Hey guys just Nate aka the foot account and welcome back to the channel happy Monday start of a brand new week and Start of probably something pretty interesting on FIFA because it is upgrade pack Monday And I think there's a little bit of a chance that we can have the first player picks of FIFA 23 today because as we're gonna take a look last year during the road to the knockouts promo We had 75 plus player picks those don't have to be added to the code There's no knowing if they're gonna be dropped maybe a leak very shortly ahead of time But those would be massive and that would be a huge huge piece of content that so many people would be interested and last year They were cracked so we're gonna take a look at that today the potential of just an upgrade SBC whether it's the 75 plus player pick or you know like we had last week during ones to watch a 78 plus upgrade some sort of upgrade SBC I think is very possible if not almost guaranteed and Team of the week upgrade base icon, you know There's still so much that hangs in the balance right now in terms of compensation in terms of a tweet from EA sports But today is a Canadian holiday. So could EA sports actually have had the whole weekend off I don't know. We'll talk about that in today's video as well And of course discuss the market with the brand new mini release of those four road to knockout cards that are out A lot of people are investing in those that has me a little bit scared So we'll talk about that and more in this video today If you're excited for it hit the thumbs up subscribe if you're new let's talk about what I mentioned first Player picks Nate.  Is that actually like potentially content for today? You know, it is I feel like it's not the biggest potential some sort of upgrade pack I would imagine is dropping today and like we have seen the content right now in this game Continues to be really good yesterday. We had the Benasser SBC 30,000 coins for a live 84 rated AC Milan card with the potential to upgrade by not just a plus one But of course one upgrade would get this guy to an 86 another one would take him to an 87 This card is like honestly kind of like a tonally box-to-box replacement for somebody that you may be having your team Really really good value and again That's just another SBC added to the list that has been such good value And I think that's going to impact the market throughout this week as well But if EA is continuing this good Content kind of push like everything in the last couple days has been pretty good last year during roads to the knockouts They also kept that going with a 75 plus player pick SBC and I remember this last year This was a huge catalyst in a lot of that market drop-off last year in the middle of October It was during the second week of road to the knockouts. I believe maybe in the first But for sure it was in the second week. I do remember that and this would be huge I mean just think about player picks on FIFA 23 this early in the game That'd be incredibly massive So I do think there's a little bit of a chance at this drop today because the content's been good If they're gonna put on a new upgrade pack SBC This one would get people excited and would get people on the game and you know also it happened last year So I think there's potential for it today, but regardless I do imagine they would rerelease like the 78 plus upgrade Of course, we saw that during ones to watch last year and we saw it even last week during ones to watch You know, there's an 80 plus upgrade pack that's in the code I just you know, I don't have my high my hopes set too high for a 75 plus player pick I feel like it's like maybe 50 50 I would really expect just some sort of upgrade pack today because EA as we know Likes to drop upgrade packs with every single promo nowadays because we like to open the upgrade packs in just about every single Promo so along with a regular upgrade pack today to try to pack some road to the knockout cards Which by the way who wouldn't want to do some 75 plus player picks to get yourself a chance at packing One or multiple of these roads to the knockout cards live upgrading nice car designs We now have all of them in packs after the mini-release yesterday So people would see upgrade packs is a very good opportunity to pack one or two of these cards If the pack luck is somewhat decent from them, of course And if you maybe get a little bit lucky, but besides those upgrade packs, you know I've been talking about this and mentioning it But there's really a potential for a team of week upgrade pack to drop in the game Foot sheriff tweeted again that the team week upgrade should come this week I think either today on Monday or maybe tomorrow on Tuesday would be a very likely day for that to happen And actually if we take a look back at last year in mid to late actually late October was when the team of upgrade was first Dropped and it was pretty cheap It was like 12,000 coins and people were like man It's not worth it because all team of the weeks are like 10k but of course the whole draw of putting a team of week upgrade out is To get people to try to gamble and to try to pack a player like a Holland like a bignette or like a la rafael liao Marquinhos a lot were from team of the week one, of course son De Bruyne Any of those players because we would believe that a team of the week pack would include players from previous team of the Weeks as well not just the current team of the week three So maybe that comes this week as foot sheriff said he it should come right we don't even know But I just think what to expect today is some sort of upgrade packs on Monday, right? That's nothing new that shouldn't be too big of a surprise The only thing that would be a pretty big surprise is a 75 plus player pick if they were to do that So again, I don't think a likelihood of that super-duper high But again like I said the content's been really really good So maybe they're gonna keep progressing forward with that content and drop us some pretty good player pick So if you want to do anything to get ready for that, I would just say stock your club with a couple rares and non I don't think you need much. I think you need just enough to get by and do a couple player picks I do believe they would require like 11 golds. Maybe a few rare The one last year actually let's double check that and see what it required last year the 75 plus player pick I did very beginning of last year actually just kidding. There's no way it requires that much number of players in the squad of four and you have to have all gold players one rare So four players in one rare. So yeah, just stock your club with some non Rares stock your club with a couple of rares again for a 75 plus player pick Yeah, it's got to be pretty cheap because 75 plus in return is your your low rating guarantee there You need to make it a pretty cheap SBC. So you can stock the club if you want to go ahead and do that I've got a lot of stuff in my club from packs opened over the weekend and we can leave rewards and stuff like that And that's kind of what I want to talk about next is this market and still we can make rewards of getting paid out Today on Monday what we normally see on Monday is a pretty solid market rise, right?  I'm going to pick up this photo right here. Oh, I missed it, man Now I'm trying to grab a photo because I do think that some of these road to the knockout cards Are going to bounce up in price and folding just being 376. Boom. I will take that center attacking me with a hunter I want to try this guy And I think somebody's road to the knockouts can potentially rise up in price this morning on Monday as Honestly, I think a decent amount of the market again If ea don't do anything today in terms of compensation Or in terms of even tweet from ea fee for direct about the whole hero situation Monday mornings on the market usually Bring some rising prices as people again, like I said, they get their rewards They go out they have some coins and they try some cards and especially this early stage of the game People are going to get right back on grinding division rivals to get those rewards and to be working on You know maintaining those packs that they can get the next set of rewards That will be upcoming and a lot of these cards have dropped off a little bit I bought a bombing uh at the content drop on sunday yesterday live on stream at about 484k sold them for 530 kind of time that fluctuation really great Now he's back down to 480 and again because people want to try these brand new promo cards Usually you see mondays after rewards in the weekend, which a lot of the supply ends But people get coins they go out they try some new players and buy some cards So i've actually picked up a couple of bremer as well because you know, of course, he was in the mini release There's a lot of hype with this Syria after the bonaster Sbc was released, which again this sbc is incredible value 2900 up votes 27 000 coins Really good box-to-box card Not lengthy or anything like that right explosive But really good dribbling and again you give this guy and one upgrade if he potentially can get one upgrade And he's going to an 86 that'd be a really solid upgrade and he would almost behold it gang besides shooting So really really really nice card You saw a lot of the ac Milan links rise like this rafael. Yeah, of course direct correlation with that card Right a compliment going from 80 000 coins all the way to set to 93 000 coins Kind of where he is now. I expect that card to keep going up a little bit today There was another oh a tamori Our boy tamori was up a lot as well But I think tamori was increased in price too because of a team of the week potential for this next wednesday So that was another reason why you saw his card go up But the syria links are just kind of hype right now So I picked up a couple of bremer a lot of people Are buying lucish paqueta and hoping to see him rise up in price today And you know, I picked up a photo because he's tried and true And that's a card that I've seen rise a lot over the past couple of days On the weekend as people try him out even flipped him myself This card was brand new yesterday as a part of the mini release paqueta is about 180 000 coins I believe his card looks great right five star skills forced our weak foot, but man I think there are so many people that are investing in this card because yes It's hype and a lot of people want to try it So I understand how people would maybe want to invest in this but this guy is getting supplied So much on the market. It's crazy So I'm being a little bit careful with paqueta It seemed like he didn't like nobody would let him go under 168 or 170 000 coins A lot of people were investing in this card And he's kind of now sitting in like 180 k So I do think there's potential for this card since it is so hype to rise up a bit into today I'm just a little bit worried about the over investment Potential here because so many people were investing in this card And even the same thing with wambasaka, although I like wambasaka a little bit more because There's just not a lot of right backs that are in the premier league, especially with halfway decent pace Again, that's why kyle walker we talked about in last night's video. That's why kyle walker is like 150 k Is because there's no other substitutes for him wambasaka's card is decent. He's not like kyle walker He's explosive. He's not lengthy. He's medium medium work rates, which you know isn't as ideal But 91 sprint speed. He is a pretty good looking card dynamic image Manchester united english links So, you know, I think this could be a card that rises up today as well But I kind of went with bremer like I said because the syria hype and just because I felt like he had less You know, like people investing in him at the time and a brazilian center back I mean, there's so many people with the syria links and so many people love this dude's base card That I just I just feel like he has a really really good potential of going up a little bit today Again, if you see cards that are going up in price today any of the roads to the knockouts Any gold cards as well? I mean, I'm not excluding golds