over. The fact that they can lay in the ground for another 30 to 40 years, maiming, you know, children, innocent individuals, simply trying to grow food or walk home or get to their cattle or goats, that's a dramatic irresponsibility.


I would like to thank the organizers for inviting me. It has been quite educational so far. Hopefully, this talk will be interesting to some of you. This is joint work with Anish Malik, who is currently in Chile, is okay. So the question, so the entire talk is about two random matrices. So random toplits and random Hankel matrices. So let me define them. So this is the random toplits matrix. And also symmetric. So the random toplits matrix looks like this. You have x1, x2, xn minus one. And it's also symmetric. So the same. And it's a toplit. So it is the same x0 on the diagonal, x1 here, et cetera. So it's constant on these diagonals. And the random Hankel matrix is the matrix which is constant on this anti-diagonals. So you have, let's say x1 here. x2 and x2. x3, x3, x3, and so on up to xn, xn plus one up to x2n minus one. And it's constant on these diagonals. Where xi's are iid, normal zero one random variables. So that will be the assumption. So the entire talk is about these two random matrices. So these were first introduced by Bai, Zidong Bai in 1999. He introduced these as more restricted matrices compared to Wigner and other things and asked various questions about it. In particular, about the limiting spectral distribution and stuff like that. So some of it was proved. So in 2003, I think, 2005 and six, so let's also let me write LTN for the empirical spectral distribution of TN. And similarly, and I'll write LTN bar for the expected empirical measure. So this is the measure which puts mass one over and at the eigenvalues of TN. And this is the expected measure. So these are, so in paper of Brick, Dembo and Xiang. This is from 2006. There's also a paper of Hammond and Miller in 2005. They showed that the limiting spectral distribution exists. So these things have a limit. So they showed that LTN and LTN bar, they converge to some measure mu sub T. And the same is true for Hankel matrices. So the Hammond and Miller did it for the top plates and Brick, Dembo, Xiang did it for both. So what are these muti and muh? So these are not random, of course. So they are deterministic measures. And this does not require the normality assumption. So under, so you only need to assume that the excise have mean zero and variance one, but they showed that these limits don't matter. I mean, it's the same for all such distributions. And yeah, and they are not random. So that's the result. So their approach was by the method of moments. So the proof was just, I mean, of course, the method of moments, the combinatorics is much more complicated here because the same excise are there in many places. And you have to keep track of many things. So, but it can be carried through and they found some descriptions for the moments. So they showed that the moments of these quantities converge and they determine a unique measure which they call mu sub t and mu sub h. But the moments are highly inexplicit. They're complicated. So it's enough to get some properties. Moments are good to get certain properties of a measure. For instance, from this one, it's firstly, it uniquely determines a measure that is one. Second, you can say something about the tails of the distribution. In particular, both of these are unbounded support. So mu sub t and mu sub h have unbounded support. All that can be got from the moments. But if you draw a picture, it's a very simple to do a simulation. So the picture of mu sub t, if you draw random topletes matrix, take its eigenvalues, draw the histogram. This is what mu sub t looks like. And mu sub h looks like this. They are both symmetric about the origin. This looks unimodal, that looks bimodal. So some things that moments don't tell us, so these are the questions. So moments are good for certain things, but certain properties are hard to say from the moments. So for example, the questions are, do they have densities? And if they do have densities, can we say whether the densities are smooth and smoothness and properties that you see in the picture, such as unimodality or bimodality? So these are questions which are not apparent. So in the very basic case of Wigner random matrix, of course it was done by the method of moments, but the moments are just Catalan numbers. And even if Wigner did not know it before, it is not hard to compute the generating function and see that the measure is the semi-circle law. But here every moment is complicated. To calculate say the k-th moment, odd moments are zero and even moment. To calculate the k-th moment, there are something like two to the k integrals. And the integrals can have dimension going from zero to k or so on the unit cube. So they are highly inexplicit. Even numerically, I was never able to compute more than up to the 10th moment of these things. Maybe if somebody is more savvy, they can compute. And the point is if you can just guess the measure, of course, from the moments, then well and good, but nobody has ventured a guess on what exactly this mu sub t and mu sub h are. So what I'm going to say may have some suggestion for that. So this question, there is not much work and the only thing I know