Okay everybody welcome to the show. We got a ton of stuff to go over so let's not waste any time just jump right in First of all, I know that There is a lot of things that are going on But as a general reminder and we talked about this yesterday is to be hyper focused on the things that you can change Now the things that you can't change. We all know there's a lot of things going on in the Middle East. There's a lot of Problems that are happening between Multiple sides and we don't know where things are going to pop off and I'm not a geopolitical expert So I'm not gonna weigh in but again as our reminder Try to focus on the things that you can actually control and all the things you cannot control what we can control It's the things that we do in our reactions to events now. We talked about Possible recessions possible depressions and possible different other things that could potentially happen yesterday and we took a look at Markets traditional markets and of course crypto and gelasset markets and how they fare in Times of panic and times of war and went all the way back to World War two and I have to tell you Again the things that we can control during times of war. There is a positive correlation with returns So I know everybody talks about, you know, these things will you know tear everything apart. Well Just watch yesterday's video and we go from there also, I know there's a ton of fake news out there and a lot of things that are being passed around on Twitter on Tiktok on Instagram whatever place it that you can find it. There is a individual journalist of BBC and he's done a great job Cheyenne So does idea I think I said that right out of the UK And he takes a look at all these difference if you're looking at all these pictures and things that are really just going down A rabbit hole first go and find this guy and I linked him in the description and he's debunked a ton of different things so far about What's going on so again all these things that are that are happening who knows if it's real who knows what it really is But this gentleman here he's actually will show you the pictures and the videos from one image And I'll show it to you from like a year or two or three years ago So just be aware that a lot of things that are out there are just fake So having said all that Before we get into the fidelity report, which I got to tell you fidelity has 4.5 almost 5 trillion assets that are management It is an enormously bullish what they just put out and this is the type of report that you can give to anybody Doesn't matter how down that rabbit hole traditional finance They are doesn't matter if they're gold bugs doesn't matter if they're in the stocks or bonds over else It is a great report to show them and just a really for them to dig in and lays bare a lot of the truths That is Bitcoin before we get into that I just want to talk about a little bit of a other bullishness in the markets and what is going on I'm not a very big. Hopium type of person But when we got a ton of negative news and try to balance things out a little bit of positive So this was Paul Tudor Jones and he was on CNBC and he talked about what's going on with the equities and how everything's in a fair as far as like with a recession which is potentially coming in and This is a minute and a half. This is from documenting Bitcoin I linked their Twitter account in the description so you can check them out But what he says right here is great and again Paul Tudor Jones multi-billionaire guy and and he was the one that has really got his nose what's going on in the world He was the one that in 2019 with the Davos and pretty much told everybody that The surveys of iris was right at our doorsteps and he was right because he essentially has some type of information The normal people like us don't have so I'm gonna have you I'm gonna play this real quick I'm gonna bring up the tab itself so you can actually hear it Just take a listen. It's about a minute and a half or so. So here we go. You take I think I Think now the barbers relics and I would lump gold and Bitcoin together. I think they probably take on a Larger percentage of your portfolio than historically they would because we're gonna go through both a challenging Political time here in the United States and we're gonna go through we've obviously got a geopolitical situation So I would I would say but high interest rates were supposed to be the thing that was actually gonna be unhelpful to Bitcoin Well, and I think on a relative basis. Look what's happened to gold. It actually has been clearly. It suppressed it So you know that more likely or not, we're gonna go into recession There's some pretty clear-cut recession trades the easiest are The yield curve gets really steep term premium goes into the back ends of Of debt markets, right into into 30 year and 10 year and seven year paper The stock market typically right before recession declines about 12% That's probably gonna happen at some point from some level and You look at the big shorts and gold more like than not in a recession the markets typically really long Assets like Bitcoin and gold. So there's probably a 40 billion dollars worth of buying It has to come in the gold at some point between now and if that recession actually occurs So, yeah, I like Bitcoin and I like gold, right? Great, so your permission lays it out. He's like look the recession is probably gonna come and there's a couple of reasons Why and of course because of that actually happening There's gonna be some type of store of value that we're going to get into him being one of them And of course a lot of his buddies and that would be digital gold Bitcoin and just regular gold I own both. I still understand the problem With people Especially with the gold bugs as they talk about like hey, you know, you shouldn't own Bitcoin like we're on the same team I'm pretty sure I don't I just don't get it. We're here to make some, you know Have a little bit of profitability, but whatever so what he talked about there and he's right He talks about the different The yield curve as it inverts and uninverts This is the treasury yield spreads against his Ben's website in the crypto verse link in the description 10% off the first month There's no sale right now, but maybe next month. Maybe then will will be so kind As to as to limit the and I'll drop the price a little bit, but anyhow, so we take a look at the the Yield spreads you can see that yes right before a recession when we blow this up They will invert and they will go down they want to invert and of course things are going good And then we'll go in this great part, which is the recession itself and that happened during the surveys of virus I stole that from George Gammon. I even check out a channel. It's great stuff. Also, let's see over here in December Oh, is this oh one during the Dot-com crash and you can see here that of course again treasury yield Inverts and an unverts everybody's happy and then we're going to go into recession And of course that is happening. All I'm getting to is that it's happening right now It's going down. It's inverting now. We're uninverting, but we aren't at that very point where it's actually at base so we're waiting for it to actually happen and then we'll probably get a recession and You know when that happens It is a natural there's a natural cycle and not only that and if you take a look at the United States with their debt to GDP ratio You know, we're at a hundred twenty two percent hundred twenty nine and we're writing things pretty high We should be around sixty sixty eight percent. Of course, that would be the ideal But of course, we're America. We love debt. We love the print money So here we are and of course in I think a couple years are the the interest on the debts Which is over trillions or trillion is the more that we're actually going to spend Into the military industrial complex. So if we think about it, there is a ripe time for that But don't despair because as a reminder and we talked about this about a week ago or so Recessions don't last forever bear markets don't last forever and bull markets They don't last forever either Everything is a cycle and we average these out going all the way back to the 50s The average for a recession is roughly 10 months now some last a little longer Some last a little bit shorter But you're looking at about 10 months and if we go into q3 and we have a recession What does that lead us into all it leaves us into roughly 2025 what happens after a Bitcoin having? I think you know the answer So not to be outdone Fidelity this was a great report. It's 23 pages. I'm gonna try to I'm trying to breeze through this as fast as possible I highlighted the good stuff left out the kind of boring stuff, but I linked this Document in the description. I'd love for you to share it with everybody who you think would actually be able to understand it A little bit and here's what it says and again fidelity if this is what they're telling their clients 4.5 roughly 5 trillion assets that are management. I think we're in good hands So this was released the end of September 2023 and just heard about it today Bitcoin first for visiting here is let me see if I can blow this up a little bit. Yeah, perfect. Here's the summary One of the first concerns investors have regarding Bitcoin is as the first digital asset It may be vulnerable to innovative destruction from competitors such as like my space and Facebook Of course They're talking about in the good old days in social media before we ever knew Facebook was gonna be a juggernaut We're like, you know my space will take over or some other thing that was our our friendster offer people remember that and of course It was Facebook so they're getting to the the crux of it Which is I know people they think that something better is gonna come along, but it's not I know people right now are screaming at that the screen going but Rob You're an idiot because there's much better technology than Bitcoin. Hold on. We'll get to all that. I got you So Bitcoin is best understood as a monetary good one of the primary investments these Thesis for Bitcoin is as a store of value in an increasingly digital world No other digital asset is likely improve upon Bitcoin is monetary good because Bitcoin is the most Relative of our digital assets secured decentralized sound digital money and any improvement will potentially face trade-offs other non Bitcoin products should be evaluated from a different Perspective and this is very true. Let's be honest Bitcoin now is the most essentialized It's the most battle tested it's been around forever and it's building number one for everybody talking about the flippening It hasn't happened yet. So I'm just waiting for that day Investors should hold two distinctly separate frameworks for considering investments digital asset ecosystem Second consider the addition of other digital assets and exhibit venture capital like properties again We start with Bitcoin then we get to the degenerate stuff, which is fine. I just think that with them telling all their customers I think this is a catalyst for growth So Bitcoin the network versus Bitcoin the asset I like how they did this because they pretty much laid it out as like this is What you have to understand and we're gonna talk about this in a second as far as like the network as it compares to like TCP IP and the asset which is the Bitcoin that we all know and love and have in our ledger or our Tangent on our ellipel walls and they said we can why we believe Bitcoin is best understood as a monetary good and they Put out pictures because it's a mixed thing simple Historians suggest the answer lies in several characteristics that make good money and you can see very very clearly here They they compare gold Bitcoin Fiat very nice durable divisible fungible portable verifiable scarce and a track record and Bitcoin has everything except for the track record We can't beat out in gold for the tens of thousands of years has been on the planet And we can't beat out Fiat currency yet as far as like a track record But if you take a look at all Fiat currency throughout the entire existence of mankind all Fiat currency Inevitably goes to zero and I don't know when the Dow is gonna go to zero I don't think it's gonna be tomorrow like like some people say