out of this as well I mean, you think about yesterday on sunday this kunday card went from 69 000 coins all the way to 78k You almost went up 10 000 coins on a nice morning rise We had a little bit of pack supply yesterday So we dropped off just a tiny bit and right now he's about 75 000 coins again That's the type of rise that you maybe see today. It's just a nice slow steady rise on the couple of these cards I'm not expecting for cards to absolutely explode today. It should be just a nice Rise into the day on monday again That is unless ea sports go out and do something like compensation or a tweet from ea if even direct We have no information still About the whole foot heroes thing Um, it's it's very frustrating and it's interesting that you know, even today on monday guys today today's a canadian holiday Today is canadian thanksgiving You know, of course if you're celebrating, you know, have a great day enjoy What what the holiday brings but you know that also could mean that ea is not working today and would Potentially be and another reason why we might not get any communication from ea sports Today on monday and maybe why we haven't gotten any communication over the entire weekend Is because they're on holiday So that's a very real thing that we have to consider With what's going on and the lack of communication that we have had so far So we'll see if we see anything today. Some people might be like Nate. Would that mean there's going to be no content today I don't think that that would be the case at all because They can schedule content days ahead of time. It used to be in the past for like holidays would would be like, no there's nothing but now Now it seems like they're they just schedule content ahead of time and something will probably come out today on monday I doubt there would be absolutely nothing So I still think the upgrade packs are very very likely to drop today also really quick as well Mondays, I believe have been days where we have had icon sbcs Um, I think sundays and either like sunday monday or thursday I feel like those are the common days for icon player sbcs We are the first icon player sbcs leaked vidich and casias were both Leaked yesterday by a foot sheriff So it seems kind of crazy early to have some icon player sbcs But if we roll back in time when was the first icon player sbc that we had last year I'm looking on uh footbins fifa 22 sbcs. We had the base icon upgrade I think this would have been at the end of october. It was during rule breakers Okay, it was during the first week of november is when we had the first base icon upgrade We had closer and alcocha around that same time as well Also, as I mentioned and as we've looked at in the code We do have the hero pack that we of course saw in the store and the base icon pack like As an upgrade we would assume this is being added to the code for that reason last year We had like I just looked at november 8th for the base icon upgrade The foot hero upgrade was ahead of that This was released november 1st the very very end of Of october and the beginning of november is when we saw that hero upgrade pack last year So, I mean ea do seem to be doing things a little bit faster this year and ahead of time And especially with how much they're boosting somebody's road to the knockout car It's like a bombing seems like they're progressing the power curve pretty fast this year as well so We're just gonna have to see if that continues today and if ea are going all out You know 75 plus player picks a hero upgrade pack in the next week or two a base icon upgrade that'd be crazy But you know, I do think it is potentially possible But you know everything that we're doing on this market right now If you have cards that are in your team with how good the content has been I mentioned this in the past couple videos as well I would just say take it take it a little easy with the market right now because yes Again the content's been very good and that usually means that a lot of the market prices are going to end up dipping down Because people are doing more sbcs and they're interacting with that great content and instead of buying players when there's You know still gameplay demand out there They're going and doing the sbcs and getting that done forming their teams around those sbc players So that's why if you see a nice market rise today, and you don't want to be In like invested with the cards that are in your club I don't think it's a bad idea at all to sell some players from your team today Not saying that they could you know drop off a ton by the time we get to the end of this week All i'm really saying is you know today and monday is usually a day where you see the market rise up a bit If it's going to be a quiet week Wednesday could be the peak but again, there's just so much unknown right now with compensation with um, you know Multiple forms of compensation. We don't know about what they're going to tweet about with the hero pack What that's going to cause in the market, um and then upgrade packs today So, you know, that's kind of the safe route if you really really want to do that But I feel like holding teams unless we get a hero or a base icon upgrade. I think holding teams should be Decent at least for the next couple of days You shouldn't lose too many coins by the time we get to wednesday If you're just wanting to hold onto your cards and use them in your team now I want to talk about fodder again as well because we've been talking about sbc fodder in the past couple videos And i'm still here to tell you right now that I think it looks pretty good Like I mean 84 ratings for 1.7 k is not bad and 83s At literally discard Is not bad either because if this team week upgrade pack does drop in the next day or two These 83s even though it'll probably seem pretty dumb to do an upgrade sbc for a team of the week I would assume it would be around the 83 rated mark as it always is I don't know if they'll require any chemistry points because last year. I think I've clicked on the requirements for the Team week upgrade and it was an 83 rated squad with 70 chemistry, which is so annoying But like this year they have not been requiring chemistry and most of the sbc's So, you know apart from some of like the pack sbc's or whatever So I I think that 83s are still a big dub and it's not like they're up a lot 84s are up like a hundred and 200 coins a card after benacer came out You can see you know, they rose a little bit But not too much and even again as we see some supply from weak and league rewards starting to hit as people finishing their games on a sunday night Um, you see these guys dipping down a little bit lower too So I would say that fodder is definitely not a bad buy by any means Right now and maybe even on the higher tier and 85s are up a little bit 86s are up a little bit 88s are not that expensive But what's really going to move the needle on the higher tier fodder is a big hero upgrade Or an icon upgrade that would be what it takes to move that sort of father fodder I think there's a better opportunity for the lower tier stuff to move Especially because a lot of the player sbc's ea has been releasing have been on that lower tier So that's something to watch out for also making coins on ones to watch cards was incredible this weekend and I just wanted to point this out and talk about it because um, I know this week we have Uh, champions league and your ropoli games that are gonna affect these live road to the knockout cards So if you learned anything this weekend From what has gone on Sell in the hype is the biggest advice that I can give you think about guys like darwin nunyes If you are watching this guy during the liverpool arsenal game, he went all the way to 110,000 coins post game He's gone down back below Um 70,000 coins because of course he did score the goal, but they did not win You have guys like antony who scored a goal as well and they even won the game But since there were so many people that had invested in this antony card, um There he went he went from like 230k all the way to 280. We were doing watching it live on stream It was mad fun and now he's back down to 225 I actually picked two of them up at like 210 sold them at 225 just a second ago for a quick flip And that's how I had the coins to go on by foden Levent dalsky, um, you know, of course did not score for barcelona So his card price is down a lot. He was like 400k now. He's 335 You know, some of these guys will end up bouncing back And then of course, I actually have a gabriel hazus right now on my transfer list because gabriel hazus Is you know a card that is arsenal is on two wins out of three for his upgrade And if arsenal win this upcoming weekend, I believe they play against leads Which would be a very winnable game for them This gabriel hazus will get upgraded next week to be an 85 rated card to get a plus two because that's a plus one Right an inform upgrade plus one So we'd go to an 85 rated card and that'd be a massive upgrade And I think the hype is going to continue to build so I don't mind setting aside a bot when I like 245k I don't mind setting that aside because I think that's a card that will rise up in price I kind of want to try him out as well. I haven't used him yet I know that his gold card is the exact same stats, but this one looks prettier So I might give him a shot in rivals or something like that Um, and you know, that's kind of an investment that I would like to watch and kind of follow But again, keep a close eye on these ones to watch cards because if you watch their movements over the weekend Also, quick note the ball is injured. So that's why he scored a goal yesterday and literally this was a crazy turn of events So the ball was up because you know, rome was playing decent He scored a goal scored a penalty went up to like 170 or 180k for like a quick minute or two And then he was injured and the injury seems pretty serious So I would be staying away from this debala card until you hear detail that maybe his injury is not that serious I hope it's not. I would love to see him play at the world cup Of course, because we're almost a month away from that. So, you know, just that's something to kind of note with that debala card But um, you know, lebendalski is still kind of low Nunez is still pretty low and a lot of these other cards, you know, they're just kind of chilling, right? And here's why I would watch lebendalski as well because manne, you know, dormant Drew in like a last minute goal drew against bayern over the weekend. So this manne card went from like 700 k All the way down to 500 000 coins. I mean, he wasn't quite 700 k But like, you know, 650 and now this card just because he's rare has bounced back up to like 550 k 540 So I think a similar thing could happen with lebendalski You've got a rafina card in the road to the knockouts People would expect lebendalski to be scoring goals during even the midweek not that that would upgrade his card Wow, there's a lot of lebendalski's. This is overnight at 349 k. Let's see if this is a trader Uh, okay, only a couple of them are interesting So like my price for this level was like 320 if he if he hit 320 Then I was going to get interested in him. He didn't quite get there But he's a pretty rare card and of course is a goal scoring machine So, you know, that's a card just like Jesus where, you know, barcelona did get a win and let me double check Are they on their second win? They are so lebendalski is in the same exact position as gabriel Jesus is This is a card that of course it went down in value, but it is now One game away from that upgrade albeit that next game this next weekend's el clasico So it's a pretty big game But you know, that's just stuff to consider with these otw cards And again, it was just a nice weekend to trade with these guys I made a decent amount of coins on them Flipping them and I know some people made bank, right? If you bought an antony and he sold when he scored a goal stuff like that That's the type of movement I want you to get used to seeing and you know Go look at the graphs if you maybe missed out on it and stuff like that because there are going to be movements With these road to