Welcome everyone again to this session. This is about visual validation, the missing tip of the automation pyramid. Not as much as a tongue twister if you slow it down, but yes, it can get interesting. Quick introduction about myself. I'm Anand Bagmar. I've been in the quality space for more than 20 years now. I've worked with various product and services organizations over this time across various different countries, and had great mentors, colleagues, friends, whom I learned a lot from, and also many whom I learned a lot of things that I should not be doing when it comes to my opportunity. But that's enough about me. You can reach out to me on LinkedIn or Twitter, and we can definitely have more follow-up conversations beyond this Agile India virtual conference as well. So let's start off. And I would really like you to try and participate in this and put in your thoughts. I'm gonna be asking a few questions. Put in your thoughts in the discuss section of your browser window over there. That would help us make this a little bit more interactive than just me rambling on. So let's start off with an activity, right? How do you test ink pen? Okay, so can you probably just write on what are the few top things that come to your mind in the discuss section? Okay, trying to write with it. Yes, that's right. Anything else? Okay, I'll give you some answers that come up first when you take a pen in hand and you try to test it, right? So of course it has to write properly. Yes, there's another thing, fill the empty ink tank. And that is you're assuming that there's a ink tank set over there, right? You don't know what type or how are you gonna really fill the ink over there? But yes, that is also very important. You would also see if the cap closes properly. It looks as expected. And of course it is visually appealing as well. You can hold the pen properly while writing. There are so many other type of scenarios, test cases that you can come up with now for this testing of pen. But the challenge is if you wait for the pen to come in your hand for testing, it is too late. And why? Because a pen is made up of many different components. It could have a cartridge or it could have an ink tank. The way Sid mentioned that is one of his thoughts around it. So there could be different mechanisms of how you're going to fill ink in the pen for it to be able to write with it. Also, there are various different components. The nib does it fit correctly or not? Is it of the right shape, the right thickness? Is it smooth enough? Do all those different smaller pieces fit in well together with each other before the final assembly can happen for the pen? And that's how you typically build a pen and how you would end up testing it eventually. But if you miss out on any of these earlier validations in place, what if that ink cartridge does not fit correctly into the pen or it is loose when you shake the pen that cartridge comes loose? The pen is of no use in that case. In fact, your clothes might get spoiled or whenever you're keeping the pen that might get spoiled. It's of no use to anyone, right? So you really have to think about how are you going to build the quality inside out, get those components tested correctly before they integrate with the bigger, larger pieces, and eventually make it a pen. And not surprisingly, this applies to software as well. You look at a website or a native app, it seems like a simple enough product, a simple enough interactions that you're trying to do. But in the back end, it couldn't be a really complicated architecture that is really enabling that kind of functionality for you, for whoever that end user is. So you have to think about how is your product really built inside out and based on that, how can you test early to get that feedback? Now, what is really missing in this case, right? Let's look at that. How do you ensure what was working before continues to work well now? And this is definitely a more applicable in software type products, not like a pen where the architecture of a pen is not really going to evolve for the same pen that you create different types of pen, but it's not the same pen. But from software perspective, we release a product at whatever point in time, and then you incrementally make changes to that product to add more functionality or fix issues based on feedback that you have got. How do you make sure that what was working well earlier continues to work well after these changes are done as well? And that is a big question that you need to really get and handle on because it's not just about how my testing the changes correctly, it's about making sure the overall product is also working well. So if you think about a typical testing approach, right? And I'm not going to preach to the choir over here. We are in Agile India. Agile has been around for a long time. The XP practices have been around for a long time. We've heard about these on far too many occasions, but we know that test automation is one of the key enablers to get that early feedback and make sure we keep validating the existing behavior with what was expected as the product changes. And with the automation, we of course need to think about the pyramid. What are the different types of tests that you can automate to get that feedback earlier? And you think about it from a technology-facing perspective or business-facing perspective, you have to think based on what kind of feedback are you really getting, right? If it's a slow feedback, can you restructure your test to get that feedback faster? And a part of all these automated tests, you also need to have a good strategy for doing exploratory testing for tests that have not been automated, cannot be automated, or certain things that you understand from a human context perspective of interacting with the product. So the pyramid actually can get broken further based on the context of the product as well, right? There are tests that you can automate from an NFR perspective, for example, performance, security, accessibility, analytics. These are all very important types of tests, including many others, again, the types of tests that you would automate depends on the context of your product. But all of these tests are, again, very, very important when it comes to building a quality feedback for your product. That said, there is a challenge that is there, right? And that challenge is mostly about how are we addressing and approaching the non-automated tests for your product. And typically the approach taken by the team, whoever the team is, usually or mostly it is QAs in various, in most project teams, but you take an approach of finding, thinking about this as what the difference, right? How am I really going to do exploratory testing? Yes, I'm going to explore, but there has to be some aspect of thinking why is this exploration results correct or incorrect, right? And one of the approaches over there, which unfortunately comes up with is for the differences. Okay, I'm going to back off a little bit from where I was in interest of time and let's get started with it again. Again, apologies for the technical glitch. This is definitely on my side, as I mentioned, internet issues and no power as well. So let's see if we can get to the next 30 minutes without any interruption from the network perspective now. So we were speaking about the automation pyramid. We know what the value it brings and how we can help look at and get quick feedback of the overall quality of the product based on these automated tests. But there's still a big challenge that remains and that is in terms of the manual and exploratory testing that is happening. And for that, one of the techniques usually subconsciously that QAs end up doing is almost like playing the game of spot the difference. So if I show you this particular image and ask you how many differences do you see over there, given a little time, you'll be able to come up with the number of differences and where exactly those differences are. But if I tell you this quickly and say, okay, tell me immediately right now how many differences are there, you may find a couple of them maybe not as well, right? But in this particular image, there are four differences that is there. Let's take another example. If I give you this particular comparison, what are the differences in these two images that are seen and how quickly can you come up with the 10 differences that are there over here, right? Maybe half a minute, a minute or so. But I lied, they're not really 10 differences. Again, there are just a few differences over here. And the reason I'm bringing this, sharing this point is a lot of approach to doing manual testing or exploratory testing is unfortunately just looking at the product and given the context of the product from your past experiences, you would see if it is working correctly or not. And what happens is many a times is, which is not a surprise, right? This happens in software as well. It's not just about looking at the image and seeing what is going on. You will see countless such examples in the field, whether it is Twitter, whether tweets are misaligned or UPS where on the tablet version of the app, the product does not show up correctly. And for those who spotted it, there are two lines also over here on the screen in the title, right? So these are differences that you may or may not realize very quickly given the context of how you're testing what pressure you're working under or what timeline you're working under. So again, many examples, financial times, the title being too long and it overlaps into the content itself. Here's Amazon webpage from the past and a big sale launch, which is gonna happen in India soon in a couple of days now. And instead of the numbers growing, they saw the numbers actually dipping in instead, right? So you look at the product and realize, oh, shoot, there's something basic that is missing that we could have found out. Also another example of HDFC bank pair on the homepage itself, we are seeing this kind of weird overlapped content, right? So the challenge over here is that the defects escape because of our approach to testing is incorrect. We are focused on a very raw ad hoc way of testing at the top layer of the pyramid. And that is the challenge that we are trying to solve. And that is a challenge that I'm trying to discuss with you with the solution, how you can look at the UX or visual testing, which is a missing piece in the overall aspect of quality that you are focused on. Okay, yes, 10 was a misleading number, but you're right, it's actually in that aspect. So now let's look at what happens when visual testing is not done. We've already seen certain examples that I shared earlier, right? UPS or Amazon, certain products, they have, there's not a revenue loss in that sense, right? So financial times the example that I showed you, what would happen if that text title is overlapping? It's fine, I'll still click on that article and I'll be able to see the content completely. Well, nothing is going to, the world is not going to end if I'm not able to read that few lines of text over there, same for Twitter as well, right? But in case of UPS or Amazon, there's actually a revenue loss that would happen as a result. And that is a challenge which comes across if visual testing is not done as part of your overall testing or quality strategy. You might end up with business or revenue loss, there's a loss of brand and credibility and more or equally important, you start losing your users because users have a very short attention span, right? So it is extremely important to think about how you can make sure the visual aspects of your product are also working correctly. Let's quickly understand for those who are not aware of this, what exactly is visual testing? So visual testing is a way you can validate the visual aspects of the screen, right? The name itself is quite indicative in that sense. You make sure that what is expected or rather what is presented on the screen is matching to what is expected in terms of the layout, the appearance, the content and the overall UI experience itself, right? That is visual testing. Now, how is visual testing typically done? This