but at some point it will so again durable Very it's non-destructible very hard to destroy especially the tens of thousands of knows that we have it's divisible 100 millions of satoshis per Bitcoin. It's fungible. Of course, you can have one Bitcoin for one Bitcoin one goal for one gold It's portable. I do all that to remember is my 24 word mnemonic phrase I can take it anywhere very tough for gold to do but pretty easy for cash Verifiable which is on-chain. It's scarce to 21 million actually. It's not scarce. That's not that's not the right word It's finite because gold is scarce, but Bitcoin is fine. It's only 20 million. We keep finding gold for some reason It's amazing and of course the track record So again as I'm going through this just think about all the people that get to read this and are gonna go through this Especially the people that are in traditional finance. They just don't get it yet They're like, why would I invest into nerd money which I've been hearing about for a decade now I know it's the best performing asset class so far, but why should I do it? That's what this is actually for and I'm again. I'm excited that we'd only put this out Bitcoin's values are imbiots enforceable scarcity and finite. It's provable finite 21 million and of course it talks about Why it's so good first is Bitcoin's centralization Don't to tell you about that and it talks about if the network is operated by mirror code Can this code be changed again? I love this because they put things in there because people are probably thinking themselves if this is just code Why can't we just change it and make it 42 million or a hundred billion? Yes, you can but only through consensus of the network participants or the node operators a change in Bitcoin supply schedule It's something that could happen in theory, but almost never will an actual practice I know people talk about this, but if people are going to vote and say, you know what? We should make it 42 million or a hundred billion You're taking away the best aspect of Bitcoin itself And you have to get all the node operators or at least 51% to agree to that and that's not gonna happen second the Bitcoin network is censorship resistant, of course because it's on an open ledger and We've seen what happens when different blocks are our fudges around with I think the Mara or riot blockchain We're doing some kind of Experimentation and they tried that and it was immediately rejected the Bitcoin network works just like it's supposed And then we get to the good stuff why you believe Bitcoin is the potential to be the primary monetary good We will not be as so bold as to predict there will only ever be one money But we do believe that one monetary good will come to dominate the digital asset ecosystem Do the very powerful network effects if investors are looking for a digital asset as a monetary good One with the ability to actually store value then they will naturally choose the one with the largest most secure Decentralized and liquid network now right now. I know you're thinking to yourself, but Rob my crypto is awesome You don't understand. It's great. It's super fast transactions per second can do all those things again Can you go through this and say that is the most secure it is the largest the most decentralized and the most battle-tested no Because Bitcoin was the first and it'll probably continue to be I'm not a Bitcoin maximalist I'm just saying I understand what they're coming from So for the case for Bitcoin the reflexive property is even more pronounced because it does not just include passive holds the asset It includes miners and I like how they break this down is so people understand that actively increase the network security As more people believe Bitcoin has superior monetary properties and not to store their wealth in it demand increases And it's just a continual effect more computing power devoted to Bitcoin mining leads to higher network security which in turn Makes the asset more attractive leading once again to more users and investors And this would have been a great time for them to put the hash rate, which is at an all-time high Which means if we're at an all-time high for a hash rate some at some point price will follow Which means that all the Bitcoin miners they're just talking about this little snippet Really believe in Bitcoin and are putting their money with their mouth is which would paint the price at some point go up Any subsequent monetary good would be reinventing the wheel and they go to some They're gonna talk about it here But I skipped it because when I talk about Bitcoin cash as far as like reinventing the wheel for Bitcoin You're gonna see why it works and why it doesn't work They talk about the Lindy effect Lindy's law is a theory that the longer some non perishable thing survives The more likely this is to survive in the future take a Broadway play if it's run for 10 years It's likely running another 10 years Compared to one that's only been around for a year and think about that for all the grip and cryptos that you're into And we actually did a report to take a look at how many different cryptos back in 2017 Were hit their all-times high in 2021 out of the top 53 only 11 did so again Battle tested and it makes sense as the risk goes down Makes more sense for people to invest into it And then it gets into the trilemma and this is where it talks about how Bitcoin of course Does have a flaw Security well the the trilemma is very simple security decentralization and scalability, right? So the more the more secure it is this is how likely it is a network can be attacked or compromised how secure is it? Bitcoin the main concern is a 51% attack which when I got in 2017 all the different miners and the nodes that were out there It was feasible It was actually plausible that that actually happened because we didn't have as much Security that we do right now and as much as many as many nodes as many Miners that are out there so the security was an issue It was a much riskier bet back then but we believed in it now here We are so and it talks about how it's way more Oh, here's the it's way more secure because the hash rate going up to talk It would take billions of billions of dollars to to attack at 51% as far as Bitcoin now other cryptos I can't say Decentralization how much control any one person entity or group may have on a system or network? Banks very centralized Bitcoin, Ethereum and a bunch of different ones much more decentralized Bitcoin the most essentialized So the less decentralized it is the user it is to change things on a system or a network because they can do what they want It's a one section and lastly scalable or how well the network can handle growth And this is where they said scalability has notably been the Bitcoin networks Achilles heel, and it's true Have you seen the transaction fees in 2017 in 2021 for Bitcoin? It's close to the roof and that was the whole point of the Bitcoin white paper a peer-to-peer transaction At that point it didn't really make sense and that's just the truth I know some people say well, Robert if I'm you know moving millions upon millions of billions of dollars I have to spend You know 50 75 bucks. I don't care. That's true, but I don't know how many of you've got millions of millions of dollars and billions I don't have billions so for me. That's not really a good state As far as a you know for a peer-to-peer I think for the majority of people that I want to spend 75 bucks to move 10 bucks of Bitcoin around just saying So then to move on not be a dead horse It's the Achilles heel because it maximized the centralization and security, which is a little bit, but as a result In the network with one of the slowest transaction throughputs. That's very true However, we believe Bitcoin is going the most secure and decentralized monetary works network So I like how they they say yes, here's the positives, but there is one downfall, but then they get into store of value And actually before they get that they go and they talk about improving Bitcoin the block size war And of course when they talked about changing the code, this is what they're getting to where they talk about Bitcoin cash And I got nothing against Bitcoin cash. I don't I know people hated Roger beer's guts when he did it in 2017 But I've had on the show nice guy and I can see why I did it Bitcoin cash case study advocates of this hard for believe Bitcoin should First and foremost be a literal peer-to-peer electronic cash system or a system that can handle large amount of transactions We emphasize that there is nothing wrong with this approach But it once again demonstrates the trade-offs made for scalability once you make things more scalable There's a problem with other parts of that with decentralization and security. I Have no problem again with Bitcoin cash. I'm just saying that even when the transactions go up The transaction fees do go up But it is a peer-to-peer transaction you use it and don't worry. We'll get the lightning network. So stop screaming at Bitcoin's market cap over a hundred times greater than Bitcoin cash Which means that investors have continued to choose Bitcoin as the preferred monetary network and therefore it appeared to be value-a-secure and Sounds store of value over faster or cheaper payments. And that's the thing. I Know when we talk about this and people will say well damn it. This wasn't supposed to be a Store of value This was supposed to be a peer-to-peer Transaction and I get it I understand exactly where you're coming from because it's easy to say right because that's what the white paper said And of course Pierce will say I am not I don't want to go outside of this because that's exactly what it is So when I think about it I really dig deep into it. I think to myself well, what about iron Well, actually, I'm gonna blow this up so you can see it and steel Think of it this way Bitcoin is a very new technology. It's only 13 14 years old, right? 2008 the white paper 2009 rolled out first blocks Genesis blocks But if we take a look at iron and steel, I mean iron was 5,000 years ago. I went early man Found it out and smelt it and started to break it down. They're very the most easy things trinkets jewelry Press plates some swords not very good though, right then around 1800 BC. We figured out. Okay, if we take iron Makes it with carbon we can make steel that was 1800 BC and of course what happens then well in the medieval times We use those for protection then as we moved on to the later 1900s. We made Look a motion We made steel tracks. We made buildings and everything else on top of that So even though in the beginning, I'm sure these guys medieval times this new technology iron They're like, this is it This is the greatest thing of all time and we can use these for just these little things as time progresses The technology catches up and they go, you know, we can do a lot more things. I think that's the same thing here With Bitcoin and moving forward so To finish up with this report Bitcoin superior monetary good The market shown a preference towards Bitcoin, which is slower as a payment system compared to the digital assets and blockchains Signals the market currently values a highly secure decentralized to revive. Okay, I read that. Sorry and then Okay, how Bitcoin positions itself against the rest of the ecosystem Bitcoin is currently the most secure decentralized network But at the base or native network layer, it is not the most scalable. That's why we have stuff like Ethereum That's all your stuff like Cardano and Solana and Cosmos and whatever your coin is don't Don't yell at me too hard if I didn't mention although no one knows exactly where what Bitcoin may become We may think it is we think it is instructive to examine two dominant narratives That have growth potential one is a multi-chain world, which we can tell right here. There's a multi-chain Maybe when it will take some maybe when it will take all maybe when it will take most But with Bitcoin we kind of see what it actually is and then of course on Ethereum Smart contracts stable coins defy NFTs all that stuff, right and of course there's other different chains So it could be a multi-chain world But they said something pretty interesting here They said just be careful with this multi-chain because people use tokens