the knockout cards this week, especially for clubs that are maybe on like the bubble, right? Um, you know, I believe that some of these clubs are not In first or second place in their group if it's a club, it's maybe in like third or fourth place Where right now it's like man, they got to step up To get an upgrade and you see them go ahead and like score a goal in a game that they need to win This is match day four this week, you know, you're going to see some prices rise because of that So we'll break that down and kind of look into that here pretty soon As we're monitoring these prices day by day We'll probably wait until tomorrow and tuesday to dive into that a little bit more when we have those champions The games actually on the doorstep But I may I wanted to make sure to talk about that at the end of the video because those ones to watches We're really good to make coins on and so are the roads to the knockouts as you can see I've been trading with a lot of different stuff And though there's the antennas right there and then again what I have my transfers right now are The photon a couple bremmer's the capital hazus and just some other stuff. I'm listing for Lazies but hopefully I mean a I wouldn't mind if 75 plus player picks came out today Because that would be absolutely fire. So we'll see if that happens I feel like the potential is kind of there but some sort of upgrade pack for sure today on monday We'll try to pack a couple of these road to the final car It's just because you got to take your shot at it, right? You're never going to pack anything stick if you never open packs So that's the video for today boys If you did enjoy smash the thumbs up comment them below if you have any questions and subscribe if you do See you on the twitch stream today. It's been Nate's foot account. I'll catch you guys later. Peace


Good morning. As Louis said, my name is Peter Cronkleton. I'm based in Lima, Peru working for the Center for International Forestry Research, but I'm collaborating on this team with funding from the from DFID to examine tendencies in reforestation in these three countries. I'd like to point out that this is a multi-author paper. There are teams working on each of the three countries where we are doing this research in Nepal, China, and Ethiopia. I won't name all of them. You can see them on the screen. The title of my paper today is Dealing with Property Rights. And so the reason for that is secure property rights are seen as a key enabling condition for a forest restoration. To change stakeholder behavior, either to get them to invest in restoration or to limit extraction to allow restoration, they need to have insurance of future benefit gains from forest restoration and confidence that mechanisms to enforce rules exist and that others will comply with those rules. However, secure property rights are more than just land title. There are several characteristics of property rights that I want to point out today. There are themes that run through the cases that we're going to examine in this paper. First is the issue of the origin of rights or the nature of those rights, whether they're formal or customary. And in most systems, you find a mixture of both statutory legal rights and rules and customary practices and beliefs. Also, it's important to understand that there are often different types of property. There's state or public lands, private that can be both individual or collective, meaning that there's some entity that's able to exclude others. But there are also open access situations that often result from either an overlap of these different types of property where people are able to venue shop or a breakdown in governance where there is actually no established property system and functioning. And in most of these cases, you have nested systems. So you have sometimes collective systems where there are customary individual property rights within them and individual property rights systems where customary customary collective rights allow the establishment of security. Also, it's important to understand that property is usually seen as a bundle of rights. So you have access rights, whether you're able to enter and benefit somehow from a property, whether you have the right to withdraw from that property, basically to extract, but without influencing the behavior of other individuals or having ability to plan long term. Management rights that actually allow you to make decisions on how a property or a research should be used and make long term planning decisions. Exclusion rights, which are the ability to keep others from using the right. And alienation, which is basically the idea that you can transfer or sell your rights to another individual or entity. When we're discussing forest property, it's important to understand that usually states embark on a partial devolution of rights. It's rare that forest resources are transferred with the entire set of rights transferred to the local communities. And this creates a co-management system, basically where there are shared rights and benefits. The local entity that receives the rights has the ability to benefit, but they also have responsibilities to comply with regulations established by the state. But also the state has obligations to provide basic conditions to allow them to manage. So I'm going to go through the three examples relatively quickly, since I don't have much time. And I want to just go through first the tendencies and the policy changes as they affected property rights, and then look at local examples to see how those played out. So in Nepal, the transaction occurred over several decades. In 1957, there was a nationalization act that placed all forests under state control with the intention of protecting and conserving forests, but instead increased degradation by creating open access situations. In 1976, there was a national forestry plan that devolved rights to local government and attempted to promote restoration programs, but these were done in a way that there was very little local participation in the plantations that were being established on public lands, so these had limited levels of success. In 1988, there was a master plan in the forestry sector where policymakers in Nepal began to recognize that communities needed to play a role in the management and restoration of these forests, but it was not immediately established as the national policy. This took place with the 1993 Forestry Act that recognized community forestry user groups that were able to gain control over forests near their residents. It required these groups to formalize by adopting a constitution using a template established by the government and to develop operational plans for the management of the restoration area that they were going to be working with. It also reduced the quasi-judicial powers of local forestry officials who had had a great deal of control over forest access, but also were channels of corruption. Very quickly, this system was very recognized and successful, and over the following decades, it was expanded to over 19,000 community forest user groups in the country covering 1.7 million hectares, basically 33% of the forest in Nepal, and almost 40% of the households, which is quite impressive. We're going to look at a specific watershed near Pokhara, and a community that I'm just going to refer to as SRD, not wanting to massacre the Nepali. SRD is a watershed that has been quite successful. There are 77 community forest user groups managing over 2,000 hectares of forest, and it includes over almost 8,000 households participating in these restoration efforts. This specific community, SRD, has 219 households managing an area of only 22 hectares, but this is a significant area of land for this household. Prior to 1993, they had no rights over forest restoration and no stake in decision making over this area. Conservation activities were designed by external experts and implemented with minimal local investment or involvement. Residents lacked interest in participation and did not collaborate with conservation measures, so typically extracted fuel wood or fodder from this area allowed their animals to graze activities that were against the official rules. After the 1993 Forest Act, the community began organizing to implement their own restoration plan, and this was in collaboration with local officials, and after 1995, they were given official recognition for management of this area. They managed this area for fuel wood, fodder, and bedding materials, so to a certain extent it's mainly for subsistence purposes, but they also sell many of these products to surrounding communities. The regulations established by the user group require members to invest labor and tree planting and to guard the forest, control grazing, and to monitor for forest fires. There are designated collection periods for fuel wood and leaf litter that facilitate regeneration, and then the rights that each member have include access, withdrawal, management, exclusion, and these rights are held perpetually, although they're required to update their management plan every five years, and if they don't do that, they're not allowed to commercialize products from this forest, but they are allowed to continue to use it. And this has significantly increased the forest quality and the community looks forward to possible benefits from payments for environmental services or ecotourism processes that are currently being negotiated. Now I'm going to switch to the example in China and quickly go over a few of the policy trends. In 1981, one policy was the household responsibility system, which allocated agricultural land to increase and increase productivity. Basically, households were given tenure certificates as long-term lease contracts, and this has subsequently applied to forest land, although with mixed results in different regions. A new tenure form between 2003 and 2008 transferred 99% of China's collective forest lands to individual households, groups, investors, and village collectives, and they were given long-term tenure security in the form of 70-year renewable contracts. They also had the potential once they had these contracts to receive other types of subsidies for forest restoration, and this reversed a trend of forest loss in southern China. I want to look, we're going to look specifically at the Chianting County and the Fujian province. This is an area of over 300,000 hectares with a population of over 500,000 people. It was once one of the most degraded counties in China. 