Welcome to nursing school explained and today's video on how to change a sterile dressing. Most of all keep in mind that you always want to gather your equipment first because once the old dressing has been removed you want to make sure that you have all the supplies that you could possibly need right there at the bedside so you don't have to leave the room or call for help and have some supplies brought in. So what I like to do and it'll depend on the facility that you work at. I like to bring either a dressing change kit and then also maybe some extra gauze. This gauze here is nice because on the side it has a little tip measure so you could use the wrapper of the gauze to measure the wound if that's needed and then I also like to maybe bring an extra pair of sterile gloves as well as some cleaning swabs just in case something happens or the kit doesn't supply everything that I need. Keep in mind if you're using a kit it usually has all the contents of the kit right there for you so that you can know what's in the package and then you can gather any other supplies that you might need. Once I uncover the patient and their dressing I can basically get ready to set up my sterile field and also assess the wound and I will do this by performing hand hygiene and then putting on just clean gloves and removing the patient's dressing but before I want to do that I note here that this patient has paper tape that they use so in order to prepare myself better I will again also use paper tape and I can measure the length of the tape strips that I'll need but just measuring the length and tearing them off and then placing them at the bedside table or some other place where I can easily get to them later on. Another trick is to make a little tab at the end of the tape which later will help you once you remove the tape off the patient's skin it's much easier to come off when there's a tab otherwise you might have to really dig underneath that tape to get it off and that might not be good for the patient's skin nor might it be very comfortable when that happens and typically we want to form a window frame around the dressing which is what I'm doing here because this dressing was set up the same way before. Okay so now I'm ready to remove the dressing so I gently want to remove the tape. If the tape sticks too much to the patient you can always look for these tabs but if there is no tabs you can take a little alcohol and wipe underneath the tape which will help to dissolve the adhesive of the tape and then the dressing will come off easier. So I loosen it up all the way around first and then I will just remove the dressing and I can throw it right down into the trash that I set myself up with and then I can remove the rest of the dressing and this time I will see if there's any discharge, draining, any kind of fluid that's on the dressing so I can put that in my charting later on. I also want to take a look at the wound and we use the acronym READER so I want to assess for redness, ecomosis, edema, as well as drainage and approximation and the approximation means is the wound, are the wound edges approximate, are they together? In the case of this wound they are not really well approximated because I have this gap right here for this laceration so if they were approximated this would be if there were for example sutures or staples in place here and the two wound edges here were to come together. So now I can take off my clean gloves, I will perform hand hygiene again and then I can open up my sterile dressing kit and this particular kit comes with a nice sterile field so we'll also see how to set up a sterile field. I always like to just fold this over here. This particular kit comes with a trash bag you could set it up right here if you open up the kit before you remove the old dressing and then use this as your trash but in this case I already took off the dressing so I can't just get rid of this. So then everything in here is sterile so now I have to be careful and the sterile drape I'm going to set myself up with and I'm going to pick up one inch of the edge of that drape so I'm going to pick it up right here move the remainder of the box out of the way for now and then hold it at the edge let it unfold and then set it up right here. Now I have a nice sterile field and I can take the contents of the sterile dressing kit and just dump it on here being careful that they don't roll out to this one inch margin. My kit can go away if I were to use additional supplies if I were to use this gauze that I talked about earlier has this nice measure tape measure I could just again open up the wrapper away from the sterile field of course now touch the inside and then carefully just dump it on my sterile field. In this case I'm actually going to use the tape measure and I could use it to visualize and see the length of the wound in this case there's about 10 so this is about 11.5 to 12 centimeters long there's not really a whole lot of width maybe right there at the biggest diameter it's about 1 centimeter and then if there was any depth of the wound I would have to take a sterile q-tip and place it inside the wound gently and measure the depth and then keep that in mind for later so that I can chart that. So now that I got my sterile field all set up I'm ready to don my sterile gloves and I'm going to use those to that away from my sterile field I don't want to put anything on top I don't want to reach over it so I'm just going to look put them aside here careful not to overlap anything and then don my sterile gloves and I have a separate video on how to don sterile gloves properly and then I can just take the wrapper here and be careful stay away from the sterile field and throw it in my in my bin. Now everything here is sterile my sterile gloves I can touch everything here but again I'm going to be careful not to go within that one inch margin but there's a couple of things that I'm not going to need which are these four steps I'm probably not going to use these scissors either I don't wear any tape because I already got my paper tape ready really all I'm going to need on my cleaning swap sticks my gauze and my ABD pad which is what was previously on the dressing so this is fairly simple going forward now because I'm just going to use the gauze and place it over the wound actually first I need to clean it and so I tear this off and this can go in my trash or I can leave it here because it's all still sterile and it comes with these three swap sticks sometimes there can be some cleaning solution in there so you want to be careful not to place the wrapper on the sterile field where the fluid could leak out of the wrapper because then you have a wet sterile field and now it's contaminant because germs could soak through there so you want to either hold on to them remove them and get rid of this wrapper or keep it here but make sure that it doesn't go upside down and then we'll typically clean the wound with whatever the prescribed cleaning solution is just like we do on catheter insertion one wound edge throw that away second wound edge throw that away and then the third wound just down the middle depending on the orders and what the wound looks like then I'll let that just dry for a couple of seconds now I'm ready to put the gauze on remember the gauze is sterile so are my gloves so I don't want to touch the patient when I put the gauze on so I can either just come here and carefully place it on there or I can grab it in the middle and do it this way I'm going to take my ABD pad and place that on top now my sterile procedure is actually complete I could take off my sterile gloves now but since they're still clean I'm not contaminated there's no blood on it I can now use the tape that I have previously prepared here in the appropriate size strips and again I will use a tab here place it on one side here use the other long strip the other side and then my third strip is shorter so it'll go again in this window frame method with my tab and before I put on my last one because I want to label a date time and initial the dressing but now I'm not sure if the gloves touched anything before I reach inside my pocket and use my pen to do that I'm going to take up my sterile gloves and by now I can just discard all these contents here and I will do hand hygiene and then take my pen and label this last piece of tape because I don't want to write on the page that might be very uncomfortable so I'll write the date and the time I'll say it's 10 38 a.m. and I'll put my initials and then I'll put this last piece of tape right there and now I have concluded my sterile dressing change remember to chart everything that you've done to make sure that you take care of your patient give them the call light do all the appropriate things and then regarding the charting always include what the wound looked like so with the reader acronym also include what kind of dressing you did how what kind of addressing was it what supplies that you use as well as how the patient tolerated the procedure please also watch the other videos in my skills playlist regarding sterile technique for catheter insertion as well as donning sterile gloves thanks for watching nursing school explained see you soon


You're listening to the ECB podcast, bringing you insights into the world of economics and central banking. My name is Katie Ranger. 2021 is widely seen to be the make or break year for climate action. The countdown is starting for the United Nations COP26 conference in November in Glasgow and expectations are high. In July, we at the ECB revealed an ambitious roadmap for taking climate change into account in our work following our strategy review. And today, we've reached one of the key milestones on that roadmap, the results of our first economy-wide climate stress test. I'm speaking to our Vice President, Luis de Guindos, about the results of the stress test and what they mean for people, companies and banks. So, again, welcome to the digital class right now, Luis de Guindos. Hello, thank you very much. It's a pleasure to be here with you. Now, it's probably right for you to explain stress testing as a tool that we typically use in our role as a point-fitting supervisor to gauge how strong banks are in the age of shock. Now, the principle for the latest stress test is essentially the time we are assessing climate change. But here, we're looking specifically at what's called my climate change, and this time around, we've all joined the company in our analysis so that we can assess the economy of that economy. Luis de Guindos, what can you tell us about the kind of news we're doing with the digital class? Well, first of all, you are totally right. That's the main goal of our climate stress test. And if I have to summarize the main conclusion and to put it in a sort of a nutshell, I would say that we need to act today because the costs will only increase tomorrow. That's the main conclusion. That's the main point that we are making. We have to act now, and our stress test findings support this even more. Concrete findings that I think that we should go to very concrete and specific points. Climate impacts are concentrated in some geographical areas and sectors. For instance, we have the example of this summer. Countries in the south of Europe are particularly exposed to heat waves and wildfire risk, while north European countries are much more prone to flood risk. When talking about physical risk, sectoral differences matter less than geographical location. Our transition risk sectors play a much bigger role, though. We found that that mining, agriculture and electricity companies could be the most impacted. Stress tests really are a key tool for us central bankers. One of the big challenges with climate change is that while we do know that it affects the financial sector, the concrete risks are currently not understood well enough. The climate shock differs a lot from previously financial crisis and can materialise over longer pre-tine horizons, so very far in the future, between 30 and 50 years. Stress tests