about this is that this answer, this was answered as yes for mu sub t. This is a paper of Arunabh Sain and Balint Vevar in 2011. So they showed that mu sub t is absolutely continuous and has a bounded density. So what we have proved is the same for also the Hankel case. And our proof works for both the topolites and Hankel. And of course, mu sub t is a repetition. This is proof of the theorem of Sain and Vevar, but our bounds are better. So we have bound something like the bounds are like, it's not important and I'll not talk about that here, but bounds are actually reasonable looking numbers like one by square root of pi and one by square root of e. So they are off, if you compare with the numerical simulation, this one by square root pi is off by a factor of something like 1.4, a little more than that, 1.45. This is off by a factor of something like 1.85 also. So it's close to, yeah, it's, so that is the theorem of which I want to explain the proof. And well, I'll not talk about other random matrices, but our methods work for some more general class of matrices. So for instance, one can, so which again, I'll not talk about this. So what is generalization here? So if you have a countable group, you can form a topolites matrix. So let's say we have XG, G in the ID normal zero one. So you can form a topolites matrix, which is just XG inverse H indexed by the elements of the group or a Hankel matrix, which is the G, H entry depends only on G times H. So these are topolites and Hankel matrices associated to a group. What you can do is you can take finite subsets of the group going to the full group and take the corresponding matrices and ask about their limiting distribution. So our methods work for the case when if you take G to be ZD and you take going boxes, then we can show all the things go through and we can show absolute continuity and stuff like that. So in the more general case, I'm quite confused about this question, whether there's a good answer or not, I don't know. Please ask me if there are any questions at any time. What I want to do is to give an idea of the proof of this theory. So the proof has really two steps. No, no, they are both unbounded. So support is unbounded, yes, both of them. Because the moments go faster than exponentially, one can see that they cannot be bounded. So there are many interesting questions about these things, like the largest eigenvalue and various questions about this, which I'll not be talking about. I have nothing to say. So there are really two parts in the proof. Step one, actually it's quite interesting and if some, I have, it's a, okay, I'll, at this level, let me just say it like this. So we can, the main idea is that we can write this toplit matrix as a sum of two random matrices. So we write Tn as a sum of two random matrices where an and bn are independent. So this is independent random matrices. And if you look at the LSD of this, both of them converge to normal distribution. So you have two independent random matrices. They're limiting spectral distributions are actually normal. And so, and similarly in the case of Hankel, we write it as an plus bn, okay, not the same an plus bn. Again, they are independent and they're limiting distributions converge to this symmetric early distribution. So this, so it's just the symmetrized version of the early distribution. Mod Xe power minus X square by two is the density. Now anybody with experience in random matrix should think at this point, the problem is done. You have two independent random matrices and they have very nice limiting distributions and you're adding them. So how can it not be absolutely continuous? So indeed, it sort of explains the picture too. You have your, there is some kind of convolution. So the limiting distribution of this mu sub T has to be some kind of a convolution of normal with itself and mu sub H has to be some kind of convolution of this early distribution with itself, which sort of seems to explain why this picture should look like this. It's clearly this density looks like this. So you can, if you take a normal convolution of this, you will see a picture a bit like this. But the point is the operation here is neither the ordinary convolution or free convolution. It's a different convolution which we sort of understand at the level of moments but we don't really understand well. Maybe if one understands it, maybe one can even tell exactly what is this mu sub T and mu sub H. And so a step is needed. So from here it's not immediate. So at first I thought maybe it is free convolution but it is not at some 10th moment they differ actually. So the 10th moment, one of them is 42, the other is 44 or something. Okay, it's not free that much is clear. So there is a second step which is a spectral averaging. I'll explain it later. So spectral averaging is a technique that is well known to many people in random operators and so on. So here there is a spectral averaging. There is a different spectral averaging we have to do in the topolitz case and in the Hankel case. So these are the two main steps and from that we can get the absolute continuity of mu sub T and mu sub H, okay? So what I would like to do in the remaining time is explain these two steps. Now, so I'll explain the first step. So the first step in the topolitz case. So this is something curious to me. I