60% of the territory suffered from soil erosion. Forest landscape restoration programs began in 1981 and focused on 970,000 hectares of eroded lands. The program focus included exclosure efforts, afforestation, and orchard plantations. By 2015, eroded lands were reduced from just over 30% of the area to less than 10%. Forest coverage increased from about 60% in 1986 to over 80%, and the annual income increased from $60 in 1978 to over $1,000 in 2015. But there was a separate policy process at work in this context that involved different levels of government and different mandates. The three-forest fixed reform from the early 1980s was intended to stabilize forest ownership. It delimitated the boundaries of mountain exposures that were then devolved through the system of forest responsibility. So 16% of the mountainous forested lands were distributed to 94% of the households, but in very small parcels of less than one hectare per household. Most of the forest remained collectively managed by the government and village collectives. Later, the Who Plant Who Own and the Wasteland Auction Policy in the 90s allowed villagers to invest in afforestation and plantations to receive certificates of forest rights. It increased participation, forest cover, and income. This was a very significant process. And then the reform of collective forest rights after 2002, and this was a decentralization of forest rights from collectives to individuals. The state maintained forest land ownership but granted access, use, and management rights to forest lands to households. Additional incentives were reduced taxes and fees and the ability to participate in other restoration programs. This allowed forest land, it also allowed forest land mortgages that increased enthusiasm for investment in afforestation and diversified participation in forest landscape restoration. So the trends in these incentives were that generally you saw a process of collective and public owned property rights arrangements provided relatively low incentives early on. The Forest Three Fixed program provided insufficient incentives for management and protection and theft in forest products continued. However, the collective forestry reform decreased thefts and illegal harvests. However, no afforestation activities either because land was managed through exposure so it was limited. But villagers were unwilling to invest in forest landscape restoration on small remote areas with limited rights. However, later the individualization of forest rights arrangements provided relatively high economic incentives to large households, enterprises, and cooperatives. Individual stakeholders willing to invest in afforestation were able to attain economic benefits. And individualized property rights arrangements encouraged public participation and diversified participation in the restoration of landscapes. Now I'm going to move on quickly to the Ethiopia example. The policy trends that we've heard a little bit about in Ethiopia started, I want to start primarily after the 1975 coup that replaced a quasi feudal system with the nationalization of forest properties throughout the country. Which created an open access problem because the nationalization did not take into account local customary practices and state agencies lacked the capacity to actually control the forest areas that were nationalized. It corresponded with an increased national research degradation due to droughts and so you had large scale government programs to conserve soil and water on sloping integrated lands, massive tree planting programs on state lands and major investments but with limited success. After 1991 there was another violent transition in government which maintained the tenure policy but introduced other reforms but also weakened governance in many rural areas. The national conservation strategy in 1994 stressed that local participation and development should be prioritized and used decentralized approach to implementing forest restoration programs. And it created space for NGOs to experiment with participatory forest management which was one of these strategies that was promoted. NGOs helped to negotiate agreements between communities and regional government agencies although no formal rights to property were transferred, it designated withdrawal rights and some management and exclusion rights to communities surrounding forests. We're going to focus specifically on the Chalimo Forest in the Oromiya State and this was while it had been designated as a national forest priority area, much deforestation during the period of the weak governance following violent change in government in 1991. So from 1982 to 1995 forests in this area shrank from over 22,000 hectares to just over 6,000 hectares. And in 1996 the NGO Farm Africa and SOS International began promoting PMF as brokers between communities around this forest and the district government. And in 2004 they were able to gain some official access and gain withdrawal management and exclusion rights and in 2004 the district officials legalized the bylaws of the forest user group officially transferring the management and use rights. The Chalimo FUG which is one of these groups included natural forest and devolved rights over plantations that had been planted as a buffer. They were only allowed to harvest NTFPs from the natural forest, this included grasses, medicinal plants and fuel wood, but they were allowed the collective sale of timber from the plantations which was less restricted, there were less restrictions on use and it's allowed this user group to have considerable income from timber sold from these plantations and as a result deforestation was reduced and regeneration was enhanced in this particular community. However there were concerns about marginalization, the government had decided on the composition of the forest user groups and so there was a lack of transparency in the distribution of responsibilities and benefits sharing mechanisms. State agencies still lack the capacity to assist with enforcement of exclusions so there is illegal harvests of small diameter trees and leakage into non-participatory forest management forests near the user group. Compared to forest user groups without plantations the timber economic returns were lower than expected in neighboring groups. However communities expect that being granted the PFM status is an incremental step to gaining recognition to stronger property rights in the future so that just the opportunity to potentially get rights in the future it continues to provide incentives for people to participate. So finally in conclusion I just want to draw what I think are four main points out of these cases. First of all secured property rights are an important enabling factor in forest restoration I think that's seen in all of these cases. However secure property rights are more than just land titles and involve multiple government scales, relationships and behavior. Generally partial devolution of rights produces co-management situations and I think that's what you see in all three of these cases. And finally efficient and effective solutions result from adaptive multi-stakeholder processes involving negotiations and balance of trade-offs. Thank you.


So let's get started. So OTA is actually an application which is provided as a source in the WB-Cube package. So it's ready to be modified and customized by anyone. It resides at the very bottom of the flash and it occupies about 24 kilobyte. And there are three main purposes to update the application or just a part of it. So it can be, for example, a configuration data that you want to change. And of course, it's also possible to upgrade the RF stack when needed. So there are two ways to do this. Currently, you can use the STBLE sensor. This app is on GitHub, also in source. So you can carry out the firmware upgrade with your phone. A second way to do this is with another STM32WB. So to make it work, you flash the OTA clients with so-called transparent mode. And this communicates with the CUBE Monitor RF running on your computer. And CUBE Monitor RF can do many different things. It can access the ACI commands of the Bluetooth stack. But in this particular use case, we are only interested in the OTA. So let's have a look more technically on how it works. It's important to understand the memory mapping and the interactions between the individual firmware. So WB is a dual core with a single bank flash. So the area dedicated for M0, M0 plus, is secured, which means the user core, the M4 cannot read it, cannot delete it, cannot write to this. So the user section starts from the bottom and ends at the security barrier. So at the bottom, we have the OTA application. So this is the firmware executed after reset. And the first thing it does, it searches if there is a valid application and it searches for the OTA request. If it finds no OTA request, it will be simply bypassed. So it jumps to the application and then the application is executed. Now what is an OTA request? OTA request is a way for the user app to call the OTA. And that's done in a very simple way. The OTA request, which is just a word in SRAM, the first memory address of SRAM, that's where we put the OTA request and then a system reset is generated. So after reset, the OTA boots, it checks the command because the SRAM retains the value between resets and it proceeds accordingly. So this is how it's done. So let's imagine a scenario when actually there is an OTA request. So when this happens, the OTA application will initialize the Bluetooth and it will start advertising. And it's now ready to be connected by the OTA client, which can be your phone, which can be any other device. OTA is actually a Bluetooth proprietary service, in this particular use case. So it's a service with three characteristics. There is a characteristics for defining the base address where we want to flash the data. There is a characteristic for the exchange of the raw binary data. And once all the data have been transferred, then there is an indication back to the OTA client saying that the upload finished successfully. Okay, let's talk about the application first. So what are the necessary steps to integrate the OTA into your user application? So most obviously it needs to be linked above the OTA. But from the BLE perspective, it's necessary to do two things. For the custom BLE service, we need to add a special characteristic, which is called an OTA reboot characteristic. And this is integrated into any BLE service you can imagine. The second thing is changing the advertising. So let's talk about these two things separately. So this is a simple example. Let's imagine the user application is a heart rate. So it's a very simple Bluetooth service, which is actually adopted by Bluetooth SICK. It has two characteristics. One compulsory one is the measurement. So this is the actual heart rate value, which is sent to the phone or your wrist health meter. Then there is a characteristic that specifies the position of the sensor on your body. And now what's important, if we want an OTA to integrate OTA into this service, we add an OTA reboot request characteristic. So in there, when the client writes into this characteristic, he can request the OTA application, which will generate a reset afterwards. We can also specify here which area in the flash will be erased. So because we need to free space when we need to upgrade, then here we can do this. We can select which sector, which is the beginning sector of flash and how many sectors we want to delete to free upspace for the new version of the application. So regarding the advertising, the OTA capability is also advertised, and this is done by a special proprietary advertising structure. This is described in the STBLE BlueST protocol. So in there, there is a feature mask, which is indicating what the device is capable of. So according to this standard, there are many bit fields related to sensors, but what interests us the most is the OTA reboot bit. So this is how the phone immediately knows from the advertising content that this device is capable of OTA. So let's have a look at the flow of the OTA. So let's keep in mind the heart rate supporting OTA. When the phone sees the advertising content, he already knows it will support OTA. When it connects, it will perform the service and characteristic discovery. It finds the OTA reboot characteristic. So it writes to it, and immediately a reset is generated. So the OTA application boots, it will erase the area in the flash, which we tell it to erase. After that, it will start advertising and the phone can connect again. Then there is the process of exchanging the data of the raw binary and storing that into the flash. And once this is done, the target sends an indication that the upload has finished. Another reset is generated, OTA reboot. It finds a valid application, so it's bypassed. That's the end. So before we go to the first hands-on, just a few words about the firmware which is running on the M0 Plus. So it's obviously the RF stacks. It can be Bluetooth, can be Thread, can be ZigBee. But it can also be FUS, the firmware upgrade services. So these stacks are provided by ST in an encrypted form. So there must be a firmware which decrypts it and install it. And this is the purpose of FUS. So in fact, when you want to upgrade the wireless stack, there are three options. You can use a system bootloader, USB or UART. You can use an OTA. And you can use also a JTAG. The first, it's actually a process which has two steps. So firstly, we need to store the encrypted binary in the flash. And then we need a code, a firmware, which calls the FUS services. And the M0 Plus will do the rest. So this firmware can again be a system bootloader. It can be OTA. It can be a custom application downloaded by JTAG.


