Welcome to the 37th session of the first module of the core signal and systems. We will now complete the continuous time convolution that we are undertaken in the previous session. By complete I mean let us write down all the outputs of the convolution in the three regions that we are identified and then sketch them.  So, we are identified three regions. The first region was p greater than equal to t1 plus t2 and less than equal to t1 plus t2 plus capital T1. Region 2, t goes from t1 plus t2 plus capital T1, t1 plus t2 plus capital T. Of course, capital T2 is greater than capital T1 so valid. And finally, region 3 was p is greater than t1 plus t2 plus capital T2 but less than equal to t1 plus t2 plus the sum of capital T1 and capital T2. And the convolution value in region 1, 2 and t were as follows. I will just write them down in this horizontal fashion. Here it was t minus t1 plus t2. Here it was a constant at capital T1 and here it was essentially a dying or reducing line. So, for the last part we had written down the output of the convolution as essentially a difference. So, you know, let us by sketching this we will get an idea. First the convolution rises, reaches t1 and then goes to the end falling off as a dying line or a reducing line. Now, the convolution is a function of t. It begins at t1 plus t2. There is a transition of behavior at t1 plus t2 plus capital T1. One more transition of behavior at t1 plus t2 plus capital T2 and the final transition to 0 at this. In this region, the convolution takes the value capital T1, a rising line here and a falling line there, 0 beyond here and 0 before here. Region 1, region 2, region 3, all straight lines, 0 here and 0 here. Now, notice something interesting. Here our convolution was simplified because you were always multiplying two constant functions and finding the area under a constant product. You could, if you wish, think of it in a metaphorical sense as all passengers having the same strength, all the passengers inside the train and all the passengers outside the train have same unit strength. So, when they hand shake, they all contribute unity and then we integrate and find the combined effect. What if the passengers as will often be the case have different strength? They have different builds and different strengths. What does that mean? For example, suppose we were to try and convolve the following two functions. Let us take an example. Convolve this function. The function that rises from 0 to 1 over an interval of t1. So, t1 to t1 plus capital T with another function that rises over an interval of t2. Let us call this x1 t and it is called as x2 t. Now, here you should think of it as again passengers and a train with passengers inside the train and outside the train. Passengers space very closely together into a continuum. The only thing is the passengers have different strengths. So, the tallest and strongest passengers are in the end and the weaker passengers are in the beginning. But you know, you have to be careful. Again, suppose again without loss of generality, let us take capital T2 to be greater than capital T1 because you can always interchange the order of the functions and the convolution is not affected. So, without loss of generality here, let T2 be greater than T1. And we can do the same. We could put the platform with the passengers which have a longer strip and the train with the passengers that have the shorter strip. And let us draw both the platform and the train. The platform would now look like. I do not need to carry out all the explanations again. I will just try to withdraw the platform and the train now. In fact, we must now write down proper expressions analytically for the passengers on the platform and on the train. So, here for this one, I would write the expression. Well, how much is this theory? It is take the difference from the point lambda at which you are from T2. So, lambda minus T2 divided by the entire interval which is covered. So, capital T2 into 1. That is the value anywhere here in this region. And here I need to take again I could write a similar expression there. So, I would have written so T minus lambda and so on and so forth. So, I can write a similar expression for this. I could write here T minus lambda minus T1 divided by T1. Now, for example, if you take lambda equal to this T minus T1 plus capital T1, you can see that gives you 1. And you take this value T minus T1 here for lambda, you get 0. Now, again here we have three regions as before. However, now the convolution integral is a little more complicated. So, regions are the same. Let us write down the regions. In fact, I will now calculate the convolution each of the three regions. Let us write down those three calculations. So, T1, you know the regions do not change. T is greater than equal to T1 plus T2, but less than equal to T1 plus T2 plus capital T1. And in that region, you essentially have the frame not quite having entered the platform. So, I will draw the platform and the phone in different colors here. I will superpose the frame which is the region of overlap. Let us mark that in green and let us calculate the product. This is the region of overlap. And we also need to write the expression everywhere. The expression for this is T minus lambda minus small t1 divided by capital T1. And we need to take the product to calculate the convolution. We take the product of this with this integrated over T2 to T minus T1, this region, integration region or integration interval. Let us write that down. We are saying essentially the convolution region 1 is the product lambda minus T2 divided by capital T2 times T minus lambda minus T1 divided by capital T1 d lambda integrated from T2 to T minus T1. So, essentially it is going to be a quadratic, but to be expected. When you multiply two line segments and integrate, you are going to get some kind of a quadratic here. Now, in fact, you know, the integrand is quadratic. When you integrate, it is going to be cubic. So, in fact, if you look at it, expand this, look at the expression here. The integrand is quadratic. So, you would have a lambda squared term and so on. So, the integral will be cubic. So, I mean, you know, it would require a little bit of algebra to work this out. And that calculation I am leading to do as an exercise. I am leading to you the key where you have to work a little hard, but it would explain to you several things about convolution when you do it patiently and carefully. Now, the same approach can be found for region 2 and region 3. In fact, the only change, the integrand is really the same in region 2. It is just the limits that change. However, here, one has to unlike the earlier example where the convolution remain constant all through region 2. The convolution would not remain constant here because there are passengers of different strength interacting with each other even all through region 2. Region 2 is the region where the train moves within the platform strip. And finally, there is the portion where the train starts leaving the platform strip and there again the expression is the same, but the region over which you integrate that expression, the integrand is different. So, I leave this as an exercise to you. I recommend that you complete this and sketch this. You expect that you would get three cubic segments in your sketch. It would be a good exercise to complete this and understand those sketches in some depth. Please do that exercise. Thank you.


Whenever I'm doing Wi-Fi testing, frequently WaveMon is my go-to tool to see the statistics on the Wi-Fi. Now, it's really simple. Most of the major distributions, you can sudo apt-get install in your WM-based distributions, WaveMon, I believe it's in the repositories for several other distros as well. Pretty easy tool to find. sudo apt-get install WaveMon, I've already got it installed, so I got the latest version here. Now, you can run it without root privileges, which we'll start it like that, and it gives you some of the details, but you're not able to run a scan. So we're actually gonna go ahead and quit, and we'll do sudo WaveMon. All right, now we're running as admin privileges, which gives us a couple more features. Now, the first initial screen out of the box, this is a default config. It's gonna give you the link quality, signal level, and I'm actually, because I'm on my desktop right here, it will default to the first wireless it finds. If you have multiple wireless, you can specify which one from the command line, but the majority of people just have a single wireless card in there. Now, my desktop is connected hardline, but I plugged in, if you haven't used them, a little alpha networks, ALFA networks, USB, just for this demo here. Great for doing wifi testing as well, that's why I have it.  Wifi is not like hardline in levels of simplicity. It is a lot more complicated layer. It's amazing it works as well as it is. I remember the early days of wifi, how difficult it was, it's become substantially better. But right away, what you're presented with is all the different statistics because wifi isn't just a connection over a certain frequency. There are channels and bandwidths and everything else. There's also this, and a lot of people sometimes don't realize what this is. Internally in the wifi stack, there are drops and retries. And there's also another profile curated by each wifi company. They create a profile for how fast the connection speed they think should be based on the signal and the gain of the antenna, which will control the link quality. So there's a lot of factors in wifi and this helps understand or see some of the other pieces of it. They're all in one easy display. So we can go here to list or scan and we can see all the other wifi's. So even though I'm connected to one, it will show all the others. It can perform a scan and see the different percentages, statistics, how far away they are essentially in terms of power. So it's kind of a nice all in one utility. It's really simple. It does have some preferences so you can change a couple things here. I'm just using the F keys to bounce around from option to option. It tells you which interface, channel signature, cycles, things like that. Now one of the cool things because this is command line, you can have a headless Linux box wherever you wanna have it and put it in an area and log in remotely via SSH and scan things. It's pretty cool. Now one of the things I wanna show you as well is because all this is being updated essentially in real time, I'm gonna go over here and we're gonna run an IPERF test. And something, even though this IPERF is pretty solid this 25, 30, you see a little bit of variance here. And here what you're noticing though is a number of like transmit retries or RX retries. It's kind of cool to be able to see this. So I'm moving the Wi-Fi around. I've actually got it in my hand now. Oh, bump the microphone with it but it's trying to find something I can do. Maybe put my hands around it. There we go. And change the Wi-Fi signal. I've got this little screw on antenna and I can take this off. And there we go. So we see the signal and what it, now the antenna is in my hand. It's got a little, I have a directional one on it. But this is what I use this utility for a lot is when we're doing the Wi-Fi testing because I can get snapshots and say this is what it looks like. This is how many retries or drops. And those little factors, whoops. I have unplugged it accidentally. No such device. So that's what happens when you unplug it while running it. So let me go ahead and plug it back in and quit, I was at the length of the USB. Whoops. Nice thing about Linux is when you unplug or plug something from USB it's pretty much instantaneously works again and reconnects. There's not, I didn't even pause the video for that. And there's only probably, yeah. Here's only the certain drops when the network interface was missing. Here's where it dropped a couple of seconds while the USB was unplugged and now it's back up and running. But no, this is just a handy utility I use. I just want to, it's a brief video. There's not a lot to it. It's really, really simple. It doesn't have a lot of options. It's got a level histogram where you can see the levels and things like that I don't use, but you can see this. Mortarsly, I will use it a lot, which I didn't run it when I restarted it. Hold on, sudo wave mom, there we go. I mostly use it for the scan list so I can find Wi-Fi networks as it'll list them all out, even hidden. This does not do any functional control though I still use the networking interface to actually join and move from networks. It's just all about display information. And more than anything else, I use this when this is the testing I was doing for the UniFi video that I did to see and understand just the different connections.  