It's hard to say exactly what goes into making a marine, or a man for that matter, but whatever it is, there are two basic elements you always have to have. One is good material, and the other is the right environment. If the marine corps has come to be known for the caliber of man it turns out, it's largely because of the value the corps places on both of these requirements. It may not look like it, but the corps is very careful in selecting its recruits. And when it comes to training them, well, you can judge for yourself. For all marine recruits, processing begins right here. You're now at Marine Corps Recruit Depot San Diego, California. You're about to start your first day of processing. There are five days involved in processing. These five days do not count as part of your training.  Unless you are asked a simple question that can be answered with a yes or a no, and then you will answer yes sir or no sir. While you are here, we will expect you to act as a man. You will be treated as a man. Now on, you will do things to the best of your ability, and you will move as fast as possible. Almost as much a trademark of the Marines as the way they carry themselves and walk is their distinctive hairstyle. It takes some time for recruits to develop the other characteristics, but they can get the haircut in just a few minutes, which is just one of the many practical advantages of this kind of haircut. The haircutting begins the processing, and in a way it's rather fitting because it graphically marks the kind of radical transformation the recruits can expect in other areas. As the processing continues, the recruits get the initial issue of clothing they'll wear during training. The first scrub down in the Corps is the first of countless showers and wash-ups of all kinds they'll undergo in the Marines. The Corps has always been zealous about cleanliness, and upholding the military tradition of neatness and bearing. No matter what you're wearing. The Corps is also very demanding about physical condition, and so examinations are an important part of the initial processing. All of these men were carefully examined before they were accepted as Marine recruits, but the Corps just wants to be sure there's nothing wrong with them now. Those that need glasses will get them. If any bad teas are found, they'll be taken care of while a recruit undergoes training. The Corps also wants to know just what its recruits are capable of, and so they're given a series of tests. Those with some special skills will get more tests. The PT or physical training tests are designed to be equally revealing about the physical condition of the recruits. Those that require it will get extra training and attention. To ensure they meet the requirements set for all recruits. The last day of processing the recruits receive their rifles and other tools of their trade which they'll learn to use during training. Processing ends with the arrival of the drill instructors, or DI's, who will lead them through training. For the recruits, this is probably the most important event of the processing. It brings them together with the men who are going to be personally responsible for their training. During the training, the recruits in each platoon will spend some 16 hours each day under the sharp watchful eyes of their drill instructor. Over the years, these drill instructors have become almost as much of a legend in the corps as its heroes, and rightly so, because they've had a hand in shaping most of them. But like all legends, they've been transformed and exaggerated into something that they aren't. And as a result, they're frequently judged on the basis of what people have heard they are, rather than what the recruits actually know they are. In any case, it's hard to exaggerate the importance of the DI's, and the corps is very much aware of the role they play in making Marines. For this reason, it carefully selects them. Do you feel that you have anything medically wrong with you that would disqualify you for this type of duty? No, sir. Steps on green, you realize that this is a very challenging job and a very demanding job. It'll probably mean that you'll have to spend approximately 80 hours a week at work, and probably have to be away from home every third night standing the duty. Do you want to be a drill instructor? Yes, sir. I would like to be a DI. Then Justice carefully trains them at its drill instructor's school. What? Period of instruction, we're going to be covering the daily seven exercise. You, as drill instructors, must know the daily seven exercise in order to teach your recruits. The daily seven exercise is nothing more than a warm-up exercise. Thank you, sir. Thank you, sir. Please take a seat. Yes, sir. Just out of drill instructor. When they do become drill instructors, they work under the supervision of a series commander who is responsible for all the platoons in a particular series. Thus, whatever he may be, every DI is carefully selected, carefully trained, experienced, and under constant supervision. Well, here in Locke's starting crews, we're just picking the series up on a receiving and we'll be able to get with them all the way through, and they'll be a very rewarding experience. It's a much better starting with them, so I'll be seeing you on the drill field. Come here, buttons on the button. Answer him. Can't hear you. How about getting your weapons fired away? And if he seems brusque and impatient, it's because he has a tough job and not much time to do it. Recruit training actually begins with the DI taking over and telling their platoons exactly what will be expected of them. The first place they run up against these demands is on the drill field. They get more of the same in physical training, where they begin with the basic exercises, and it continues in their classes. This part here located in gray in color