think this must be, there is an observation about topolitz matrices, nothing random which probably is known but I could not find anywhere and so first don't, let's think of just a general topolitz matrix with not even Hermitian. It can be a general topolitz matrix and so this is not random, not symmetric, okay? So there is a presentation that we found for general topolitz like this. So to explain that let me say the main character in all this is this matrix L which is zero one, one's on the super diagonal and zero elsewhere. So clearly everything, the topolitz matrix can be written in terms of this as X naught times identity plus X K times L raised to the power K. L raised to the power K will have once on the Kth diagonal here and X minus K, so if you want it on the other side you just transpose it L star raised to the power K. So this any topolitz matrix can be written like this. Now a lot of things in topolitz matrices, I mean for instance also the same in Virak paper, the general idea is it looks almost like a circulant matrix, okay? Which would be much better but it is not circulant, it's a in fact a slightly problematic matrix, it's not normal. So the Kajia step here is to actually write this zero as one plus minus one. So we'll write it as zero one, one, one and put a one at the N comma one entry and everything else is zero plus you consider a similar matrix but put a minus one here, okay? So this matrix I call C and this matrix is D, okay? It's actually two times L, sorry. Two L is two times this and that is C plus D, okay? So I just put a one here and a minus one here. So this is very, this representation, what is the point of it? So here are some basic points. C and D are unitary, they are unitary matrices. It's quite clear, C is a circulant matrix. So this one I'll just call it twisted circulant. So what is C doing? If you think of a discrete cycle, C is just a shift operator on the discrete cycle and D is also a shift except that at one location it flips the sign, okay? So C and D are both unitary. In fact, C to the power N is identity and D to the power N is minus identity.  And most importantly, not only is L is half C plus half D, but also if I take L to any power P, it is just half of C to the power P plus half of D to the power P for, okay? Because if you take L square, L square is the one with ones here on the next diagonal and C square has ones on the next diagonal as well as two ones here and D square will have two minus ones here, et cetera. So this works. So for all P less than equal to N minus one and if you take the transpose, you just get that C star is same as C inverse. This is unitary, C to the minus P plus half of D raise to the power minus P. This is true for all P up to N minus one. So the point is this L is written in terms of these two unitaries. So the entire topletes matrix can be written also in terms of C and D, okay? So what does that lead to about the matrix itself? So this implies from this we get that T is, well, it is some polynomial of C and a polynomial of D because you write each L power K as and L power minus K in terms of C and D. So what we get is, let me write it as A plus B where A is summation Aj C to the power J, okay? So here I'll make an assumption. Let me take N to be odd, okay? This is just convenient. There is a slightly different representation when N is even but let me take N to be odd. Then you can write and this is of the form BJ D raise to the power J, J equals minus M plus one to M minus one. So where you can write down exactly what Aj and BJ are. Aj is something like XJ plus, okay? So you have this matrix. So these two matrices as you see A is just a polynomial of C. So we know it's full spectral decomposition. So C, it has the same eigenvectors as C. Only the eigenvalues change. So the eigenvalues of C are in fact, okay, we can, I did not write it here. Maybe I should say what are the eigenvalues and eigenvectors of C? So let's write V theta for the vector one e to the i theta, e to the i N minus one theta. Then C eigenvectors are just C V theta is e to the i theta V theta for any Nth root of unity. And for D, the eigenvalues are it's similar, i T V tau where e to the i N tau is minus one. So the eigenvalues of C are roots of Nth roots of one, eigenvalues of D are Nth roots of minus one. And eigenvectors are just these things. So it's just very explicit. So thus of course A will have exactly the same eigenvectors as this except the eigenvalues change. And B will have the same eigenvalues as, eigenvectors as D, eigenvectors as D, eigenvalues change, that's all there is. So in particular, so this representation, so it may be of some use in general, I don't know, but if you, for example, a basic theorem, this is just a small digression, if you think of the Ziegolimit theorem, which is a theorem about determinants of topolitz matrices, the Ziegolimit theorem is completely obvious separately for this A and for B. Because if you know exactly what the eigenvalues are, if you start with a topolitz matrix with a certain symbol, and you write down this A, the eigenvalues of A will be the values of the symbol at the roots of unity. And the eigenvalues of B are the values of the symbol at roots of minus one. And so the determinants are just these products which if you exponentiate right as e to the log, you get the Ziegolimit theorem. I