is done manually. We saw that example, right? We are manually trying to figure out if there's something wrong with this. And the reason this becomes a challenge is because of it being done manually. It is a very tedious process. It is extremely error prone and it is impossible to scale and repeat. And if it is any of these conditions satisfies in your approach of testing, then you are going to be a blocker for enabling CICD, okay? And that's the part that we really need to focus on. How can we avoid, right? How can we remove the blockers and enable the team to move forward faster? So you can use functional automation to help in certain ways, but there are still challenges of how much functional automation can help in this case, right? So over here, this is where I would like to present to you how a visual test automation can work to solve this problem, okay? So the first thing that visual automation needs to do is create baselines and that is typically done by taking screenshots of the expected UI. When you have created these baselines, you would compare the screenshots when the test runs the next time with the baselines and see if there is a match or not. This can be done at a whole page level or snippet of a page level. Now the whole page itself can be what is seen on your screen versus you scroll and take a full page screenshot and compare against that as well. That is also a further level of detail about what type of validation can be done. When you do the comparison, you would find out if there are any differences reported in this either that is because your product has evolved, that means functionality is changed, so you need to update your baselines or you've actually found a defect of which is going to be a problem and you need to fix quickly. That defect could be just a visual defect because there is overlapping text or it could be a functional defect which means that, oh, I expected certain values to be seen over there, a certain data to be seen over there but it is not there and we'll see more details of this in a demo as well, okay? Now the challenges of visual testing is the false positives and negatives and this is extremely important to understand. Basically it comes down to how the visual test automation itself is being done. If you're going to use Pixel comparison for comparing your UI, that is going to be a big problem because browser version changes can create updates in the rendering engine which means the way pixels are rendered for the same page could be different, hence you will get differences over there or dynamic data becomes a problem or also the responsive web design, right? Or even if you have native apps across all different types of devices, we've got devices right from 4X inches to six and a half, seven inch screens or tablets as well. How many such baselines will you take for each of these specific viewport sizes to do the actual pixel to pixel comparison and make sure everything is fine? So the false positives and negatives is one of the biggest reasons why visual validation fails, automated visual validation fails. The second aspect which is a challenge is how do you really create a baseline and maintain these baselines? And again, as I mentioned, this could be for different browsers and devices and resolutions and viewports as well, right? You need to have a baseline for each of these combinations, otherwise I'm trying to compare an apple with an orange and just because both of them are fruit does not mean they are represented the same on the screen, right? So you need to do an apple to apple comparison in order to get results from a visual validation and that result analysis itself has to be rock solid and give you the correct results, no false positives, no false negatives over there, only then can you really take action on that, okay? So this is what is really important from, these are the challenges from an automated visual validation perspective. So I hope this resonates with you in terms of what is a problem statement that I'm trying to highlight over here for you. A quick thumbs up if you're still with me. Excellent, thank you so much. Okay, so how can we really solve this problem in a better way, okay? And this is where I want to talk about one of the options what you could use which fits in very well with your agile way of working where agile or not for that matter, right? It's a matter of getting quick feedback and accurate feedback about what exactly is happening with your product. And that's where I would like to show a quick demo of one of these tools, aptly tools, which is a visual AI tool and how it can solve the problem. Again, there are a lot of other tools as well. This is the tool that I'm using from a demo perspective point. What I have over here is on the screen, hopefully my browser is visible where I have integrated aptly tools with my functional testing tool. Now, in my functional testing, I could have, you can see from this page there are more than 40, 50 different SDKs based on the choice of your functional automation tool. You could choose a particular SDK of aptly tools to integrate visual testing along with your functional testing. And the advantage it brings out is you are using your functional testing tool like Selenium or APM for example, to drive your application under test to do the various different functionalities. You open the app, you log in, you navigate to different screens, you interact with the screens or do actions on them, right? And that validation is happening from a functional perspective if your workflow is going through correctly. But what those tests do not do for you is the screen seen correctly on the device itself. Remember that Amazon example, right? I'm pretty sure the Amazon team ran all the tests possible on the page before doing a release. And the test passed because Selenium is going to pass saying that, okay, I'm still able to click on a particular element or find those elements over there on the browser. But Selenium will not tell you if there is a CSS that is broken which is causing that weird rendering issue where users cannot even use the product at all, right? So that's where you can really integrate visual testing along with functional testing where you use a functional testing to drive your application on the test to simulate the end user scenarios. And then you will use the visual testing aspects at relevant points, whenever you say I want to do a visual validation done of this functionality, the results will be captured, the data will be captured sent to apti tools where the comparison happens. So let's take a quick example. And here's an example of a cross browser test where we are comparing the baseline which is on the left-hand side. We're comparing the screenshot which was captured as a checkpoint on the right with that baseline. This is running on the baseline was captured on Chrome. The screenshot that was captured as part of the test execution was an Internet Explorer. Now, if I use a pixel matching algorithm to do this validation, and if I highlight the differences, you will notice that the whole screen is being shown in pink over here. And that is a big problem. This is a problem of pixel-based validation. In this case, of course, it is going to have the whole page different because it's one browser versus the other. But you will see certain types of false positives even between browser versions at times, depending on what has really changed in that browser. So this is a reason why pixel matching never works. However, if you look at a AI algorithm called the strict algorithm in this case, you will notice that all the region in pink over here that is highlighted is actually the differences that the human can see. The strict algorithm is, show me the differences what a human can see as differences, right? And as I switch between the baseline and the checkpoint, you will notice that all the differences highlighted in pink are actually what the human eye can see. Now, again, in this particular case, this is not a good example because you're comparing one browser with the other. And the strict algorithm also is not a good algorithm in this case. So if I use a layout algorithm, in the layout algorithm, you will notice that all the pink has gone off, but there is a difference highlighted, which is on the bottom right-hand side of the screen. And that is a defect caused, captured by the layout algorithm. This is actually a functional defect and a visual defect in that sense, right? So because this particular text is missing here, the user will not be able to use this functionality. If I have a Jira integration, I can just create a defect over here, report it in Jira, mark the test has failed, and I can move on with my next execution. The similar approach will work with your native apps as well. This is a dynamic data app, Yahoo Finance app, but the data is different. And you see that again over here, the strict algorithm has captured everything that is different. Now, there are techniques that you can use over here to say, I don't have control over this section of the page where the data is dynamic. So I want to use a different algorithm for that screen. And I'm using layout over here. So layout is ignore the content, focus on the structure of the page. And based on that, I still found there is some one difference that is there in the button over here, which is a problem from a layout algorithm perspective, right? So again, these are some of the examples of the power of AI algorithms that you can get to use, to see if your functionality as well as visual aspect user experience is working correctly. And this will work regardless whether it is web apps, native, or even PDF forms for that matter, for teams which are from a compliance perspective, it is very important to make sure that PDF documents are also validated. And the same algorithms will work for PDF as well. There are use cases that it will support from a localization perspective. For example, I'm checking a login page for Facebook in different languages. And because I'm using a layout algorithm, it is saying the structure of the page is valid. There's no problem. If I change it to a strict algorithm, you see that all these differences are shown. Now, the other, a very important aspect from this is what is important from a scaling your test perspective, right? The users are not just on one browser or one device. You want to scale that execution across all the different browsers and viewport sizes. But there is really not enough value in running your functional test against all the different browsers or viewport sizes as well. So you could use another feature from Apple Tools called AppAsGrid where you run the test only on one browser, but you configure it to say I want to do the rendering on all the different browsers as well and viewport sizes. So just by two tests executed, the visual validation is done for all the different browsers and viewport sizes that you have specified and you get the value from that immediately, right? So your feedback cycle reduces drastically. You're running the test just once in your CI machine or on your dev or through a laptop itself and you will be able to get visual validation results for all the different browsers that are important to you. There are other interesting aspects again from a shift left perspective, which is very important, is a root cause analysis. Now, what this does is if you click on any of the differences highlighted, Apple Tools will tell you what is the difference in the DOM and CSS, which has caused this difference to come up in the first place. Now, this again becomes a very powerful way to not just run my tests in CI, the test will fail if there is a functional defect or a visual defect in CI. So you get that feedback over there, but it's not just important to find what has failed. It's also very important to know why it has failed and take corrective action against it. And these are some of the features from Apple Tools that will help you find those, get that quick feedback and fix the issue as quickly as you can, right? I don't want to get into other features over here, but I hope this aspect you're able to relate to in terms of the kind of problems