And so you'll see some future videos because I want to do some more Wi-Fi testing because a lot of people have been asking about it. Wi-Fi testing is just so hard because people say, yeah, but I had a tree in the way. When I was doing a site to site, it made a big difference, it does. And it's, I've almost wondered if there's a difference in Wi-Fi signal penetration from different types of tree. Do pine trees more than oak trees? I do know one of the sites to sites that we've worked on the seasons here in Michigan make a huge difference. Cause as the leaves come off the tree, their signal goes up because they just don't have a clear line of sight but they have good enough to get the data they need across. So there's little factors that play into Wi-Fi. I mean, you're transmitting through the airwaves, you've got density of moisture in the air and many, many other factors including a lot of potential outside interference causing issues with the Wi-Fi. So future experiments, I'll still be using this tool and when everyone messaged me in there, what tool, what tool is this? I'll just reply with this video real quick. Like I said, not much to it. Just a handy, great utility to put everything in one little window and easily screen-cord-corded, screen-captured or when I'm doing things remotely, plugging it in. And I think Wave Man will work fine on a Raspberry Pi. Now I say, I think I haven't tested it cause I don't have, I don't know if I have a Pi with Wi-Fi? Maybe? I don't remember. I have a couple of them laying around that I've been playing with for mostly games. This is for my retro Pi video on a while back. Maybe I'll do some more Raspberry Pi videos but it is because as long as you have a little institution that supports it, this is also kind of a novel thing you can do if you wanted to use a Raspberry Pi and the Wi-Fi on it to leave it somewhere but remotely check Wi-Fi signal strength and changes. Another use case you could use it for. So that's it, Wave Man, real simple to use. Not a lot to it but very, very useful in terms of when I'm doing all this Wi-Fi testing. I've not found really in Linux any graphical tool that I thought was substantially superior to it. And it's been a while since I looked so if someone has a comment or one that they think is really amazing graphical tool, cool. If not, I'm gonna keep using Wave Man because it's handy and easy to read and concise and I know where all the things are. Thanks for watching. If you liked this video, go ahead and click the thumbs up. Leave us some feedback below to let us know any details which you like and didn't like as well because we love hearing feedback or if you just wanna say thanks, leave a comment. If you wanted to be notified of new videos as they come out, go ahead and subscribe and the bell icon that lets YouTube know that you're interested in notifications. Hopefully they send them as we've learned with you too. Anyways, if you wanna contract us for consulting services, you go ahead and hit LawrenceSystems.com and you can reach out to us for all the projects that we can do and help you. We work with a lot of small businesses, IT companies, even some large companies and you can farm different workout to us or just hire us as a consultant to help design your network. Also, if you wanna help the channel in other ways, we have a Patreon. We have affiliate links. You'll find them in the description. You'll also find recommendations to other affiliate links and things you can sign up for on LawrenceSystems.com. Once again, thanks for watching and I'll see you in the next video.


You know the story of Joseph is very peculiar because Joseph when he was a little boy he got this nice garment from his dad it was a coat of many colors and he this coat symbolized that Joseph was the favorite.  That's kind of what it was it was an insult to the rest of the kids and and this kid he got a coat and the Bible says when he got that coat he started to get dreams and in his dreams he saw everybody bowing to him. It's kind of hard to dream bad dreams when you got nice coat when you have people speaking over your life and saying you're awesome you're beautiful you're handsome you're strong you're gonna make it people like that tend to have dreams not nightmares dreams not fears and Joseph gets this beautiful coat and one day his brothers they ripped that coat from him and they dip it in blood and then Joseph goes into Porifar's home and they give him another coat it was a coat of a slave and we know Porifar's wife she didn't waste any time she ripped that coat from Joseph as well Joseph goes into the prison where he is now a prisoner he is a coat of a prisoner and the moment Pharaoh had a dream the Bible says when they called Joseph into the Pharaoh's court they ripped that clothes from him as well and then we see last time when Pharaoh puts a clothes of a prime minister on Joseph that's a lot of changing of clothes four changes of clothes it's very interesting because in every season when his clothes changed Bible used this word and the Lord was with Joseph in a dry pit and the Lord was with Joseph when Joseph is in jail and the Lord was with Joseph when Joseph is a servant he has a death certificate laying in the house and the Lord was with Joseph when Joseph was a prime minister and the Lord was with Joseph your seasons will change God will never change God will never leave you and God will never abandon you God will never forsake you can somebody say amen and that's why i want to challenge every person tonight do not become attached to your season your season may be today a season of being on the top of the mountain don't think God loves you more because you're happy your season may be today in the low valley don't think God left you because you can sense him or feel him or see him no more and the Lord was with Joseph God's character God's will it never changes it stays permanent that's what makes him God that's why he's trustworthy that's why he beckons faith in him because he is unmovable unshakable but his clock is always ticking that means that your situation today tomorrow it could be completely different that means that your problem today in the next five minutes that could be completely shifted that means that whatever you are in today in the next minute God can completely shift the situation around God's clock is on the move because God stands still can somebody say man have your faith anchored in God's character and always know because God is immovable my situation is gonna move joblessness is gonna move the fact that you're single ready to mingle and you can't find nobody that could move the fact that maybe your children are serving God and they completely have nothing to do with God listen that is able to move what because God does not move hallelujah God's clock can move amen


All right. All right. All right. We are live live live. I think I'm live on Instagram, too Let's see. Let's see how it's going. All right, y'all. So this is the end of day 6 5 5 then a 5 so Monday Tuesday Wednesday Thursday Friday Saturday 6 I read it in wrong. This is the end of day 6. Um, oh, I'm super excited We are kicking this thing off for one of a reason One of a reason Instagram isn't working so a whole tight Facebook. We're gonna be talking about day 6 I want to talk about yesterday and today and what's coming up tomorrow. So really quick live challenge Okay, let's go Instagram. Where you at? Where you at Instagram Instagram just not working y'all. So what's uh, let's just go at it So here's the what I'd love for you to do if you don't mind So this is the end of day 6 now yesterday We did the burpee challenge and it was amazing seeing how many people that were basically how many people out there that Were doing burpees in their offices and getting it done and they're like I haven't done burpees in years That's inspiring y'all like you have every reason not to do it and you did it. That's pretty dang awesome That is super super cool.  I'm proud of me. All right Let's see if we can get this up and running There we go Instagram Instagram is live now Instagram is up too. So y'all we're this is day 6 wrapping it up day 6 Tomorrow's father's day. So before we go any further.  No neither of my fathers are either along with us But I want to say happy father's day to them Because without them I wouldn't be here Without them I wouldn't I really wouldn't be the person I am today Now I'll be the first to tell you that they probably on paper Robbie weren't the best fathers That a son would be looking for there Let's just say that they weren't the fathers that I would try to be for my sons or my son Sorry, we'll have one, but I will tell you this is that They taught me a lot because they gave me what they gave me right at the end of the day And so I'm just truly grateful for that So I thank them for as many things that I've created in my life because without all those Experiences I the wisdom and information today to hopefully go out and change more lives. So So in the chat do me a huge favor Just say happy father's day if that's all you want to say, but let's just do something really cool today We did the we did the 20,000 stuff. It's Saturday Saturday. We should get out and move get out and move no audio I don't have audio. Hey in no audio there. What's going on? Instagram's being really really really really weird. I don't know why But if there's no audio, I will try it again. So Anyway, but so let's do this. So today was it was it was basically two miles and or 20,000 steps, so I'm just a little over 20,000 or 10,000 steps. I'm probably at 12,000 right now I got some work to do. Yes, I hit the two miles, but I'm going for the 20,000 steps I didn't realize there's there's more than 20,000 steps and two miles actually did pay attention But either way, I'm gonna hit 20,000 tonight. That's my goal Hopefully you hit those or at least set a standard for yourself set a goal for yourself. Like I said Dwayne Daner's 72 years old body doesn't do burpees anymore. Hey Dwayne Daner. I'll tell you I'll tell you Christy Sandy in Iowa. Are those iowegens. They did some burpees. I mean you're Minnesota boy. Come on now Come on now Get 10 get 10 you can do a little ones if you want to but good. I'll get let's get some walks you out today 100 ounces of water today. Hey listen if it's late at night. You didn't hit your goal. Just take that down as a check mark I hope that makes sense. I don't want you to pound a hundred thousand a hundred ounces of water right before bed bad idea Just because you want to accomplish your goal. That's not the way that's not the intent of this The intent of this challenge is to challenge you to do things that you've ever done already do Some of you did but guess what? I don't need to tell you to do more because you do more anyway And that's a lesson and there's a lesson for tomorrow and I got a challenge for you The hardest challenge we're going to do the hardest challenge We're going to do for me is tomorrow the hardest challenge this whole 10 days is going to be for me tomorrow And I'm going to say what that is in a second. So What else would you do? We got back to the two meals a day super super excited About that and we're a post on facebook our post on social media So hopefully you did a post about your family something exciting about what was going on Something just about your life. Hopefully that's what you posted today Be grateful that we get that right be grateful that we have all this thing my first time doing burpees Tammy that's awesome.  