don't know if for instance one can prove the Ziegolimit theorem for T from this, this I don't know. But maybe there is, so it's an elementary looking observation, so it must be somewhere, but if somebody knows, I would like to know it afterwards, okay? So in particular, what happens when you apply it to the random matrix? So in the random case, xj and x minus j are the same, and that is some normally distributed random variable. Therefore, aj and bj are independent, so it can work out everything. So this is the claim. So you have broken that matrix T into some of two independent random matrices. And okay, what are the eigenvalues of A? They are of the form, well, they will look like, so you take any nth root of one, and then you form this polynomial, so that is an eigenvalue. So you get this, you have this eigenvalues of A, which are very explicit, and they are all linear combination of the same edges, so they are all normal. Actually the eigenvalues of this big matrix A and B are actually normal, and they are almost independent, in fact. So I'll just write that A is, so I'll just write the conclusion, because I want to tell a little bit about the second step. So let me write what is the conclusion. So this A and B we can exactly solve using this.  These are rank two. When you work out, you see that one eigenvalue occurs with multiplicity one, others occur with multiplicity two, because of the n odd case. If n is even, then there are two eigenvalues of multiplicity one, et cetera, not so important. But these are rank two projections, and this is rank one. And their P's are not random at all. They are completely coming from the eigenvectors of C. And lambda J are almost IID normal, zero half random variables. So this is, I write almost, one can work out the correlation of these things. It's very small. So for the talk, I'll just pretend that they are actually IID. And the representation for B is quite similar. There are some, and mu J are almost IID normal, zero half. And Q, these are rank one, and these are rank two. So P J and Q J's are not random, that's the point. So this is the representation. This is step one, where you have written the topolitz matrix as a sum of two matrices, which are completely understandable. So from this, it's obvious that the limiting spectral distribution of A and B are actually just normal zero one. Sorry, normal zero half. So the Hankel case is similar, except that maybe I don't write it now in the interest of time. In the Hankel case, we can do the same. Yeah, what is the difference? So maybe I finish the topolitz case and in the end, I'll mention the Hankel case. So this is what works in the topolitz matrix. So from this, how do we see the absolute continuity of the, of T, for example? So we have written T as A plus B. And we want to, okay, so the main way in which we will show that the absolute continuity of this is to show that the still just transform of the expected empirical measure is bounded. Uniformly, there's an N. So we will consider GN of Z, which is the expectation trace, ZI minus TN inverse, one over N. And we show that Z in the upper half plane, that is imaginary Z positive. So there is a uniform bound for the still just transforms of the expected empirical distributions of all TNs. So from that, it is immediate that the limiting spectral distribution will have exactly the same bound. And it is a well-known fact that if you get a bound on the still just transform, that means the density has exactly the same bound. Because when you approach the real line from the upper half plane, the imaginary part of the still just transform converges to the density at the point. So you get exactly the same bound maybe with a one over pi factor for the density. That's what we have to show. So how we do that is, so we have this. So let me write what the spectral averaging is. So let me write the spectral averaging lemma. So this is the general nature of spectral averaging lemma. Incidentally, in the work of Arnab Sain and Balint Virag, where they proved this, they also use spectral averaging, but it's a much more complicated one. Ours is a very simple one-dimensional spectral averaging. So let's consider M. So we have a, so this is a real symmetric matrix. And then we add, so this is a projection and lambda is a parameter. So we think of lambda as random distributed according to some density. So this is a probability density function on the real line. So think of it as a random operator where you have a fixed one plus lambda times a projection. This will be relevant here since we know how to, the spectral decomposition of A and S, what we are going to do is just fix one of those lambda case, a condition on all the rest, then we have a matrix in this form. So if we condition on everything except say lambda one, we have lambda one P one plus the entire rest of A and B together will be M naught. So that will be the idea. So then the fact is that if you take trace of, P times Z i minus M lambda inverse P expectation, well expectation is with respect to phi. If we can, if we average this over the density phi, then we just get pi times, okay. Let me put absolute value pi times the sup norm of phi times the dimension of the projection. So this is the spectral averaging lemma. No, I mean, so of course, if pi is not a bounded density, I don't get anything, but