in an arcade for ease of use and utility And attribute value to them because they know they represent a certain dollar amount or can be traded for other goods and prizes However outside of the native arcade environments the tokens have no value little to no value So again think about that when you're investing into crypto and digital assets I can't give you financial advice, but think yourself. What's the utility here? What's really being used and if I get out of this little system. Is there any kind of value outside of this? This world leaves non Bitcoin tokens battling to do other viable use cases Yeah, and then a winner take all or most world another scenario that could arise if the ability for apps and scaling solutions To be built on top of the base layer or layer one if apps can be built on top of an existing blockchain network Rather than be forced to start a new network users would arguably want to build on top of the strongest Most secure network out there. This is what Adam back's always talking about. I couldn't really understand Till I read this Bitcoin is arguably the most essentialized and immutable blockchain and exist and appears as a prime candidate to be one If not the main winner, and this is how they compare it and it's beautiful. I did it TCP IP is the internet space layer provides the perfect example TCP IP is an open source base layer for communication to flow through and Subsequently applications and content on top of which it was built TCP a protocol is not owned by anyone It's open source allows the internet for a flow of information Does not allow ownership of the base layer. I mean it's here right here. TCP IP was created I was around that time and what was built on it everything that you see right here YouTube Facebook Amazon Google Apple Netflix all the webtoons that are out there, but you couldn't own the base layer But you could build on it Ownership is only possible for the applications and technology construction on top of it right ownership the base layer is Possible in the digital asset world. So again, the base layer will be Bitcoin or whatever layer one is zero that you got Then there's Bitcoin the actual network and you can be a part of that too You can be a miner. You can be note operator or you can build on top of that with something like lightning An investor can own part of the base layer of this new tech and be relatively agnostic about what apps are built on top This is why I like Ethereum too because whatever is built on Ethereum. That's a use case. There's utility there I know we just talked about it But I just want to bring that in so people don't think that you know This is the only thing I'm talking about as far as Bitcoin, but for this report makes sense It will be akin to being able to own the base layer of the internet and getting exposure to all the innovation built on Top of it Google and Amazon without having to try to pick specific ones Won't that be awesome if you get on TCP IP and then everything that's built on it You get some got a cutback. Ooh Good thing you were early, right? Bitcoin lightning is built using smart contract functionality allows off-chain transactions between persons with the ability to make a final Settlement settlement on the base layer. All it is is this me and you want to open up a channel We trade back and forth. Okay, Pete. You owe me a dollar. Okay. Here's two bucks. Here's $3 Here's $1.75 and we go back and forth for like a month. Then finally we settle off on the base layer, which we Bitcoin That's lightning in a nutshell. Hopefully it works out but It comes out of this Where people should Expand their portfolio so they make a base case for everything and this makes sense digital assets placed in the full portfolio Investment in the space are likely to benefit from segmenting Bitcoin and all the digital asset instruments as separate decisions allows for two simultaneous yet separate decisions made by allocators the importance of holding exposure the scarcest monetary assets or Other types outside of Bitcoin and then they talk about the risks Many of the risks and criticisms that could have been used to create a case for this demise of Bitcoin are gone or diminishing And each day the network grows stronger with more users miners and infrastructure is being built Which is what they laid the groundwork in the very beginning of this report There's also a problem with protocol bugs and I didn't know this Did you know there's a $1 trillion bounty for anyone capable of exploiting Bitcoin and no one's collected yet? I didn't know that so there's a protocol bug and it says the Bitcoin's case It is arguably the arguably the least likely protocol to encounter a major bug at this stage Have you heard of any double spend? Have you heard of blocks not being produced? Have you heard of any kind of hack in Bitcoin? I haven't In its life because it has existed longer than any other project and it holds an Intentionally simplistic code and again a trillion dollar bounty I didn't know that was even existed and it talks about nation-state attacks and in 2017 I kind of saw this would work But I mean now it's just I don't think it can happen potential for large countries to oppose the growth of digital assets Now actually that can happen because America is not too keen on Bitcoin and crypto Good old Joe Biden and good old Gary Gensler kind of despise it In other words, it's not that we think an allocation of Bitcoin does not come without risks But we think some investors are overestimating the downside of Bitcoin when compared to the digital assets And it talks about the growth of digital asset economy and everything's gonna happen Not Bitcoin risks and return drivers and it takes a look at Between what I looked at 2017-2023 Actually, if you go back all the way Bitcoin's always number one and it takes a look at and just reminds people that yeah In 2017 these were the top 10 steam Number nine was mates. I don't know what made save coin is And I was around 2017 auger a counter member dash. Yeah, he's classic. Yeah, I'm an arrow. Yeah Like coin XRP Ethereum Bitcoin 2023 Bitcoin Ethereum XRP BNB doge Which has been the top 33 since its inception in 2014. I might remind everybody Cardano, Solana and Tron so Jazz it kind of just points out and then they talk about the conclusion. They said look As a monetary good Bitcoin is unique therefore not only do we believe that investors should consider Bitcoin But that Bitcoin should be considered first and separate from all the digital assets that have followed it And that is it a nutshell. I know that was a little bit long That was a great report again. I linked this report in the in the Section underneath so you can find it very easy The description That's right today comments, but that is what we have for today and then lastly as a quick reminder I'm giving away sweat coin and that's gonna be in three days amazing how things Sneak up on us So we're gonna have the giveaway on October 13th or she was a cut-off is October 13th I guess isn't well going today October 14th. We'll give you the giveaway I'm giving away a hundred thousand total sweat coins. That's five thousand to 20 lucky people Also, we're giving away ten of their NFTs and then as a little snippet of Interesting pieces because I'm biased and I own a bunch of sweat coin You know sweat coin was ranked 548 or 534 depending if you're looking at coin get her a comarcap in June and now it broke into the top 300 So just saying on top of that. We take a look at DAF radar. It's number four In all the wallets and all the apps being used and the only one that's beating them is Pancake swap and a couple of games Stargate and Galaxy. I don't know which they are but looks interesting So that's all we have and that's what we have for today. So I know it was a bit long, but I do like that That document so look like today's video give it a thumbs up consider subscribing I'm gonna talk about this very time sensitive. Thank you so much for stopping by I do really appreciate


Well, it's over, it's all over. And I come to you today now as a broken man, an empty vessel of a hust out individual who at once had things going for him. And those things were episodes of succession. Four brilliant seasons, now wrapped up. I'm gonna be talking about it today. There's gonna be spoilers, so if you haven't seen it, just go ahead and subscribe to the channel.  All right, let's talk about succession. The easiest way I can summarize this show for people that aren't familiar is to say, it is the business equivalent, the white collar worker equivalent of Game of Thrones.  These are broken, miserable people, scratching and clawing their way for power. They will throw their friends to the wolves if that means getting ahead. They will toss each other under the bus if that means getting a promotion. There is nothing they won't do. A couple things that will turn people off as succession. One, there's no heroes here. There's no good people to root for.  There's different layers, there's different levels of it for sure, but not a single one of these people sets out on a path to do good. It's all about their internal struggles, often about the presentation and the window dressing and how best to step on people to get ahead and advance their own careers.  And that's exactly what Roman Roy says in the final episode.  We're all nothing. None of this matters at the end of the day. He actually knew this since the first episode, but it takes four solid seasons for him to get back to the place where he knew he belonged all along, which was a drift. Outside of the family, hanging out at bars, just live in life as a playboy philanthropist. Brian Cox brilliantly plays Logan Roy. He's basically Robert Murdock. The Murdock's own Fox News and a bunch of different corporations under that umbrella. The Roy family owns Waystar, that's the name of their company. Under that umbrella, you have the news channels, the networks, you have a cruise line. There's lots of different cogs and lots of different key players involved in each one of those. Much like Game of Thrones, or I guess more appropriately, House of Dragon, this show follows several characters, but they're all under one house crest and that's the Roy crest. We're gonna be following his three kids. There are four, but Connor just kind of comes and goes. He's not as intricate to the plot. He's more of a comic relief type character. And he's played by the always delightful Alan Ruck. The big focus is on Kendall, who's often considered the oldest brother because he's playing the game with the others. Then there's Roman and Shiv. Kieran gets to flex a lot of acting muscle with this character because there is a lot of depth to him.  Then there's Sarah Snook as Shiv, also a powerhouse actress here. This woman so desperately wants her father's approval and she is the most like him. She's ruthless, she's cunning, but she doesn't know how to play the game like the boys because she's not a man. And that's really always what it comes down to at the end of the day. Let's circle back to Kendall. He's played by Jeremy Strong. I love this guy.  It's hard to watch him. He really does become a lame duck. But season one and season four, he is fantastic. He's psyching himself up, listening to rap music, trying to act like the big dog, but he's not. None of these guys ever could be. And the big dog is of course Logan Roy. It all boils down to this. All of the kids of Logan Roy want what he has, power. Those around them worshiping at their feet because they already have billions of dollars. They can get any woman or man they want. They can buy all that. But you can't buy the type of power, influence and commanding presence that Logan Roy has. And unfortunately, Logan Roy is a douche and he raised his children with a false sense of worth. He wants them to compete for his love, for his affection, for power. It's all part of his game. It's all part of his plan. And he desperately wants a kid to step up and be him. But he knows deep down, none of these people are. They're all a disappointment in his eyes. Logan Roy's not doing well when we open up the first episode. He's got some definite issues going on health-wise. And this is going to lead the family to not only band together and be there for their dad, but also to step on each other and break each other's backs in a madcap dash to get the power, the CEO of the company. There's double crosses, triple crosses, constant backdoor deals going on. But ultimately it all leads to the final conclusion we all knew was gonna happen.  