is known as... There are also practical applications such as guard duty. Sir, right here, report to post number four, all secure. Post and orders mean the same, nothing unusual to report. Sir, report to post number five. Training in close combat, so hand-to-hand combat is constantly tired and aching these first days of training. Still, the exercises get progressively harder, but they keep at it, and for most of them it pays off. For some, however, it's too much. As soon as the DI spot individuals who are having trouble, they usually work out a program of their own to give them special help. However, when a private's inability to progress hinders progress of the platoon and other recruits, he is assigned to the special training branch. That's just a small part of the contract that each and every one of you people sign when you come into Marine Corps. That's part of the reason why you're here in motivation. Here the recruits work and live with others who have the same problems and special programs are set up to help them meet the training requirements. Some may require additional motivation. Others need help in physical conditioning. Some have medical problems which keep them from participating in the activities of a normal training platoon. For those who find it difficult to obey the rules, there's correctional custody. By the time the final days of the first phase of training roll around, everyone is beginning to feel that they're a part of a team. By now, the soreness and stiffness have begun to disappear. So have confusion and uncertainty. All right, sir. Most recruits manage to find the strength and energy for sports and for competition with the other recruits in training. Drownproofing is a vital part of recruit training. With every man required to swim at least 75 meters, fully clothed and carrying a rifle. By the time they've completed the first phase of training the recruits are considered ready to be introduced to another old tradition of military life. Mess and maintenance duty. The recruits have a week of mess and maintenance during their training. They spend the next two weeks at the rifle range. First, learning how to use their rifles. Weapon into your shoulder, rotating up, keeping the right elbow up high, straight up, bring the elbow well underneath the piece, aiming in, getting a good natural point of aim, squeezing the trigger straight to the rear. Then we're practicing to develop skill. This is one of many opportunities the recruits will have to qualify with their rifle. Fire for score, once a year. Also included in second phase is an introduction to combat training. Here the recruits are trained in basic skills they'll need in the field. They learn how to use a compass. Now then, what we're going to learn today is how to shoot an asthma. Before we can do this, we might not have enough points. Such as the point, if you look to your rear, where the radar, little radar is set up on the hill. Here they have a chance to actually work with mines and demolition charges. The recruits also learn to use grenades properly. Prepare to throw. Infiltration training. Combat training introduces the recruits to the kind of food and living conditions they'll encounter in the field. Practically all training is in the form of exercise. With the recruits actually doing what they're learning, of the training activities take place at night. Tracer displays show the various kinds of coverage produced by different fire patterns. The men return to the recruit depot for the third and final phase of their training. This is a spit and polish period and everyone is very much aware that there are only a few weeks of training left. With the recruits expectantly looking forward to the end of their arduous and demanding schedule. And the drill instructor struggling to smooth out the rough edges in time for graduation. In the meantime everyone continues to drill. The physical training is harder than ever. Still everybody does it. Their schedule is tougher than ever but now they can handle it without straining. For those who display a potential as leaders there is a special program to develop it and make them aware of the challenges and rewards as well as the responsibilities of leadership. Almost before anybody can believe it, graduation day arrives. As far as the recruits are concerned there are really no special preparations. Their barracks are always spotless. Branks and uniforms display the same daily meticulous care. What family and friends of the recruits see here today is no special show but actually the same conditions they could see any day. The big difference of course is in the recruits themselves. For parents and relatives it's well worth the long trip many of them have made to be here. It's a proud and happy day for families and friends. The recruits pride and feeling of accomplishment seems to be contagious. Even the seasoned old mentors who have gone through this many times before feel it and some of those tough stone-faced characters will even sheepishly admit that they feel a great sense of loss every time graduation day comes around. It's an especially proud day for the recruits who receive awards and there are many ranging from the most outstanding recruit to those who have excelled in the different areas of training. But whether or not they received a special award all the recruits have a feeling of achievement. They've earned the right to be called Marines. It takes good men to get through the Marine Recruit Training Program and everybody knows it. There are two facts you can't get away from. It's that the core obviously started with some pretty good men. And it's equally obvious that it did a pretty good job of training them. The whole thing is nicely summed up in the words of one mother who wrote, We sent you a boy and you sent back a man. She could also have said, you sent back a Marine.