help us better understand what climate change can mean for people, companies and banks. The economy, as we have said, as a whole. Very interesting and above all, career for adults indeed. Now, we've talked a little bit about the what, let's talk about the how. The setup of these stress tests is new and quite different from past exercises conducted by other central banks. Can you explain a little bit about how it was conducted? Well, I think that this is quite that unique stress test, and as you have said before, it's different from, let's say, financial consideration stress tests. This one is much more tailor-made in order to try to pick up the costs of climate change. And it's quite unique in scope and methodology. Starting on the scope, it was an economic-wide stress test. This means that we don't look only at banks, we also include companies. In fact, it was the largest of its kind, looking at 4 million companies worldwide and more of 1,600 banks in the Euro area. So the level of richness of the database is huge. And we looked at the time horizon of 30 years into the future. This is the most comprehensive collection of climate and financial data in a central bank. On the approach, this is different to other exercises. We performed a centralized stress test. This means that we didn't ask banks to self-assess the potential impact of climate change on the balance sheet. But we performed this calculation ourselves for all banks, and companies in our samples. This way, we were sure of the consistency in the approach. It also allowed us to look at such a large number of companies and banks. And finally, on the methodology, for these 30 years, we looked at three scenarios and what they could mean in terms of the impact on banks and companies. The first is the best case, what we call the best case scenario. Climate policies are put in place in this scenario in a timely and effective manner. The second one is what we call a disorderly transition scenario. Measures are put in place, but late.  No policies are implemented, no action is taken. So, just to go back, you mentioned that this is a centralized stress test, and our experts often call it a top-down stress test as opposed to a bottom-up. And that's this idea that the data is collected centrally quite fast, rather than it being provided by the banks and companies themselves, as we traditionally do with the supervisory stress test. You are totally right. The top-down is that we have our information, and we make a sort of comprehensive assessment for the whole sector. But we don't receive the data from the banks or the companies. So, I would say that perhaps this top-down or centralized exercise is much more, let's say, neutral than the bottom-up. The bottom-up is when we ask to the companies, we ask to the banks. So, in that respect, the outcome, we can say that is not affected by any sort of bias in terms of the answers and the responses of the banks. Now, you've also mentioned the three different scenarios that we looked at and the effects of them. And what in fact we've already seen over the past month that climate change can indeed have tangible and dramatic consequences. But it does seem that we, as a society, are lagging behind on taking action. Why is it so difficult to set the green transition in motion? Obviously, the bulk of the responsibility lies with government. But what is actually the company from banks actually doing to get this going? Well, I think that this is a very important issue, the one that you have mentioned. What are the costs of investing in doing things differently today? And how do they compare, for instance, to the longer costs that will arise from climate change? These are the two main questions that we have to ask ourselves. We urgently need to transition to a greener economy. And there are different ways of financing this. We have taxes, we have incentives. Even we can put a price on carbon emissions while there are different ways. But we shouldn't forget that the transition also comes with a lot of benefits. First, technological developments can bring energy efficiency and revenue gains for companies and banks. And second, acting now helps us avoid future costs due to the increased physical risk. As for examples, you know what the floods and the wildfires that I mentioned before. Examples of what banks and companies can do, they can invest in green technologies, for instance, make their production change and processes much more sustainable over time, shift their portfolio investments towards green counterparts. Our climate stress test captures all these aspects in the modeling framework. If policies to transition towards a greener economy are not introduced, physical risks become increasingly higher over time. They will increase exponentially. And due to the reversible nature of climate change, such an increase will continue over time. We really need to start this transition now to mitigate the costs of both the green transition and the future impact of natural disasters. That's perhaps not the main message that we can send. Well, we found that climate change is a major source of systemic risk, particularly for banks with investments concentrated in sectors and regions highly exposed to climate threats. For example, imagine an area with a lot of industry that is located near a coast or a river. We have so many of them here in Europe, think in the Netherlands, for example, the north of Germany or even Italy. With climate change, extreme weather events are becoming more frequent. We have seen terrible floods in central Europe this summer which cost a lot of damage to people, companies, to the whole infrastructure. The same goes for the wildfires in Greece and other southern countries, for instance, I come from Spain and we have had quite a few of them. What does this mean for banks? Banks give out and grant loans to people and companies living in these affected areas. The effects of floods and wildfires can lead to people not being able to pay back these loans, which in turn means losses for the banks. The impact on banks' expected losses is mostly driven by physical risk and it is expected to become more severe over the next 30 years. This is why an orderly transition to a greener economy is so important and so beneficial for companies and for banks at the end. This stress test is a very relevant part of the ECB's action plans, to consider climate change in our work as a central bank. Climate change can affect financial stability, as our stress test shows, but also price stability, which is, as you know, our primary mandate here at ECB. Therefore, we are committed to do our part within our mandate to tackle it. This action plan is one of the outcomes of our big strategy review and was announced earlier this summer in July. We put a lot of attention and a lot of emphasis on climate change in our strategy review. The action plan looks at all the different aspects of our work. It covers how to consider climate change in our monetary policy operations, how to better understand climate risk in our micro-economic models, how to check banks and companies' exposure to climate risks, as well as our own exposure. For example, the climate stress test methodology that we have used and the results that we have obtained will fit into two other important ECB stress test initiatives. The first one will be the supervisory climate stress test, that it will be using our terminology, a bottom-up. We will ask the banks and afterwards we will aggregate the responses of the banks. And finally, we are going to also to stress test our own balance sheet. Before we wrap up, we always ask our guests for a hot tip next to the topic we are discussing today. What tip would you like to share with others on the topic of climate change? Well, it's difficult to give a tip, no? But in my case, well, I have two granddaughters, five and two years old. And perhaps, you know, whenever I deal with this kind of things, I try to look for, let's say, a human aspect, a human consideration. And I think that sometimes, you know, I think that perhaps the best legacy that I can give to my granddaughters is, you know, a clean planet, a planet that is dealing with the problem of climate change. And I think that, you know, this, you know, solidarity with future generations is perhaps, you know, one of the main aspects that I would like to recall and to bring to the fore. Because I think that sometimes we do not consider that our actions are going to produce consequences in the future. So everything that we do in order to fight climate change is paving the way for, you know, a better world for the future generations. Thank you very much. Bye-bye. Let's now look more generally at our commitment here at the ECB in the fight against climate change and the next steps on the action plan that we've already touched upon. I'm joined now by the head of the Climate Change Center here at the ECB, Irina Hemskerk, who joined in June when the center was set up. Irina, welcome to the ECB podcast. Nice to see you joining virtually from Amsterdam. Thank you so much, Katie. A pleasure to be here today with you.  Now, perhaps you can tell us a little bit about the center's purpose. What's the idea behind it? Yeah, so how I see the purpose of the Climate Change Center is really to shape and steer the ECB's climate agenda as we start to tackle the issue with more and more urgency and determination and to able to realize this. The Climate Change Center, we will focus on three things. First is coordination. We bring together the work that is being done on climate issues in different themes across the ECB from statistics, monetary policy, economics, financial stability, and so on and so on. So like really connecting the people and the content. Our second focus is strategy. So we are creating an overview of all the climate-related activities inside ECB and we're also monitoring the developments that are happening outside in the markets and at the political level. On this basis, we identify priorities to enhance the ECB's strategy to address climate change. Thirdly, and lastly, we have a central role in steering the work across the ECB in order to implement the strategy and reach the climate priorities that we've agreed on. So it's kind of like bringing it all together and driving it forward at the same time. It sounds like you're going to be really, really busy over the next few months as work really starts to get going. How's it going so far? I mean, to what extent is the center already up and running? Yeah, so I joined in June, so indeed, still pretty fresh on the job and most team members just joined last month. This of course means that we are still a bit in the startup phase of our work as we can build upon, but yet as we can build upon the climate work already done, I do expect we can be quickly up to speed. Okay, Irina, I'm curious to know what kind of people you're actually working with in the climate change center and what kind of profiles you're looking at. Maybe you can take us a little bit behind the scenes because, well, I've got to be honest, I have this kind of idea of a central banking expert that's also a climate scientist and knows everything about the environment as well at the same time, but that's probably quite unrealistic. So maybe you can just give us a bit of an insight into what kind of people you've got in the team there. Yeah, happy to do so. And to start off with, in total, we will be a team of 11 people and will be a very diverse group as typical for the ECB. My colleagues are from different countries across Europe and we all bring in different perspectives with various backgrounds. Five experts in the team are seconded to the climate change center from these different areas within the ECB. They are really their liaison between the technical work that is happening in the different business areas and the climate change center. They are key for the coordination. And then we have three team members focusing on horizontal topics. So one is communication, the other one data, and what you mentioned also climate science. We