They're not worthy to take up the mantle that Logan Roy had planted. There are a couple of solid supporting characters. Greg Hirsch being one of them. He kind of reminds me of Jimmy from South Park.   He's definitely the kindest and the most well-intentioned out of all of them. But by the end of this, he's just as trash as the rest. When push comes to shove, he will absolutely do what's best for him. Bullying him through every season is Tom. Shib's husband. I do air quotes because they are married, but it's rocky, it's rocky at best. In fact, these two pretty much hate each other. And by the time the finale rolls around, it's just a loveless marriage that's completely for show. And I think it kind of always was. They might've had well-intentioned at one point. There might've been a small part of them that yearns for love and companionship, but it will always be steamrolled by their ambitions to climb, to reach higher up the corporate ladder. The big twist in season four is that Logan Roy is killed unceremoniously in the third or fourth episode. Out of 10 episodes, we have a lot of time where Brian Cox is no longer in the show. That hurt. That stung. It was incredibly out of nowhere, but it was real world. It wasn't some over-the-top extravagant death.  And we spent an entire episode of the kid's morning has lost. Going through every single step of the emotion, grief, loss, acceptance, anger, all that stuff. And this is really where these actors get to stretch their muscles. Sometimes maybe a bit too over the top. If I did have one criticism about the show, it's that sometimes it felt like the characters maybe weren't themselves anymore, but they were actually the actors putting themselves in those positions instead of playing the character. At times the tears go a little long. It feels like they're really looking for that Oscar. But small hang up beside, some of those episodes are really rich. You have the whole episode on the cruise ship where they're just reeling from everything that's going on. Their world is crumbling around them. And then we have a full funeral episode where we get to see Logan Roy his many different fiance's over the years, all of his trophy wives. And it's through these episodes that we see just how complicated their relationships are with each other and with their dad, whom they truly do love, but also despise at the same time. I think every kid deep down wants to love their parents and feel rewarded by them and feel noticed by them.  And Logan was so good at not giving them an inch.  It was usually for some bigger purpose. Whether it's covering up an accidental murder for his son Kendall, so that Kendall will basically be the reek of the show. Do whatever he says like a robot.  He doesn't go after his son really. Sure, he scolds him, calls him a weirdo. But at the end of the day, he's gonna protect his most important assets, which are his kids. And whether that's out of love or for the appearance purposes, it's hard to know what this guy. I do think when all is said and done, there was a compassionate side to the character. They do showcase this in the final episode when the kids all sit down and watch a home movie where he's singing a song around the dinner table, incredibly well done. Another one of the many amazing moments of the show where we see these kids react and get the softer side of their dad for once. In the final season, everything crashes together. We have Luke Mattson, played by Alexander Skarsgard, who's this tech genius billionaire. He's like an Elon Musk type.  He might have fake numbers, but it doesn't matter. He wants to acquire Waystar. And the kids are at a crossroads. Do they sell, cash out, make even more money? Or do they run the company the way that their dad would want them to? Shiv is on the fence.  They become co-CEOs, Jim Helpert style on the office. And she is left on the side of the road, left out of the big conversations. So what other choice does she have? Either become a lapdog for her brothers who she deems unworthy of the positions or she gets hers. Team up with the competition, take over the company and become a key figure. Signing a nice little sweetheart deal ahead of time for a cushy position. She will find out in the final episode, Mattson never intended on putting her as CEO or CFO or whatever the hell it is. I don't even remember the exact position. She's fucked. The Roy siblings are gonna take Mattson down. And to do so, they have to have enough people on the board that poo poo this whole offer and put them as the new kings. And when we finally get to that moment, it is as awkward, uncomfortable and embarrassing as one would expect from this family. As not Roman, but Chiv backs out in the final moment. It is a tie vote six to six. She can break it. They can get everything they want. She falters. She leaves the room. Kendall follows followed by Roman. This leads to a five minute sequence, a confrontation that is just so hard to watch. Because right in the other room, the board can see them all fighting with each other. At one point, Kendall puts Roman in a choke hold. It's just brutal.  He's abandoned his wife and his child. He has burned every bridge all for this power because his dad promised him when he was seven years old that he would one day have the company. Of course, Logan Roy promised each of the kids this at different points in life. And they will latch onto this because their daddy said so.  And it makes you feel kind of good that you're just a middle class dude that doesn't have to worry about all the politics and shenanigans up top. You're just more poor and dealing with more small scale things. These people though, as Roman says, are nothing at the end of the day.  Now I saw online some people arguing about Chiv's choice not to do this because she cared for her brother Kendall. She knew he wouldn't be a good CEO and that it would end up destroying him. That is not the takeaway I got. Not saying they're wrong, but they're wrong. Chiv doesn't think either of her brothers are capable or worthy. She thinks she's the one that should have had it. Her dad promised her only a year or so back. It was her turn to shine. It wasn't about whether Kendall would be okay in the role.  It's all about them at the end of the day. So she looked at the landscape. She knew that Tom was gonna be the new guy in charge if the deal went through. And she decided to be a trophy wife. She has the ear of Tom. She already knows she can bend this guy, break him because he does love her way more than she loves him. And that will be the way that she clings to power.  They're buffoons. They're broken. They will make mistakes. They will slip up. Tom is consistent. Tom is a yes man.  Kendall could fall back into alcohol. Roman could go off the deep end as well. They are wild card individuals. And Shiv is a practical, functioning, responsible adult with a kid on the way. She needs stability in her life so she does what's best for her. And this absolutely would kill Kendall way more not getting it than it would getting it. So we leave this show in an almost handmade tale scenario where she's just sitting there broken but she has what she needs to thrive and to grow with Tom by her side. Roman is back where he started. He's reverted. He's back at the bar drinking a martini.  Now it's maybe more clear sailing for him. Out of anyone, he's probably the most well-adjusted going forward. Kendall, however, this will always haunt him forever. This will be the one thing that slipped away. He might start another business. He might, it doesn't really matter what he does. He will be haunted for as long as he lives. This will kill him. This will eat at his soul that he did not achieve what his father did. All the money in the world doesn't matter to these people. They've always had it. They've always had it. They can do whatever they want whenever they want. So what do people want that have everything? They want more. And for Kendall, there's no way to get it. And that kills more than actual death. If I didn't make it clear, I loved succession. I loved everything about the finale. I thought it was so well-executed. Not a fairy tale ending, but these people don't deserve one. I think it's kind of also like Veep. If you didn't watch Veep on HBO Max, which is now just stupidly called Max, definitely check that one out. That's, I mean, that's 100% comedy though. So freaking funny. But it's another show that follows a bunch of broken, awful people that just want power and it's hilarious. There are my glowing thoughts on succession. A brilliant show that you absolutely should watch if it's your style. It's not like action packed. There's no exciting, amazing moments. It's really just a bunch of people backstabbing each other and a lot of great little stuff that adds up to a very, very smart show. Let me know in the comments your thoughts. Like the video if you had a good time and please subscribe if you haven't. I post tons of movie and TV show content each and every week. I'd love to have more people stick around. Take care.


So we learned that if you have a solution A, the concentration does not change if you have one liter of that solution or two liters of that solution. But what happens if you add more solvent? Remember solute is the thing that gets dissolved by the solvent and solvent is the majority of the solution. So the relationship between the volume and the concentration is on indirectly proportional relationship. That means if you increase the volume without adjusting the amount of solute, accordingly the concentration will decrease. So say you have a cup of salt water. If you add more water into the cup without adding more salt, you will say that the salt water is now diluted. And that means the concentration of the salt in the salt water solution has been reduced. So the relationship is initial volume times initial concentration equal final volume times final concentration. So let's do a question so we can have a better understanding of what that means. So you have 200 ml of a 3.0 molar sodium chloride solution. If you diluted to one liter, what would be the new concentration of the sodium chloride solution? So let's summarize the question. Vi the initial volume is equal to 200 ml, equal to 0.2 liters. So let's convert to liters so you can see that we are dealing with liters everywhere in the question. You have 3 molar means 3 mol per liter and you have 1 liter over here in the question as well. Ci equal to 3 molar. Okay next if you diluted to one liter so that means Vf the final volume is equal to one liter. What will be the new concentration? So our challenge is to find the final concentration Cf. Let's apply their relationship approach. One simple way to think about this is whatever you want to find let it be Cf or Vi. Keep it there in this side of the equation and move the term next to the other side and flip it. So what do you mean by that? So you have Vi Ci equal Vf Cf. So if you want to find Cf then the term next to Cf is Vf. What you need to do is move that Vf onto the other side and flip it so you divide. What if you want to find Vi for example while already knowing Ci, Cf and Vf? Well you simply just keep Vi there and bring Ci to the other side and divide that term by Ci. Okay let's get back to the question. The final concentration of the Sodium chloride solution is therefore Cf equal to Vi Ci divided by Vf and that will be equal to 0.60 moles per liter. So after adding more solvent to the solution the concentration is diluted down to 0.6 moles per liter instead of 3 moles per liter. Now if you take 200 millilitres out of this 1 liter of diluted solution put in a new beaker then make it up to 1 liter again will be the new concentration. So I would like you to calculate this but the answer is that the final concentration will be 0.12 moles per liter. Now notice the volume ratio so you take 200 mil of a solution and diluted to 1 liter. Now the dilution factor of that dilution is 0.2 to 1 or 1 to 5. It means that every time you take out 200 millilitres and diluted to 1 liter we are decreasing the concentration by 5 times.