you need to, you'll be able to solve over here, okay? So moving on from the demo itself and we'll take the questions. I see there are some questions over here already. So it's good, we'll get to those shortly. I'm almost done. I want to have as much Q&A as possible and interaction with you as possible on this. So the test automation pyramid we already saw, right? So basically what we're saying is we need to add a visual component to this pyramid and that visual component basically is user experience validation and that has to be automated. And remember what I showed as a demo, right? The validation is automated, but taking a decision on that validation is still a human aspect required. You as a team member know if the difference that is seen is that because of a regression caught in your product or that is because of your product has evolved and you need to take a decision, you need to update your baselines based on that, right? So it's very important to understand where the value of tools can come into picture. It's not about AI solves all the problem. AI in this case, when used for visual testing is able to tell you the difference with accuracy, but you as a team member know why that difference has come in and how you need to address that, right? So tools have to be used in the correct fashion in order for you to get that feed. And overall, this is what the product quality is. It's not just about UI testing. It's not just about unit testing. It's all aspects of testing that is done including the non-automated testing. That all comes together to understand is my product of good quality or not? And you have to look at all the results of these tests or rather the results of all of these tests talk to all the different team members who have collaborated to implement these tests and get the results. Together you have to take a decision about what is the quality of my product. Remember, we always say quality is a team responsibility. How do you enable that? It's just a big word. This is a way that you can start enabling that. You have to ask your development team, how is your core quality? What is the tech debt over there? What is your branch coverage that you have from your unit test coverage before you get to your web service test and so on and so on? Together all of these results combined will tell you the value of your automation. That will help you make your pyramid really like a pyramid instead of ice cream cone which is unfortunately the case in many, many organizations. So in summary, what does this really mean? You need to think about a holistic quality strategy for your product. Don't think about it, I am a QA or I am an ASTET and this is my scope of influence. This is what I'm going to be doing or I'm a developer, this is how I'm going to do TDD or whatever implementation that I'm doing and then I'm going to throw it over the wall to some other role who will do whatever else is required. No, have a holistic quality strategy for your product. It's product actually not produced. Aha, interesting defect I found there. You need to think about how can you shift left to get quick feedback and shift left can happen at various different levels. You have to get all the different roles involved over there to make sure that you are actually getting feedback faster from your test and it is extremely important to think about if visual testing is going to be an integral aspect of your automation journey of your automation strategy. It may not be applicable in many cases but in many cases the brand reputation, the revenue loss or the risk of losing a user because of the short attention span of your users. If something doesn't work well they'll go to some competitive product. What is the risk to your product if any of this happens? Based on that you think about what are the risks you can take on and what are the risks that you need to mitigate for sure before the next release of your product goes out and including these as part of your strategy is going to be a very critical thing to look at. So here are some references that I have spoken to or referred to in the slides and with this I'm going to stop talking. So though we had some hiccups I've managed to cover the content in time I rushed a little bit in between but now we can get to the questions and we can have further conversations around that. So please do put in your questions in the discuss panel and we'll get to that. So let me start looking at the questions over here. Okay so the first question is why can't functional tests cover visual testing issues? There is a big limitation of what the functional testing can do from a visual perspective. How are you going to check from your functional tests if there is an image that is loaded correctly or not? Or if there is some overlapping content or not? So that is a big challenge from a functional testing perspective and in some ways maybe you can write a lot of code for validating those types of issues but you'll quickly run into issues when it comes to what about different viewport sizes, right? If I'm looking at a mobile web versus a laptop versus a 27 inch monitor the layout is going to change because my product is responsive. So can I really do justice by writing how much code can I write to get that validation if it is even possible? So that is the first part I hope that answers the questions actually that was a few quick examples why functional testing cannot really do visual testing to the level that is required. Also from aspects of color and everything, right? You need to think about that aspect as well. The next question is how to monitor KPIs across builds as part of CI CD pipelines that is login time, time to check out, et cetera. Again, a very interesting question not tied to visual testing but I'll take a stab at answering that right now is you need to be able to capture metrics which are going to add value to you. So some of these KPIs that you're talking about these are metrics, right? What are the metrics that are going to add value to you? And value is in terms of not to understand just what your test execution has been but clearly about what information does it give that can help you take decisions about your product quality or your test automation itself. So you need to look at, identify what are these metrics that are important to you? And then when you have identified these metrics use the 80-20 rule and see how can you automate capturing of these metrics into dashboards or reports automatically as part of a test execution. So you don't have to spend time in capturing that data and taking decisions on those. So the 80-20 rule is extremely valuable over here to think about it which what can you do to get maximum value automated results capture or metrics capture based on what you'll be able to take decisions and maybe the rest of 20% metrics for which you haven't been able to automate getting the values directly. Is it okay if we live with just 80% and skip the 20% because do you have enough data in that 80% that will allow you to take decisions, right? So maybe that is an approach I actually take many a times. The next question is how localization testing can be done. Now localization testing itself is a very different topic and I will add just one aspect to this right now, right? Localization testing it is very challenging for the team to do in terms of is this content correct? So I showed that example of the Facebook login screen, right? So if I just quickly go back over there. So in the Facebook, so in this particular screen, I don't understand either of these languages. So does it mean that I cannot do any testing over here at all? So this is where your strategy again comes in, which is very important about in which environment what type of testing will I do? So maybe in my dev environment or in my QA environment where I have control over the data for that fixed data if I use a layout algorithm, the layout should not break regardless of what data is fed into these screens, right? When I'm comparing between different languages. However, if I want to check for a particular language itself, that's a different strategy. You can use a strict algorithm and say, I'm comparing a French login page with a French language login page itself. And is there any difference when the data changes? I'll be able to capture that. So there are different aspects from a localization and automation perspective that you can think about. More in terms of automation for localization, we can talk about separately. The next question that are there first is a comment, I guess more is, I think all of these testings are still reactive until and unless people start working towards TDD, VDD. I do not think it makes sense with the legacy kind of automation testing. I would differ over there. You have to start somewhere. Not every project is going to start Greenfield. Or from scratch, you have to start somewhere. And how can you get the most value from your automation in that legacy product also can be a big win as that legacy product evolves into new legacies that it is creating, right? So even for existing products, you would start adding automation. You would start potentially adding visual testing if it makes sense in that context. And then as that product evolves, you will start seeing the value of that. The second aspect is even for legacy products which had limited automation and you add more automation to it after the fact, that becomes an opportunity for you to say, I have a test safety net now. Can I do refactoring internally in the product? And as long as my tests are still working fine, maybe that is a good value or that these tests are also bringing to me. So in fact, that's a strategy that I've taken in multiple projects in my past experiences, where for legacy products to enable certain change in the product functionality, the big risk is it doesn't have any automation. So first we build automation based on what we know about the product functionality to as much level of detail as possible. And then using that as a safety net, we start refactoring bits and pieces and make sure our test continues to keep passing as that refactoring is happening. So hopefully that helps answer that particular comment itself. Thank you for joining us today. Thank you everyone and again apologies for the technical glitch. Thanks everyone, bye bye.


The Senate has approved the sum of 22.7 trillion Naira. It was spent by the Executive Am of Government without the initial approval of the National Assembly. The 22.7 trillion Naira is money borrowed by the federal government from the Central Bank of Nigeria, through the ways and means advance. The Senate also approved an additional sum of 180.4 billion Naira being balanced of the supplementary budget, an interest accrued to the ways and means advance. The Senate's decision followed the consideration of an introduction by its members. Mr. Weshkeleks, the Special Committee of the Excessive Deliberations recommends as follows, that the structural sum of 22 trillion, 719 million, 703, 774,306.9, only for ways and means advances be approved because the advances were made to ensure that the government does not shut down. Two, that the Senate further approves the sum of 180,463,162,187, being the money, I mean the interest accrued on the money. The Senate also sounds a note of warning to the Executive that the National Assembly will not condone any future increase in the ways and means without seeking the approval of the National Assembly. The National Assembly will not condone the ways and means accrued over a long period of time. Ways and means is not peculiar to our country. They become necessities but there are procedures and processes and better ways of incurring them. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