assumptions on which, no M is much higher dimensional, it's okay, no problem. Yeah, but here we are not actually studying the full steel just transform. It's only on the projection in this P direction that is important, yeah. So for instance, how does that help here? So when we come to the random situation, so how is this useful? So let me indicate how this is useful. If you apply that with some say, you fix the kth one and so on. So we get that the expectation of trace P k, zi minus T inverse P sub k. From this, we get that it is bounded by pi times here, okay, so phi is the normal zero. So here I'm fixing say lambda one, so some kth one, then we have the normal density. So let me just write it as some constant times two, because rank of the projection there is two or one, depending on which one you take. So you just get a constant for each k up to, yeah. So I wrote almost IID. What it is is that when you condition on the rest of them, the variance of this is still very close to half, okay. It is always more than one fourth, but if with n going large, it is in fact, you can make it as close to half as possible. So what we do is we condition on the rest, then we still have a normal random variable with that much variance, and that is what is used in the spectral averaging. And then you take a further expectation over all the variables to get this. And then when you sum it over k, you get the sum of all these with all the projections will give you the still just transform. So you just get that the still just transform, which is the average of these things will give you, that's the, that's all. So this is the key point in the proof. Now, those pks, they sum to identity, right? This is the spectral, yeah. That's the spectral decomposition of A. So the sum of those projections is identity. When you add them, you just get the trace of Zi minus T inverse. No, no, but we have to average. G of Z has a one over n also. So it is the number of summands is also n and it's exactly canceling that. Any other questions? So this is how it works. Now, yeah, okay. How many minutes do I have? Two, three, four minutes. Okay, so yeah, so I'm thinking whether to indicate a proof of this or to just tell what happens in the Hankel case, maybe I just mentioned what happens in the Hankel case. So in the Hankel case is actually similar but a bit more complicated. So in the Hankel case, the first step is actually quite similar. Maybe I just say it in words. So here what happened was we take any toplit matrix. We could write it as a sum of two matrices. One is a polynomial of C and one is a polynomial of D. In the Hankel case, we can, you take any Hankel case without randomness. We can write it as a sum of two matrices, a and b. Now, the point is a is, everything is slightly more complicated. So in the toplit case, a can be reduced to diagonal form. I mean, the eigenvectors don't depend on the entries of D. That was the point. But here it depends, but you can bring it to block diagonal form where these are two curves to blocks. So this matrix A can be brought to two curves to blocks by a unitary transformation conjugation which does not depend on the entries of the matrix. In the toplit case, the same could be done up to diagonal but here it is only up to two curves to block form. And the similar thing for B, we can bring it to two curves to block form, et cetera. So the spectral averaging also got a bit more complicated because well, there is a spectral averaging glamour where this quantity that we do spectral averaging over, this is not a positive definite matrix. So at least when I asked a few spectral averaging experts, they said it only works when you have a positive definite perturbation. But in our case, it's a very small rank perturbation. It's only two. Therefore, we could handle it directly. And we have an analogous spectral averaging glamour from which we can get the conclusion. So the key point is the proof of this but okay, I don't have time for that. So I'll stop here.


Rowing in color, an organization designed to support diversity in rowing, had their first all-Latina team at this year's head of the Charles Regatta. The coxswain of the team, Sebastiana Lopez, tells us about the challenges as a minority in rowing. It takes a lot of people. It doesn't only take minorities and rowers of color to push our own weight. Some people are exhausted of fighting this fight. People are exhausted of always talking about why you shouldn't be. Why microaggressions aren't okay. Why racism is okay. People are tired of fighting this fight. Jeanie Trace, the chief community engagement officer for U.S. Rowling, talks about how diversity can still be improved. So we are putting education, training, resources together. So I would say the culture piece, but then also visibility and representation. So we know that there is diversity in our sport already, but maybe there's a lack of visibility in terms of social media or the website and storytelling and bringing those stories to life to say, I walked onto the team where I didn't know about rowing until I was 50 and it's changed my life and bringing some of those to life. U.S. Rowling says that almost 7% of their athletes are people of color and more organizations are offering scholarships to increase opportunities for minorities. Reporting for BUTV, I am Aisha Kulibari.