In the previous lecture we introduced the fundamental principles of 4D war algorithm which is also called the first order joint method using a linear deterministic dynamical system as a strong constraint. We solved the constraint minimization problem using the Lagrangian multiplier technique. The whole aim of the exercise is to be able to compute the gradient of the cost functional in the context of the linear equality constraint and once we computed the gradient numerically we then have to use the gradient in an optimization minimization algorithm such as gradient method or a conjugate gradient method. So since we have seen conjugate gradient method as well as gradient method how they work we did not elaborate on that part of the problem that is the one half the bottom half of the problem the top half of the problem relates to computing the gradient itself. So 4D war adjoin method are essentially methods for computing the gradient of the cost functional with model as a strong constraint that is the deal. Now I am going to provide an extension in the previous case we considered linear perfect model deterministic we considered noisy observation observations where linear functions of the state we remember we considered 4 cases model can be linear non-linear observation can be linear non-linear both being linear is the easy case both being linear is the more complex case now I am going to go over to the non-linear case when I say non-linear everything is non-linear model is non-linear observations are non-linear functions of time observations are noisy observation so using non-linear noisy observations I have to determine the initial condition based on a given set a finite number of indirect information about the states. So given that I have the non-linear model deterministic initial condition is x naught m is a model map m of x is m1 of x m2 of x mn of x so m is a function from Rn to Rn is the vector valued function of a vector observations are non-linear functions h is the forward operator again h is a map from Rn to Rm so h of x is also is equal to h1 of x h2 of x and hm of x transpose Rk is the observation noise we are assuming white what do you mean by white vk so if I consider 2 instances in time k1 and k2 I have vk1 I have vk2 I have vk2 vk1 vk2 are uncorrelated that is what white means white means the temporarily uncorrelated but at a given instant the covariance the matrix covariance matrix for the noise is given by Rk so vk is normally distributed with mean 0 and Rk as the covariance what do you mean by mean 0 mean 0 means the instruments that measure the states do not have any bias that means if there is a bias in the instrument I have already calibrated the instrument against known standards I have I have I have subtracted the bias therefore observations are bias free observation noise are mean 0 the observational covariance Rk Rk is at a given time and observations at different times are temporarily uncorrelated these are the standard assumptions I want to make a comment if the observations are temporarily correlated the analysis becomes much more complex therefore in trying to solve the problem we would like to be able to make assumptions that are necessary to make the problem non-trivial if you keep adding various levels of assumption the model the problem statement becomes so difficult we may not be able to mathematically solve it in a meaningful way so what is the trick in modeling you make all the necessary assumption to make the problem interesting but at the same time not too complex so if you stand if you analyze the standard versions of the problem you get a feel for the solution based on which we can then tag on other assumptions other conditions to further explore the impact of assumptions like if what if the observation noise is actually correlated and so on so the cost function is again j of x not it is given by z minus h of xk transpose Rk inverse z of zk minus h of xk so this is the forecast z of xk is the forecast error so this is a sum of weighted sum of squared errors the problem is to be able to minimize j of x not where x not is related to x a xk is related to x not through the model dynamics again it is an implicit minimization problem in the linear case we could replace xk implicit explicitly by xk is equal to m to the power of k x not in the non-linear case it is much more difficult so we need to be able to handle this case with little delicacy which with little bit delicately not delicacy with little bit delicately I am sorry delicately so while we could use the Lagrangian multiplier method we illustrate an alternate strategy called the adjoin method I would like to distinguish between adjoin equation and adjoin method the adjoin method is a class of algebraic methods by which I can compute the gradient rather explicitly in a beautiful way so first perturbation analysis of the model is key to the adjoin method that we are dealing with so let x bar not be a base state a base initial state from that I can generate a trajectory which is called the base trajectory if you give me the base trajectory I can compute h of xk bar as the model predicted observation the actual observations are zk if zk is very close to h of xk then xk bar arising from x not is pretty good and x not bar could be a decent initial condition to start the forecast from but in general but in general sk not x z of xk may not be equal to h of xk z of xk may be large zk minus h of xk is equal to ek and ek will be far from being small if ek is far from being small that means I have a large forecast error our aim is to be able to annul the forecast error or reduce the forecast error the forecast is xk bar the forecast was generated from x not bar so how do I and h is known fixed zk is known fixed so how do I reduce the forecast error the only way to reduce the forecast error is to xk bar but how do I change xk bar xk bar is the state of the model at time k but xk bar depends on even the model equation is fixed so I would like to remind you xk bar is equal to m of xk minus 1 so that is the model equation so starting from x not bar I calculated xk bar so look at this now my aim is to minimize or reduce the forecast error ek the only way to reduce forecast error is to change xk the only way to change xk is to change x not so x not is called the control element it is called control because by changing the initial condition x not bar I can change xk if I change xk I can hope to change the forecast error so with this in mind I am now going to change the initial condition by adding a correction delta x not x to x x bar not so this is the old initial condition this is the correction or the perturbation term this is x not is the new initial condition so delta x not is called the initial perturbation so I am changing the initial condition from x bar not to x not now if I run the model forward in time from x not I will get x1 from x2 xk so what is the hope zk minus h of xk must be smaller than ek I have already computed if this can be made smaller by moving the initial condition then I am going the right direction to be able to reduce the forecast error so here is the idea of basic perturbation analysis so let me summarize the only way to reduce the forecast error is to be able to change the model solution the only way to change the model solution for a given model is to change the initial condition I am assuming everything else in the model are fixed so by changing the initial condition means I am going to add a perturbation to the initial condition so this is the base trajectory this is the base trajectory this is the perturbed trajectory I would like to be able to find an optimal perturbation at an optimal increment in the initial stage such that zk minus h of xk is small small in what sense in the sense of least squares so I would like to be able to minimize the norm the weighted norm of zk minus h of xk where the weighted norm is rk inverse the square of the norm so what is this this is the sum this is the weighted sum of squared errors at a given time and by if I sum it up over k is 1 to n I get the total errors coming forecast errors coming from all the observations so I would like to be able to decide how I should perturb the initial condition to be able to to be able to annihilate the forecast errors at specified insertion time so that is how we can look at the 40 bar problem I hope I hope the statement and the view of the problem is clear right now so I am now going to be talking about first order perturbation theory this is this is all this is also called variational analysis that is why the notion of 40 bar variational method came into being so first order perturbation analysis how does it go let x not be the initial let x not be the initial x not bar be the initial condition this is the base state given by 20 the base trajectory I am going to perturb the initial condition I am going to get the new initial condition by adding a perturbation to the this is to x not bar I am sorry this is x not bar so I can now compute the perturbed trajectory the perturbed trajectory is given by the equation 21 so the base trajectory is given by 20 the perturbed trajectory is given by 21 now what is the whole idea let me go back to the picture now if x not is the perturbation at time 0 let x 1 be the perturbation at time 1 delta x k be the perturbation at time k delta x not is the first perturbation I am giving up at the initial condition that induces a perturbation at time 1 that induces a perturbation at time k so what is our first goal our first goal is to find out how delta x k transforms to delta x 1 how delta x 1 transforms to delta x k in other words I am interested in understanding the dynamics of propagation of the initial perturbation through the model so that is the first task. So in trying to write the dynamics of perturbation let us consider how delta x 1 is a relative to delta x not please understand delta x 1 is the induced perturbation at time 1 induced by the initial perturbation delta x not at time 0 to this to compute delta x 1 from delta x not we are going to invoke to the first order Taylor series we have already talked about first order Taylor series for maps in one of the previous modules. So delta x 1 by definition is equal to the perturbed state at time 1 with the unperturbed state at the base state at time 1 x 1 is m of x not x 1 bar is m of x bar x not bar but x not we already know x not is equal to we already know x not is equal to we already know x not is equal to x not bar plus delta x not. So that is what delta x not is all about I am now going to apply the first order Taylor series expansion for the first term when I apply the first order Taylor series expansion I get m of x not bar plus the Jacobian of m at x not times delta x not minus m of x not that first and the third term cancels I get delta x 1 is equal to the Jacobian of m at x not times delta x not please recall the Jacobian is a n by n matrix Jacobian of m is n by n matrix it is a partial derivative of the ith component with respect to this I must say the following this is x I am sorry this is not m this is x x of j not so x not of j is the jth component of the initial condition m i is the ith component of m so i varies from 1 to n j varies from 1 to n so that is the Jacobian of m at the initial base state. So if you know m I can compute the Jacobian I can evaluate the Jacobian therefore you can readily see equation 22 that relates the perturbation at time 1 to the perturbation at time 0 is a linear relation. So even though the model is non-linear the perturbation dynamics is linear that comes out very easily from equation 22. In general let delta x k be delta x k plus 1 be the perturbation at time k plus 1 at time k plus 1 this is equal to x k plus 1 minus x bar k plus 1 this is m of x k m of x k plus x bar k now please remember x k to a first order approximation is equal to x bar k plus delta x k so that is essentially this then you have the m of x bar k by applying the first order Taylor series you get this. So now you can see this is the perturbation dynamics this dynamics in mathematics is called variational equation this is also called perturbation equation but in meteorological circle they have a very different name called tangent linear system they call it TLS. So TLS is a linear system it is a non-homogeneous system because the Jacobian matrix varies along the base state so even though this is the matrix the matrix changes in time therefore you can try to relate delta x as this is equal to a k times delta x k where a k is the Jacobian at x k of yeah so a varies with time therefore this is a non-homogeneous system is a linear system it is a non-homogeneous linear dynamics that gives you the evolution of the perturbation this is the first order perturbation equation. By iterating 23 so by iterating this equation you can really see delta x k is equal to the product of Jacobians along the trajectory the product of Jacobian along the trajectory times the initial perturbation I am now going to concoct a new solution a new notation d subscript k minus 1 colon 0 to m essentially represents in this product this is the product of k matrices going from time 0 to time k minus 1 so with this notation you can readily see delta x k the perturbation at time k is related to the perturbation at time 0 through the product of Jacobians