are still in the process of hiring a climate scientist, but I believe it will be quite unique and yet also very much needed to have someone in the team that can help us better understand how the climate is changing and the effects it will have on the economy as well on the financial sector. The other three team members are the deputy head, the assistant and myself. We are there to ensure everything is managed smoothly and we can deliver on the expectations. And I'm just really pleased that the team is almost complete and the colleagues are just a pleasure to work with. They're all very highly motivated and great experts in their fields. But next to the great people I work with, what I also really like about my job is that the work of the ECB has moved beyond acknowledging the importance of addressing climate change. So the work now is more in a stage of focusing on implementation and action. And I'm just very much motivated to contribute to that. Let's focus on what you've just mentioned, Irina, the work itself. And Vice President Deguindos mentioned earlier in this episode that the stress tests, the results of which came out today, was just one part of our climate action plan. Another are the stress tests that we'll be conducting next year on climate risks for banks, so on the supervisory side of things and also for our own balance sheet. What are the next steps on these two tests? Yes indeed, two other stress tests are planned for next year and they will be based on the methodology and results developed for the economy-wide climate stress test that was published today and introduced by the Vice President already. But firstly our banking supervisors, they will be looking at how banks self-assess their own climate risk. So the idea is to test how prepared banks are to assess climate risk but also to understand their potential vulnerabilities to climate risk. And the results of this stress test, this so-called bottom-up stress test exercise, they will also be used to inform their annual supervisory review process. Officially we call it the supervisory review and evaluation process or in short SHREP. And the preparatory work for these stress tests has already started. Today's result of the economy-wide climate stress test offer a useful basis for the different scenarios our supervisors will be testing the banks against. And now I could also say something about the other stress tests we're doing on our own balance sheets. So we are currently collecting data and specifying the methodology for a climate stress test in 2022 of the Euro system balance sheets. This is the first time we'll assess our own risk exposure to climate change and this stress test will also be based on today's results. So in total we will execute three different stress tests, the top-down economy-wide stress test that was published today and next year on supervisory site and also on the Euro system balance sheet. Let's talk a little bit about our core business now, monetary policy. In this area we hear quite a few demands that we should be taking a bigger role in the fight against climate change and that some of these are quite unrealistic given that we're a central bank. In fact, executive board member Frank Elderson said on this podcast back in May, we are the policy taker here, not the policy maker. And governments are essentially the ones primarily responsible for fighting climate change. That being said, following our strategy review, we did pledge our commitment to include climate change considerations in our monetary policy framework. And one element that people look at quite closely there is our corporate bond purchases. Irina, what concrete steps are we taking here? Yeah, before diving into these two concrete steps, I think it's good to emphasize that at the ECB we take climate changes very seriously. Governments do have more powerful tools at hand to combat climate change than we as central banks do. That's true. But we are convinced that every policy maker needs to contribute to tackling this global challenge. With the tools it has at hand and the mandate it has been given. So our action plan on climate change and monetary policy very much reflects that. Concretely, the two actions I want to mention related to our corporate bond purchases. The first one, the first action is taking into account climate risk in our own financial risk assessment. We want to reduce the risk that we face as an asset holder. That's what we need to do to consider climate change as one risk aspect in our due diligence procedures for our corporate asset purchases. This we have already started to do. Secondly, we start to do more analysis if and how we could include climate-related eligibility criteria in our corporate asset purchases. So what does this mean? For example, we look at whether the issuers of corporate bonds that we hold or want to buy or are complying with the Paris Agreement or similar goals to reduce emissions. This is not something that we can implement overnight. We will first have to assess the possible effects. For example, buying fewer or even no bonds at all from high-emitting companies could help redirecting funds to low-carbon activities. But it could also hinder transition away from carbon if it takes funding away from large polluters that have made firm and near-term investment plans to reduce their carbon footprint. So here we think careful analysis is just very important. Well, that's quite interesting. It's actually not as black and white as it might seem that you just stopped buying bonds from these polluters because actually that might stop them from making the progress that we want them to make in the near term, right? Yes, indeed. Now another aspect that we hear a lot about in discussions on this topic is transparency. And the Vice President just mentioned that while we know for sure that climate change has an impact on the financial sector, the exact risks aren't necessarily that clear. That's right, Irene and I. Yes, exactly. And it's also important in the context of monetary policy. So this is the third aspect of the action plan I want to touch on. It relates to the much needed transparency in the field of climate change data. And we also want to practice what we preach. So in this regard, we have decided to start publishing climate-related information on our corporate asset purchases as of 2023 and as well as for our non-monetary policy portfolios. So these three actions I just mentioned and also the stress tests, the three stress tests are part of a broader climate agenda of the ECB. And I can imagine that listeners might want to know more. So I would like to really like to refer you to the information on the website of the ECB. Absolutely. And we'll definitely link to that in the show notes as well. Well, it certainly sounds like you're going to be busy getting work underway. And before we wrap up and I let you get on with said work, we always ask our guests for a hot tip about today's topic of climate change and climate risk. I think for this one, I really would like to share the story behind the picture. I have hanging behind me on the wall here in my home office. It's quite large and it shows the ocean and the horizon. And in the middle of the picture, in the middle of the ocean, there's one lonely mangrove tree with green leaves and its roots are standing out a bit above the water. This tree used to stand on the beach. The picture was taken on the other side of the road in Fiji where the shorelines are already heavily eroded due to rising sea level. It was taken by Kedir von Lohausen. He's a great photographer who traveled to places around the globe to capture with his camera the impact that rising sea level is already having today. And the forecast, you know, it's not looking good. A report published by the World Bank last week concluded that climate change could force 260 million people to move within their countries by 2015. And hotspots of internal climate migration could emerge as early as 2030. So the reason I have put up this picture in my home office is to remind myself just every day that even though the wildfires that were raging over Europe last summer are extinguished, the flooded areas dried up. But we should not lose sight of the urgency to act now and prevent as much as possible that the impact of climate change is getting worse. This also brings me back to the topic of today. The results of the economy-wide stress test that were published. They show that climate change impacts us all, including the economy, be it companies or banks, and we have to act now. Well, Irina, I can see this picture. This is an audio-only podcast, but we're lucky that we can see each other as well. And it's a beautiful shop, but I would call it tragically beautiful. And sadly, it's all too easy to forget what's actually happening as a result of climate change unless we have it in front of our eyes. So I think having a picture like that in front of you is very useful. And thank you so much for being on the podcast and giving us an insight into the work of the Climate Change Centre. And I look forward to speaking again when the work is up and running. Thanks so much. It was a pleasure to be here. This brings us to the end of this episode. Check out the show notes for further reading on this topic. You've been listening to the ECB podcast with Katie Ranger. If you like what you've heard, please subscribe and leave us a review. We'd love to hear from you, so do share your feedback and ideas with us via social media. Until next time, thanks for listening.


Is the devil using the narcissist to hurt you? Narcissists are evil. They are immoral and wicked. They are morally bad, cruel and unpleasant. They are the opposite of good. So naturally, we might assume that they are possessed by the devil. We might assume that they have been sent here to hurt us. But I actually believe that God is using narcissists to empower us. To help us to learn and grow. To make us stronger. And this is something that I have experienced in my own life. There are times in my life where I have been manipulated and abused by narcissists. But I didn't let it define me. I got back up and became better than ever before. And it may be the same thing in your life. God may be using narcissists to strengthen and empower you. Because narcissists can force us to take action. They can force us to reassess the things that are meaningful to us. They can remind us of how lucky we are. They can remind us of the goodness in other people. They can teach us how we want to love. So our bad experiences are just as important as our good experiences. There is a place for negativity in our lives. We need to have a contrast. There is no light without darkness. I believe that God uses narcissists to isolate us. Where there is no one to validate what we're going through. Because although validation can be good sometimes. It's best for us to validate ourselves. When there is no one around to validate you. It forces you to go within and self reflect. It forces you to find your own inner strength and courage. By realizing that you don't need anyone's permission to validate yourself. You can direct your own life. By not always putting your faith in other people. And instead by putting your faith in God. Trust in God. Because although people may disappoint you. God will always be there for you. I don't believe that the devil is using the narcissist to hurt you. I believe that God is using the narcissist. To turn you into the person that he needs you to be. But for you to become that person. You must go through the trials and tribulations. You must experience pain and suffering. You must validate yourself. Instead of seeking validation from external sources. You must feel like you can't depend on anyone. Other than yourself and God. Thank you for watching. I hope this video resonated with you. Please like, comment, share and subscribe. If you would like to donate. My PayPal link is in the video description. Coaching Inquiries. You can email me at coachingatnaxviver.co.uk Thank you for watching. And I will talk to you soon.