Tammy? Did you go like this? Did you did you pat yourself on the back? I hope so be proud that you did something for the first time Because the alternative was you sat on your butt and do nothing. That's the alternative The point of the challenge is for you to do things that you don't normally do Uh sarah is at 17 000 steps walked at 10 k this morning for miles for a migraine virtual race Awesome job sarah. It's migraine and headache disorder awareness month. I did not know that I actually been having a little headache right here. Uh, we're working on it though. We're working on it. All right y'all so Who's ready for tomorrow tomorrow is going to be a little different day tomorrow a is sunday Um, if you don't know the history of sunday a lot of people look at it as a biblical day But the real big history of sunday was a day of rest, right? That was a big Component of sundays was a day of rest Because most people didn't work four days or three days or five days a week They worked six hard days and they took a day off. So sunday Is going to be our day of rest. So I want to kind of add to that So this is the challenge for sunday for nutrition. We're going to do two meals a day Preferably two ketones tomorrow preferably two ketones. You can do one I don't know where you're at with your rations if you don't have enough to finish the 10 days I want because we're going to need a couple extra ketones next week. So stay tuned for that We're also going to be introducing the 24 challenge in the reboot tomorrow night But I'll be doing that virtually over recording because I'm going to be with my family for father's day And that's part of the agreement for tomorrow. So tomorrow. It's two meals Um, if you're somebody that's doing a special father's day brunch, right? We like to do special meals on father's day brunch Well, all I want you to do is do that modify don't worry about the time because the time's at 10 o'clock in the morning Still do your two meals have your ketones have your first meal and then have your ketones and then have your last meal That's fine. Just modify the times do not try to be perfect with anything because it doesn't work Doesn't work, but I want you two meals tomorrow tomorrow Your your kids are making you something special. It's a little bit not keto friendly Don't worry about it. Enjoy tomorrow.  No I don't want you to do that. But I do want you to enjoy tomorrow. Okay. Enjoy this holiday Allow yourself the flexibility and give yourself permission to not feel bad about being perfect I hope that makes sense. I hope that makes sense Okay, now I'm talking to a lot of fathers But I know guess what if you're a woman on here, you might have some component to that Right, you might be along the ride with your husband with your father Whatever that looks like and I want you to take that serious. Okay The reality is this is anytime, you know, I've watched with weight watchers for a long time And I watch these people and if you didn't weight watchers and it's worked for you awesome I haven't seen that happen yet. Most people are very miserable around food because they they're married to this number In these outcomes and they think that it's like they always have to be perfect And that's not the way it'll ever work. There's always going to be a holiday.  There's always going to be a vacation There's always going to be something going on that's going to throw things out of the routine Allow that to be And allow all the other times to be perfect. But here's the deal It's the guilt you feel about those things when you aren't perfect that actually causes more harm than the food itself So this is where we can start making those little adjustments So I want you to enjoy tomorrow be be cognizant be responsible. I guess if that makes sense Don't purposely start to binge eat because you think you have freedom. That's not that's not the intent The intent is is to be relaxed about tomorrow and there's a keyword in there relaxed Okay, so I know I'm going to be doing something fun tomorrow. I don't know what it is for sure They're trying to trick me with some stuff. I have some ideas. So tomorrow the goal is just two meals I don't care when you eat them time doesn't matter. Okay time doesn't matter now The only time that matters is nothing later than seven o'clock. How's that? I'm going to resay that the only time What's up wheels? The only time that matters is don't eat your last meal after seven o'clock now if it's 7 30 So be it, right? Um, that's number one number two Um, number two, this is what I want I want this is gonna be a little different for a lot of you number two if you are doing a father's day Fun fun fun time and you know that you're gonna have some carbohydrates I want you to drink an extra serving of ketone.   Just go about your day. Okay, so that's what we're doing. Um, that's tomorrow nutritionally Okay, here's what we're gonna do for the rest of the day tomorrow Is I want you it's a day of rest is day relaxation so No exercise if you want to go for a hike or do something fun good if relaxation for you is exercise Do it My point is is there's no goal around exercise or fitness or walking or burpees or push-ups none None Monday on the other hand, we're gonna have some fun Monday on the hand We're gonna do something really really cool and stay tuned. I have a video coming about that tomorrow But and you'll get tomorrow night So this is a day of rest, but what I do want you to do This is what I do want you to do tomorrow.  Just deflect if you start to think about something just turn it off and come back to here Right the zen moment right Tomorrow, I want you to go within and just start to see if you can find peace in yourself just find quietness yourself It's hard for me to do. I'm always I like a lot of stimulus being around It's the hardest thing for me to do is to be quiet and sit still I do 10,000 steps in my house just in my house without going for a walk true story I walk like six miles a day in my house. I don't slow down So for me, it's really challenging something. I'm constantly working on but tomorrow's a day of rest I want you to encourage that the second thing if you're a cell phone Uh jockey if you're always on your phone and you're always on your phone Put it down for at least one hour tomorrow Take schedule an hour where you put it down and you just forget about it for one hour For one hour now if your life depends on it, uh, and you use it for another reason I hate guess what you can you can do 30 minute bouts But or have a special ringtone but literally put it down and don't touch it for one hour tomorrow Second hardest thing for me to do second hardest thing for do as I have a global business I spent a lot of time on it to to do what I do. Um, so so those are the challenges for tomorrow So here it is two meals tomorrow two key tones preferably tomorrow And then what we're going to do is you're going to do rest five minutes of quiet time You can do as much as 35 minutes. I said five minutes because that's my challenge That's my challenge if you're somebody that's used to doing that then do a little bit more And then put your cell phone down for one hour tomorrow. That's your challenge Okay, it's a little different challenge than we're used to but I think it's as valuable It's not more valuable than going out for the two mile walk today. True story. I got a little crime baby I'm going to jump over to here. So you guys happy father's day. What we're going to do tomorrow night I'm just going to give you a sneak peek tomorrow night. What we're going to do is we're going to be launching a fast tomorrow night So tomorrow night we're going to be launching the fast. So starting tomorrow night Um, a roughly you're going to start your fast tomorrow on your last meal So maybe between six and seven or eight o'clock at the latest Um, you're going to be doing do we going to ignore the fact that it's 180 degrees? I don't care how hot it is. You can walk I don't know who said that. Hey, listen, you can walk two miles in your house because I do it Listen, I've been doing around. I've been walking around the the thing to get my 20,000 steps in That's what that's what's so great about this.  I'm starting my 24 fast I'm starting my 24 fast 24 hours without food. You're going to post that whenever you start Okay, that's you're going to do tomorrow night Now if you have a reboot kit and you didn't do the reboot with the company You're going to start the reboot tomorrow night for 60 hours through your story Okay, what I want you to do is I want you to message me if you're doing the reboot But we're going to do 24 fast now if you have the reboot kit There is a little twist You could do with the reboot kit you could do 224 fast if you want to so you can do the first 24 Eat one meal do another 24 and we'll use the reboot kit as a double 24 fast So i'll give you some i'll give you some outs on sunday on monday night So stay with me i'm at but we're going to do 24 fast now if you do not have the kit We're still going to do 24 fast and what you're going to do on monday And i'll give you the details on monday.  I gotta say by them. I gotta go say hi to my little girl cheers y'all. Good night Hey peg could you hear me? Are you having a hard time hearing me? Can you put your phone on speaker? Kathy uh smith and tammy are you guys having a hard time hearing me? Okay. Oh hi, Kathy. So peg it might be that you need to put on the upper left hand side of your phone


Welcome back. So we're going to talk about how we can add a third variable to our bar plots today. So in the previous bar plot video, we showed how to get plot a categorical variable with counts on the y axis, and then a categorical variable with a quantitative variable on the y axis. But if you wanted to add a third variable, you could do that through adding fills, which is what we will demonstrate here using the plot nine or GG plot plotting tool. So we are here in the Google collab file that we started in the previous video, we've got our libraries, we've got our data that has already been read in. And at the end of the previous video we melted the data set and this will become very important when we go to use GG plot to make this bar plot. And so we can go ahead and just get started with our GG plot. So, similar to the previous videos. We start off with listing our data frame. And then we're still doing a bar plot so we say GM bar, and we still need an AES. So in the past, we specified an x axis will say category. We specified a y axis emissions. And then we did stat equals identity to say we want the actual data, we don't want to do any calculation on it. And then we added the fill outside of the AES. And that's how we got to variable plot. Remember, if you want to add a third variable, you need to do it within the AES statement. And so here, we say fill equals source. So if we run this. We can see that now we've got emissions, we've got category, and we've got source. And it automatically creates this legend for us. So we don't need to worry about that. And we can see how it works. Now this plot isn't the most descriptive, nor is it the most readable. And so, to show you a few other things that you can do within GG plot. Flip the coordinates with cord underscore flip. So if we run that. We can see that now, because it's on the y axis we can actually read what those categories are, which makes it a lot nicer. And then we can actually add some labels. So we can say X slave equals emissions scenario, and note that I said X label, it needs to follow whatever you mapped your x value to in the AES statement. So in this case, when I run this, the X label is actually on the why, because I flipped those coordinates, but the program is able to track where you, which value you coded as the X value and attach the actual value to it. So we know that that's what value you mean when you do the label instead of assuming that it goes on the X axis automatically. So instead of tracking a specific axis at this point, we're tracking a variable and the program knows where to put that label based off of the variable. And so this is an example of how you can add a third fill based variable to your bar plots.