Richard, what was your part of it? So back in 2020, people did not expect that it's actually very easy once that we have 5G network to help people understand that even though we have different positions, we can very easily do common values if there is a mechanism to do so. So my part is like a digital peacekeeper. We made a space where everybody can share the reflections on what the problem is. And instead of talking about how to fix it, we first have people share what they mean by fixing it, what they feel about fixing it, and so on, so that we have a common map of the issues upon. And very quickly, people understood that there are certain pathways that are very thin, that are very difficult, but that's the only way out of the weakening problem. OK. And did it, if you look at it more universal, is there an idea how people kind of connected and cooperated on this level? Certainly. Back in the 20s, people had this idea that we have direct democracy on one side and representative democracy on the other. And they're kind of fighting each other instead of complimenting each other. But in Taiwan, starting from the 2010s, we're starting to prototype a new political system where instead of these two systems competing on fixed resources like budget and things like that, we have them work in conjunction with one another with participatory democracy set the agenda. It's like the first diamond in design thinking, which is, by the way, required reading for everybody educated in the 20s. So for the first diamond, it's participatory democracy and for the implementation, that's the development and delivery that's representative democracy. And once we fix on the same structure and everybody understood that this is a how-might-we question, that is the thing that democracy is supposed to produce. It became very easy for all the different democratic systems. It could be liberal democracy. It could be central democracy. It could be authoritarianism to converge on this new political system. And when you say direct democracy, did kind of the digital help us? Did it help us? The digital helped us a little bit by making sure that people, when we are having face to face understanding, listening, and so on, these could be amplified so that people can enter the same empathy space. Previously, before digital, it's easy for a room with 20 people to end up, if you have good facilitation, agree on each other's values. But these 20 people cannot bring that feeling back to their comrades, back to their communities, and so on. So digital helped a little bit by putting us in each other's shoes when we're forming the common understanding. But around the year 2025, quantum really helped a lot more. Because with quantum, we can now have people enter the space but just tailor-made to their personal feelings so that they can voice all their fears or their doubts or their misunderstandings or their uncertainties and participate in a tailor-made virtual conversation with everybody trying to not convince them but also just listen to them and provide a good overview of fact feedback so that people can feel that the Earth itself is talking to them, and that became only possible after quantum computation. And these different kinds of democracies you were talking about, are they upscaled? I mean, are they, the values might be more communal? And then, but they are everywhere, in a way. Yes, so around 2020, we introduced this idea of Internet of Beings. And so it is not just people, like adults, humans that participate in the democracy, but gradually all around the world, people starting including like rivers, mountains, animals, and so on. All the different species capable of sentience as well as collection of environment that could be translated into an avatar that speaks on behalf of them. All these were included in the participatory deliberations that we talked about. Of course, on the final decision implementation in the 20s, because of technological restrictions, these are still mostly human, but including the environment and the social and future generations in the first diamond is already helping a lot in the 20s. Of course, by the 30s, we now have pretty good sentient quantum simulations of future generations as well as of the environment so that they can also participate in the second diamond, although this is somewhat experimental at this point. Wow. And the democracies, are they still based on a market-orientated economy? The market has been expanded so that it is not just about trading services or products and so on. We use this simple idea called quadratic voting, making sure that people understand that each of our strengths or preferences is best if we just share our private assessments of common issues with the community because that ends up resulting in the best possible outcome. And this solved the old election paradox, the arrow paradox, because there was built on the idea that the person only had a limited number of votes and one vote per candidate. And that was because the bits were insufficient. The uploaded information is not sufficient, and that is the cause of the paradox. When everybody switched to quadratic voting, people discovered that they can save their voting points, they can save their voice credits, and everybody understand that it is the best for everybody if they evaluate only the parts that they actually have an idea about and also learn from the other analysis that found other people that they care about and just almost magically because each increasing return of each vote is the same as the increasing expectation of the cost. And so because the cost and the return are the same in this voting game, people are motivated to disclose their true feelings. And so without a top-down of the return and distribution of political budget and so on, a good, fair, sustainable distribution just emerged because of this market of votes. So there's no price system as we know it in a way. There's no, not this thing, people make prices and compete. There is less competition. It's not competition oriented. In a zero sum world, which is the battle days, I think it was last century. It's so long ago, I didn't remember. People had this idea there's limited resources and you'll have to compete on a win-lose mechanism and people who have lost make it a loose-lose mechanism to basically get revenge because of the systemic imbalances. But using quadratic funding, quadratic voting and other methods designed from the radical exchange movement, we discovered that if we, instead of playing game theory on zero-sum games, we can do reverse game theory, which is mechanism design. So once you turn mechanism design into a participatory game, everybody start devising games that are truly win-win for everybody involved. And because of that, people now engage in a lot more creative pursuits when it comes to politics. If people detect that there is a win-lose dynamic going on, they will say, hey, let's just have jam and hack us on and come up with a better mechanism instead of focusing their energy on winning the game and making other people lose. And next year comes out this serenity from Ethereum. I mean, it came out in 2020. And was that part of the solution? Yes, the serenity fork actually prompted people to have a new imagination about what a rough consensus-based governance can do because previously people understood blockchain or Bitcoin in a very fixed term. Like they are here to provide a public ledger that are self-funding, which sounds okay, but it doesn't really expand to other part of the society. But with the serenity, people now understand that the Ethereum naming system, for example, it could be adapted and used for legal identities. Those legal identities don't have to come from a top-down government or bureaucracy or a bank, but rather can be gain-nified so that people or authorizes, authenticates each other using what we call at that time a distributed identity system or social identity system. But nowadays we just call it the identity system because the old top-down fixed single point-of-failure identity system has just rendered obsolete after the new serenity system came about. And so that became one of the key points that enabled people to have multiple jurisdictions across jurisdictional identities and the imagination of alternate governance system become not something that you have to render out but can do right away in your existing communities and are compatible with existing contract lines, that one. Wow. Fantastic. Really? Yes. Thank you so much. Very convincing.