What is going on guys welcome back to the channel, and I appreciate you being here now I bet you're wondering why why the heck are you undestined new one? Well, I am people to bring users a loot and location because there's something special Here this week for us Xbox players now if you're in an Xbox player This would probably have no interest for you whatsoever, but if you are people This is the must watch but before we go any further guys Do you want to win some exclusive epic loot in the form of emblem and sparrow codes gift cards and much more? If so simply drop a like on this video leave a comment down below and join my discord server linked within the video Description okay, so there this week within destiny one is located right next to the crucible water master And this week people this week Xbox players guess what he has many loads We have the Jade rabbit We have the finally people and I know most people have moved on from destiny one But still if you want that Grimoire well at least a grimoire card Then you get the Jade rabbit from here from there. You don't have to come on and go on the game You just simply come on week in week out check Zerzer weapons and you know never know next week He may have the Zen meteor who knows but yes this week He has the Jade rabbit people and what house is it got? Legacy engram we got insurmountable school for we've got crust of alpha loopy, and we also have the claws But yeah this point let's run through that but you also has people look this is how this is how destiny 2 should be laid out We should have Ornaments exotic ornaments we should can purchase before shards. We should have all of these things right here I'm not sure about three coins. I don't know if they're needed exotic struck way too often in destiny as it is But still and definitely ammo packs for sure and whatever else we could they could fit in but yes But other news people on other news besides the epicness that Zer has brought the Jade rabbit within destiny one or us Xbox people This is this is actually kind of big. Okay, so if you guys follow true achievements on Twitter This is what they tweeted out yesterday the incredible amount of Xbox one enhanced content that came with our review console a massive Thank you to Xbox UK and they tweeted a picture of and you can see people at the top We have Assassin's Creed Origins, which has been confirmed to be running at 4k on the Xbox one X Call of Duty same thing, but it's also got their people a picture of destiny 2 So does this mean mark knows whether you're stuck by his word insane We will put out a game capable of what a console can handle well along them terms There's something like that. He said but yes He said something like we will we won't hold back on a console's power And we will put out a game to fulfill that power That's basically what he said when asked about the Xbox one X So yes, will we get when the Xbox one X comes out an enhanced version of destiny 2 running that 4k true 4k Well, we don't know they actually backtracked with the tree and I'll show you guys on screen now They stated some clarification on this tweet not all games featured in the pic are currently confirmed to be Xbox one Enhanced but I think they're just backtracking here because it's just crazy if you read the original three again the Incredible amount of Xbox one enhanced content that came with our review console a massive. Thank you to Xbox UK The incredible amount of Xbox one X enhanced content that came with our review console and destiny is there So does this mean people does this mean destiny will get a 4k version on the Xbox one X I truly hope so indeed me being an Xbox player and then basically our only plan Xbox the Xbox one X It's something I'm super looking forward to the destiny to my game is enhanced It's just super great news for me seriously is but yes guys Obviously not confirmed as they try to backtrack with their second tweet, but hey, it is what it is Hopefully though it does come 4k. That would be great But yes guys that is it for another video if you enjoyed it leaving a like really does help me out If you are new around here and enjoy daily destiny videos Be sure to subscribe if you never want to miss a video upload hit that bell button next to subscribe button to receive email Notifications of when I do upload but thanks as always for stopping by people and I'll catch you on that next one


In a bold move towards a healthier future, youth in carnal states under the ages of protecting and activating communities against tobacco-packed, of cold and higher institutions to enact smoke-free spaces in campuses. The call was made in an event tagged Paint the Change which featured a variety of educational activities including the use of art to raise awareness of the harmful effects of second-hand smoke and the link between tobacco use and cancer. This is in a bid to stress the importance of creating a smoke-free environment. According to the World Health Organization, modern 16,100 Nigerians are killed by tobacco-cost disease yearly and modern 25,000 children aged 10 to 14 years old and 7.4 million adults from 15 years and above continue to use tobacco each day. I am calling on highest petition, especially in Bairi University, Kamau and Yushu Mekama Suley University, though we hold advocacy with them to enact laws on smoke-free spaces. And then yes, we have gained commitment towards securing that due to the alarming statistics whereby 27 million Nigerians, especially youth, are being affected by second-hand smoke. There are a lot of youths in university and most of these smokers we are seeing are youths. So when you control the smoke intake among youths, I think you've made a very big change in the environment. That's why we focus on institution and universities. We are even targeting secondary school students so that we catch them young. There are actually three types of smoking. So there's first-hand smoking in which the person is the smoker and then there's second-hand smoking, which the person is sitting around people that smoke. Both are equally dangerous. Maybe second-hand smoking in some cases is even more dangerous. And then there's one that has been recently discussed is which is the third-hand smoking, which is the type of smoking that when people smoke in a particular area, it is, research has shown that the residue from the tobacco smoking, the chemicals will still pass it in that environment and they can still cause harm. I call on all the school management actually to take heed of these places and enact laws and make sure that they stand by the law so that people actually follow the laws instead of harming everybody. And meanwhile, Governor Aguilque has plans to invest more in tourism development to boost the state's internal generated revenue, IGR. But if tourism can fund the administrations free education policy and other projects across the 16 local government areas, the governor aims to change the negative narrative of exploiting mineral resources and labeling the state as poor. Professor Leslie Rogers promises to use his connections to attract investors and reveal the state's excess wealth in tourism and agriculture, which if harnessed will significantly improve the IGR. I came seven years ago was money and economic development by and large. I want to highly comment on his excellence in Dr. Aguilque first for dampening into trying to diversify the the sausage of revenue of the state. Tourism is one aspect we are very blessed with here in Naraba state and I count it as the welcome development, trying to divert our source of revenue swinging into the tourism. I'm sure an optimistic that bringing in tourism Naraba is going to restate and regenerate more revenue that will lead to us meaningful development. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


This is where we stopped yesterday. We have an oscillator with a Hamiltonian which has eigenfrequency, omega naught as a parameter. The mass is 1, p is the momentum, this is the Duffing nonminiarity, and this is the drive. So we talked about it yesterday and Yaroslav today very nicely summarized these results that we had. And we derived essentially these equations of motion doing the RWA, which is the conventional abbreviation for rotating wave approximation. So at this point there is no approximation, we just switch to the rotating frame and then we make an approximation by looking at smoothly varying parts of QNP which are the biggest part. QNP also has smaller, but fast oscillating part. So we are looking at the big part of QNP, we have these equations of motion and now it is our choice to essentially rescale variables in the way we like. And there is no unique way to do it, we can do it in several different ways. The way I used in the notes was to switch to the dimensionless time which is determined by the frequency detuning. The frequency detuning, delta omega is omega f minus omega naught. Obviously this is a bad choice if you drive your oscillator exactly on resonance because if omega f is equal to omega naught, it's really a bad choice. I will not be considering this case, I can choose a different scaling, I'm a free man, it's just my first choice. So I switch to this dimensionless time and I will choose my parameter C. So now I have to choose my parameter C and I will choose my parameter C in such a way that, which is incorrect here, so far it's good. I will choose it in such a way that this coefficient will become equal to one. Now what happens when I change to this time? I essentially divide this equation by one over delta omega, one over delta omega. And then Q dot which is dQ dt, if I divide it by delta omega it becomes delta omega and this is dQ detail. So once I have done this, I will call my C squared equal to, in such a way that 3 8, so I divide this whole thing by delta omega, I will choose C so that C gamma C squared over omega f delta omega is one, which gives me the scale of C. So this is omega f delta omega 8 over 3 gamma to the one half. This is the typical amplitude of my oscillator. Because I want my variables Q and P dimensionless variables to be over the one.  Therefore if Q and P are over the one, C is my characteristic amplitude. So essentially what I am doing, I am scaling my variables in such a way that their typical values are over the one. C squared is the vibration amplitude. Now my Hamiltonian. My Hamiltonian I can transform it accordingly. And what will happen with this? I look at these equations, which now I will write one of them in these dimensionless variables. I will also introduce parameter kappa, which is gamma over delta omega. And then look what happens for example with first equation. It becomes minus kappa Q at gamma over delta omega minus P divided by delta omega. This coefficient becomes one. It's C squared gamma 3h over omega f delta omega.  And we know that this is minus kappa Q plus some auxiliary Hamiltonian over Dp. I call this auxiliary Hamiltonian G. And essentially what happens is that G is again a scaled Hamiltonian, which I construct in the following way. I rewrite, I have to make a canonical transformation of this Hamiltonian H and change to scaled variables. The easiest way to see what will come out where the parameters are coming out is just to look at this term. I have gamma, so I make again canonical transformation, scale. And the result is some typical scaling energy times function G of Q and P. This typical scaling energy, the easiest way to see what it is, is just to look at this term. Because this term we know that because of the scaling we have instead of omega naught squared we have delta omega. We have changed the rotating frame and this is a non-inertial frame. So there is if you like a Coriolis force when you change the, you know, Coriolis forces? Again, speaking of micro-mechanics, when you rotate your iPhone the picture changes. How does it happen? It's one of the applications of micro-mechanics. So Coriolis forces are important. Because of that this term is ugly. This term is good, nothing happens to this term and therefore you can see the scaling. Gamma Q, the scale of Q is C. So my E scaling is gamma C to the fourth, right? It's Q to the fourth. And then there is this parameter of 3.8 which comes from averaging. Cosine to the fourth, Yaroslav was talking about it today. So this is 3.8. And with this 3.8 I know what my Hamiltonian has become and my equation of motion for the scale variables have the form dQ d tau is minus kappa Q to the decay rate plus dG dP. And dP d tau is also minus kappa P, we have that before, plus minus dG dQ. Let's try to understand the form of this Hamiltonian G because this is one of the miracles of the nonlinear oscillators of the rotating frame. So this Hamiltonian G has some terms which are very clear. So this is the derivative of G over P. So let's try to guess the form of this term. So G is one quarter P squared plus Q squared squared. If I differentiate this over P, I will have P, 2 times 2 is 4, over 4 is 1. So I have this term here. I will have that same term here with the right sign. And I'm done with this part.  