So thanks everyone for joining today. Today we're very happy to have Professor Seamus Davis with us. Seamus is a professor at the University College Cook and University of Oxford. His research focuses on the fundamental physics of exotic states of electronic magnetic atomic and space time quantum matter. His group speciality is the development of innovative instrumentation to allow direct atomic scale visualization or perception of the quantum many body phenomena that are the characteristics of these states. So today he's going to talk to us about machine learning in electronic quantum matter imaging experiments. So yeah, Seamus, the floor is yours. Please go ahead. Thank you very much. Thanks to everyone for being here. I'm in the Beacroft building at Oxford this afternoon on a beautiful day. And happy Jubilee to the queen. I hope she will be not too dissatisfied with us. But in any case, let's get on with our business here. So I want to talk about how to use machine learning to analyze high data volume electronic quantum matter imaging experiments. OK, so first thing, how do we image electronic quantum matter? So here's a schematic picture of the Beacroft building. I'm over there on the left hand side looking out at Keeble. So three stories underground, more than 30 meters underground, there are our ultra low vibration labs. And in those labs, we have a two story space in which we can build. Here's the scanning tunneling microscope, a spectroscopic imaging tunneling microscope. It's inside its ultra low vibration millikelvin refrigerator inside the first stage of vibration isolation, which is about 10 tons, weighs about 10 tons. And that's sitting on the second stage of vibration isolation, which is a massive 30 ton brick of concrete, which is itself supported by vibration isolators above the foundation of the building. So in terms of acoustic and vibrational noise, these are some of the quietest places on earth. I mean, a cave a mile underground is quieter. But in any human habitation, these are some of the quietest places on earth. And we use that to do the visualization experiments. So inside one of these microscopes, you have some complicated refrigeration. Then right down at the bottom, you have the scanhead. This is a drawing of the scanhead. In the scanhead, there is a very sharp needle. Here's an SEM image of the needle right at the tip. There's only one atom. When I started in this field, I always thought that was a very intimidating requirement. But a Greek philosopher could have told you that if atoms exist, there's always one atom at the end of every object. So it turns out that that's not too difficult to achieve. However, cooling it down to millikelvin temperature and scanning it is tricky. So we've built several new quantum microscopes here at Oxford. Here's a picture of the Gemini spectroscopic imaging microscope, which I took this morning. It's in the B2 corridor, North corridor of B-Craft underground. So we use such systems in the following way.  Now, conventional STM, you scan around and take a picture of the atoms on the surface. We don't do that. We turn off the feedback system. And then we can vary the voltage between the thing we want to study and the metal tip. And by varying the voltage, we vary the electron tunneling current. So we get the current as a function of voltage. If we take the derivative, dIDV, from theory, that's proportional to the amplitude squared of the quantum mechanical wave functions of the electrons at this location. Location R in the sample. So by imaging dIDV as a function of location and voltage, we can measure basically the amplitude squared of the quantum wave functions of the electrons as a function of energy. The energy is controlled by the voltage. And location, the location is controlled by scanning the step around over the surface. OK, so here's a result. So this is the surface of lithium iron arsenide. These are lithium atoms. The little light dots used to here are lithium atoms. And these weird-looking things are actually iron vacancies in the layer underneath the surface. But if instead of imaging the atoms, you image the differential conductance, which is the amplitude squared of the electronic wave functions, as a function of energy, it looks like this. And when we first produced images like this, people really couldn't believe them because you're not taught to believe that the electronic structure of real materials looks like the Battle of the Somme or something. But it does. All real materials look like this. They're highly disordered. There's no perfect material except in a theory textbook. Now, you might think that that chaos is not useful, but it turns out to be extremely useful for the following reason. Suppose you have a quantum mechanical wave function, and it scatters from an impurity or a defect, and it rebounds. So that produces a wave function of the opposite wave vector. That means the same wavelength but pointing in the opposite direction. And these two, the incoming and the upcoming wave function, interfere. And they produce a standing wave in real space. And then the amplitude squared of that standing wave modulates at half the wavelength, or twice the wave vector, of the original electronic wave function. So if you can image the standing waves around the impurities, then you can deduce what was the wave vector of the electrons. And since we can image as a function of energy, the way we do it is image the random disorder as a function of energy, take the Fourier transform to find the wave vector of the standing waves, and then deduce that from the standing waves, the wave vector of the electrons is typically plus minus half the wave vector of the standing wave. So like this. You image the electronic structure as a function of energy, take the Fourier transform as a function of energy, and then deduce what was the wave vector of the quantum mechanical wave that was producing this pattern. OK. So if you go back to this highly disordered mess I showed you here, the electronic structure of lithium iron arsenide. But suppose we take the Fourier transform of that exact data set. It looks like this. It looks much more ordered. We're inside the gap of the superconductor here. When we exit from the gap, we see this nice contour here. That contour is the Fermi surface. It's the wavelength of all the electrons which are at the chemical potential of this compound. So even though you take a disordered image in real space by using Fourier analysis and theory, you can deduce what are the de Broglie waves in momentum space. Now, for any theorist listening to this, the reason why this works is that if you have a scattering potential v and you have some greens functions representing those de Broglie waves and you consider scattering to all possible orders. So here an electron scatters once. Here it scatters twice. And to all orders, then it turns out in a Dyson-like equation, you can find the new greens function after all the scattering. It's the original greens function multiplied by this product. And this product is a free particle greens function multiplied by the scattering matrix multiplied by a different free particle greens function. And the theorists in the audience know the constraint upon which we can represent this sum by a matrix, but it usually works. If that's true, then here's the greens function after all the scattering. Here's before. Let's subtract this from that and just get the change in the greens function. It's just this nice triple product here, original greens function, scattering matrix, another original greens function. Now, the utility of that is that the perturbation to the density of electronic states is just the sum over momentum space of that triple product. It's this sum here over k. And now I've written the second wave vector k prime as k plus q. So after I sum over k here, I get some function which depends on energy and wave vector q. And that's the one we measure. So the reason why this all works is because of quantum scattering interference. And the movie I just showed you is actually an image of this theoretical product of greens functions with their scattering matrix. A very powerful technique. Now, so why do I belabor this? I'm going to show you a lot of real space images, but it's important to understand with this technique you can simultaneously determine what's happening to the electrons when they're stuck in real space and what's happening to the electrons in momentum space. And that's the thing which begs the question that we needed machine learning to answer. Okay. So I just showed you this one. Here's a different one. Here's wave functions of a heavy fermion compound. Like all real materials, they look like a mess. Here's the Fourier transform. That circle there is the Fermi surface of a heavy fermion metal. Actually, that's the first time the Fermi surface of a heavy fermion metal was ever observed. Here you have a different material. This is iron selenite. It's a very exotic and strange metal. You can see the disordered impurity scattering on the right-hand side. If I take the Fourier transform, it looks like this. Quite simple, beautiful, straightforward and analyzable. And we were able to discover from this that this material is an orbital selective metal. Only the electrons from some orbitals of the atoms contribute to the metallicity. And this was the first orbital selective metal visualized. So this is a very powerful technique. Okay, now let's talk about cuprate superconductivity. So most people know you can put as many bosons as you like, as long as they don't interact into a single quantum state. So that allows us to take a large number of bosons in a container, let's say a Bose gas. And by cooling it down, remove the randomization. And then eventually, as Bose and Einstein predicted, all the bosons will fall into a single microscopic quantum state and it's the ground state. That's so beautiful. But, you know, fermions can't do that because one of the identifiers of a fermion is that only one fermion can be in each quantum state. So it would appear like this condensation isn't possible. However, other nature is very, very, very clever. And what she knows is that if you take two fermions and let's say they're distinguished by having opposite spin directions, their intrinsic angular momentum number of opposite direction, if you cool them down, the two fermions can bind together. And when they bind, they make bosons and the bosons can condense. That's a charged 2E macroscopic quantum fluid. That's what we call a superconductor. Okay, superconductivity now more than 100 years old, all superconductors are zero resistance, infinite conductivity, perfectly dissipationless electrical and electronic materials. And they're of tremendous potential utility for science, for technology, for the economy. And they're still a very hot topic of study. Here is the critical temperature to it below what you have to cool if you want to get superconductivity. And in the first decades of the field, it was like minus 250 or minus 260 centigrade, not very useful. By the 1990s, it got up to around minus 100, minus 120 degrees centigrade. And again, that's in the copper-based compounds I'm talking about today. And the same is true for the iron-based compounds discovered in the early 2000s. And in recent years, hydrogen-based superconductors have reached to a critical temperature near room temperature, which is psychologically very important. It proves that room temperature superconductivity is not ruled out by