In the previous two modules we reviewed the fundamental concepts from finite dimensional vector spaces and then various properties of matrices one would normally come across in the analysis of data assimilation algorithms. In this lecture we are going to be also providing a broad overview of the fundamental tools that we need from multivariate calculus. The reason for including this is as follows almost all the students who take a BS degree in basic sciences or engineering in any part of the world they have done calculus 1234 in equivalent of calculus 1234 they have been introduced to univariate calculus differentiation integration differential equations all in one variable. But when you formulate a problem in a data simulation framework the problems have to be formulated using multivariate analysis. The state of a system is defined by a vector x the dynamics of a system could be linear or non-linear for a linear system the matrix defined the state of state transition. So we need to be very familiar with the multivariate analysis. The tools for multivariate analysis include understanding of finite dimensional vector space a thorough understanding of matrices and properties and also a good facility with dealing with multivariate calculus which is an extension of the ordinary univariate calculus that anybody who does a BS degree should be familiar with. So our goal is to be able to provide you a broad based introduction to fundamental concepts from multivariate analysis. So let us start with from fundamentals we are going to start with the notion of functions to be able to define a function we need different objects one is a set A another is a set B A is a F is a function from set A to set B we call A the domain of the function we call a B the range of the function this is called the domain of the function this is called the range of the function. So I need a domain I need a range then I need a function what is function your function is simply an association of points that the domain with the points in the range by definition F has to be defined for every member of the domain the value of F in the range need not take all the values in B that is where the distinction between various functions come to be. So by definition F is defined for all members of the domain that means you cannot leave anybody here by definition a function is also called single value what you mean by single valued if you think of function as a black box if you give an input it gives an output FFX for every x there is a unique FFX there is a single value what is the difference between a single valued function and a multivalent function this is a single valued function what is the multivalent function this is the multivalent function if I took x so this is x this is x here for x there are 3 values this is a single valued function. So while in principle one can have single valued functions and multivalent function in mathematics we exclude multivalent function from consideration so when a mathematician says let F be a function he already has at the back of his mind a domain a range a range is also called co-domain and an association between points in the domain of the co-domain by single valued means it is unique so that is the broadest possible way one can define functions. Now there are special classes of functions such as special class of matrices so F is a function is called 1 to 1 it is called injective what does it mean if x is not equal to y FFX is not equal to F of y that means distinct points are mapped into distinct points in the range that means y is equal to x square so distinct values of x have distinct values of y so that is what is called injective F is called on to or surjective means F is maps all the points of a on to complete set b F is called 1 to 1 and on to it is also called by injective it is both injective and by injective. So let us give some examples of functions FFX is absolute value of x x square sin x e to the x sin x e to the x these are all examples of functions and these are different classifications of functions we will more often be interested in 1 to 1 functions which are both injective and surjective because it is for these functions we can have inverses so if F is a function from here F inverse is a function from here to there that is the inverse function in order that the inverse is defined we need to be able to have further constraints the constraint is F must be 1 to 1 or injective these are all facts essentially come from basic definitions of functions. So now I am going to talk about other classifications of functions F is a scalar valued function of a scalar so what does it mean here is a black box sorry here is a black box F this is x this is FFX x is a scalar FFX is a scalar that is what is called scalar valued function that means the domain is real the core domain is real. So what are the examples of functions which are scalar valued function x is equal to x log x 2 to the power of x e to the x these are all scalar valued function of a scalar the input is a scalar output is a scalar so you can think of F as a transformation as a black box something goes in something gets out F is a scalar valued function of a vector so in this case what happens F x belongs to R of n but FFX comes in FFX belongs to R it converts a vector into a scalar so that is what is called scalar valued function of a vector such a thing is also called functional we have already seen the notion of a functional when we talked about vector spaces so what are examples of scalar valued function given a vector x the norm of x a norm is a number associated with every vector there is a number so a norm is a function is a scalar valued function quality form of x is a scalar valued function in the product of x with a for a fixed a that is a scalar valued function so these are all examples of scalar valued function of a vector the input is a vector the output is a number but in dynamical systems theory as well as in data simulation we are going to be interested in a third class of function which are called vector valued function of a vector so what does this mean here I have a box F x gets in FFX gets out x is a vector FFX is also a vector this is called vector valued function of a vector in general F is also called a map map is a very technical term used in dynamical systems theory let F be a map what does it mean F is a scalar valued function of a vector input of the vector output of the vector so let us okay in general these two n did not be the same it could be a n vector this could be a m vector I want you to see the difference the input of the vector output of the vector then the vectors could be of same size or of different size. So let us work an example give an example let n be 3 that means input vectors are size 3 let m be 2 output vectors are size 2 the x is equal to x1 x2 x3 so FFX is F1FX F2FX so what is F1FX x1 square plus x2 square plus x3 square what is F2FX x1 x2 x3 so you give x1 x2 x3 you get this vector given by this so that is what is called a map or a vector valued function CAB denotes the set of all continuous functions defined over the interval that is an huge set it is an infinite set CK of AB is the set of all continuous functions with derivatives of order up to K if I say CAB continuous function need not be differentiable but in the second set CK AB it not only be differentiable but also I would like you to be differentiable up to the order K so what does this mean I have C I have C1 I have C2 I have CK continuous function is the largest set differentiable continuous and differential function is smaller functions which are twice differentiable smaller so you can think of a relation these are supersets C1 is a subset of C C2 is a subset of C1 which is a subset of C I am putting greater conditions and the behaviour of the function so functions come in various shapes and forms functions are of various types continuous function differentiable functions set of all continuous functions set of all differentiable functions of order up to K where K is an integer if K is infinite what we call such functions are called analytic functions for example polynomials are analytic function they have they have derivatives of all order exponential functions are analytic function they have derivatives of all orders and so on with that as a background now I am going to introduce various concept that we would need in trying to do data simulation algorithms especially optimisation algorithms we are introducing the notion of what is called a gradient of a function so in this particular case we are concerned with yes I am sorry we are concerned with a scalar so what is the starting point let F be a scalar valued function of a vector the type 2 let X and Z be 2 vectors in Rn we say X F of X is differentiable at point F if and only if there exists a vector U such that F of X plus Z minus F of X is given by U times Z see this Z and this Z are same so the definition is contingent on the existence of a vector so this is an inner product hot means higher order terms higher order terms in Z and what is the proper to higher order term the ratio of the higher term to the norm of Z they go to 0 as Z goes to 0 this is the limit so such a U is called the U is called the gradient of F of X with respect to X so this is the most general definition of a gradient this gradient algorithmically can be computed as a set of partial derivatives of F with respect to X 1 F with respect to X 2 F with respect to X n so this is a n vector the derivative is denoted by the inverted delta subscripted by F F of X this is called a gradient you can call it so we use the term derivative for univariate gradient for the multivariate so even though F is a scalar valued function of a vector its gradient is a vector in R n so I want you to be able to see the importance of introduction of vectors and matrices very soon so you cannot do multivariate calculus very well until and unless you understand finite dimensional vector space as well as matrices very well so what is gradient in simple terms gradient is simply a vector of partial derivatives that is a simple form of being able to describe what a gradient is this operator inverted del which is the gradient operator it has lots of interesting properties let F be a scalar valued function G be a scalar valued function the gradient of the sum is sum of the gradients so gradient is additive as an operator it has an additivity property gradient of a constant times the function is constant times the gradient of the function that is called the homogeneity property gradient of the product has this rule which is called the product rule which is the extension of the product rule in univariate calculus we are used to d by dx of u v is u dv by dx so we already know this right d by dx of u v is equal to u dv by dx plus du by dx times v that we call this product rule so this is the analog of the product rule from univariate to multivariate in the multivariate calculus we are also interested in another concept called directional derivative so F is given F is a scalar value function of the vector I pre-specified direction Z I would like to be able to compute how the function varies in this direction so it is called the directional derivative that is defined by F prime X, Z X is a function so FFX is a function F prime X, Z is the directional derivative of FFX along the direction Z and that is given by the inner product of the gradient with Z by Cauchy Schwarz inequality this inner product is equal to the norm of the gradient times norm of Z times cos n theta theta is the angle between Z and the gradient you can ready to see that so Cauchy Schwarz inequality we already saw in the previous lectures so this is essentially an application of Cauchy Schwarz inequality that tells you how the directional derivative the magnitude of the directional derivative can be obtained by computing these. Now we are going to be talking about a slightly related concept until now we assumed X is a variable in itself but here X is not a variable X is a function of another variable so X of t is a vector each component is a function so Xn of t is a scalar valid function of t X2 of t is a scalar valid function of a t Xn of t likewise so I have a vector function