Hi, we have over there. Congratulations. Hello. Good to see you. Good to see you. How are you? Good to see you. Good to see you. How are you? Well this is a great place to be. Hello. How are you? Very good. Good to see you. Hi. Good to see you. How are you? Yeah, that's great. That's the time for the hand to roll. And you were there. And I enjoyed it. In a few years I didn't know that, but I enjoyed it. Thank you. Can you come over here? Thank you. Here's a photo of me sitting there. Here's that. And I'm going to show you. Thanks, Dan. I love you. Thank you. Thank you. Thank you. Dan, I love you. You're my idol. You get here. Press conference. Come over here. Meet the press. Why don't you... If you didn't see it, why don't you meet the press from yesterday? I think I saw it all there. It's all right there on NBC. That was an investigation. That's all I answered. That's what he said. Another commission. Another second. Why don't they take what they've already got? I think he made a pretty good plan. Nice. A good lesson for the kids who worked in it. I'll be watching this evening to see. How do you feel? Let's get started. Have you seen this before? Very interesting. Well, it's just in Japan and down to Indonesia and India, Pakistan and yesterday and Oman at the Gulf Gulf. That's the long trip. Did you come back this way or did you keep on going? I came to the west. Well, it's the same. Who's one day? I'm going back to the west. Oh, we've been saying that. I don't know. I don't know. I don't know. I don't know. I don't know. I don't know. Kristine is not right now. No. Okay. It's so wonderful to be here again. Thank you. Thank you for telling me. Well, listen, I can't think of anything. I'm just trying to get a picture. You should ask her if she needs it. She might have it in the library. No. She brought her to the world. If you wouldn't mind before we leave. Me, I would be very pleased to be here. And they also have something with glass jarring as the seer of the presidency on it. But inside the jar of jelly beans. You think she can make use of those? Uh-huh. She's right here. That's wonderful. And her autograph is right here on this picture. Oh, I was waiting. Do you want me to hold that for her? Maybe in the gap. Amy, I'm going to take your jelly beans. Thank you very much. Oh, I see. The names where she would like to use them. What's that? Please help us stop our Fridays. I will and a lot of other people, and you're going to help a lot of other people find out about it. And stop it from what you're doing. And what you're doing. And we will. But we maybe have a family picture. Why don't you like that? We're actually just going to buy you a beer. Okay. Thank you. Thank you so much. Thank you, Mr. President. Mr. President, may I pose for you? May I pose for her? Thank you. Mr. President, Mr. Malone is the chairman of the foundation. Thank you very much, Mr. President. I understand that there's been a lot of talk lately as to whether the games have a chance of success. Well, let me just say that it's unfortunate that some of the governments of less than free countries have decided for reasons of politics in spite that their athletes will not participate, but let there be no doubt that games will go on and the games will be tremendously successful. Here are God's most magnificent creations. And the final analysis, the goal of those participating, is to do their utmost and to put them at excellence. Our athletes, as you're aware, are not supported by tax dollars. Instead, they depend on all of us, their fellow citizens, to contribute voluntarily to the effort permitted to attend this year. We never have to worry that members of our team will, if given a chance, decide not to come home. This year there's a program which is being operated at no cost to the government that provides a certain proceeds from the sale of these coins are divided equally between the Los Angeles Olympic Organizing Committee and the U.S. Olympic Committee. To date, this program can also want to thank the Congress and the business community for their active support. I'm certain that our athletes deeply appreciate them and every American citizen who purchases these fine coins and does so. Thank you, Mr. President. As you noted, this program is the most successful coin program in history. However, we don't intend to rest on our laurels. We hope to make more Americans aware of these coins, and I'm confident that as we do, Americans will be buying more and more of these valuable and very impressive coins, as well as supporting our Olympic athletes. Mr. President, I'd now like to give you, for you to present to Colonel Don Miller, the Executive Director of the United States Olympic Coin Committee, the first strike, 1984 Gold Eagle, which is also the first gold coin minted in the United States in 50 years. I should add, Mr. President, that I had the pleasure and privilege of striking this beautiful coin at West Point last September. It will have to be taken on at place in the new Museum of the United States Olympic Committee. And in closing, Mr. President, I'd like to thank all of those in Treasury, both in the 1984 Gold Coin. I used to, you want to leave that in my hands, I used to run a quarter-mile. You may find that I'll break 45 on a quarter-mile after. Present this to you. Mr. President, Mr. Secretary, distinguished guest, on behalf of the United States Olympic Committee and all our fine young amateur athletes, I would like to thank you, Mr. President. Ladies and gentlemen, if I may have the pleasure of introducing Melissa Ballott-Hamlin, former gold medal winner, and also Frank Maisley, who was our flag bearer in the 1980 Olympic Games in Sarajevo. In the years of export, we figure 25,000 jobs are created. And those in 1961, there have been over 1,600 recipients of that award. We have 11 of the tenured excellence in export, and three of those are represented here today. Joining me on the podium here are Mrs. Anishin, the American economy, and our local banker, Bill Draper, the president and chairman. Ladies and gentlemen, the president of the United States. Sit down. I don't know about you, but all morning I've been sitting there watching the sky, recognizing the need for increased export efforts. America's future growth and prosperity depends on how well we develop and compete in foreign markets. One in eight manufacturing jobs is related to exports, and 25% of our... far 25% of the total value of all goods produced in this country. Exports mean jobs for our people, profits for our businesses, and growth for our economy. And that's why it's going to be a pleasure to present the well-deserved E and Free World out of recession, and this will increase demand for American exports. But occasionally, the interests of diplomacy and the interests of American industry seem to conflict. Well, our administration sees it as our job. In 1982, we passed the Export Trading Company Act, aimed at opening foreign trade opportunities for medium and small-sized companies, more efficiently and more effectively. We're also implementing an international investment policy to reduce the number we can to get government out of the way to make sure that you have the opportunity to compete effectively in world markets. And there's something else. And I'm beginning to feel a little like an export product myself. But one of the key purposes of these trips is to see that all the export trading doors are everything I can to promote U.S. exports, except possibly wear a Buy American bumper sticker on my bag. We're committed to keeping markets open to free trade. These are our awards. Our award winners are making it happen in a fiercely competitive environment. You have good... President of Belco Industries, Incorporated, of Carrizozo, New Mexico. Mr. John Vontos, President of Vontos Corporation, Monticello, Minnesota. Emery G. Alcott, President of Canberra Industries, Marathon, Connecticut. Mr. Sergio DeArmas, President of Florida Exporters and Importers Association of Miami, Florida. Mr. Leonard Kunzman, Director of Agriculture Development and Marketing Division of the Oregon Department of Agriculture of Salem, Oregon. Mr. Reece Pfeiffer, President of Pfeiffer Wire Products, Tuscaloosa, Alabama. Mr. Richard D. Messinger, Chairman of the Board of Power, Kerber's Incorporated Salisbury, North Carolina. Mr. David Ziminak, President REC Specialties, Camarillo, California. Dr. Leonard Skolnik, President Spitz Space Systems, Chadsford, Pennsylvania. Mr. John Walker, Tennessee Department of Economic and Community Development in Nashville, Tennessee, I assume. Dr. Donald Turville, President, Zeus Scientific Incorporated, Raritan, New Jersey. Mr. President, those are the 11 E awards, and we have three star, E-star award recipients. They are Mr. Harold W. Godberson, President, Gomaco Corporation, Ida Grove, Iowa. Mr. William Donahue, Commissioner, New York State Department of Commerce. And last but not least, Mr. President, Mr. Steve Perry, General Manager, Toledo Scale Company Division of Reliance Electric, Worthington, Ohio. Congratulations to all of you, gentlemen. Thank you very much. Now I'll go back to work. Good job, last one. Thank you very much. Right on the mark. How are you? Good morning. Good afternoon. How are we doing? Good. Well, that's what we're going to find out. Oh, good. You've, and you've seen that. I don't know this guy. Yeah. How are you, sir? How are you, sir? How are you doing? Good. How are you doing? Good. How are you doing? Good. How are you doing? Good. How are you doing? Good. I see you're just a hot-sink. I'm not an hot-sink. But you're going to be a better fit. That's all right. Hello there. Oh, it's magic. Thanks very much, sir. That's there for a picture. And then why don't you all come in and join us for a family business? Sure. This, this's the bridge. In ancient days, it had a ship water. That was sent there. But we refurbished it and ship it.


One concept that can be confusing when deciding whether information needs to be cited is that of common knowledge. Common knowledge, simply put, is information that is so commonly known that when you include it in a piece of writing, it does not need to be cited. But how to know if something is common knowledge? One way to decide is to ask these two simple questions. Is the information factual and not controversial? And, is it widely known among your readers? For example, if I state in a paper, George Washington was the first president of the United States of America. This is a fact that isn't controversial, and it is also very widely known. You might consider this piece of information common knowledge and choose not to cite it in your paper. As a second example, what if I state, the gravitational pull of the moon as it orbits the Earth affects the ocean tides. It is factual and not controversial. But is it widely known and accepted among your readers? If you are writing a paper for your astronomy class where you've discussed or read about this fact in your textbook, you might consider it common knowledge among your class peers. When in doubt, ask your instructor if you should consider a piece of information common knowledge. Let's consider a third statement. A vegetarian diet is healthier than eating meat. First, is this statement a fact? Although you might argue that many people agree with it, this does not mean it is a fact, and it does not mean that there isn't debate about whether it's true. If you make a statement like this in your own writing, make it clear that this is your opinion, and then back it up with evidence. If it is someone else's opinion, make that clear and cite it according to your citation style guide. One final note on a frequent misunderstanding about common knowledge. If a work is free to access, or if there isn't a specific author as in crowdsourced sites like Wikipedia, this does not mean that it's common knowledge. These are two completely different concepts. Information found on a site like Wikipedia or other free websites still needs to be cited. Now, whether Wikipedia should be used as a source in an academic paper? That's a question for another video.