mother nature. However, those compounds have to be at millions of atmospheres of pressure before they superconductor. They're not very technologically useful. The highest temperature ambient pressure superconductors are the copper-oxides that we're talking about today. And so there's still a big push to understand how they work. And indeed, superconductivity is extremely important, not yet for the economy, but for science. It's extremely important. If you ever have an MRI, you're inside a high-field superconducting magnet. And now they're becoming very important for understanding how the human brain works or any brain works. They're important as a source of the most sensitive quantum devices, the most sensitive photonic devices, the most sensitive astrophysical detectors, the most high-power accelerator sources, the highest magnetic fields for producing, cyclotrons, high-current cyclotrons, the highest magnetic fields for physics and other kinds of research. And today, in fact, high-temperature superconducting confinement is being used for Tachymec fusion reactors by commercial companies. It's no longer just governments who can do this. Because of high-temperature superconductivity, commercial companies make a compact Tachymec for fusion power. And of course, as most people know, superconductivity is the source of our present capability to carry out quantum computer. All functional, commercial quantum computers at the moment are based on superconductivity. Okay, now let's talk about copper superconductivity. Why do we have to delve into this because it's the highest temperature superconductor we have available at ambient pressure? We need to understand it. So in these compounds, they're dominated by the CO2 layer. So that's a layer of copper, oxygen, copper, oxygen, copper, oxygen, copper, oxygen, no problem. The coppers are in a 3D9 electronic state. They have one electron missing from the D-shell. And that means they should be a metal, but it's actually an insulator. And the reason is the energy for another electron to arrive in the 3D10 state is about three electron volts, that's called U. And so just there isn't enough energy available. At room temperature, there's no way for one electron to hop and to doubly occupy a copper side. So each 3D9 electron gets frozen at its own location in a mod insulator. And I'll tell you in a second that this is an anti-ferromagnetic mod insulator. And for the experts here, the 2P6 band of the oxygens is in between the empty upper 3D10 state of the copper and the field 3D9 state of the copper. So the top of the chemical potential is actually in the oxygen P-bed. Okay, all right. So now when you, so these are insulators. So how do you make them into conductors? Well, you have to remove some electrons from the environment and you do that by removing an electron from the top of the 2P-bed, which is the same as removing an electron from an oxygen atom. It creates some quantum mechanical state we don't understand, but this axis here is the number of electrons removed are holes introduced. It's called hole doping by material scientists. So when there's no holes, the copper is the oxygen is in the 2P6 state, but as we increase the number of holes, more and more electrons are removed from the oxygen atoms. As that happens, the insulating state disappears very quickly. And soon with enough holes in the system, the high temperature superconductivity state appears. This is an extremely well-established phase diagram and the background theory for this is called the theory of a charge transfer insulator for the experts. However, if we want to understand the mechanism, we have to consider carefully what happens between the coppers and the oxygen. So consider the 3D9 electron on one copper and the other 3D9 electron on the adjacent copper. So here it is on one, here's its neighbor. In between there are two 2P6 electrons in the oxygens. That's an insulator. We know it's Hamiltonian. In fact, you can solve the Hamiltonian for these two electrons in this simple model. And if you do so, you'll find there's a powerful anti-ferromagnetic magnetic interaction between the two copper electrons. The simple Hamiltonian is Heisenberg-like and J is a large positive number. It's equivalent to around 500 Kelvin. So what that means is there's a powerful magnetic interaction causing each spin on the copper side to be opposite than its neighbor. And we know the magnitude of that super exchange interaction. So take that picture and now consider a square lattice. Well, you could guess, and it's mathematically true, that in order to have every copper spin opposite to its neighbor, the simplest way is just to have an anti-ferromagnetic insulator. This is an anti-ferromagnetic square lattice where each electron is frozen in space and it spins our opposite to its neighbors. That's what the super exchange theory would tell us and indeed that's what the neutron scattering experiments tell us. This is exactly how an undoped cube rates work. So that tells us that this exchange interaction is predominant in the insulating state. Now, however, whole doping means that you're going to remove one electron from here, from the 2P60. So when you do that, the anti-ferromagnetism disappears almost immediately and the high temperature superconductivity appears Phil Andersen proposed in 1986 that the reason why that happens is that the anti-ferromagnetic super exchange interaction survives, but instead of making a magnet, it actually binds these two electrons to make the electron pairs, which are necessary to make a superconductor. So this is a very powerful and almost unique mechanism for binding pairs. And if it is the mechanism of high temperature superconductivity, it explains why the temperature is so high. And to understand this mechanism would give us control of these materials and hopefully would bring us to room temperature superconductivity. So at least for me, that's still a very exciting goal. So no problem. Anti-ferromagnetic insulator phase understood. Check. D-wave superconducting phase actually very well understood. Check.  That's also pretty well understood. Check. But in the phase diagram of hold-up CO2, there's another phase. It's called the pseudogap phase. We don't know what that phase is, or at least the identity of that phase is contentious. And it's part of the problem we're trying to solve today. OK. Now let's think about electronic liquid crystals. So liquid crystals are part of our lives. Pierre-Gilles Dijen solved this problem. I got an Nobel Prize in 1975 for finding the theory of classical liquid crystals, which we all use in our working lives, in our information technology. It's a vast industry with an amazing number of applications. And the reason is these states are controllable. You can alter the properties of classical liquid crystals. Now there are two basic forms of liquid crystals. So one is called asmectic. It breaks rotational symmetry. All the molecules are aligned in the same direction. But it doesn't break translational symmetry. There's no pattern in real space. And so there's no wave vector that's called wave vector q equal to 0, breaking of rotational symmetry. That's an ematic liquid crystal. Asmectic liquid crystal is one that breaks both rotational symmetry and translational symmetry. It's got a periodicity in real space of lambda or a wave vector of 2 pi over lambda. And Dijon explained both of these states with his habitual genius and beauty in his theory. And we understand them very well for classic liquid crystals. Now just about 20 years ago, these two colleagues, Eduardo Franken, Steve Kievelsen, and Vic Emery, God rest his soul, who has passed away since, they proposed that when you dope holes into a correlated anti-firm magnetic insulator like CO2, instead of getting a superconductor, you would get an electronic liquid crystal state. And they provide very good theoretical reasons for imagining that that's the case. Furthermore, during those years, much evidence has appeared that when you go from this metallic phase into this mysterious phase, as you cross this line, there's a breaking of rotational symmetry at q equal to 0. And there's a breaking of rotational symmetry at finite q. There's a breaking of translational symmetry at finite q. That would mean that this phase here is some combination of a pneumatic and a smectic if it is an electronic liquid crystal. In fact, I mean, if you just look at the empirical facts, you have to conclude that both broken symmetries, both rotation and translational, exist in the electronic structure in this part of the phase diagram, so far so good. All right, now I want to examine this state using our techniques and see what does it look like at the atomic scale. So on the left-hand side, you see the picture of the atoms in one of these materials. This material is called bisco, but the name doesn't matter. It's a canonical high-temperature superconductor. And with conventional STM, we can see where the atoms are. Okay, now the next thing I'm going to show you is a movie of the density of electronic states as a function of energy in this identical field of view. It looks like this. So for some energies, there's no changes of the pattern. It's highly static. Then for other energies, the pattern starts to evolve, the wavelengths are changing as a function of energy the way they would be for a de Broglie wave.  So this way we can visualize the broken symmetries in real space of this high-temperature superconductor in that strange phase, the pseudo gap phase. So let's look at this a little bit more carefully. So again, this is a picture of where the atoms are. And this is a simultaneous picture of the electronic structure. And it's a mess, no doubt about it. It's not your father's or your mother's beautiful periodic density wave and neither is it a simple metal like copper or gold. It's some weird mixture of the two, which is very hard for a human being to diagnose. If you look at these images, it's hard to state. What actually is the phase that I'm looking at here? Okay, now we can get, we can advance our understanding of it by using Fourier analysis of this image. If we Fourier analyze this image, it has four important peaks. Two peaks are the Bragg peaks. They have the same periodicity of the crystal. And there are two other peaks which are the peaks associated with these periodic patterns which are to first order four unit cells periodically. So we can separate the properties of the lattice from the properties of these longer wavelength modulations by using Fourier analysis. So let's just first focus on these two red peaks which are the Bragg peaks. And they measure what's happening inside the CO2 unit cell. And now that's a little bit complicated because inside the cell there are three atoms. There's the copper atom and two oxygen atoms. And that means there's different ways of breaking the symmetry at Q equal to zero inside the unit cell. There's a S symmetry way of breaking it and there's a D symmetry way of breaking it in which case the two oxygens are in different electronic states. And although the real space images look approximately the same, the Fourier transform is really quite different because the symmetry of these states is different. Okay, I won't belabor that too much. If we take an image of where the atoms are, we take a Fourier transform of that image of where the atoms are and we compare the amplitude of this peak to that peak, we find them to be virtually identical. In fact, identical. That means the lattice itself