the product taken along the trajectory starting from x 0 to x k minus 1 this matrix is the product of Jacobians along the base trajectory starting from x 0 bar to x k minus 1 bar notice the order of multiplication please remember matrix multiplication is not commutative therefore you have to take great care in trying to when you want to involve matrix matrix multiplication you have to worry about the order and be sensitive to the order now come back to so what is that we have done so let me quickly summarize we stated the problem we saw the problem of forecast correction is equal to changing the initial condition change the initial condition is equal to adding perturbation to the initial condition so we were interested in trying to quantify how an initial perturbation propagated through the model in time so we have simply the original model equation we also have the forward dynamics which is the tangent linear system that describes the evolution of the perturbation forward in time that is what we have accomplished so far sorry I am going back instead of going now I would like to come back to my J of x 0 the thing to be minimized please recall J of x 0 is given by this summation this is given in equation 20 so equation 20 when you multiply that all the things now becomes equation 25 25 is simply a re-return version of 20 now I would like to change the notation to make the application of multivariate calculus lot easier so let me call the linear term let me call the linear term like this let me call so A is RK inverse ZK so from module 4 I do not think it is module 4 the number is slightly different I will compute the number later recall from one of the modules in multivariate calculus which is to point something I am now concerned with what is called the first variation you remember the notion of first variation the first variation is simply the inner product of the gradient and the variation XK so the first variation of A transpose H of XK is the gradient of A transpose H of XK times delta XK the A transpose XK is given so its gradient is given by this equation A by substituting this is given by this equation therefore the first variation of the linear term is given by 27 so what does first variation means I would like to be able to talk about that for a moment before we go further I have A transpose H of XK so if I change XK to XK plus delta XK and if I compute the difference between this and that term and that is what is called the difference between A transpose H of XK plus delta XK minus A transpose H of XK that is called the first variation actual difference this difference is equal to the gradient of A transpose H of XK times delta XK that comes from the basic definition of the notion of first variation. So how is the induced variation affects the linear term and that is going to be affected by this where DH is here DH is the Jacobian of the forward operator H I hope this idea first variation is very clear why am I talking about the first variation look at this now delta XK depends on delta X naught I have already related delta XK to delta X naught through the tangential linear system. So if I can relate the first variations of each of these terms with respect to delta X naught of delta XK sorry I have already related delta XK to delta X naught so I can relate the variation of delta X naught to the initial variations so that is the basic principle that is at work here. If I consider the second term if I consider the second term the second term is a quadratic in H from the module on optimization from the module on multivariate calculus we already know the first variation of this quantity with respect to XK is given by the right hand side of 28. The first variation of ZK transpose RK inverse ZK is 0 because it does not depend on XK so substituting the whole thing we can readily see substituting 25 through 29 in 25 the first variation in the cost function induced by the first variation in the cost function induced by delta X naught is given by this expression in equation 30. Now, how do the right hand side depends only on delta XK but the left hand side I am talking about variation induced by delta X naught through the tangential linear system I already know delta XK is related to delta X naught so combining tangential linear system and 30 I now know how to relate the first variation in J to delta X naught so that is the line of arguments again I am going to define to simplify notations F of K is equal to the forecast error this is the forecast error this is the normalized forecast error this is the forecast normalized forecast error viewed from the model space the same F of K as we have used in the previous case. So, I can rewrite the equation this equation 30 succinctly as the variation in the variation sorry the variation in delta J induced by delta X naught to the sum of the variations induced along the path all with respect to delta XK K running from 1 to recognizing the fact delta XK and delta X naught are related through the tangential linear system and that is 32. So, this is the first and the most fundamental relation in a joint approach to 30 y. So, let me go back to the picture to illustrate it little bit further I think it is very useful so I have when I change from X bar naught to X naught my J function changes. So, originally I had sorry I originally I had J of X naught bar now I have J of X naught the difference between the two the difference between the two is delta J this delta J is induced by delta X naught therefore I would like to be able to talk about the induced change in J at a given time through the initial condition and that is what we have a complete so far through this variational analysis through the tangential linear system if I wish. So, that is what we are now I would like to remind you that delta XK is given by the tangential linear system in 24. So, let me go back to 24 remind you what is the so 24 essentially relates delta XK to delta X naught through the product of the Jacobians. So, 24 so using 24 I am changing dependence from delta XK to delta X naught let me come back here. So, I am going to substitute for delta X naught here if I did that this is the expression I get that is the expression I get now you can really see delta J induced by a change in the initial condition is related directly to the change initial condition itself everything becomes explicit. Now, we are going to go back to matrix algebra to define the notion of an adjoint operator adjoint. So, if A is a matrix the inner product of AX comma Y the inner product of AX comma Y by definition is AX transpose Y which is equal to X transpose A transpose Y which can be written as X comma A transpose Y. So, that is what this relation is therefore, AX the inner product AX with Y is the same as the inner product of X with A transpose Y this is the so A transpose is called the adjoint of A the transpose of a matrix is called the adjoint of A. So, that is the definition of the adjoint of a operator or a matrix A. So, using this adjoint property I can now apply to 33 so you can think of 33 as F of K comma A of K delta X naught which by adjoint property. So, let A of K be equal to this matrix let that be equal to A of K therefore, by applying the adjoint property in the reverse way I can essentially say this is A K transpose F of K delta X naught this is delta X naught. So, A K transpose is D of K minus 1 colon 0 transpose F of X K so by adjoint by applying the adjoint property 34 to 33 I get this relation this relation is one of the most fundamental relation the method is called variational methods because I am talking about variations induced by the initial variation I am also talking about this adjoint method because I am using the adjoint property of matrices. So, is adjoint and variational schemes all put together it uses many number of interesting properties of the adjoint from matrix theory recall some of the basic things from again linear algebra. If I have the inner product X 1 plus Y plus X 2 plus Y that is equal to X 1 plus X with Y if I have X is inner product X and Z is equal to inner product Y Z for all Z then that implies X must be equal to Y it comes very. So, first is a linearity property second is the property there essentially tells you if the inner product X with Z is equal to the inner product Y with Z for all Z X better be equal to Y. So, that is the basic property by applying the first property the sum of the inner product is equal into the inner product of the sum. So, the inner product of the sum with X naught so I have applied the first property the first property is sum of the inner product is inner product the sum that variables essentially. So, if I have a first variation is given to the inner product also from first principles from variational calculus we have seen in multivariate calculus delta j is equal to the gradient times delta x naught. So, I am now going to have two expressions two different expressions related to delta j and these two expressions are equal for all delta x naught delta x naught is an arbitrary therefore by applying the second property I can readily now conclude the negative of the gradient is given by the sum which is summation k is equal to 1 to n transpose of the product of matrices along the trajectory times f of k and f of k is the forecast error mu from the model space. That is the whole idea my idea is to be able to find an expression for the gradient and we have achieved it. So, instead of using Lagrangian multiplier and equating the gradient we have walked the path of being able to use the variational analysis the variational analysis is very intuitive in the sense that the only way to be able to correct the forecast error is to change the initial condition change the initial condition is equal to perturbing the initial condition if I perturb the initial condition the initial perturbation propagates through the model. So, if I can quantify to a first order accuracy the propagation of model errors or model perturbations along the trajectory I have handle on one of the issues to be tackled using tangential linear system. The other part of the story is to be able to compute the induced first variation in the cost function itself then we relate these two first variations in trying to relate this we use several properties one is the joint property another is the linearity property another is the property where the inner product of x and z and y and z are the same for all z x is equal to y all these three basic properties are intimately related and they are applied and that essentially gives you an expression for the gradient which is given in 39. Now look at that everything on the right hand side of 13 is computable f of k is computable the Jacobian of the model is computable but what is the only thing that we do not like it involves product of Jacobians Jacobians are matrices matrix matrix product is a no no so you never multiply matrices unless that is what you want you never invert a matrix unless that is what that is what you want these are some of the golden rules in numerical analysis in numerical in linear algebra because these are two expensive operations. So in theory you may involve matrix matrix multiplication but when you practice you should avoid as much as possible whenever wherever possible. So even though we have gotten x 39 for the gradient still we are in the same boat as we were in the linear analysis we still involves matrix matrix multiplication we want to avoid matrix matrix multiplication matrix vector multiplication is cheaper than matrix matrix multiplication let me talk about it for a moment now. If I have two matrices if I want to multiply c is equal to a b the cost is o of n cube if I have y is equal to a x when a is the matrix x is a vector this matrix vector computation is o of n square o of n square is much cheaper than o of n cube. So whenever there is a matrix matrix operation avoid it whenever you can get away with matrix vector multiplication instead of matrix matrix multiplication introduce them. So now we are going to rewrite the computation of 39 without doing any matrix matrix multiplication but involving only matrix vector multiplication very intelligently. So we are going to talk about in a very efficient way this way is essentially the joint equation we already saw so the rest of the problem rest in computing 39 efficiently essentially involving only matrix vector multiplication to bring this to bring the structure of the expression 39 let us assume n is 4 just to be able to look at how this one comes up this is in here we have involved a product of two Jacobians in here we are involved with product of three Jacobians in here we are involved with product of four Jacobians that is how the terms come in. So please understand these Jacobians these are all product of Jacobians from the computational point of view these Jacobians if you did it like this that is deadly. So 41 is simply an explanation but 41 while it is meaningful to interpret it is computationally disastrous but to understand the kind of challenge we have I have simply expressed 39 in a simple form of n is equal to 4 and expresses 40. So you can see how much of computation involved in computing the gradient. Now how do we avoid a matrix matrix multiplication and introduce matrix vector multiplication that is done very cleverly by what is called