Well, this is also easy, minus 1 half P squared plus Q squared. If I differentiate this over P, I will have minus P, this term. And similarly, over Q, I will have the right term there. And the only thing that is left is this fourth term, the term of the fourth, which I will write as minus beta to the 1 half Q. Beta to the 1 half is for historical reasons. This has been used in so many papers that I prefer to use in so many people that I prefer to use this notation. The fourth amplitude is a bad characteristic. Amplitude is essentially a square root of P squared plus Q squared. So it's better to use squared amplitude. F can be positive or negative. So I use squared amplitude and the squared amplitude will be beta, will be F squared over 4C squared omega F squared, delta omega, because I divide by delta omega squared. So with this, I have a full description of my dynamics for P and Q in slow time in the rotating frame. So now I am absolutely clean. I have two equations of motion. These equations have two parameters. We started initially with a lot of parameters. We had omega naught. We had gamma. We have field amplitude. We had field frequency, four parameters, right? And I have reduced these dynamics to just two parameters, which is much better and much easier to comprehend. Now I have to understand how these dynamics evolve in time. And the first question that I want to ask you. Do you think this is useful at all to have these equations? And if it is useful, tell me a single measurement where these equations can be used. So let me give you a hint. Q and P are the quadratures of the oscillator, right? This is what you measure if you are measuring quadratures, or sometimes you call it in-phase and out-of-phase components. So these are Q and P. So tell me of a single experiment that you can think of where these equations can be used. Go ahead. Homodyne, right? And what will you measure in homodyne? You will measure quadratures, right? And will you see the evolution in time? How will you observe what do you do to see that your quadratures evolve in time? So clearly, if you wait for sufficient a long time, the system will come to a stationary state and they will be constant, and you can measure them. Can you measure the evolution in time, any idea of any experiment that would tell you that they vary actually in time? When you turn on the field, the system is not in the stationary state, right? It has to evolve to the stationary state, and you will see how these quadratures evolve in time, approaching the stationary state. Or you change the field, or you change the frequency of the field. So when you change parameters, this is when this time evolution becomes important and comes into play and becomes observable.  This is minus. It's p squared plus q squared with a minus. And if it is not with a minus, then I made a mistake, but I think I did not. I think it's correct. No, no, this is correct. This is correct. And so this will be minus, time minus will be plus, and this is a plus, and dp is minus. So this is correct. This is correct. It's right. So this is something, thank you. This is something that I keep in my back pocket. The other one, not the one where I keep the mic. So I just, just for convenience, it makes no difference.  What is important to have by stability is to have that delta omega times gamma is bigger than zero. This is necessary for the by stability. And I kind of imposed upon you that gamma is positive. And therefore I quietly presumed that delta omega is also positive. I can choose delta omega the way I want. And as I said, this is just the choice of my scaling. It's not, it's not card and stone. And that is connected to the minus, right? But, okay, well, let me move on. And I will, yes, formally, yes. And there is a slightly deeper reason. So what happens with this Hamiltonian and what happens with this evolution in time? So let me try to rewrite these equations now in the explicit form.  And this expression for g. So tell me something. So g is the energy, the Hamiltonian. What is the most striking difference of this Hamiltonian from this Hamiltonian besides the time dependence? So this Hamiltonian is time independent. Okay, look at this Hamiltonian. There's kinetic energy, right? And potential energy. What about this Hamiltonian? It's not a sum of the kinetic and potential energy. Can a Hamiltonian be not a sum of the kinetic and potential energy? Do you know a system where the Hamiltonian would not be a sum of the kinetic and potential energy? It's independent of time. But okay, potential energy can depend on time. That's fine. It's still a potential energy. So think of a system where the Hamiltonian is not a sum of the kinetic and potential energy. You know this system very well. Everybody knows it. The simplest one. How about a spin in a magnetic field? So once you have angular momentum, it becomes three-tier. And it's not a sum of the kinetic and potential energy. So for a spin, it's not a sum of the kinetic and potential energy. For a relativistic particle, this is actually the first term in the relativistic Hamiltonian of a particle in the magnetic field. So you cannot separate potential and kinetic energy. And you have to live with it. That's life, life of stuff. But also nice. And now what I want to do, I no longer need this line. I will try to describe how to understand this motion. Except that this thing doesn't do anything. Let's try this one. Not much better. Well, as I said, by looking at the Hamiltonian, of course, I cannot tell if I made a canonical transformation. And as I said, I had a canonical transformation and scaling two things. Now, the transformation that I did, and I didn't want to write it and don't want and will not write it in the classical terms because it's a mess. But in quantum terms, it's actually quite simple to write the canonical transformation from the lab frame to the rotating frame. And I will do it later on when we will be working on classical effects more closely. So how do you describe a motion of a system? And one of the buzzwords today is, well, suppose you open the archive and you look for the most frequently used term. What do you think you will see? Let's vote. My vote is for topology, right? So actually, topology emerged in the linear dynamics well before it became a buzzword in physics. And let's see how, where this topology is coming from. So suppose I have just a harmonic oscillator with just a free harmonic oscillator with a friction force. Then I know that the equation of motion is q of t is a e to the minus gamma t cosine omega naught t plus y. And p of t is, if gamma is much less than omega naught, then it's a omega naught e to the minus gamma t sine omega naught t plus y. This is the solution that you know for a for a demharmonic oscillator. It is pretty ugly and hard to picture because it has the amplitude, it has phase, and it evolves in time. So I know, I know that q of t depends on time, something like that. And p of t depends on time in a similar way. And I change the amplitude, this plot will change, somehow change the phase, this plot will change the mass. I can do what is called parametric plot. Now, how many of you have been using Mathematica? How many of you have seen this command? Okay, almost, almost everybody on that side of the room. Just one or two persons on this side of the room. That's for you about credibility theory. So what I can do, I can, from this equation, I can express t, this gives me p as a function of t. But I can solve it and find t as a function of p, and then find q as a function of p, or vice versa. And that's what I will have is the following thing. What I'm plotting is called phase plane. It has p and q variables. And I know that as the system evolves in time, ultimately it comes to the point where p and q are both zero. But it starts somewhere here, and then p and q evolve in time. If there were no decay, what will be the dependence of p and q? I will tell you that energy is one half p squared plus one half omega naught squared q squared. Energy is constant. This is the expression for a very special curve in Mathematics. Do you remember how this curve was called? An oval circle. Ellipse, correct. So this would be an ellipse. And what it tells you that in this case, the system just moves along the ellipse as time goes. So rather than plotting these complicated functions, I can just, where there is no decay, I can just draw an ellipse. And this will tell me how the system evolves in time. If I change energy, what will happen with this ellipse? It will become just smaller or larger, right? And therefore, essentially, if I have this ellipse, if I have one, I have all of them. I know the topology of the phase portrait. Now, if I have decay, I understand that instead of an ellipse, what will happen is that the ellipse is correct. The ellipse will become a spiral. So it will be spiraling, spiraling in. And again, this is my initial condition. I start from this point, I know how it will spiral. If I have different initial conditions, I start from this point, I know that it will still be spiraling, spiraling, spiraling in. And therefore, this spiral is the phase portrait. This is how it is called phase portrait of the system. Now, when we are talking about phase portrait, think about your portrait. What do you have on your driver's license?  They have a particular shape.  So they are all in some sense similar. And therefore, what I have to say if I want to characterize my system is what its phase portrait looks like. If I know phase portrait, I know I can start from different points. I can start from different initial conditions, but I know how the system will evolve in time generally along this. So let's see what is the phase portrait for this system that we are dealing with now in these variables Q and P. Again, I will be trying to compromise with the bottom line. So now Q and P. And first of all, I want to understand what are the stationary states of this system. So I have to set this equal to zero, this equal to zero. And if I want to find the phase portrait, I have to find how many eyes my system has and maybe noses. And there's a stationary state. And as Yaroslav told you, and I told you too, this system can have three stationary states. So let's see what happens when it has three stationary states. So it has one stationary state, it has another stationary state, and it has another stationary state. So these dots are dots where this Q and P don't change in time, stationary states. But now I want to understand how the system behaves. And to find it out, I have to look at trajectories on this phase portrait. What you will find is that these trajectories are peculiar because I can start from this point and approach this. And from this point and do the same. But if I start from here, I will move like that. And if I start from here, I will also move like that. I will approach a different stable state. So these states, which the system approaches, they are called stable states.  