each component is a function of t so if I am going to be computing the total derivative of X with respect to the time t df by dt is df by dx1 times dx1 by dt so what is that I am now talking about I have talking about f of X of t so if I am interested in so f so I would like to talk about couple of things now f of t of X of t these are all different functions f of X so let us talk about all these functions f of X X is a simple variable f of X of t f is a function of X X is a function of t so it is a function of a function f depends on t in this case only implicitly in the third case f depends on t both explicitly and implicitly so this is no dependence implicit dependence implicit and explicit dependence in these cases we should be able to carry out the computation of the derivative of f with respect to t so derivative f with respect to t is the total derivative derivative f with respect to x1 x1 times derivative x1 with respect to t so on and so forth so this is called the total derivative f with respect to t by chain rule so chain rule additive rule homogeneity rule product rule that we have learnt in basic calculus all carry over there is nothing new but the old concept take a new form when you go from univariate to multivariate that is the idea next is the notion of what is called second derivative if f is a function of a scalar second derivative we simply say the second derivative is simply given by so f df by dx d square f by dx square we are done but when f is a function a scalar value function of a vector like this x is not one that are n variables x1 to xn so I can gradient is a vector I can consider the second derivative matrix the second derivative matrix look at this now the first row of this matrix second partial of f with respect to x1 second mixed partial of x1 x2 second mixed partial of x1 to xn likewise each row such a matrix is well defined this matrix is a special name is called the Hessian of f so you can see matrices arise very naturally not only that we know from basic calculus the mixed derivatives are essentially the same that means del f by del x del y is I am sorry del square x by del so del y del x the mixed partial derivatives if the partial derivatives are continuous the mixed partial derivatives are same the order in which you compute the partial derivative is a material so given that this matrix is a symmetric matrix so n by n symmetric matrices naturally arise when you consider the second derivative matrix which are called Hessian matrix of functions of scalar variables so Hessian is not so symmetric so symmetric matrix so where do symmetric matrices come from symmetric matrices come from various directions one of the simple ways in which symmetric matrices arise is by computing the second partial derivative matrix of a scalar valued function of a vector and this matrix is singular because the mixed partial derivatives are the same and that is what I told you a minute ago so this is called the representation of second derivative matrix for a function which is a scalar value function of a vector now we are going to vector value function of a vector we are going to move to the next level we are so let f be a function from Rn to Rm look at this now I would like to be able to keep this picture of the back of the mind what goes in is x what comes out f of x x belongs to Rn f of x belongs to Rm so f of x is f1 of x f2 of x fm of x x is x1 x2 xn so there are m functions each of which is a function of n variables I hope that is clear now what is that I can do now I can take f1 and compute the partial derivative of f1 I can take f2 I can compute the partial derivative of f2 I can compute fm I can compute the partial derivative of fm now this partial derivative when written as a column is called the gradient so what is that this is the transpose of the gradient so this is essentially transpose of the gradient of f of 1 this is simply transpose of the gradient of f of n so what is that we do now we take component by component we compute the gradient which is a column vector you transpose it to your row vector you stack these rows there is one row for each component of f there are m such component so there are m rows there are n variables so this matrix is a m by n matrix there are m rows there are n columns therefore if you have a vector valued function of a vector from rn to rm this is the collective first derivative matrix for the entire function the collective first derivative matrix is in general rectangular matrix this matrix is given a special name it is called Jacobian so Jacobian of f Jacobian of f is defined only for vector valued function of a vector Hessian of a scalar valued function of a vector gradient scalar valued function of a vector so these are all the various quantities associated with functions in terms of their derivatives now I am going to give some examples let a be a vector let x be a vector a be a constant vector so I can define a function so look at this now I pick I pick a I pick a in rn I keep it fixed so I am going to define f of x equal to ax which is equal to a transpose x which is equal to summation a i x i i is equal to 1 to n so it is a function of x it is a scalar valued function of x because it is an inner product the also the output is a scalar input is a vector a is a common vector that transforms every input vector so what is that this is simply a linear function because the right hand side is linear in each component of that so what is the gradient of f of x partial of f1 partial of f2 partial of xn and partial of x1 is a1 partial f2 is a2 partial of xn is an so that is equal to a so we have enunciated the first rule of multivariate calculus what is that if f of x is equal to a transpose x the gradient of f is a this is very similar to what the univariate calculus person does d by dx of e to the x is e to the x d by dx of sin x is cosine x we develop a table of differential coefficient of various standard functions so in data simulation we need to have such table this is the first entry in the table so if f of x is a transpose x the gradient of f is a now let us compute the gradient of x transpose a that is a quadratic function a is yesterday we talked about with respect to quadratic function we need to consider only symmetric matrices so let a be a symmetric matrix f of x is x transpose ax so f of x is ax1 square plus bx1x2 plus cx2 square let me compute the gradient of this f of x partial of f with respect to x1 partial of f with respect to x2 a simple calculation shows is the this vector you can rearrange it at 2 times this matrix times this that is 2 ax therefore we got the second entry into our table if f of x is equal to x transpose ax its gradient is 2 ax then f of x is equal to one half of x transpose ax minus b transpose x the gradient is ax minus b by combining 2 1 and 2 anybody who has done 3d war should immediately recognize that these terms very naturally occur in 3d war so when you read 3d war without recognizing that these are all tools from multivariate calculus you will have more trouble now if you know this 3d war will become a simple exercise and that is the reason why I believe that it is necessary to understand many of these basic concepts before you start data simulation algorithms. My examples continue now I am going to I am getting little bit more sophisticated x is a vector h of x is another vector so h is a function so in this case h is a function from Rn to Rm so h is a m vector h has m components h1 h2 hm each of the components are functions of n variables x is n variable x1 to xn so let us fix a vector so let us define a function f of x is equal to a transpose hx or hx transpose a this is simply an analog a very simple analog of what we did in the previous case a transpose x here a transpose h of x h of x is any general nonlinear function so what is gradient of this f this gradient of f can be this gradient of f is given by the transpose of the Hessian of h times a you remember already we have talked about a Hessian so this is how you are going to be able to compute the gradient of this again I am not in my class I will derive these things in this lecture we may not have time to derive all these things but it is very necessary that each of you what these examples have that aha in your mind to be able to handle some of these things to develop that independence and dexterity in trying to make this calculations and manipulations. Now let us extend it even further I am going to take the same h now I am considering h transpose a h look at this now this h here we consider x transpose ax here we are considering hx transpose a hx this is again very often come across you come across in 3d war especially with respect to the nonlinear observation operator so h is generally used as a nonlinear observation operator I am using the same kind of notations in here. So in this case what is the formula for the gradient of h the formula for a gradient of h I am sorry gradient of f f is given by this is 2 times the Jacobian the transpose of the Jacobian of x times ax if you it is very imperative to me to me these are all the nuts and bolts yesterday someone was observing after the class who are the people who develop algorithms for data simulation those who understand and have good mathematical skills are the one who are going to be able to invent new or algorithms. So there are 2 ways one is to use somebody else's algorithm another is to be able to invent your own algorithms to be able to invent your own algorithms you have to develop all kinds of mathematical skills and that is one of the underlying purposes of doing this preview of very many different tools. Now consider the next case hfx is the composite function function of a function hfx is g of ffx and this we denote as so x you apply f first and then g first in terms of picture there is rm there is rn there is rd f takes you from rm to rn g takes you from rn to rd hfx is in fact a bridge goes from rm to rd so hfx must be related to f and g in this way so this tells you the relation between h and f and g so what is the Jacobian of h the Jacobian of h is simply product of this Jacobian of g at x and Jacobian of f at x. So this is a this is a kind of a chain rule for Jacobians this is again a fundamental result these all are important things that we will apply when we talk about algorithms. The next topic in multivariate calculus the notion of a Taylor series expansion Taylor series expansion for a scalar valid function of a scalar scalar valid function of vector vector valid function of a vector again there are t 3 layers of Taylor series which are important. So let x and z be real numbers f of x plus z is f of x so what is the basic idea the basic ideas as follows. If I have a domain if I have a point x if I know f of x the derivatives of x all at the point x if I am given a point very close by x plus z this is x this is x plus z is small how can I infer the value of the function at x plus z given the value of the function and its derivative at the point x that is a question Taylor answered. So the value of the function at a neighbourhood point is given by the value of the function at the point plus derivative times z so you can think of z as a perturbation. So first derivative times the perturbation second derivative times the square of the perturbation kth derivative times the kth the power of the perturbation. So this is a Taylor series in a small neighbourhood under super appropriate condition this series will converge this is one of the fundamental theorems in in in in in multivariate in in calculus this is the infinite series by truncating this infinite series at the kth degree term this is not the n kth the degree term in z we can get the kth order approximation this is kth order approximation. So normally we do not use k more than 1 and 2 we talk about first order approximation second order approximation. So that is the general rule with respect to approximations in analysis either you compute exactly there are not too many things we can compute exactly in life approximation is the order of the day. So Taylor series based approximation is often a very useful approximation computationally so this Taylor series is is absolutely plays a absolutely fundamental role in computation. Now we are going to consider the next class of functions the next class of functions are functions which are scalar valid the input is a vector output is a scalar in this case x is a vector z is a vector again the z is a vector z which is rn. So here again I have x I have z I have a point here the distance this is z so this is x plus z sorry this is x plus z again if I know the value of the function at x and its gradient and its Hessian Hessian is second derivative I can approximate the value of the function at x plus z by this relation. So this is called the second order approximation second order approximation we also know the gradient and the Hessian are related I am sorry gradient of the Jacobian related by the transpose of each other. So I can rewrite this using replacing the transpose by the by the Jacobian so it is this form we will use in our analysis so this is the second order Taylor series of it of a scalar valid function of a vector. Now I am going to extend it further the second order Taylor series for vector valid function of a vector you can see there are so many intricacies in here.  