that joint equation. So let us look at 41 so in this case the gradient is given by the sum of these products sorry the sum of these products. Now look at the beauty of the structure of this now we are going to successively expand the matrix matrix multiplication involved in here recursively. So this is the structure I want to be able to compute efficiently in order to compute this efficiently again I am going to give an example let lambda 3 so I am going to introduce some new variables these variables lambda are related or somewhat related to the Lagrangian multiplier that we have seen earlier. So let me set lambda 4 is equal to f of 4 lambda 4 is equal to f of 4 let us say lambda then I will compute lambda 3 to be equal to d3 transpose lambda 4 plus f3 so that gives raise to this formula lambda 2 is equal to d2 transpose lambda 3 plus f2 that give us to this expression lambda 1 is equal to d1 transpose lambda 2 that gives raise to this expression you can see that is delta action. Therefore when I have only 4 observations I can compute the gradient simply by involving matrix vector multiplication what is the matrix multiplication look at this now lambda 4 is f4 there is no multiplication to compute lambda 3 this is d3 transpose m is a matrix lambda is a vector. So that is matrix vector multiplication addition of a vector 1 matrix vector multiplication addition of a vector 1 matrix vector multiplication addition of a vector. Now if I did this like this involving only matrix vector operation you can see by iterating backward in time I have gotten the explicit expression for the gradient. So what does this suggest this suggests that we can avoid matrix multiplication by introducing a backward recurrence relation much like that joint equation that we had earlier and that is the essence of the story. Therefore generalizing so I have given you a specific example to be able to get a handle on the problem with n is equal to 4 for a general n I am going to define lambda n is equal to f of n I am going to define lambda k using dk transpose m lambda k plus 1 plus f of k. So compute from lambda n to lambda 1 if you compute lambda 1 then you can come you can verify that delta the gradient of j x0 with respect to x0 is given by minus d0 transpose m delta of lambda 1 if mfx is equal to mfx that means if the model is linear you can see this equation reduces to the one that we did in the Lagrangian multiplier technique. Therefore this relation is a generalization of the backward adjoined dynamics that we considered for the Lagrangian multiplier technique that is why this is called adjoined again adjoined dynamics. This whole idea of using first the propagation of the perturbation adjoined principles from matrix theory and combination of adjoined dynamics within the context of nonlinear system provides a very simple and an elegant means of computing the gradient of the cost function with respect to the initial condition once the gradient is available we can again use it in a general gradient or conjugate gradient method. So here is the summary the 40 watt algorithm for the nonlinear case start with x0 compute the nonlinear trajectory only for the sake of illustration we use the base state perturbation state and other things now that we have understood everything I am now going to encapsulate all the analysis into a form of a algorithm this is called 40 watt algorithm for the nonlinear case start with the initial condition start with the initial condition x0 compute the nonlinear trajectory from the model then compute the Jacobian and evaluate the Jacobian along the model please understand computationally is it could be it is expensive why is that each Jacobian is a n by n matrix there are n square elements. So I have to evaluate the n square elements of the matrix at each of the n instances in time so that is going to be a pretty demanding computationally so the question comes in do you compute these matrices and store them that is a no no why storing these matrices which requires n square space when n is of the order of million there is no space in the world in computers to be able to store all these matrices for all time so what is that you do you have a general expression for the matrix someplace you evaluate that matrix on demand whenever you need the value at a given state. So there is a notion of a space time trade off involved in implementing these and one has to be very clever in not to burn the space requirement by storing too many things but I also want to recognize if you can store few things you can speed up the computation but the demands of the space becomes too large it makes no sense because it will eat up all the memory and then some and you may not have much space left for doing anything else. So great caution must be exercised in trying to be able to evaluate you have to evaluate the Jacobian the question is should I store them or not you probably cannot afford to store them you simply compute them on the fly and use them whenever you want wherever you want that is the basic idea. So once the Jacobians are computed I can compute f of k f of k are vectors say f of k can be stored matrices expensive f of k is it could be a million million million by vector million by a million vector is easier to store than million by million matrix. So that is a trade off between trade off between storage and time and now what that I need to do I need to be able to start the backward dynamics starting from f n is called lambda n and lambda k is equal to transpose of the Jacobian at time k times lambda k plus 1 plus f of k. So once I have lambda 1 I can compute the gradient by this simple formula in step 5 once I have the gradient I can compute the optimal x naught by simply repeating this until convergence using a minimization algorithm the gradient algorithm or the conjugate gradient algorithm. But one thing I want to remind you the j function that is being minimized is not a quadratic function I would like to be able to bring that part of the argument very carefully I want you to appreciate that the j of x naught let us go back yeah j of x naught is given in 20 h of x is a non-linear function so therefore if you multiply both sides it is not quadratic it is much more non-linear than quadratic. So if the function j of x is not quadratic but much more non-linear than quadratic what does it mean the performance of the gradient algorithm and conjugate gradient algorithm are guaranteed only on quadratic functions the function that is of interest here is not yeah is not a quadratic function therefore the performance of gradient algorithm or the conjugate gradient algorithm for the non-linear case model non-linear and the observation non-linear could take longer to minimize because there is no there are no general results guaranteeing convergence. So when to stop how far to go all these things are questions whether one has to content with in trying to decide once the in trying to decide what kind of stopping criterion one could use to stop the minimization process that is a problem quite apart from the theory that we have developed but I want you to understand that is an integral part of the overall development of the package if you are interested in trying to program this. So with this we have come to the end of the introduction to 4D var so let me quickly summarize of 4D var or adjoin method is essentially a solution of the inverse problem within the dynamic context given a bunch of n observations noisy observations that contain information about the state I would like to be able to determine the optimal initial state we pose this as a minimization problem is a constraint minimization problem this can be solved in one of two ways either as a strong constraint Lagrangian multiplier problem or by using variational methods and trying to understand and quantify propagation of variation through the model and the joint properties of a joint operators. So I have illustrated these two complementary methods of analysis by one using linear model linear observation another using nonlinear model nonlinear observation this covers pretty large area of techniques that is known for solving deterministic dynamic inverse problem where the model is deterministic and assumed to be perfect but the observations are noisy. We would like to we would like to encourage you to perform several computational related experiments I am going to go over this in some detail let us spend couple of minutes on this consider a very simple scalar model xk plus 1 is equal to a times xk consider an observation zk is equal to vk please remember the model is linear the observation is linear there is no h h is identity is the simplest of the possible model the model m is the matrix is simply a scalar a vk is the observation covariance which is sigma square I am going to ask you to make take it as 0.5. So my suggestion to you is to pick a is equal to 1 pick x0 is equal to 1 generate a sequence of state with n is equal to 50 generate observations from 1 to 50 by adding noise to that store this sequence of observations once you have chosen a set of sequence of observations now I am going to consider different observation sets 1 o1 I am going to consider assimilating all the observations another one I am going to consider assimilating only a subset of observations spaced 4 this 4 units apart and then I am going to ask you to assimilate even a further subset 1, 10, 20, 30, 40 and 50 so what is that we are trying to do we are trying to assimilate different subsets of observation smaller larger and the largest possible observation what is the idea I would like you to be able to perform the data simulation experiment with different observation sets and I would like you to be able to compare the quality of the recovered x0 initial condition. So in order to do that once you have developed the observation now I would like to be able to start the forecast mode to start the forecast mode I do not know what is let us forget about the states that are used for observation so I am going to assume I am going to start the forecast model with 0.5 I am still going to use a is equal to 1 I want to use each set of observations and estimate the optimal x0 using the procedure we talked about I would like you to in particular use the gradient method being the linear case the j function is quadratic if the j function is quadratic gradient method should work reasonably well so I would like you to discuss the impact of the num varying the number of observation and the quality of estimate this I would like you to do with one variance then you could once you program this you can then change sigma square we can make sigma square less sigma square more so you can discuss a variety of cases the impact of the estimate on the observation noise you can also discuss the impact of estimate on the number of observations so one can create quite a variety of computer related projects so this is a very good example that can be used to test your understanding of the basic mechanics of the 4d war this problem can be solved using Lagrangian multiplier technique so I would like to encourage you to be able to apply the grand general player technique to solve this linear problem I believe it will be a very educative exercise to do this pencil paper and program and plot and and and and discuss the results then I am going to give you a nonlinear dynamics which is which is which is again a very interesting dynamics this is called the logistic equation when the parameter is for this logistic equations is supposed to exhibit extreme sensitivity to initial condition the model actually exhibits chaotic behavior for any initial condition in this range so the previous problem is an easy problem this is simple this is a slightly more difficult problem but still I would like you to make your hands dirty by doing this start with x0 is equal to 0.5 generate a set of observations again I have given you observational covariance u sigma square is equal to 0.5 generate 20 observations then start the model from a wrong initial condition then assimilate all the 20 observations into the estimate and find the optimal estimate now look at that the observations were generated using 0.5 the forecast is used started from 0.8 so forecast will have the error we are going to use the 4d war method to be able to correct the forecast error in the nonlinear model so I would like you to utilize the joint method that you have described in solving this problem I hope you will spend enough time to be able to solve these two problems if you solve these two problem by applying this method first pencil paper and then program it you can say you understand 40 war methods with that we conclude our coverage of an introduction to solving inverse problems within the context of deterministic dynamic models with noisy observations thank you


My name is Salatah I'm good I'm from Egypt and I'm an English instructor at El Hat international courses in Abassaeber I completed and finished my Tifle Tested International course at Tifle International Egypt 6 months ago Also yesterday I completed and completed my teaching business online course Really, both of them were really beneficial and fruitful I learned new things I learned for example EFAA methodology I really appreciate your courses, your materials, your books that you provided us Thank you. Thank you.