But stable is good enough for a physicist. But what I see now is that apparently this behavior is very different. What happens? These two kinds of trajectories have to be separated somehow. And it did. There is a line here, which is called the separatrix. It separates these two groups of trajectories, one that goes to one state, the other that goes to the other state. And this is the phase portrait. This is what you want to know about the system. The rest are details. If you know the phase portrait, you change parameters a little bit. This phase portrait changes slightly, and you have this topology of the system, except. Except. I go back to what Yaroslav was saying before. And let me try again here. I said that my system has two coexisting stable states, and one stationary state, which is unstable. But I know that my system has two parameters, SCAPA, the decay rate, friction coefficients, and beta, the squared amplitude of the driving force. Therefore, I can ask myself a question on the plane of beta and CAPA. Where do I have three stationary solutions? And as we were talking yesterday, it is clear that for very weak drive, that is for very small beta, my oscillator is linear essentially. The amplitude is small. The oscillator is linear. I can have only one stationary solution. For very large beta, for very strong drive, again, as we discussed yesterday, my oscillator can have only one stationary state and one stable state. And therefore, there is a region here, which you can find. Actually, there is a simple trick, which I don't have time to show, that allows you to find these boundaries of the region where there are three states. And here is one state. And here is one state. These lines are the lines where the topology of the phase portrait changes. And the changes in the following way. So I was telling you that if I change parameters, my stationary points move around. My phase portrait changes a little bit. But what happens if, for example, this point merges with this point? Then this whole area disappears, right? And then you have only one state left. And then the topology of the phase portrait has changed. This parameter value where this happens is actually this line. On this line, this point, which is called saddle point, merges with this point, small amplitude, and they both disappear. And this point can merge with this point. And then they also both will disappear. So these are bifurcation points, or bifurcation lines. Bifurcation, bi means two. And we have two states which merge together. Now I want to reproduce the plot that I did yesterday when I was plotting a squared versus f squared. And I can now write it as beta, which has this form. And this is the bifurcation point. This is the amplitude at this state. This is the amplitude at this state. At the bifurcation point, they merge together. This is the bifurcation point for a given frequency of the field. So for a given frequency of the field, it's this point. For a different frequency of the field, kappa is different. It's this point, it's this point. This is what happens. So this is another bifurcation point where these two points merge together. So these bifurcation points are the points where the topology of the phase portrait changes. And this is a buzzword for you in this sense. Now it turns out that these bifurcation points are very useful and they have been used in quantum information, in particular for what is called bifurcation amplifiers. And if I have time, which I doubt, I will tell you how it works. But this is a very important device, which essentially was one of the first devices to do, probably the first, correct me if I'm wrong, experts here, to do measurements in circuit QED to measure the states of qubits in circuit QED environment. They were based on bifurcation amplifiers. And they are still used in this area and in other areas too. So this is the picture that is totally done by mathematicians. Mathematicians knew it all, I don't know, probably at the beginning of the 20th century, maybe later. So far not much physics. Now let's put physics into it and let's see what it is interesting for and what we can learn about it. Well, the physics here comes from, yes, a question? Okay, if you don't ask me questions, I will be asking you questions, okay?  What is good about this system? It's that this system is far away from thermal equilibrium. I drive my oscillator strongly. This poor guy, which without a drive, was just a particle in a potential well, very simple. Now with a drive can have three states, complicated dynamics. It's a very, very different thing that we got almost for nothing. Now we understand the dynamics of this system. We want to understand what happens with fluctuations. And another buzzword that you can find less frequently in comparably less frequently, but still quite frequently, is fluctuation theorems. Have you heard this? No. Jalsinski equality? No. Okay. Well, I tell you that these are less busy words, but they're still used very frequently, particularly by people who study processes away from thermal equilibrium. And this system actually demonstrates that these buzzwords have a much narrower range of applicability than people who use them claim. Yeah, I tell them in their face, so I can tell behind their back. But it allows you to understand what happens if the system is away from equilibrium, because if the system is in thermal equilibrium, we know that the probability distribution is e to the minus Hamiltonian of p, let me use small, q and p, e to the minus Hamiltonian of q and p over kt and one of the partition functions. So if I have the Hamiltonian of the system, I know where I will find it with what probability. Now, I don't have this distribution for the system that I am talking about. And to understand where the distribution is coming from, I have to understand where fluctuations are coming from. So here fluctuations are coming from temperature. Here, so far, there is no temperature. Temperature comes classically from the noise. Now, the difference is, and we will come to it, that these equations classically are fully consistent. I can say that I have, I can think of a classical system that would be completely described by these equations, except that this system has to be, the dissipation has to come from coupling to a thermal reservoir at zero temperature. Quantum mechanical, as we will see, these equations are incorrect, incorrect because they don't take into account quantum fluctuations which come into play invariably if you have a non-equilibrium system. These quantum fluctuations have a different physical origin from thermal fluctuations, not entirely different, but they are irreducible. Their intensity doesn't go to zero if temperature goes to zero. We will see how it comes about. But in the meantime, if I want to study fluctuations, I have to add noise that comes from the same coupling to a thermal reservoir that leads to dissipation. So where does this dissipation come from? It comes from the fact that I have my oscillator coupled to some thermal reservoir which has a lot of degrees of freedom, you can call this back-action of the reservoir. The oscillator perturbs the reservoir, the reservoir reacts, and this reaction is friction. But when the oscillator is coupled to the reservoir, the reservoir on its own has, it has a lot of degrees of freedom, they perform thermal motion, and therefore the reservoir exerts a force on the oscillator. The miracle is that this force comes from the same interaction as the back-action which is dissipation. Now, you are familiar with this language that relates dissipation to back-action because my impression is that many of you are in quantum optics and have it background in quantum optics, so you throw that familiar with this terminology. Not really. Where does dissipation come from? How does friction come about? If you have a particle in free space, absolutely free space, not coupled to anything, will there be any friction? No. Where does friction come from? Of the environment, from the coupling to the environment. And you have these lectures that Orel is particularly talking about. So you can think of Brownian friction, you have this particle, it collides with molecules, and when it just doesn't move on average, there are collisions from the right, there are collisions from the left, it is shaking back and forth, but if it starts moving with a regular force, there are more collisions from the right than from the left, and therefore there is a force, and this matte force is the friction force. So this friction comes from the interaction with the environment, and you can write far more sophisticated model than that, and usually this is what causes friction in nanomechanics. But friction comes from the interaction with the environment, and that same interaction leads to some random force, some noise, which I will now add here. It leads to the noise that drives my both quadratures, Q and P. And we can say, as I said, there is a wonderful theorem which is called the fluctuation dissipation theorem, and you have heard this term used here several times. And fluctuation dissipation theorem tells you that there is a relation between this decay rate and the properties of this noise. This relation is that if I look at the correlation function of the noise, it is KBT, Boltzmann, delta of tau minus tau prime. Let me make sure that I'm not missing the scaling factor. I think there is lambda over h bar, something like that. Yeah. Yes. Two lambda... times two lambda over h bar. This is from the scaling. You remember that lambda is our plan constant, scale plan constant, so this ratio is independent of the plan constant. We're in the classical world. And the correlator of Cp is exactly the same, and these two noises are independent of the classical limit. So what these two noises do is the following. So suppose I have waited for some time and my system has approached my stable state, for example, this stable state. If there is no noise, it will just approach the stable state and stay there. But because of noise, it is fluctuating around it. And these fluctuations have very specific features. First of all, you have heard about squeezing in the lectures before that. And squeezing is essentially that the average value of q minus q stable squared is not equal to the average value of p minus p stable squared. That is, if I look at the distribution of my system about this stable state, it is not a circle. It is an ellipse. And moreover, it is even tilted. So squeezing is inherent to driven systems. Your stable state, fluctuations about your stable state are necessarily squeezed. Second thing is, well, I don't know, has anybody in this room ever measured a power spectrum, a spectral density of a nanotube? Some people have. So what you do, when you measure power spectrum, for example, of a harmonic oscillator, I think of my harmonic oscillator as a very tight spiral and it oscillates and weakly decay. If I measure the power spectrum, it's q over omega. I will use different letter. q over omega, which is defined. Now, you did the experiments, right? So what you do, you integrate from some time q of t, the coordinate, times e to the i omega t dt. You use fast Fourier transforms, don't you? OK. So this is what your fast Fourier transport does for you. Then you square it, and then you divide by 2t. This is how you calculate the power spectrum of the coordinate q. This is the operation where you do it in the experiment. The theoretical way is to write it as the integral from minus infinity to infinity dt average value q of t, q of 0, e to the i omega t, where these angular brackets indicate for this oscillator without drive, thermal averaging. These things, this is called Wiener-Hinschen theorem. So you measure for an oscillator, what is the shape of the power spectrum that you measure? Somebody told me that he or she measured the spectrum. You told me. So what is the power spectrum of the oscillator? What did you see in the experiment? Lorenz and Pick at frequency omega naught, right? Well, I can do the same measurement for my driven oscillator, which is close to this stable state. I will just do the measurement of what? q of t? That's what I would do in the experiment, because what else do I have? But before we look at the answer, let's think about the physics of what is going on. So here, the physics was that my oscillator is fluctuating in time about this equilibrium position. So if I plot q of t as function of time, these are oscillations, frequent oscillations with slowly changing amplitude and phase. And because of this slow variation of the amplitude and phase, this spectral peak has a finite width. If the oscillator were just oscillating at frequency omega naught, it would be a delta function. Because it does not maintain constant amplitude and phase. It has noise, it has volume. So here, about this point, I can have a motion which is very similar to the oscillations of the oscillator. That is my q, capital q of t. So q minus q stable as function of t is almost like oscillations. What is the typical frequency scale of these oscillations in real time? In dimensionless time. What is the scale in dimensionless time? Look, there are no parameters here. So the scale in dimensionless time is 1. Therefore, the scale in real time is delta omega. So there are these random oscillations at frequency. On the order of, it's not equal to delta omega. It's on the order of delta omega. And therefore, if I made power spectrum of q, capital q, it would be a Lorenzen type peak at frequency delta omega. So this is gq. What will I have in the spectrum that I measure in the spectrum of q in the lab frame?  