Hi, I'm Mark Hall with the Alabama Cooperative Extension System here with John Fulton and we're talking about sprayer technology. John, tell us about keeping your precision spraying on target, minimizing your expenses, minimizing your exposure to litigation. And it's just, that's going to grow.  But at the same time, we talked about it the first part of this, about just the size of the machines, but the dynamics and the terrain and everything else that machine encounters in the field. When you couple all that together and you've got an operator and you're potentially could be driving at 15, 18 miles an hour, there's a lot going on. And when we think about what GPS has done, which we've talked about all that, and the ability of utilizing some of this technology to really improve placement, reduce overlap, verification as it relates to the collecting that as-applied data becomes very important. So, you know, we're going to talk about technology, let's talk about some of these technologies that could help out. And this is just an example of some of the technology or pretty much a majority of the technology that could be put on a sprayer today, Mark. I mean, we talked about the importance of having a good field computer and in-cab display and having that information to the operator and that if you're off-target, on-target, and that's important, right? And if I got to get out and fix or make an adjustment, we talked about telemetry. That's in there. I mean, these sprayers, some of them are coming day with that telemetry piece already embedded in them. And so, but we've got other things in there that we're going to talk about today is boom height control, you know, when we select the nozzle, a lot of times there's a height above canopy that nozzle needs to be run. And again, at the size and the train variation out there, some of the boom height control maintains that. So, if I need to be two foot or I need to be 28 inches, 30 inches, whatever that is, that just automatically maintains independently across that boom, the proper boom height, regardless of the conditions. And so that becomes very important to make sure that we're getting uniform application out there. We've got product control or rate control that we'll mention. That's section control where it automatically turns off and we'll define and look at that just real quick. We've got guidance and now even today, you know, companies are providing and you can put a miniature weather station on. And so you can actually record the current conditions into your in-cap display beyond just what you're applying, where, when and the timing and such. And then the new thing that's really coming on is this pulse width modulation or nozzle by nozzle control mark. You know, we've got companies like Capstan that are with their pin points. So it not only maintains the proper uniform droplet size or attempts to do that, it can change the flow rate. And so all of a sudden we've got all this technology that potentially could provide some value depending on your operation and the type of things that you're, you know, doing out there in the field. Just to give it kind of a tangible thing, our GPS guidance, and this is kind of things that on average is going to give you a 10% overlap reduction. You know, in the old days, we used to run a little bit of overlap just in short coverage, right? Well, that at times got pretty, you know. Dangerous. Pretty, you know, it was 12, 15% overlap. And so we can get that down to almost one to 2% and be consistent. That's a gain. That's money I keep in my pocket when I adopt the guidance. And I think when you look around the least of the United States, majority of the spreaders, especially the large ones, are running GPS. I mean, so that's it done. The rate controllers where it can actually meter product and of course record with the displays. And then the big thing and anxiety is automatic section control where it automatically will look at some examples to explain that a little bit better, but you can just see in that illustration, look at those nice straight lines and even with the train differences that a spreader is going down through that field as straight as an arrow. And so that's the kind of things that not only give me savings, but I just do a lot better job out there in the field during the spray operation. We mentioned automatic section control. We're going to talk about that next, but at the bottom there, that boom height, again, it's so important not only to have the right nozzle for the right product, but boom height control keeps that boom. And you know, usually a boom could be broken up into two, three different sections and independently make sure that each one of those sections are retained at the proper boom height. So you're getting that product applied accurately. That's very important. And I really don't know too many of the least the higher end spares that don't come with boom control, but that becomes a real necessity if you want to do a high quality job and you got a lot of train variation out there in the field. Just an example here, let's talk about automatic section control. It's just, again, using GPS, it turns sections on and off. So if I spray an area and I drive the sprayer into that area, it just, it shuts it off and it reduces overlap. It reduces application in those conservation structure areas, waterways, buffer strips. Today, most of this technology is I can preload the spray area, map the boundary of where I want to spray. And so that is just a real tangible. So in that case, that blue waterway on the left, I can map that out and a controller knows that as soon as it gets to the field when I load that boundary. And so again, it just takes the guesswork out of this and really improves your ability to do a good job and also the savings aspect. Just again, another example, when we think about guidance, you see there in the blue, there's light blue areas are where we've overlapped or we've double applied. But you see where without the technology, I'm kind of driving. I've got a cart a bit of overlap on the adjacent passes. I correct that through the guidance scenario. There on the ends, you see where I'm