Americans and Australians blasting the Japs in the campaign to take Boona from the turret of an American tank. Our cameraman brings a dramatic record of war as it is fought in this wild jungle country. Cautiously troops advance against an unseen foe. For a month, they pushed forward across the Owen Stanley Mountains, mounting the Japs from foxholes and pillboxes concealed in the jungle, firing blasting at every moving leaf. Boona mission is won. Southeastern New Guinea was an important Japs stronghold in the South Pacific. From here, they planned the invasion of Australia. Now, their equipment, their bases are in allied hands. For General Douglas MacArthur, it is a victory of major importance. Taking terrific toll of the enemy, Australians and Americans met the Japs on even terms and hurled the enemy back into the sea. Streets of the capital are throng as Santiago hears the news that Chile has severed relations with the Axis. The United Nations have reassured this important South American Republic that they can and will help her protect her 3,000 miles of coastline. Flags of all the allies are in evidence as Santiago reflects the sentiments of Chile's 5 million people. President Rios looks upon a cheering populace, hailing Chile's defiance of the Axis. In this British Columbia, the fishing fleet makes the biggest haul in 16 years. Millions of herring, 500 tons in this one catch alone. Bob, formerly done by the Japanese, and they're bringing in enough fish in one day to fill 80 railway freight cars. Every pound will be packed and canned for United Nations soldiers overseas. A welcome wartime catch. Madison Square Garden as 16,000 enthusiasts turn out to see national collegiate champions set new records for speed. Here's Warmer Dam, world's champion pole valder. Tonight the Californian is aiming for better than 15 feet. A new mark for an indoor meet. Max of the evening is the mile race. Stars are entered from leading American universities. New York University's Frank Dixon is setting the pace. The national champion is now in front. Trailing up to this point, Earl Mitchell is overtaking the leaders. Sprinting to the front with a magnificent burst of power, Mitchell steps out to win by four yards. Time four minutes, eight and six tenth seconds. United States man of war makes a trial run before joining the fleet. 41,000 tons of fighting ship. She's the fastest, most powerful battleship afloat. And 2,000 trained men go to battle stations to test the big guns. Powerful 16 inch rifles swing towards the target. Observers hooded and dressed for below zero cold are at their posts. America's greatest, the mightiest dreadnought ever built is going into action. West of Darwin, Australia, the Pacific Island of Timor has been held by the Japanese for nearly a year. But behind enemy lines, deep in the interior, a force of Australians have held out against all efforts of the Japs to locate and dislodge them. For months, Jap planes soft their hideouts. And while Australia gave them up for lost, the men assembled a radio set from bits and pieces stolen in raids on the enemy. Finally, they hammered through their message to Darwin. SOS, Timor to Australia, Timor to Australia. And the message flashed across the Timor Sea is heard in Darwin. On the mainland, officers suspected Jap trick. No white men are supposed to be alive on Timor. Darwin radios the cautious question. What is the Christian name of Jack Sargent's wife? Answer immediately. And the men on Timor flash the answer, Joan. In this way, Australia was satisfied. Secretly, food, clothing and ammunition were rushed to the beleaguered Australians on their 7,000 square mile outpost. Letters from home for men long given up for lost. With fresh supplies and friendly native help, the Australians launch an attack on Japanese occupied territory. Moving up over mountains, through jungles, they take the enemy by complete surprise. Hardy rugged fighters, they've won every skirmish against the Japs. And they're staying right there to carry on the fight. No longer a lost battalion, the men of Timor are living symbols of the United Nations determination to smash the Japs.


Chinese legislation system legislation in legislation in the cyber domain for example protecting data protecting privacy and how to control the traffic of the data and they should controlling of data in in their country or they on the on on having countries who has own a view about the authoritarian mechanisms so that kind of issue is going to be making things difficult thank you very much and thank you all for for your questions and I'm sure we'll get to some of the technology and trade issues as well in the in the afternoon panel my my quick final prediction question will will I be able to gamble at a casino in Japan before the end of the year? No no how about certainly not with a cabinet member okay all right yeah so sorry we didn't get to casinos but we will we'll leave a few issues for for next year to discuss thank you panel terrific start please join me in thanking our panel thank you we are going to take a break for lunch we have sandwiches and salad and things we're going to start the keynote speech session at one o'clock so you have a half hour for lunch


So essentially we own a restaurant. We have to make hot dogs here. Take this It isn't cooked right for it. Are you kidding me Bonnie? Give me just give me a sausage here That was a great meal another sausage coming right up Okay The customer Okay Okay, we're going green here at the hell's hot dogs, so we're gonna go ahead and just use that plate It's fine. It's fine. They're friends The food is great when I play this dirty We're actually doing a really killer job right now I'm not throwing this is one of the easiest levels wait wait. Can we lose? Yes, oh my gosh here I think we're actually already losing. That's a great meal. Yeah, I'm glad you like it What do you do Oh There's a fire Bonnie I think there's too much collision that crashed the game The bonjour no The cheese a better get a two cheese better get a one hand better get We rats We already have rats already Already have rats. I'm putting them in the trash can. Oh my god It's on fire, Bonnie.  We're gonna make whatever we want. Okay. This is very simple Do you want to make a hamburger? You have to uh do it my way Bonnie's way is as you're about to see Oh fric oh fric beautiful over here Just like the steak. I did not the game's over the game is over already Yeah, you want to try for real this time? Uh, yeah, I was practicing. I was practicing hamburger I'm not that far behind Uh, is your picture on fire or is it don't worry about it. It's fine. Why is it three hot dogs again? Wait hamburger. No I thought it's an hot dog I literally won. No I think if we keep doing it give us up because look it says level one and i'm level two I don't play anymore. Let's go play the other version. Let's play pb I'm gonna make a beef taco two cut onions raw one cut ground beef cooked one taco shell cooked I don't I don't like uh Why you already set it on fire? It literally just started Where's uh, where's the uh, oh there it is cut ground beef Some more cut ground beef Yes, friend How your spot you put the groceries away. I'll do this Okay Okay Wow, look how pretty this is look Look this looks legit.  What you're sabotaging Okay, it went so fast That was so fast. Okay onions onions onions. Oh my You knocked my food off my plate gentleman gentleman, please The second I went out to put our first plate It's not our fault as fun. It's management. They're not tiring. I'll stop to go back. We need to go This game is actually so funny.  What do you what can we get you? Okay, we need one sausage one plain hot dog I'm the hell's hole open up Oh, I just threw that saw dude.


The Covid-19 pandemic has had a significant impact on the mental health of children and adolescents worldwide. In particular, those from vulnerable populations, such as those with disabilities, traumatic experiences, migrants and those living in poverty, are at greater risk of developing mental health issues due to the pandemic. Additionally, the economic downturn caused by the pandemic has led to increased levels of anxiety, depression and other mental health issues among children and adolescents. To mitigate these risks, child and adolescent psychiatrists should work together with other professionals to provide access to mental health services, both in person and through telepsychiatry, to ensure that children and adolescents receive the support they need. This article was authored by George M. Fiegert, Benedetto Vitello, Paul L. Plena and others.