So if q is oscillating at frequency delta omega, at what frequency does this thing oscillate? Cosine delta omega t times cosine omega f t. At what frequency does this product oscillate? Plus and minus. Exactly. Therefore, if I look at the power spectrum of my oscillator that is fluctuating about this state, what I will have is the following thing. So now my gq of omega. Here is omega f. Now, in principle, there may be a delta function of omega f which you can always subtract. It's just force vibrations which are always there. And then I will have a sideband here and the sideband here, they are not of the same height, which are separated, they're equidistant, and they're separated by roughly delta omega, of order delta omega. So in my spectrum I will have two peaks. Well, this is if I'm here. Now, here is another question for you. If I am prepared in this state, will I stay there forever? Not necessarily, right? Because if I think of a particle in a double well potential and I prepared my particle in this state, will this particle stay here forever in the presence of noise? No. It can switch, right? Has anybody seen such switching? It's hard to see. But people who are trapping, optically trapping particles have seen this and measured it and again in this bifurcation amplifiers people are seeing this. So it switches from state to state. If my system is in thermal equilibrium, I can estimate the probability to switch, right? Because to switch my system has to gain energy which is equal to this barrier height. Therefore my rate of switching is proportional to minus delta u over kBt. This was discovered by Arrhenius at the end of the 19th century. Then there was a very famous paper by Kramers. Now the name of Arrhenius probably have not heard. Has anybody heard the name? You have. Good. I'm pleased to see that. Who has heard the name Kramers? Okay, many people. So Kramers actually showed how this works for a Brownian particle and calculated what is skipped here, the p-factor. So for a particle in thermal equilibrium this has been done. Here, as I said, I don't have anything that would tell me what is the distribution far away from my attractor. And actually this is today a micromechanical system. These experiments have been done in micromechanics. The only system away from thermal equilibrium where this basic feature of non-equilibrium system, the probability to switch between the states, has been measured, carefully measured and characterized. It was done in the work by Chen in the classical limit and it was also done essentially with the interval, I don't remember to what side, in the group of Davare and Siddiqui who was at that time at Yale. So it was about 2004-2005. Davare and Siddiqui did it, I think, a little bit earlier for a Josephson junction, for a driven Josephson junction. And Chen did it for a micromechanical system. And this is the only system that I know of which is far away from equilibrium where these rare events leading to switching between the states have been measured and compared with this area that exists for this system. People who are, this is another buzzword that you have heard, protein folder who has not heard this word. Everybody heard, right? We are all eating. Very energetically folding proteins. So protein folding occurs in a non-equilibrium environment and therefore you have to develop means to calculate how this folding occurs. And there is a lot of numerical algorithms which are, proteins are very hard to characterize in the lab. So there are non-equilibrium, there are many factors that come into play, you have to be very careful to reproduce results. With this non-micromechanical system in Josephson junction, this has been done and today this is the only system where it has been carefully done. This is a basic thing in systems away from some of equilibrium, basic insight into statistical physics from some of equilibrium. And the method that were developed to describe these processes, they are now used in all this biochemical and blah, blah, blah science. Now I want to switch to quantum phenomena and any questions? Of course not. Of course not. And therefore when I'm saying that you prepare the system depending on where you prepare the system, it will go to this state or this state, I'm saying about something that will happen on a short time scale. If I wait for sufficiently long time, my system will most likely be in this state or in this state. It will switch as this system will ultimately, you will find it here much more likely than here. There is a special parameter range where these wells have equal depth and this is the analog of the first order phase transition. Does it sound familiar to the first order phase transition? You have two phases and their free energies are equal. The probability to switch from one to the other is the same as back. This is what you do when you boil water to make tea or coffee. So this is first order phase transition. And when you have these two minimum of equal depth, this is the first order phase transition. Here you can also find the value of the parameters beta and kappa where the probabilities to be in both states are equal. And this is the analog of the first order phase transition. And people who work with stochastic resonance used this as a kinetic stochastic resonance and so on. So it's a whole world based on this phenomenon. But let me switch to quantum. Yes, that's a very nice question. In this problem, no. But in nanomechanical systems, this onset of oscillations, when you drive a nanomechanical system, you drive it and all of a sudden you see that instead of a stationary state in this P and Q, what you have is what is called a limit cycle. The system starts self-oscillating. And I am not allowed to say where it happens, am I? So Eva has seen it. And it's quite a miracle. So it's beyond this simple model and remains to be understood. I think it's an outstanding observation. Now, Zyosha has seen it in the situation where you have coupled modes. So people have seen this. But in this simple model, no. Excuse me, it doesn't happen. So quantum world. Quantum world. What I want to start with is yet another buzzword. This is a buzzword day. And here is the buzzword. There are two groups of people, one group who knows this and the other group who doesn't know how to read it. So this is Red Plaquet. He's French, a French mathematician of the 19th century. And this has become a buzzword again. If you check on the archive, I think it was the second after topological. Probably, right? Very, very frequently used. So Floquet states, what I did, I started with the Hamiltonian H, which was equal to I reproduce it. And this Hamiltonian is a function of time. But it's not just a function of time. It's a periodic function of time. It is equal to H of t plus 2 pi over omega f. If I increment time by the period of this oscillation, my Hamiltonian reproduces itself. Because this Hamiltonian is a function of time, I try to solve the Schrodinger equation. What we have for time independent Hamiltonian is that psi of t is e to the minus i e t over h bar psi of 0. The dependence on time is determined by the energy for the eigenfunction. And I have eigenfunctions, which are called stationary states of the quantum system. How does an atom have stationary states? And all other systems, which are not driven, also have stationary states. If the Hamiltonian is independent of time, you solve the problem h psi is equal to e psi, and you find stationary states. No such luck if my Hamiltonian depends on time, obviously, right? So there are no stationary states. And it's tempting just to give up at this point. But we should not rush to give up. We almost have our chance. We notice the very important property, the property that the system is reproducing itself over a period of time.  Block theorem. So several people know, and several people don't. Who you know about electron transporting solids? So electrons move through a solid, and you're talking about electron momentum. But does an electron have a momentum if it is moving in a potential which is periodic in space? It's not a free electron. It moves in a non-uniform potential. How does it have a momentum? The answer is it does not. It does not have a momentum, but it has a quasi-momentum. And this fact that it has a quasi-momentum, which is called the block theorem, is a consequence of the periodicity of the crystal. Crystal is, you should just take an elementary cell and repeat it, repeat it, repeat it, repeat it. Ad infinum. Now I look at this Hamiltonian, and what I notice is there is an operator of time translation, which acts on the function of t so that it becomes, and I will call tf is 2 pi over omega f, but I will use essentially a more general, it doesn't have to be the Hamiltonian of this form. It can be of any form. So I will write tf. Now this operator t commutes with my Hamiltonian, right? Because if I act with this operator t times h of t, it becomes h of t plus tf, which is h of t. So I can as well move my operator t to the right. Now if you remember the basic quantum mechanics, you know that if an operator commutes with the Hamiltonian, you can think of the eigenfunctions that they share. And in this case, I will be thinking about eigenfunctions of the operator t, and the eigenfunctions are called Floquet states, and they have this property that tt psi epsilon of t is identically psi epsilon of t plus tf, right? This is the definition of the operator. And you write it in the form which is exactly the form of the block theorem in solids. So in solids, you have an operator that moves you from one elementary cell to another. And since the solid is infinite, when you move from one cell to another, you don't know that anything has changed. So your function has to be an eigenfunction of this translation operator. And this eigenfunction is defined in exactly that same way. And so I will be talking about these eigenfunctions. I want to make sure that I use the same notation that I am using in the lectures so that the sectionals can be of any use. Yeah, I used tf, right? So this is what I have with my states, and I call these states Floquet states. And this quantity is called quasi-energy or Flakek eigenvalue. So quasi-energy, because as I told you in crystals, momentum of the oscillator is not really momentum, the structure is not a momentum and quasi-momentum. Same here, epsilon is not the energy of the system. The system doesn't have conserved energy because the Hamiltonian depends on time. Instead, it has quasi-energy. And the major difference, which I want to emphasize because sometimes it is hidden again under the rug is that the values of quasi-momentum in a crystal are just determined by the boundary conditions. They are quasi-continuous set of numbers. The values of quasi-energies are found from the Schrodinger equation because after all, what I have to do, I have to plug this function into the Schrodinger equation and to find this function psi-epsilon. So before I do that, I want to show you and to persuade you that I can write psi-epsilon of t in the following form, e to the minus i-epsilon t over h-bar, phi-epsilon of t, and phi-epsilon of t plus tf is phi-epsilon of t. This is again something that people who worked with condensed metaphysics have seen in the blockchain. And you can see that if these two conditions are equivalent, if this condition holds and I increment time by tf, what I will have here, I will have this factor. And this will not change. So this function is the eigenfunction of my operator t. And now to find this function phi-epsilon, to find the value of epsilon, I have to plug in this function i-h-bar dt e to the minus i-epsilon t over h-bar phi-epsilon of t is equal to h of t e to the minus i-epsilon t over h-bar phi-epsilon of t. I have to solve this Schrodinger equation with this boundary condition. So the periodicity of the wave function is the boundary condition for the solution that I have to find. And this will give me the values of epsilon. This is a nasty problem and people have been working on it in various limitations. We are in a privileged position because we can find this quasi-energy very easily. So to show this, let me remind you what we were doing in our problem. When we started the analysis, I told you that this transition to the rotating frame is a canonical transformation. And because this is a canonical transformation, I have a relation pq, what is going on? pq is minus i lambda and lambda is the dimensionless Planck constant. Now I have a quantum mechanics for my variables p and q. And this quantum mechanics has the Schrodinger equation in the rotating frame. The Schrodinger equation is i lambda d psi dt d tau. Remember that tau is delta omega times t is equal to g psi.  