doesn't break any rotational symmetry inside the unit cell. However, if we take a simultaneous image of the electronic structure and compare those two Bragg peaks, they're different by 30 or 40%. That means inside the unit cell, modulations in the X direction are density of states in the X direction is more powerful than density of states in the Y direction. I actually didn't believe that when we first visualized these effects. So I asked the team to look inside each unit cell and check is the density of states in one direction different than the other direction? And indeed it is. Inside the CO2 unit cell, there's a breaking of rotational symmetry. So that means there's an electronic pneumatic state Q equal to zero in the copper superconductors. And this came as a big shock. Several major papers came out in 2010, 2011. This came as a big shock to the community to realize, wow, there is an electronic pneumatic state. So the other two peaks are the ones which you would call a density wave, a periodic modulation of the electronic structure. It happens to be near four unit cells in periodicity. So we can look at that. You saw it here already. That's four unit cells and that's four more unit cells. But let me turn off my movies now. So here's two completely different copper superconductors, chemically different, but at the same carrier density. And if we image those standing waves, they are virtually indistinguishable. They have, so this is four unit cells, four unit cells, four unit cells. And these dark lines here are along lines of the oxygen atoms, which turns out to be important. And then the other material, we see the same thing, four unit cells, four unit cells, four unit cells. But of course there's no long range order. So it's still difficult to understand what we're looking at here. You know, one can zoom in and examine one of these objects with subatomic resolution looking inside every unit cell. We know where the copper atoms are. They're in black. We know where the oxygen atoms are. They're in blue. So when we do that, at the end of a long sequence of study, we were able to conclude that it is a four unit cell density wave we're looking at, but it's got a deformed factor, which is a tricky thing. It means that the modulations of the X oxygens are pi out of phase with the modulations of the Y oxygens. No state like this had ever been seen before, but it isn't surprising to theorists that it can exist in nature. So you can see for yourself, it's unidirectional. I'm telling you that it's locked to the lattice to a line of oxygen atoms. It's four unit cells periodicity, and it has an internal symmetry, which is a de-symmetry form factor. And those facts are not belaboring those facts. We need those facts for the machine learning part of the project. All right, now at last we get to the question. Are the phenomena occurring in the cube rates due to the existence of an electronically crystal? Or are they just having to do with Fermi surface effects, the wavelengths of de Broglie states, which exist in the momentum space of these materials? Now I haven't shown you many de Broglie states, so let them, and oh, so here I make them, the question even clearer. So suppose the Fermi surface is, and the Fermi surface is of this compound does look like this. It's four whole-like pockets around the pi-pi point. There are flat regions here, which the solid state physicists would know are called nested. And that means scattering between those regions can produce a density wave. The wave vector of that density wave is the difference between the wave vector of the two electrons. So it's this red arrow. And so that wave vector is related to the wavelength of the density wave. Q is two pi over lambda. So Fermi surface effects have these properties shown on the left. Now, electronic liquid crystal is quite different. Its periodicity is fixed. It's set by localization of the electrons in real space. The wavelength is set by some microscopic Hamiltonian, probably the MRE three-band model for the experts. And so the Q vector isn't set by the Fermi surface, it's set by the microscopic wavelength. It's lambda is two pi over Q in this state. So here we're trying to distinguish between electronic eigenstates, which are localized. That's on the right-hand panel or delocalized, that's on the left-hand panel, as the driver of the electronic structure in the phase there. Now, so here is an image of, you know, for it. Well, here is the real space image of the amplitude squared of the wave functions in this compound in Biscoe. Resolved by energy as the energy changes, the wavelength of the de Broglie wave changes and even their wave vector changes. The scattering patterns change. It's all what you would expect for a metal. None of these phenomena are too strange for a metal. And in fact, this is a superconductor. We understand what should be happening here. It's a D-wave superconductor. We know where all the primary momentum space scattering wave vectors are in the model of the D-wave superconductor. When we take the Fourier transform of the previous image, it looks like this. Energy result Fourier transform. It has all of the necessary wave vectors and they do all the mutually correct things. So what you're seeing is that there are lots and lots of states throughout momentum space. By using data sets like that, we can deduce where is the Fermi surface. So at whole density, 6%, we measured where is the Fermi surface in this compound. And now in a heroic series of experiments, Fujita-san measured what happens to this Fermi surface as a function of carrier density. And here you see the answer. As we increase the carrier density, the whole pockets grow, we're putting more holes in. So the whole pockets grow and the moment the Fermi surface moves to a new location. I'm gonna show you that movie again though. And I want you to realize that the Q vector of any density wave should be diminishing, right? Here the Q vector is large. As we increase the whole density, the Q vector linking those locations is diminishing with increasing carrier density. So Fermi surface would predict that, okay. And here's a summary of what happens to those Q vectors as a function of carrier density. Now we go to an image of what appears to be the static electronic structure. It's in the same sample. It's in the same field of view. It's just at a different energy. We take the Fourier transform of this image. It has a peak. It has a peak near about 0.27 to pi over a naught. That means very close to four units cell periods. Very good. Now let's measure that wave vector as a function of carrier density throughout the phase diagram. And when we did that experiment, so here's the peak at low carrier, sorry. Yes, here's the peak at low carrier density and here's the peak at higher carrier density. So the Q vector of this peak is diminishing as the carrier density is increasing. And again, that's what you would expect from a Fermi surface effect. And that's what everyone deduced from the data like this, which we published now about 12 years ago, 15 years ago. However, it's more complicated than that. If you actually look with human perception at what the electronic structure is at the atomic scale, and I draw some boxes here to draw your attention to things that at least the human being would look at. If you zoom in on those objects, you'll find that they are static, okay? They don't change. They just remain where they are. They're four units cell periodic. They're bond centered. That means they're fixed on the oxygen sites and they're clearly unidirectional. And that is also a fact. So, okay, so now you want to say, okay, now we have cognitive dissonance. You're telling me that a certain Q vector is evolving with carrier density, but on the other hand, real space electronic structure is not evolving with carrier density, okay? That must be cognitive dissonance or multiple personality disorder or something. But it's actually not, right? The thing you forget is that when you do Fourier analysis, you focus on one peak, but there's data elsewhere in the reciprocal unit cell and all of that gets thrown away. Fourier analysis throws away all the other data, which is called disorder, background, diffuse, whatever, however you want to bad mouth it, you just throw it all away and focus on the Q vector you like. But in a real material, all those other wave vectors contain information about the electronic structure. So you shouldn't make a profound deduction just from the evolution of a single wave vector. Actually, what you should do is look at the whole electronic structure, okay? So here's the question now we're trying to answer. Is the electronic structure of underdoped bisco and underdoped cuprates, is it dominated by this momentum space, Fermi surface style effect, or is it dominated by this real space, electronic liquid crystal effect? And there are two famous papers which prove mathematically that you cannot answer this question in the presence of disorder by using Fourier analysis. It's provable that your traditional Fourier analysis of these images can never succeed in answering this question in the presence of disorder. And look, there's tons of disorder. So formally, you cannot answer this question by using Fourier analysis, enter Una Kim. So Una Kim at Cornell proposed an alternative approach. She said, consider the raw unprocessed data. It's a real space image and that image changes with energy. So in this stack of data here now, the vertical axis is energy, but they're all in the same field of view, but the wave functions look different at different energies. The question is, could you define a machine learning approach which would not focus on a single wave vector but take all the data and find out is this set of images consistent with real space electronic liquid crystal physics, this one? Or is this set of images consistent with momentum space, firm structure, this one?  