ITU, in partnership with the Digital Impact Alliance, has shaped a sustainable development digital investment framework for policymakers and donors investing in ICTs. The framework will help government and donors identify and fund more efficient and effective ICT investments and accelerate progress towards the attainment of sustainable development goals. The framework calls for a whole-of-government approach to take a 360-degree view of citizens needs to deploy common reusable ICT building blocks. Sets of ICT building blocks are common between different use cases within or across sectors. They can be deployed only once but used to deliver multiple services across different projects and sectors, improving cost-effectiveness and integration. The framework is a holistic cross-sector and cross-organization approach for digital investment which can be leveraged, by governments to put in place strategies to coordinate digital investments, by donors to adopt cross-sector digital investment strategies, by technology providers to research and develop ICT products that meet cross-sector requirements, and by stakeholders to integrate best practices for digital development. The framework can assist initiatives such as the Smart Villages Project, initiated by ANSI in Niger, to deploy and scale up a set of reusable and interoperable ICT building blocks to empower rural dwellers and help achieve the SDGs. Adopting the framework calls for a timely change of digital investment mindset and action in the service of the SDGs. Innovative uses of ICTs have the potential to propel government programs to far greater effectiveness and deliver on the SDG promise to transform our world by 2030.


Okay. So thanks everybody for making it out to the first first meeting of our seminar. Before we get started, I want to say if anybody wants to give a talk or has recommendations for people for me to send emails out, please, please reach out. I don't want to start pressuring the people who are here yet to talk as I've got a good bit of people lined up the next two or three weeks are settled. But if you have any recommendations for people for me to email please send them my way. Okay. So today we have Josh Cooper continuing his lectures on the Broward conjecture. I don't think a round of applause is a good thing to start or something I don't know be kind of weird so I guess Josh go ahead and just take us away. Thank you. Thanks everybody for joining. This is kind of excited to see how this pans out. This is a new day in the discrete seminar. You can attend, no matter where you are on the planet. It should be interesting. It looks like I mean we've got quite a crowd today and it seems like 10 days 15. So, Yeah, so I'm going to talk about some, not not so recent anymore fairly recent our conductor, some circles is considered important. It's a very interesting question. And because this is a talk that is really it's the he's a third talk in a series of a last semester. On this topic. I'm going to do a brief overview, not even so brief overview of kind of the, the context here the questions being asked what's known etc. Before getting to the piece of the, the story that I wanted to talk about today. Because it's the first week of classes and everything is not some just this is going to be a blackboard talk, meaning a whiteboard talk over zoom. So, let's see, can I share my whiteboard. Is that everybody said okay. Yeah, looks good to me. All right, so yeah this is I'm going to talk about Broward's conductor. And this is actually appeared first in Broward's book with hammers hammers from 2012. Although, it's funny you can actually find some papers in the receiving year or two on the topic because it was already being discussed and being called Broward's conductor. And, by the way, everything I talk about today is it's basically in this manuscript that currently being revered but is visible on the archive at this number is this one follow up on a number of archive. So, yeah, the idea here so this is a this is a conjecture about the properties of the Laplacian eigenvalues of a graph of an ordinary simple undirected graph. So, it's funny how little is known about Laplacian eigenvalues. And this is one of these questions that you'll see it sort of looks weird initially depending on where it's coming from. So let me define suppose you have G is just a simple undirected graph. And I'm going to find a few associated matrices, of course the game and spectral graph theory of you have your graph and you associate some of your favorite kind of matrix of it and you study the spectral properties of the matrix and related back to the this is the adjacency matrix. And there, of course, the idea is that the rows and columns are indexed by by the vertices of the graph and entry in the matrix is one if the corresponding row and column are adjacent in the graph and zero otherwise is a very standard way of treating matrices for computations, but also for theoretical purposes also learn to find d of G is the diagonal degree matrix. And it's just the diagonal matrix you get by putting the degrees on the degree vector of the graph, but those on the diagonal and zeros of the rails. The only thing to be careful of is that the adjacency matrix and the degree matrix have the rows and columns index the same way so that we can use a consistent labeling for the rows and columns. That's a and D and then L of G is just d of G minus a of D. This is the Laplacian matrix of G. And actually there's there's a couple of different Laplacian's out there. Sometimes called San Diego Laplacian normalize Laplacian. Or to you to Fanchong, but there's also the service people call this one that the combinatorial Laplacian and actually just differs by a similarity transformation from the normal normalize Laplacian but it's combinatorially the simplest although sometimes not best for Laplacian use any other applications you have in mind. So this is the combinatorial Laplacian. And of course, it's a real symmetric matrix and so it's eigenvalues are real. And so we can we can number them let's lambda one is the biggest maybe and then and the two and then well there's going to be end of them right because it's an end by a matrix. And so there are n eigenvalues Laplacian eigenvalues and the some things are known about these these lambdas. So, for example, these things will be the important the biggest one is always at most n and lambda n is always zero. Actually, the reason for that is that you might say okay well so where's the zero eigenvalue coming from. It means that there must be something in the null space of LG. The null ones vector, think about it for a minute, adding up the rose the adjacency matrix gives you the degree and so line LG by the all ones vector gives you the zero vectors that's where that's coming from. And in fact there's this well known property that the number of zeros and multiplicity of zero as an eigenvalue is equal to the number of components of the graph so if you have a connected graph you only get one. I can value at the very end zero but if it's disconnected there are more zeros that occur at the end of this list of eigenvalues, Laplacian eigenvalues. Okay, so those are the some basic properties of the Laplacian. Let me state the rower conjecture and then talk a little bit about where this is coming from. So, Rower's conjecture says, and it says that for any graph and these Laplacian eigenvalues, the sum of the key largest eigenvalues is bounded by the number of edges. This is a weird statement for a lot of reasons. You may not see the motivation immediately. I certainly didn't. And the reason for the just one of the sort of weird aspects of this is that, in addition to this being highly inhomogeneous and going out of nowhere. The left hand side of this expression is adding up a decreasing sequence, which means that if you plot them, you get something that's concave down. You get some concave down expression because the lambdas are decreasing. Of course, this is not always exactly what happens because you can have lots of lambdas that are equal and so there's black parts occur. And speaking of this, because they're decreasing, they are, well not flat, they're, well, they are flat in the sense of being aligned. Because these lambdas are decreasing, we just ordered them that way, the sum of them is concave down. And this is one way of saying that the sequence of chi-phan norms of your Laplacian or concave down because actually the sum is the kth chi-phan norms of your matrix L of v is the most written L of v, chi-phan are actually not even obvious that it should be a norm, but it's the sum of the k largest singular values, which in this case just correspond to the eigenvalues. In particular, these are, all these eigenvalues are non-negative and real. So that's the left-hand side. It's concave down. The right-hand side is concave up and doesn't even start at zero. It's in homogeneous. So you start at, you know, e of g, number of edges, which I'll often just call that m. And then you've got something that is a parabola up in k. And so the fact that the left-hand side is at most the right-hand side is sort of a strange fact. You might wonder where's the, what kinds of graphs do these two curves meet? And I'll talk about that in a moment. I just want to get this picture in your mind. So just to point out, there are some easy observations you can make right away about when this holds. Let me call this condition e c k of g of r r conjecture kth version by v g. So when k is zero it's trivial. When k is one you just get lambda one and we already said lambda one is less than or equal to n. And so, well on the right-hand side, you also get something that, well, the number of edges is at most, at least n minus one because we can assume that g is connected because it's easy to show that if Rauer's conjecture is true for some graphs and it's true for their distraught union, essentially because of the convexity of the function of k plus one equals two. So we only have to really consider connected graphs in order to prove Rauer's conjecture or special cases of it. And so we can assume the graph is connected, which means it's got already a tree in it, which means it's got at least n minus one edges, which means this m right here has at least n minus one. And well then the second sum and is then one. So some of those then so the left-hand side certainly gone to the bottom by right-hand side. With quite a bit more work, Rauer and some co-authors showed that this is true always also for k equals two. And then also something that I am not going to prove today actually I think it did in the first lecture in this report series, plus four report series, that if it's true for k, it's not hard to show that if BCA is always true, then that implies that BC n minus one minus k also it's also true there and it's quite complimenting the underlying graph as you might expect. So the idea is that if it's true for k equals one and k equals two, like I just said, so it's true for k equals one and it's true for k equals two. Well then it's also true for k equals n minus two and then minus one. So that's a few of the things that we know about this. Like I said that comes from complementation. We also know that eck g is true when G is a threshold graph. Actually there's a number of characterizations of threshold graphs. One of them is that you're starting from a single vertex and then you're allowed to take disjoint unions and complements. That's one way to do it. Another way to do it is what I call the threshold graph is you just define G to be, you have a vertex set B and then we have a function from the vertices to the reels and we're going to put an edge into the edge set of G, let's say x, y, whenever f of x plus f of y is greater than or equal to some alpha that we've also chosen in advance. So if you can, you get a class of graphs this way they're called threshold graphs, it turns out so very easy to show that threshold graphs are, they satisfy the grower conductor and in fact they're tight so you can hit the bound for any k, you can always construct a threshold graph which hits that bound. And so that's one reason for believing this conductor is that that's an upper bound for threshold graphs and threshold graphs are sort of widely believed to have the largest of these sums of eigenvalues, these chi-fan norms of Bola-Plaussian. And actually there's a larger class of graphs called split graphs where these contain the threshold graphs. These also, it's known by the master's thesis of Myoc actually, that the Brouwer conductor is true for split graphs. Split graphs are graphs where you can split it into some complete graph and a complement to the complete graph. So it looks like a complete graph on one side of the split and an independent set on the other side of the split and then something in between. So anything in between is fine, that still counts as a split graph no matter what which goes into the edges in between. So if you guys have this structure, notice you can, what is the split for a threshold