So once you know how to compute the second order expansion for a scalar valid function of a vector you have conquered the Taylor series expansion for the vector valid function of a vector cos a vector valid function is simply a collection of m independent functions whatever you do for one does not affect the other you do everything same for everybody so expand everybody in second order term take them all together collect the term you got that so that is the basic idea. So with that in mind the second order Taylor series expansion for this is given by this that is the Jacobian term this is the second order term this second order term is little bit more complex look at this now so look at this now f is the vector this is the vector this is the matrix times of vector this is another vector one half of a vector and how this vector is is is designed this vector is given by this look at this now I have f1 I have a hash enough f1 this is the quadratic form a hash enough f1. The hash enough f2 this is the quadratic form the hash enough fm stack them all together so you get the Taylor series expansion simply by concatenating or putting together the Taylor series expansion for each of the component please remember these are all Hessian also please remember this is quadratic form. So you can see quadratic form occurs in many many different ways one of the natural ways of dealing with quadratic forms is second order Taylor series expansion of scalar valid functions vector valid functions and so on. So that is where these things come into play it is unfortunate that once you finish BS you take our special disciplines and masters electrical engineering mechanical engineering meteorology, oceanography and other things when we take oceanography or meteorology for example they run you through lots of dynamics and so on which are very necessary. So many of the meteorology courses are very strong on models some of the meteorology program very strong on collection of data but there are not many there are not programs at all where much emphasis given data simulation models are necessary data are necessary but data simulation is something beyond in my view data simulation is an engineering discipline sitting inside the science of prediction. So this aim of this course is to be able to bring out the mathematical underpinnings of this engineering discipline called data simulation why do I call engineering discipline engineering always concentrates on developing a product what is the product forecast the development of forecast product in my view is a branch of engineering the product for public consumption and I would like to be able to create a good quality product by doing a good quality engineering which is called data simulation. The next concept is the notion of variation 3D war the war refers to variation 4D war refers to variation. So the notion of variational calculus first variation second variation is fundamental to the development of many of underlying algorithms I would like to highlight some of the fundamental properties of this notion of first and second variation within the context of multivariate calculus.  So change in X induces a change in F the change in F is called delta F. So what is delta F delta F is the resulting change in the value of F of X induced by the increment in X the increment is delta X. So what is that you can think of now there is a black box that is F if you give X it gives you F of X if you give X plus delta X it is going to give you F of X plus delta X but F of delta X I would like to be able to express it in terms of F of X itself I would like to be able to compute approximately what F of X and that is where the notion of computing the induced variation. So what is delta F delta F is the difference between the new value and the old value the induced perturbation. So input perturbation induced perturbation delta F is called the induced perturbation this is the input perturbation. So if F is a smooth function smooth function means what it is differentiable up to order 2 that is C2 you remember the notion of C2 C k functions. So to be able to do Taylor series expansion a function you should not only be continuous but also by differential at least once differentiable if a function is k differentiable I can consider the kth order Taylor series expansion. So I am assuming a better minimum a function is in C2 if a function is in C2 then I can compute the increment delta F to a second order accuracy. So F of X plus delta X that the actual value of the function at the new point is approximately equal to the function value of the old point plus increment one correction this is second correction this is called the first order correction this is called the second order correction. This first order correction is denoted by delta F the second order correction is denoted by delta which is within bracket 2 of F. So this is called the first variation this is called the second variation likewise I can consider the kth variation the larger the order of variation I can add more accurate the value becomes if you chop off at any level it is only an approximation that is why approximation symbols are important in here. What is delta F delta F is simply the inner product of the gradient with delta X what is the second derivative it is a quadratic form delta X transpose this looks like X transpose AX what is this this is the Hessian please remember this is the Hessian this is X transpose AX. So that is called the second variation term so I am I have given you the definition of first variation second variation the first variation is linear in delta X second variation is quadratic in delta X therefore when you are talking about very variational methods 3d var 40 var we are interested in computing the increment suffered by the output resulting from increments the input and that is where the notion of first variation second variation comes into being and these are essentially the so so the variational calculus within this setup is derived out of the fundamental concept that underlie Taylor series expansion here we are concerned with second up to second order in principle I can also go up to kth order. So given this now I am going to give you formulas for computing the first variation much like I gave you formulas for computing the derivatives so these are the tables of variational calculus just like tables of multivariate calculus tables of univariate calculus. So what are the differential coefficient of standard functions what are the differential coefficient of standard function multivariate calculus what are all the first variation formulas for our various cases and that is what I am trying to so these again help you to develop that skill to compute all these quantities which are fundamental to applications. So let us fx be look at this now X is in Rn sorry that is correct X is in Rn f is a vector of size m so f is m vector n I am sorry f is m vector x is n vector I am now going to be concerned with the first variation of delta f. So the first variation of f is simply the first variation f1 f2 fm f1 f2 fm are all independent compute the first variation f1 compute the first variation f2 stack them all together you get a you get the first variation of that first variation f1 is simply the inner product of gradient of f1 with delta x gradient of f2 with gradient of f1 with so you get the formula and this delta x is a common factor and the resulting one is a matrix it can be very easily verified this is the Jacobian times this so the first variation of a function is related to the matrix vector product the matrix being the Jacobian the vector being the increment. So this is a beautiful formula that we will use repeatedly in the derivations of 3D or 4D or that is the reason why they are called variational methods here are some examples again if ffx look at this now I am using the same example through to compute the gradient to compute the Hessian to compute the first variation to compute second variation the reason I am keeping the same example is because then you can see the interrelations between the gradient and the variations I think it is it is the ability to knit together a picture how these relations are built is fundamental to a thorough understanding of what we are planning to achieve in this course. So if ffx is a scalar valid function of a vector so the first variation is simply the inner product of the first variation of a with delta x again this is the first formula in variational calculus if ffx is equal to one half of x transpose ax delta f is equal to the inner product of ax with delta x here a symmetric obviously a symmetric because of quadratic form. Now the third example should be very familiar to all those who have done 3D var z is the observation hfx is the model prediction z-hfx is the error so this is the sum of the squared errors this is the function that we are often using in least square methods to minimize so given z given h we would like to minimize this with respect to x so this function is the cost function of the linear least square problem so not to be able to compute the solution for the linear least square problem I need to be able to compute the first variation I need to be able to compute the gradient I am giving the formula for the first variation of f is given by the inner product of this vector again these are simple exercises these are obvious I did not go into the derivation of each of these things I am trying to hit on various important themes and you have to fill in the blanks for a thorough understanding of all these things the aim of a course like this is not to provide all the details we will not be able to accomplish much if that were the case the aim is to be able to tell all the important concepts to see how things are needed once you understand once you have developed a bigger picture then you can dig deeply into each of these so I would like you to be able to develop that digging deeply as you go through the modules with this we come to the end of this part I have given several exercise problems these are exercises are essentially extensions of the concepts we were we had talked about look at this as an example the first problem essentially ask you to compute the first order Taylor series and second order Taylor series not for any arbitrary H but for a special H when the forms of H are given in a specific way so this will these are concrete examples if you did it you will have that final aha again compute the first variations again verify the different formulas that we have already talked about so doing this in long hand in pencil paper would help to complete the picture here what is the standard reference for multivariate calculus my favorite is a slightly older book but it is still a classic in my mind Apostle mathematical analysis I have a copy of it whenever I get into difficulty which I do very often I fall back on Apostle Apostle is a beautiful written book on multivariate calculus with that we will conclude this discussion and overview of concepts and and and and and and properties that are often used in from multivariate calculus in data simulation thank you