And that's the primary thing that I'm gonna describe now for the rest of this talk. So at the end of the day, we're attempting following her lead to find an unbiased identification of the fundamental characteristics of the broken symmetry in these images, very complicated images of the electronic structure. Okay, so identifying complicated images is something that billions, probably trillions of dollars and euros have gone into over the last 10 years. Everyone knows that neural networks are incredibly powerful at identifying images which have no periodicity. You know, when the security services are searching for your location, they don't use Fourier analysis, right? They snap your photograph and they use neural network or several neural networks which are designed, which are trained to identify your face. And so Ouna wanted to use the same strategy but for electronic structure images. Okay, so they used a relatively simple architecture. I'm not a neural network person. So let's see. I looked up what the description of this architecture is. Let's see. So each neural network is a fully connected feet forward network just with a single layer. But as you'll see the training of these neural networks and they trained 81 of them independently, the training of these neural networks is quite rigorous. But the mathematical internal structure by modern standards of machine learning is not that extraordinarily difficult. Although it's pretty difficult because there is a lot of data in each image. Okay, so the challenge is present a neural network with an image like this. This is real data on the left hand side then train the neural network to identify the characteristic structures which are hidden in this disordered image. And then to give an output, which tells us what's the fundamental state which is actually constructing that image. Now to do that, so they did this to some degree by brute force, they trained the neural networks to identify a wide variety of different things. So what they did is constructed training sets which comprise something very close to what we know exists in the cube rates, but they diversified it with noise, Gaussian noise, fluctuations, physical disorder, chemical disorder, topological defects. They also diversified it according to the orientation of the pattern. There's two possible orientations. And they also diversified it by the internal symmetry of the density wave. So the number of objects that the set of neural networks were designed to detect is really quite large after the whole training process. So here's some examples, these are training images. And what's happening here is they're taking a de-symmetry unidirectional density wave image plus Gaussian disorder plus topological defects and what they're changing is the wave vector, the periodicity in real space. They're continuously changing it, different categories have different wave vectors. And the neural networks are going to be trained to identify which category is predominant in a real image of the electronic structure. So under those circumstances with that fairly massive training set, which I'll show you the people who did this work just a little bit later at the end of the talk, with that massive training set, then they used a reasonably conventional training technique to end up with, since our training with something whose content they know, they can check whether the network is making the identification correct. They only consider the networks to be trained if they were 99.9% accurate in detecting the image presented to them whose characteristics were known by the training operators. But they independently trained 81 neural networks presumably whose internal parameter sets were different even though they were trained to identify the same training set. Okay, that took about a year actually. Okay, once those set of array of 81 neural networks had been trained, then we conditioned the experimental data sets, which are images in real space, very complicated images as a function of energy, multiple sets of data like this at each different carrier density across the phase diagram. And in fact, they used virtually our whole data archive which had taken us approximately 20 years to acquire as fodder for this set of 81 neural networks. So that was fun, conditioning all the data to match the requirements of the neural network was also a challenge. That was for the experimentalists and the data scientists. But at the end of the day, so this is a sequence, the left hand column is a sequence of images of the electronic structure at different carrier densities. The central column is a column showing the Fourier transform of the data and you can see from the Fourier transform that gosh, you'd be hard pressed to distinguish between these images by using Fourier analysis. However, the categorization, so which category, the neural networks identified, category two, I can tell you is the four unit cell, de-symmetry, unidirectional density wave. So category two was predominantly identified over all the other categories throughout all the data sets until the carrier density reached about 20% and then category two was no longer predominant. So what this says is that the neural networks think that there's a four A naught periodic de-form factor density wave throughout all of these images. That's what the neural networks found. And furthermore, we could present these images in two orientations to neural networks which were designed to detect the density wave of only one orientation. And what that actually revealed is that one orientation, that the neural networks identified the density wave in one orientation far more often than in the other orientation. So that tells us that it's a predominant unidirectional de-symmetry form factor four A naught periodic density wave which is the dominant object in these images if you don't relapse into Fourier analysis, if you take all the data and use machine learning for the identification. All right, so the end of the day, this suite of neural networks which are now being used for other studies and this strategy is being generalized, this suite of neural networks identified a carrier concentration independent unidirectional lattice commensurate, four A naught periodic density wave because it's disordered, the name for that state is a vestigial pneumatic state which had been predicted but never detected. So that was great. Actually, the neural networks detected a state which had never previously been detected. You know, if we plot the wave vector deduced from the neural networks as a function of carrier density, it's four unit cells. It does not evolve with the Fermi surface. It's a fixed property of the electronic structure. Okay, so the end of this process, we deduced and reported that we believe the broken symmetry state in the underdoped cuprates that we can access is definitely or at least is highly consistent with the theories of electronic liquid crystals of a dope mod insulator and is not consistent with theories of Fermi surface nesting to produce the density wave. All right, and that strongly supports the hypothesis and the growing belief in this idea in our research community, which is the community of strongly correlated superconductivity and has influenced new directions for that research community. Now, one thing to say at this point which no doubt many of the experts and the audience might resonate with is that many professional condensed matter physicists looked at these results and said, great, this is a new piece of information. It's a step in the right direction. It confirms the electronic liquid crystal hypothesis, et cetera, et cetera. They were willing to give credence to it, but admittedly there was a significant group of people who said, well, unless you can tell me how the neural network made its decision, I don't believe that it achieved anything. And we have to have a self-training neural network to get around that objection. We have not reached that point yet. But in trained neural networks, this procedure is a powerful new technique for visualizing electronic and understanding electronic structure in wheel space. This was a big international team. It took many years to do this. The samples across the whole phase diagram were made by the Esaki group in Scuba. Much of the experiment and analysis was done by Fujita-san, who's now at Bokeh of the National Lab. The data management and analysis to match the requirements of the neural networks were done by Andrei Mezoros, who's now at Saclay. And the programming for the neural network to match the data was done by Izan, who's now at Beijing. And Una Kim at Cornell was the PI of this project and the creator of this fascinating idea. And so that's all I want to say on this subject. Thank you very much. Thank you, Sheyma, it was really interesting. Any questions from our audience? So I had a quick one. So I was wondering whether you, during the evaluation of the neural network, whether you could see what are the features that the network picked up on to, like picked up on that was most discriminating in terms of the classification. Right, so during the length of this project, which finished about two years ago, we did not know the answer to that. I kept asking that question and Una kept politely telling me, we don't know the answer and we don't know how to find the answer. But now she does know the answer, which is beyond my area of expertise, but now they're reasonably confident that they know what internal parameterization this single hidden layer neural network requires in order to do this type of discovery. So if you want to know the details, you can send her an email and she'll be happy to tell you. Cool, thank you. There was a question in the chat, I think. Yeah, the question was, did you encounter failures of machine learning approaches while you were going towards this result? Oh yeah, right, absolutely. It was very difficult to find the optimum architecture which could indeed be trained to detect an object that's complicated as a commensurate, de-symmetry, unidirectional density modulation with Gaussian disorder and topological defects. So there were a lot of challenges in the first year of the project, finding an architecture. You know, architectures for identifying human needs, you can download now. Architectures for identifying quantum density waves, you still can't download, you have to invent yourself. So it took a while to get over that challenge. And then for the experimentalists in the audience, it turned out it was a great deal of labor to convert the format of the experimental data as stored in our large archive to the correct format that a machine learning algorithm can use to do the identification. So we had challenges on both sides. So if I may ask another question. I mean, very, very superficially, there is some analogy with radio astronomy imaging and what you are doing. In both cases, the Fourier transform seems to suddenly elucidate rather weird patterns. That imaging process is also a big computational problem, but to my knowledge, it hasn't been attacked very well yet with machine learning. And do you feel there might be a chance to get that right also, or is it? I presume so. So Una's research program at Cornell now has grown tremendously because throughout condensed matter physics of quantum materials, there are vast data sets. You know, the archival data sets from synchrotrons for x-ray scattering and from neutron sources for neutron scattering of uncountable different materials. All of them have only been analyzed by focusing on one or two wave vectors in the Fourier transform. So now there's a great deal of interest. Of course, yes. But in the old days, a human being, all they could look at is a peak in the Fourier transform. So now what the quantum condensed matter people are doing is trying to generalize this scheme to access the vast archives of data which already exist. I hope that they're collaborating with their astrophysical colleagues, but I don't know about that. I'm an experimentalist myself, so I'm not involved in that part of the situation. But condensed matter people think that this could be, I'm not sure it's gonna be revolutionary.  But I'm sure it can be a powerful new tool. It was definitely a powerful new tool for us to analyze our own dataset. Yes, by the way, coming back to the first part of the question, it isn't perhaps really hopeless to get a self-training model of increasingly complex patterns, right? Because it seems you could generate a lot of them and there's ultimately some system behind it that it may not be hopeless. I believe that Una has a strategy already developed to do that for this class of data, but I don't think it's ready to execute at the moment. Presumably when she's ready to execute, then we'll try again presenting this archive with no preconditioning and see what pops out. Yes, yes. Thank you very much, it was a great talk. All right, any other questions?  Yeah, I can't see any. So thank you so much for talking to us today. The seminar was recorded, so it will be available on the YouTube link. So thank you very much. All right, thanks very much, bye.