graph? It's, you take all the vertices whose value according to F is greater than or equal to alpha over two. Those all have, they're all adjacent to each other because of course the sum of any two of them is at least alpha. On the other side, in the independent set, if f of x and f of y are both less than alpha, then there's some, sorry, alpha over two. So one is less than alpha. So, those don't have any, then things in between. Okay, they may or may not have edges. So yes, that's threshold graphs are also split and those are known to satisfy the Brouwer conductor. We also know things like if you have at most 10 vertices, it's true. Actually, I was able to extend this using some of the results in this manuscript to 11 now. So all of the graphs on the left of the vertices satisfy the Brouwer conductor. And by the way, if you're interested in research topic that is probably just a matter of putting in some work and not too much luck involved you probably get it to 12 without too much breaking too much of a sweat. It's going to be more efficient with the computational efficiency of the algorithms. So, we also know this the Brouwer conductor is true for trees, and Horus, Horus I already mentioned, once you know, for some graphs, you know they're just right union. And it's also known for regular graphs and random graphs. And also things like unicyclic graphs and bicyclic graphs one cycle cycles. I discussed in the previous talks about this, this Brouwer conjecture and some of the results around it, able to show that if K is at least four times the, the arboricity minus one. Then, it's true and so in particular, K granted 11 constant 11, the planar graphs, and also able to show that if K is at least, remember K is varying from one up to and so K is at least the square root of 32 and that's for G bipartite so it's true for almost all the case, just maybe a few at the beginning, you think it is true but I can show that for once you get past 30m for bipartite. Actually, it's not important that it be bipartite it just has to belong to a hereditary class with some forbidden sub graphs basically. So you get a class with a classes of graphs, which the new sub graphs belong to the class as well. Once that happens you get a class of graphs for something like this occurs. Essentially, this changes the constants. Also, same thing for bipartite graphs and just using bipartite. So if K is at least square root of 32 ended the rehabs, then also hold the bipartite graphs. And just to point out right like the number of edges could be as much as quadratic and so this is saying it's, it's anything more than very sparse and it has been sparse graph. If you have a bipartite graph it's reasonably dense. So, I'm able to show that if the variance of the degree sequence I'll tell you exactly what I mean by that in a second is at most. Actually, it's not quick there's a little pickup here it's not quite that it's almost that. The variance the degree sequence I just mean, you know, think of them as samples and take the variance of that. That's of examples or if you like, it's the take a random variable which so uniformly a random pickup vertex of the graph, and then output degree, the variance of that is. And so on the right hand side, you know the variance in general it's going to be order and squared so this is beta. Beta is. It's going to be order density so I'm over the fraction of possible edges which actually are. Number m always means the number of it is not graph. So, if the variance is not very high. Then Brouwer holds, and so this by the way this implies the result about regular graphs because they're the variance is zero. Also implies it for air dish rainy random graphs because the variance of those sequences is much smaller it's linear instead of quadratic. And so, yeah so it also graphs where the max degree in the mid degree and out far apart. Things like that this applies to lots of different kinds of graphs. And it's another one of our results and another case where the Brouwer conductor, I can show it's true is when the splittance which is often written sigma I'll tell you what splittance is in a second is at least the three halves of the splittance of a graph is the edit distance to the class of split graphs. This is the minimum number of edges that you have to flip from well from edges to non edges or from. In order to make your graph split. So, the splittance that's the splittance of the graph and it as long as it's at least end of the three halves over to know that you're reasonably far from being a split graph, then, then the conditional so it's only graphs that are very close to being split that that we don't know. And also show the slightly different flavor that this number we're comparing the sum of the first J Eigen values to this question is this at most this quantity. So, in complete generality for any G, the left hand side, minus the right hand side, it should be always not non positive right that's the conjecture the left hand side but it's right hand side is non positive, but I can show this is it's certainly never bigger than some calls and times and what's where again that both sides could be quadratic so that's small compared to n squared. So, for bipartite G, again, like it's not. It's just that it was a hereditary class but for bipartite G same thing left hand side by right hand side. I can show it's the most linearly off. So we're always even in the case where you're very close to the splittance and all those other conditions fell. So the annihilation of the conductors, the most end of the five boards and bipartite and and finally, I can show that for any G. The set of case, so that, you know, the BC architecture fails for for G is contained in an interval case are the very from zero up to add a lot and dated an interval. It holds everywhere except short interval namely one that has length and most end of the reports, we're comparing the end possibilities are k varies from zero up to and or one up to and and show that, well, in general, it's everywhere but the most for end of the three, what's values a and they actually fall in an interval actually you can kind of see how you prove that from a picture. The picture I do previously, consider this and how could you know a downward concave down curve. How could that go above this concave up curve. And not exceed the value by very much. So this is basically taking these facts and noting that if you're going to not exceed the this this upper curve by at most, you know, and or end of the five boards. Well, you have to kind of turn around immediately after you cross the curve you can't go too far. And so the interval where you pass. It's an interval where you could potentially pass the browser conjecture. It's, it's the most length. And it's really just because the two curves are one of those content about the other ones down. So yeah, that's just just the results gave you feel for what's known about this and something to note is that there's another matrix associated with graphs that doesn't come up as often and isn't as highly studied but it's definitely of interest. It's this unsigned process. So this is it'll look almost the same. It's not the degree matrix minus. As you know degrees on diagonal and minus ones everywhere. It's instead plus. Now you've got ones everywhere. It's conjectured that the same statement is true there. And so we're for the, but now instead of the lambdas being the plus and I do the sinless Laplace. Even less is known about the sinless Laplace. So it's conjectured this is true and not in a keeper off had a interesting thought. So the way to kind of interpolate between the sinless Laplace in and the, and the unsigned Laplace in. Namely, what if we flip edges from pluses to minuses one at a time. So what I want to do is I'm going to define a signed graph. The graph is it's a pair G and how how takes the edge set to just plus minus one. So we're going to give a side to each edge. The degree matrix is what you think it is. It's just the usual diagonal of the degree sequence of G. And the adjacency matrix though is now. It's really great. So it's the you've signed. A of G tau. This means the matrix which is, let me just tell you for a given pair of EW vertices. It's. Well, it's just tau of EW if EW is an edge. And it's, it's zero otherwise. And then we'll define the signed Laplace in. How the, you know, do you minus. So, right, so the idea is that if, if tau assigned all ones, the edges, this is just the ordinary Laplace in. If it's assigned assigns minus one solid edges, then it's the unsigned Laplace in. And so by considering all the sign graphs are kind of interpolating between these two regimes that unsigned Laplace in the sign process. I have for a question, if you think that the Brouwer conjecture is true for Laplacian's and you think it's true the analog of it is true for the sign supply so well then maybe it's true all the way in between. And I'm a key for off started looking at examples and very quickly found a graph with I think it's I vertices and six edges, which violates the conjecture. You found a small graph to the property of a small signed graph to the property that the left hand side to some of the signed Laplacian eigenvalues exceeds the right hand side that M plus K plus one to two. And so I was wondering, you know, is this, is this a common phenomenon or maybe this is only true for some very small graphs only graphs with most eight vertices and then it's true or more. So no, it turns out, it's usually false. It was kind of a shock. True one and true the other it's probably true in between but nope. So, here I'm, and just says that one way to say it is that the Brouwer conjecture for G. The complete graph assigned complete graph is false for almost all. Actually what I mean is asymptotically almost early. Right so, namely, as n tends to infinity the probability that the Brouwer conjecture fails tends to one. That's what this is. Once you once you make n big enough you can make the probability of failure it is close to one of your life. So usually fails this. Usually not true. Signed graphs. It's somewhat surprising.  So it's, it's certainly true there Brouwer true what does this look like. Well, on the left hand side, some goes from one to land the J. And then on the right hand side. And then on the right hand side, you get a number of edges plus two. Well, a number of edges is and choose to. And on the left hand side. What is that. Well, it's not hard to see that the Laplace and I can values of a complete graph are these are the And minus one. And that these are all equal and minus one, and then of course that zero, which means that the left hand side here until you get to k equals and which we already know. And so what are these two curves look like, you know, if you think about a going from going to keep drawing this graph where we're going from K is going from zero to n. So, this, the right hand side. It starts at about n squared over two and then choose to, and then it goes up to well when K is is n. It's n plus one choose to, it's basically n squared over two again. And so the sum of them is n squared. So we think of this is going up to n squared, the upper bound looks like this. That's the upper bound. And then this quantity, the left hand side lower bound, but it's just a line slope and minus one and actually, when K is, and K is n minus one, he's meat. It's a line that basically hits it right at the end, but it's a little, the last value it does. I don't want it to go over the curve. There we go.  But it actually meets it. And these threshold graphs they meet the Rower bound it looks like that right that's left hand side certainly must be right hand side. So you can imagine what's going to happen as we add the signings to our, our complete graph. And we're going to perturb this red line somehow. And the question is what does that perturbation look like. And you can it down you see actually it makes the red curve go over the blue curve. Only very, very slightly turns out it's pretty delicate actually a couple of days of sitting in this plane with the calculations to get this right. Find, find detail in the calculation. This is really in the lower order terms of this happens. I'm going to try to convince you of this today, although I'm not going to do all the details if lots of nasty rigorous details.  So, what's the idea here. You think about it right the Laplacian of the signed graph. What, what does this look like well Laplacian of the complete graph is, you've got what ends on the diagonal. And minus ones and minus ones on the diagonal. And so, take the identity matrix times a minus one, and then. And then we're going to subtract the all ones matrix is often represented J. So actually, in order to get this to work I did one. So 10 times the identity matrix minus this. This J matrix and all ones. And by all ones. So right that's the, that's the ordinary Laplacian what happens when you, when you give it the signing. Well the degrees don't change so the first term doesn't change. The second term is going to change though. So, it's instead. And then, okay, you're going to, you're going to be adding and subtracting some kind of symmetric plus minus one matrix right so it turns out that it's N times M, where M is an I ID. Symmetric matrix with entries plus minus one of a root N.  