Is this an operator?  Is this an operator? It's an operator. It's not just that I have to multiply it by a function of q. What should I do to reveal its evil operator nature? If I'm solving the equation i h bar d t psi is equal to h psi of q psi of q is equal to h psi of q. This is an operator, right? So it's just not just multiplies psi of q by a number. It does something to psi of q. What does it do to psi of q? So I have to say p is minus i h bar d d q. Then it becomes an operator. Now here we have this commutation relation which tells me that capital P is minus i lambda d d q. Again, this is the property of this canonical transformation that we have made. And therefore I have the Schrodinger equation of this form in which g I have to use for p this form. Any pitfalls? I want to show that this operator g has eigenvalues. And I want to relate this eigenvalues to the flow-care eigenvalues, the quasi-energies. And then I want to understand this tells me what the dynamics of a quantum oscillator is. Because otherwise I have found the classical description. I want to find the quantum description. And the quantum description of a periodically-driven system is done in terms of the flow-care states. So I have to find these states and I have to find the flow-care eigenvalues. So this is the goal of what I'm doing. And what I will claim is that if I solve this Schrodinger equation g Psi is equal to Epsom g N Psi is equal to g N Psi N these eigenvalues g N will give me the eigenvalues Epsom. Which is essentially obvious. The obvious thing is that as you remember, when I worked with this Hamiltonian to make from this change from this Hamiltonian to g, I did two steps. First, I did a canonical transformation which is a purely causal step. Nothing wrong about it. Then I did the scaling and therefore what I have and then I did the rotating wave approximation. So I have my h has become the scaling energy number times g operator of P and Q. And therefore I understand and I can show it more carefully that the eigenvalues of this operator g are related, simply related to the eigenvalues of this operator in which I disregarded post oscillating small post oscillating terms just by the relation that Epsom N is E scaling g N. Therefore my quantum formulation in the rotating frame immediately gives me the spectrum of the quasi-energy, of the eigenvalues. So this is a full description of the quantum dynamics that I have obtained almost for free just from this transformation from the nature of the transformations that I have made. And what I have next is now the set of eigenfunctions psi n, the set of... which will be flocated eigenfunctions because when I increment time I change to the frame which oscillates with period omega f t which oscillates as e to the i omega f t. So if I increment time by omega f nothing happens to the frame. The only thing that happens is this spectrum that comes out is this energy g n. Therefore I have a set of flocated eigenstates. I have a set of flocated eigenvalues. And essentially this is as complete description of a non-equilibrium quantum system as it gets. And so on tomorrow that is we will see unusual consequences of this description which come about when we start talking about fluctuations and somewhat unexpected things. And just to tease you I will tell you I know that if I have a particle in a potential well which has energy levels I couple this particle into a thermal reservoir at zero temperature. What will happen to this particle after some relaxation time? In what state will I find it? In the ground state here, right? So should I expect something like that for a given oscillator? If I couple it to a thermal reservoir with zero temperature I will persuade you that no, it doesn't go to an analog of the ground state because quantum fluctuations are in some sense irreducible. They are always there. There is always quantum noise and this quantum noise heats up the system. This effect is called quantum heating which has been seen in the experiment. And there are other very weird fluctuations phenomena in this quantum system with no analog at all in systems in thermal equilibrium. On this, thank you very much.


Hi everyone, in this video, we will talk about in operator in Python programming language. In operator is membership operator in Python. Python's membership operators tests for membership in sequence like strings, lists or tuples. In operator returns value of true if it finds a variable in the specific sequence, otherwise it returns false. In this video, we will write simple example with if else statement, which takes a list of numbers and iterates once for each number in a list and if number 3 is in that list, it will print the message that number 3 is presented in that list, else it will print that number 3 is not in the list. I'll write that example to be very simple, you can code it to be better later. We will start with typing our code, first we will say that variable that keeps our number, we will call it number equals 3. Then we will define one list of numbers, list of numbers equals inside brackets. We will put 5 numbers, 1, 2, 3, 4, 5. Now we will iterate list of numbers in if statement asking if number is in this list of numbers. So we will start with if number is in list of numbers, so if our number 3 is inside our list of numbers, if number 3 is inside that list of these 5 numbers. We will print to the screen 3 is in the list, otherwise we will print else, print number 3 is not in the list. That was very simple code, let's say in operator example.py. Now we will run that code and we will see that number 3 is in the list. That's all in this video, this was a simple example for in operator in Python for iterating list of numbers. Thanks for watching, please like, share and subscribe. Happy coding.


Thanks Ryan Aaron you had to cover an awful lot of ground to get to that ball How in the world did you get there? I don't know man. I just uh, you know, it's running hard Want to make sure I made the catch I was able to what was the reaction by your teammates there in the outfield And did you realize at first that it still remained in your glove? Yeah, I definitely knew I caught it And they're excited man.  Is it personally satisfying for you to have the night you had against your former team? Of course, you know, uh, whenever you're out competing especially against your former team, uh, it feels awesome Well, you mentioned that this one was a bit of a crazy one. Just what was it like participating in this slugfest? It was awesome. You know, both teams were fighting. We were able to come back and continue to come back keep fighting You know, that's what the best part about that game was You mentioned the fight five lead changes in the final three innings What does that continue to say about your team's resilience in coming back?  Thanks for the time Yeah, definitely. You heard it from him Yankees once again savages, right?


The path to success is comprised of many ideas, ideas that inspire you to do something different in your business or to behave differently in your life. And as a result of behaving differently or acting differently or implementing some new concept, your life, your business, your life changes. A lot of these ideas actually come from within you. Yes, sometimes you read ideas, you hear ideas, but a lot of them actually just kind of come to you from out of the blue when it often times in the times when you're least expecting it. You're out on a walk. You're, you know, watching something. You are working on an entirely different project and you have this idea about something else. Now, my question to you is what do you do with those ideas? Do you at least capture them? Do you write them down? And that's what I want to talk with you about in this short video. I've been doing this practice for more than 15 years. This practice of writing down most of the ideas that occur to me. Now, it's not that I write down every thought, of course not, but ideas that say, oh, this could be something I do in my business. I write it down. And sometimes they're not always good ideas. Many times they're not good ideas, but they're out of every 10 ideas I write down. Inevitably several of them are ideas I'm grateful that I wrote down because have you noticed that we don't write it down? Chances are you'll forget them. Now they may be occur to you some later months from now or years from now, but or days from now sometimes.  Once you write it down, the nice thing is you can then evaluate it at a later time. Maybe at the end of the week or at the end of the day, whenever you organize your ideas. Or once you write it down, and then at the end of the day you're clearing your to-do list. You can put each idea in its rightful place in the right folder or right document about whatever project it's working on. And then when you work on that project, say once a week when you work on that project, you pull out those ideas that you've written down about that project. And you can then evaluate it then because distance provides perspective. And so when you have an idea, oftentimes when the idea first comes to you, it's an aha moment. So you think, oh, it must be a great idea. But it's important to write it down, evaluate it later because distance provides perspective. Now, how do you capture ideas? I want to share with you a couple of ways. One way is to use one of those small wire bound notebooks, maybe it has 50 to 100 sheets of paper. You can get this at a stationary store or like a drug store, supermarket, a little wire bound notebook.  And just carry it around with you everywhere, especially when you're out walking, ideas will come to you. Or wherever you're working on some project and an idea about another project, write it down. You could also use voice memo on your phone or your voice memo on your phone. Or what I do now is I use an iPhone and I use the app called Wunderlist, W-U-N-D-E-R-L-I-S-T. So the key I want to leave you with is the more you respect your ideas by writing them down, the more your inner self will respect you by giving you more ideas. I grew up being really shy and what I felt, I felt like I was dumber than other kids. I didn't have as many thoughts or ideas. And I think through this practice of writing ideas down over decades now, my sense is that I have more creativity and ideas than probably many people my age. So I really encourage you to respect your ideas and write them down.


Czech Republic took down the defending champs, Canada, with this ricochet shot with 11 seconds to go. Oh my goodness, that gave them the lead. They are exuberant, their bench is happy, their coach is banging, the other coach is giving them a big ol' hug. Canada can't believe it. The Canadian fans are like, what? What happened? They show the replay, it hits one stick, another stick, deflects the other way, it hits the post and goes in and all of Canada puts their head in their hands and goes, oh no. That's brutal.