Crypto is incredibly volatile when everyone is trying to reach for the moon There will always be turbulence along the way, but a few crypto currencies aim to do the exact opposite They try to keep their prices steady and solid the earth the cryptos move these are called stable coins wait That's actually a brilliant idea for a project make a stable coin token pair Where the stable coin is named after the earth and the token is named after the moon But as Luna goes into free fall below a dollar. Oh, it fell below a dollar today Absolutely wild Tara halting their network for a second time Luna and UST face extinction. Oh shit Yeah, we'll explain why that happened a bit later in the video because that involved a special type of stable coin called an Algorithmic stable coin before we get into that we need to first understand what a stable coin actually is I'm Jackson Dumont director of video at coin telegraph in this video We'll explain how stable coins work and why they're one of the most crucial parts of crypto If you haven't done so already, please consider leaving a like and clicking that subscribe button We are the leading media for news coverage and education Let's start with a simple definition a stable coin is a cryptocurrency whose value is tied to an outside asset Such as the US dollar or gold This tie is called a peg and it stabilizes the price for example The company tether issues a US dollar peg stable coin called USDT at a one-to-one ratio to the US dollar one USDT equals one USD That means if tether wants them in 10 billion USD tokens They need to have 10 billion dollars in reserve. They can't just mint money out of thin air That right is reserved for the US government This collateral keeps the one-to-one peg because it ensures people are able to redeem their USDT tokens for actual US dollars at any time Despite this maintaining the peg can sometimes be difficult, but more on that later So you might be thinking that stable coins just sound like copies of other assets and you're right That's exactly what they are but with one key difference. Get ready for it. Here it comes They're on the blockchain Never gets old But even though I've said this in a lot of videos the distinction is pretty important because it gives the underlying assets some unique properties minimal volatility as We are all well aware the crypto space is incredibly volatile Cryptocurrencies can pump 10x or just as easily lose all their value overnight in this world of chaos There needs to be a stable benchmark where investors can keep their money safe from risky price action Let's say crypto enters a bear market where every coin is crashing Kind of like what happened in the first half of 2022 There needs to be a place in the ecosystem or on chain where investors can hold tokens that don't lose value Exiting the crypto ecosystem into real-world assets for every trade will be far too costly and time consuming So it only makes sense that most trading pairs are against US dollar peg stable coins like USDT Because the US dollar is the global reserve currency If the crypto market is a machine then the US dollar peg stable coins are the grease that keep it running They are the benchmark against which most other cryptocurrencies are measured without them the crypto market would collapse be your own bank This brings us to the next unique feature of stable coins You don't need a bank to hold them or transfer them. This opens up a world of opportunities Imagine you live in Venezuela where the recorded inflation rate at the start of 2022 was 1198% that means that the official currency of Venezuela the boulevard is losing value faster than any other currency in the world The absolute last thing you want to be doing is holding that currency But maybe your local bank doesn't let you open an account for any currency other than boulevards or maybe you don't even have a local bank What can you do? Well, you can go online to a crypto exchange and buy a USD euro or even gold back stable coin Now your money is sitting in a far more stable currency This will help you fight inflation and not lose the purchasing power of your money low fees no border But maybe that's not enough you need some extra money from your cousin who moved to Canada and you need it fast You don't have time to deal with slow wire transfers and exorbitant exchange fees Instead your cousin can send you a stable coin directly to your own wallet not a banks within minutes for a very small fee Easy peasy problem solve now You can see just how powerful tool stable coins can be and this is only because these crypto currencies exist on global Decentralized networks that are not controlled by governments banks Corporations or any other centralized entities the hardest part is helping people understand how to use it So now that we know what stable coins are good for how do they actually work? Well, we can break things down by dividing stable coins into four different categories Fiat backed commodity backed crypto backed an algorithmic Fiat backed stable coins work exactly as we explained a bit earlier in the USDT example Fiat collateral must always be in a one-to-one proportion to the number of tokens issued The collateral is held in reserve by a central issuer or financial institution Regulators require these issuers to frequently disclose the reserves to make sure they always have enough backing for the tokens They meant commodity backed stable coins work in a similar fashion these stable coins are Collateralized with physical assets like precious metals oils and real estate rather than with currencies the stable coins price reflects the value of its underlying asset For example each token of Paxos gold Pax g represents one ounce of gold However, because the prices of these stable coins are tied to commodities They are more volatile than their fiat pegged brethren two of the most popular commodity backed stable coins are tether gold and Paxos gold Holders of these stable coins can sell them for cash or the underlying gold This facilitates investments in assets that may otherwise be out of reach locally However, both fiat backed and commodity backed stable coins require a central issuer to provide collateral for each token In the world of cryptocurrency, we seek to decentralize as much as possible Crypto backed stable coins seek to do just that by using smart contracts instead of relying on central issuers If you're not sure what smart contracts are check out our video here as the name suggests Crypto backed stable coins use other cryptocurrencies as collateral when you purchase these stable coins You lock your crypto in a smart contract and the smart contract gives you tokens of equal representative value This is called a collateralized debt position. The prominent stable coin in this category is die Usually these kinds of crypto backed stable coins require over collateralized positions Essentially, you have to put more crypto into the smart contract than you are taking out This is to protect you against price fluctuations, which could cause liquidation However, sometimes even over collateralization doesn't save users from liquidation during extremely volatile market conditions The final category of stable coins are algorithmic stable coins These are the newest types of stable coins to emerge and they are still finding their footing to put it lightly Contrary to previous categories algorithmic stable coins do not use fiat or crypto as collateral Instead, they use a complex system of algorithms and smart contracts to manage the supply of tokens and circulation thereby Controlling the price when the price of the stable coin deviates below its peg Tokens are burned from the circulating supply pushing the price back up Conversely, when the price of the stable coin goes above the peg tokens are minted into the circulating supply pulling the price back down Terra was a great example of this. It combined a governance token called Luna with a suite of fiat peg stable coins such as UST Terra incentivized its users to take advantage of small differences in price of the same asset across different marketplaces Essentially if UST was valued at one dollar and one cent instead of one dollar Users could burn one dollar worth of Luna to mint one dollar and one cent worth of UST Investors could then sell the UST for one dollar and one cent earning a profit of one cent for their efforts Burning Luna tokens reduced the number of overall tokens left in circulation Making them more scarce and therefore more valuable by minting more UST tokens it had the effect of Diluting the existing tokens and circulation and bringing the overall price back down to its one dollar level Ideally users would keep this process going until the UST value decreased back to one dollar The opposite would occur if UST fell below one dollar Think of it like a seesaw Constantly trying to balance itself. The problem is that this system failed big time. It crashed the whole market What happened was this a lack of demand for UST drove the price below its one dollar peg Traders saw this opportunity and began burning UST for one dollar worth of Luna which was then sold for a profit So far everything was working as intended However, the continued selling of Luna led to its price plummeting not only canceling out the arbitrage opportunity But increasing the amount of Luna in circulation while the price continued to crash Investors saw the system crashing and immediately tried to sell their holdings which only caused the prices to crash even faster When the dust settled Luna and UST had lost a mind-boggling 100% of their value in just a few days costing investors billions of dollars This event was a sobering reminder that even experiments aimed at stability can have devastating consequences But it also goes to show just how key stablecoins are in the crypto ecosystem They are faster than banks transcend borders and oil the crypto machine Imagine if an even larger stablecoin like USDT or USDC suddenly collapsed a black swan event like that would make the UST fiasco look like a walk in the park and remember those stablecoins are issued by centralized Corporations they look safe for now, but they still have a single point of failure and are at the mercy of the regulators Who knows what can happen the need for a decentralized stablecoin hasn't gone away and although Luna failed that Failure will pave the way for better smarter stablecoin systems when that happens coin telegraph will be here to cover it I'm Jackson Dumont. If you enjoyed this video, please leave a comment below and what you'd like to see me cover next