I decide well I mean is that you choose all of the entries above strictly above the diagonal independently and identically just just uniformly 5050 for the coin. Assign these one of these two values according to the outcome of the coin and then copy all those values in the lower triangle. That's M. And so this is an expression for the Laplacian of that matrix of the signed. And the reason to write it this way is that the spectrum of N is well under of M is well understood. And in fact, by this relation, you get that the case Laplacian Eigenvalue of the side Laplacian is there in bijection with the Eigenvalues of M. So just this, take a, take an eigenvalue of M, and let's call it new K, take an eigenvalue of M and multiply by root N and then add N to it, get an eigenvalue of the sign Laplacian. And, okay, well, again, the matrix M is real symmetric. And so the eigenvalues can be ordered. And, like I said, it's actually very well understood what these news look like what the eigenvalues of a random symmetric matrix look like. There's a very famous result known as big news semi circle law. It says what the news look like. Oh, keep in mind M is a random matrix right so these these news are also random. And we can only describe their probability distribution. It turns out that the, the PDF of the eigenvalues is, it's a semi circle. It's one over two pi square root of four minus x squared. If you have one of these matrices, the reason that this this one of a root N, you might wonder why am I multiplying by root N divided by root N. Well it's so that this matrix has a norm one. It's just normalization so that it fits the standard statements of figures semi circle law. So this is the, this is what this curve looks like. It's one over two pi times square root of four times x squared. And the idea is that the height of the curve height of a circle is the probability density of the eigenvalues that you get lots of eigenvalues near the middle. Right and then they sort of Peter out near the edges, but you get, you get the most of them near the middle and if you plot a histogram of these things you will get a in the limit, get a semi circle. And even I'm not going to be precise about that's the statement of figures semi circle law it says that essentially any ID symmetric matrix, symmetric matrix has its eigenvalues distributed this way not just plus minus one, huge class of matrices. Even like if their entries are Gaussian distributed. So that's bigger semi circle law. And, okay, so that should give us a way to compute approximately at least these new case. And then that gives us by virtue of this expression, the lambda case and then we can add them up and see how it compares to number of edges which is then choose to plus a plus one choose to. So that's kind of a game plan. So, by the way to do that, you need to know where the new case are with quite a bit of precision so it's not enough to know just the semi circle law and it's sort of classical formulation, which is a, it's a limit theorem. And it says that the essentially that the number of eigenvalues up to a certain point. Mark an X here on the line officer is just equals the fraction of eigenvalues to the left of the value X is the integral under this semi circle. There's a local limit law version of that that's known. And quite a bit is known about these the spacing between the eigenvalues a lot is known. This is precise. This is true in a very precise sense of the location of the eigenvalues is sort of exactly what you would expect from this picture that I did. Of course, they're random, but you can put the eigenvalues in a very small window. And, okay, so actually, where is the key to eigenvalue that you might wonder, you know, given this picture, where does the key to eigenvalue fall. The alpha and I can go I sort of think of alpha is varying from zero to one right so we have the, the first eigenvalue and alphas one of around, think of this Europe, all the way up to an alpha is one. Right of course that the subscript is supposed to be an integer but we're going to pretend like it isn't for the moment. When does this happen when when is lambda. When is new alpha and to some value T well it's when approximately local limit window that it's inside of. So that'll be true that new alpha and it'll be about T if, well, the integral from T up to two of, let's call this function row of X of row of X. The X is alpha, right if you want an alpha fraction of the eigenvalues where you have to integrate up to the point where you get an alpha fraction of the area under the curve. And notice by the way I'm indexing backwards or I'm indexing from right to left. So, that's why the, this is integrated from T up to two instead of negative one or negative two. That's happening. So, okay, if we call this function, this integral, all it, let's say f of T, then we're really saying is that new alpha and will be about f inverse it off. Okay, so we've got our. And then so what does F look like to F of T is the integral from T up to up to two of row. If you integrate this function. You get, you get, this is one negative two to two. It looks like this right so all the eigenvalues are negative two and none of them are good. So that's what this integral looks like this is your F, and then right and so the new alpha and as well it's about an alpha. And so what does F inverse look like well okay. All that. So, if you draw F inverse okay that looks like this about a minute graph inverse, and it's going from zero to one and negative two to two. That's the graph of F inverse. And. Okay, so what does the sum of the eigenvalues look like one up to. Alpha and think of K is being multiple. Third of an or two thirds of an etc. Well you're going to get. Remember the lambda K is n plus root and times new k so you get an end for each one of these lambda so it's n times alpha and, and then you pick up something from the new end. The new ends, namely, you get end of the three halves because the root and gives you a factor of end of the one half and then there's a factor of and because I'm rescaling everything from zero up to one notice I wrote it up to one here instead of up to one. So the rescaling gives you another factor of M, and then it's just the integral under this curve now. So this is the integral from zero to alpha of inverse of x. And if you plot that. It looks like this. Think about think about integrating this integrate the whole thing you get zero because the symmetric about a half. And so that's why it comes back to zero over here, but this curve is concave down and it's, it's positive. It's just the integral. A lot of the integral that so okay so that means that we should expect here that the, the alpha and I can value looks like this. The integral from zero to alpha inverse of x, the x. And so, now you can see in that that picture that I drew where there's this line from the complete graph and then a parabola from the upper bound in our conjecture. So if you add something to that line, which is positive and concave down, it will do something like this and cross the upper bound, but it'll cross the upper bound near the end, because this term is really small compared to this term. It's really in a much, much lower order so you really should see this crossing of the bound, much, much closer to the M, or M. You know, so what's what's the upper bound, you know, M plus key plus one choose to this is, well, it's, you know, and squared over to Amazon choose to, and then plus, if we have alpha, then it's, you know, alpha m squared over to about and so you get what n squared over to one plus alpha squared, right, or if you write beta to be one minus alpha. So we're starting from the end instead of starting from the beginning, then you get that M plus a plus one choose to is about n squared over to plus and times one minus beta squared over to which is n squared one minus beta, then squared from both of the terms and then n beta times two all over to that's where beta comes from, and then as a lower order n squared beta squared over to. And so okay so I want to consider both of these expressions and want to compare these two that expression and that expression. If we take beta to be about one over root and so we're getting really close to the end, it's not quite zero zero would be all the way at the end one over root and as close. Well, in that case, the, this express I'm really running out of room. So, this expression is what it's about n squared one minus beta plus some constant times and right because we're getting alpha is about one over root and and we're integrating something that's, you know, just some some positive value that you just replace it with the average value on that interval. It's about we're getting something it's about one over root and because this distance is one of a root and right here that's what it is chosen to be. And so you get one of a root and times end of the three have that gives you a linear term right, but if you compare it to the the other term, what do you get so this the second term is n squared one minus beta I'm going to leave that as it is. And then the second term is, well beta squared is now one over n, one of our n times n is times n squared is also linear. So you get some other constant C prime times as you see it is very delicate because now we're just comparing these two linear terms. And it turns out because of this convexity this the idea of this this thing is is actually it's positive down. It turns out this C here is is three halves. Whereas this C prime is one half one half no it says one. And so the upper back this the upper bound is exceeded by the thing that's supposed to be an upper bound is exceeded by the left hand side by about n over two. And I don't know if that's optimal but it's fairly close. And so yeah so the that implies right that the average, the average case or almost all signings of a complete graph. So some of the Laplacian eigenvalues, the sign Laplacian eigenvalues exceeds the Brouwer bound, when K is very close to and namely it's about root and less than, and so the most most signings actually finally. And just a comment, I think that's not true of almost all graphs because a random graph is quite far from violating the Brouwer conjecture they all satisfy the Brouwer conjecture, but maybe it's true for random signings of threshold graphs, I'm not sure. It was essentially it was easy to show it for easy, but it's just this calculation to show it for complete graph, because all the degrees are the same. Okay, so they have very tight control of the form of the Laplacian, but for other threshold graphs I may not be the case. So one question follow up question is, is this true is it true that the Brouwer conjecture fails assigned to Brouwer conjecture fails for random signings of Brouwer of threshold graphs. Thanks, Josh. Maybe everybody turn their mics on and saying thanks would be too much or collapse or something, but maybe some thank yous in the chat would be would be nice for Josh. If anybody has any questions go ahead and we'll open it up. Are we going to get cut off the 330. I don't know Lincoln, do you know whether this will just shut us off to find out. I think so as light no other sections coming up. So we should be can be like it's not problem. That's a question of whether it's simply employed to stay on or whether we're actually. Yeah, well, we schedule this seminar we put some buffer between this is searching, so you can somebody spend longer than one hour. Hi, well, if nobody has any questions. A lot of the classes of graphs you mentioned up front that satisfy the Brouwer conjecture, I think are also distinguished by low dimensional vice filer layman for graphs for graph isomorphism. And in particular two dimensional vice filer layman distinguishes non co spectral graphs so the eigenvalues are determined by two dimensional vice filer layman. I'm wondering if there any combinatorial properties that are picked up by two or three dimensional vice filer layman that would be useful in informing us about why these graphs do satisfy the Brouwer conjecture that we possibly leverage and generalize from that. Yeah, so I know virtually nothing about the year you're referring to. Interesting. Yeah, I guess I mean somehow that you know it's the split graphs that are also threshold graphs are specifically are the most dangerous right they're the ones that things are close to come close to split graphs are only grass. So I wonder what is what is what is what does look like. Do you have any other questions. We'll get a chat a second to back out some questions if we have anything otherwise we'll go ahead and close it out here. Thanks everybody it's like amazingly smoothly circumstances. So I guess I'll have another one next week. Yep. Thanks again. Have a good weekend. Yep.


Hi, this is Erin Wiens with CalTV Entertainment, and today I'm here on Sprout to talk with UC Berkeley students about their struggle against campus squirrels. Tell us about your most traumatic experience with a campus squirrel. I'd have to say the other day I heard a loud squeak from the trees above as I was walking to class and an orange, like a full orange just dropped right by my head. Well last semester I had a lot of nature valley bars and I'd always sit in front of Dwinell Hall and I'd sit down and be doing homework and steal my nature valley bars but I wasn't too mad because it was a great personal experience. I felt like out of connection with them and I like the way their cheeks look when they're chewing. I decide to avoid squirrels at all costs because those creatures probably have rabies, okay, and if I get rabies that is not okay. I don't think my parents would be very happy so.  Definitely a squirrel. I would have to take my chances with a snake just because I wouldn't want to hurt the campus squirrel. I would choose a hawk snake. Why? Okay, because I haven't slithered in two so just kidding. Anyway, all right so we're here with Juniper the dog. Juniper, do you like squirrels? Do you think they look tasty? We've interviewed the students now it's time to interview the squirrels. What do you have to say about all the allegations of you stealing food? Nothing. This is Erin Wins with CalTV Entertainment on Sproul. Squirrels don't care.


Hi everyone, this is Kess from Doji smartphone and I would like to introduce you to our flagship model. This is the V20 Pro and this is the flagship model. You can see it feels like a retro but actually it's glass. Glass? Yes, it's glass. It's unique technology and also you can see here we have a formal image camera. So it's glass, it's not plastic? It's not retro but it looks like retro. Alright, cool. So this is using the, if I can come here behind you, it says here diamond. That's specimen 7,000 chipset. Yes, only 6,000 for the battery and I have a big memory like telepros 256 and we also have enlarge on the shockwave 8GB which means in hardware the memory is new and you can start the shockwave. 20GB? Yes, together 20GB and in case you have the formal image function, I can show you. Here, you have an inflate. He has no weapons. You can see the temperature and when people go outside for hunting or for some outdoor activities, you can feel the heat here. This way you can also check if people have corona, right? Yes, right. No corona. You are healthy. You are healthy. Okay, that's good. And also the screen is amyloid. Amyloid? Yeah, amyloid. So high quality, high brightness, sharp and will not break. Yeah, it cannot break. Impossible. It takes military 810. So that means, waterproof, that's proof and drug proof. That means somebody who is 810 kilos can walk on it and it's not a problem. Yes. The car will drive on it. It's okay. The car, yes, but we have the standard for the military 810. Okay, cool. Is there a price? It will be good price? Yes, the price will be good. The RP price is about 500 to 600 USD. That's the retail price, yeah? The retail price. All right. But the distributor contact you, make a minimum order quantity and you give a good price for them. Sure, sure. So welcome to contact me. All right. And this is just one of many products you have. You also have here the V31 GT. Yes. This right here. This one. With a big camera lens area. And big battery. Also big battery. And over here you have another one. S100 GT. All right. Also the big battery series. This is a 10800 MAH. Yes. Huge battery. Yes, huge battery. You know people going for the outdoor they will need a big battery. So that's why we had a series designed for the big batteries.  Yes, yes. All right. And this one. S100 Pro. This one we have 2200 MAH. Yes. Huge. It's huge, but it can long use for the battery. Would use for three weeks. Yes. And you can see we have camping light here. Camping light. If you open the light then you can light up the whole room. Nice. You can set up the shortcut for the light. Yes. Somewhere in the settings. Yeah. This is the... What kind of market? Who's your customer to buy this kind of product? The people for outdoor activities, policemen, hospital, logics and many all kinds of different professional fire. Like also like people like hunting or outdoor activities. Nice. And you show some smartwatches here. Yeah. What is the coolest new smartwatch? The smartwatch. Yeah. I need to ask my colleague to my watch. Introduce us. Which one is a nice new one? New one. All of this is a new one. This one is a new one. All right. So what this can do? Yeah. What are you doing? Is it running a special software connected with the Android iOS? I mean also you buy smartwatch or only you are... We just do a YouTube there. Yeah. Reporters. Reporters. Nice. This one. This one. It's cool. And this design also. Design. Yes. You can interview our boss. Boss. Nice. So what's your latest cool smartwatch solution? Solution. This one. Real tech. Real tech. Real tech. Yes. Is Wi-Fi only? Bluetooth? Wi-Fi? Bluetooth. All right. And how long is battery life? Fifty days. Take a picture. Fifty. Nearly two months. Yes. Two months. No, no, no. Two months. Half a month. Yes. Fifteen days. Half a month. All right. Well, which one is the best seller? Best seller. This one. This one also. This one. Best seller. This one. The case here is limo. Can you show how to do this? Yeah. Not so easy. Can change. Can change. Nice. Yeah. Different colors. Yes. And this four included in the package? Yes. So when you feel like a gold style, you can go. Yeah. If you like sport style, you can go. You can choose as a addition, which color, which type you want. And we can add it into the box. Nice. Cool. What do you show over here? Oh, this one also. Nice one. Big display. Also 15 days battery. Is it OLED? Yes. OLED. What is the software solution in the CPU? Real tech. Red tech. And it's an embedded software solution. No APP, right? On it. Yeah. No APP. Did you talk about prices for these or it depends? At the price, the price, they allow $10 to $20 for the FOP price. $10 to $40? $10 to $20 for the FOP price. $10 to $20. Depends which one exactly and everything. So very affordable. Yeah. Yeah. And then very low cost smart watch solution. Cool. People are around $40 to $90. Maybe you can sell for $49. $59. Something like that. Yeah. Cool. Thanks a lot. Welcome. And you. Oh, you want to show more? This one? Nice. Cool. All right. Signage. Some man size. If people use it a lot, can they change the battery at some point? No. No need to buy a new one. Yeah. You need to buy a new one, but our battery can last a long time. Many years maybe. So we don't have to worry about this part. Cool. All right. And then here you're showing some big power solutions. Yes. Yes. Which one is the most popular right now? 3,600 watts. Yes. So is it expensive? Or you provide the best price for this kind of solution? Yeah. Yeah. Sure. You need two guys to carry it, right? It's a little bit heavy. You can roll. You can draw it. You don't have to carry it by your man. Just put it down and then carry it. Nice. And here you have this kind of design also? All right. Cool. Thanks. Thanks a lot. And we have the tab rig. Oh, let's check it out. Okay. A regular tab rig and a non-lucky tab rig. So what is this tablet? Yeah. It's a regular one. It's a T30 Pro. Yeah, this one. We have the TUV certification. Right. Certification. It's a 2.5K for the display. Oh, high resolution. Yes. High resolution. People request the high resolution for the tablet because they use a video for pictures. So that's why we made a really high resolution. And good quality sound. And very nice design. And long battery. Good battery life. We'll see if it has a high-density. MediaTek solution. Even camera on the back. Yes. And it can use the SIM card, not just for Bluetooth. 5G? 4G? 4G. We have the lucky one. A lucky one. The lucky one. Okay. Yeah, here it is. Madeleine. Oh, it's powerful. Okay. What is the most popular regular phone you have? Regular phone. Yeah. Which one is the most successful? The most selling? Back selling. Actually, the regular phone we focus on the Odeon. This is what we're making for the South Korean market. Korean market. Nice. So 2G N70 Pro with Helio G99. It is on the screen. Fingerprint. 20 Baht. See this one. So high quality. Still good price. Yeah. It's also good price. Better price than Samsung itself. Sure. You can check it like you. Nice. This is the high range. Cool. Thank you very much. Thank you. Give me a contact with you.