shooting boom section on and off. That's what automatic section control can give to a grower. Looking at that a little bit different way, we get these application areas at the top there. The blue represents double applied areas mark. The red is missed areas. And so when you drape the technology in particular, the section control over that bottom shows you the same area sprayed without or manual decisions being made by the operator versus the technology. But look at the improvement made. Big improvement. So and you can do that consistently, right? At the technology, as long as it's set up, property is going to be able to do that in morning, afternoon, night, whenever you're out there. And so a lot more consistency as well. Just an example, you know, we say 4.4%. But these are 22 fields that Dr. Luck and Dr. Shearer, when they were at the University of Kentucky. But look at that. Blues manually spraying those fields and the overlap. And look at that one is up into 30%. But you see a lot in that 10, the 20% area. Whereas when you put the section control, look at that. You're down in that below 12%, if not below 5% in a lot of times. But look at the savings, but also going back to being a good steward and not overflying. Tremendous. But the point here is it's all dictated on field size and field shape. And that's why you see those variations across those fields. But again, that's a good way of showing that there's a real tangible. And then of course, we've got these 120, 20 plus booms out there. Now what we see is we've got nozzle by nozzle control. We have cap stand. We've got Raven's Hawkeye system. Deer just introduced their nozzle control. I mean, we're basically similar to what we talked about in the precision seating technology. We're breaking that big sprayer rather than being 120 foot boom. We're basically potentially getting it in the future down to 15 or 20 inch where we're going to control it. And so we can think about how much better we can do with the nozzle by nozzle. This is called Pulse Width Modulation or PMW technology. We basically put a solenoid on each one and then it's regulated of how much comes out to be simple with it.  So if I put a target rate, I'm trying to put 10 gallons, 15 gallons per acre. Now the fact is, and it shows in the picture, the inside is not being over applied and the outside being under applied. So it automatically compensates and maintains that across the boom even when you're doing a current linear. So again, big machines, what it gets into, it's going to be more precise to maintain that target rate that we entered into the display. This is what this, this is a sprayer that was equipped by nozzle by nozzle, maybe a little bit difficult. But again, the operator's coming down, I'm standing on the edge of the road, there's a buffer strip.  He comes over into the buffer strip a little bit and the nozzles turn off. I preserve that vegetated butter for strip. So this is what this can do, it preserves these conservation structures. And by doing it on nozzle by nozzle, you're pinpointing on and off of that very, very accurately. So that's kind of what this pulse width modulation or section control can actually do for you is to help minimize this spray and not where you don't want it to spray. So the other big thing is, and again, thinking about what the crops and what we put this through is the fact is that most of these cab displays, basically with the guidance coupled with GPS, you're going to get a detailed as applied. When timing, you can enter product, any of that and this shows you where you were out in the field and you can have that for tomorrow if someone stops in or if you need, like you were saying, litigation. Hey, I've got a tangible record. Rather than maybe sitting on a piece of paper that I either lost or I got a file and fine, it's right here on electronic verification that I can send someone. I can email that to you as verification mark if I needed to. Would it be handy? So pretty much all the manufacturers, all the technology providers are providing something similar. The nice thing is, is not only do I have it as a map, like a shape file that I can use in analysis, but they give you PDF summaries of everything that went on in that field. So you kind of get a report, plus you get the data that you can kind of use as a spatial data layer for some things too. Well, and if you were trying to cheat and do something off label, this would be, no, no, no, don't do that. Yeah, but. That would resist that temptation. That's right. But again, I think having the records are going to probably suit you better than not having records, so. Some things that I just want to go through some new things to think about today.  Well, today we've got technology, as an example, this spot on sprayer that basically, I just stick it underneath and it takes about three or four seconds and I actually know what the flow rate out is of each and every tip. So calibrating, checking nozzles basically preseason. If you got a season on some nozzles, you better check them so they're not worn. This is an easy way to do it. But again, just new technology can really help us better manage our sprayer and the components, in this case, nozzles out there. The other thing is, this is just an example, TJET provides this technology today, Mark. I mean, it's going to happen, right? There's going to be clogging. And this technology, you see a flow meter in the bottom left, it's mounted right on that spray body and they basically can tell you if you detect clogging, wear, damage, or anything out of the nozzles and it identifies that piece now for you. And so again, we're really getting information that can improve our opportunity here to do the best job we can and may never know in some cases, right? Yes. So, and then the other thing is, there's not an app out there that either a tip company doesn't provide. So when you're talking about selecting tips from this case, just an example, TJET, could be Hypro, it could be Leckler, any of them. They all got apps. It's right there in your fingertips. You don't have to carry that big book around, but if you're out the field, there's calibration information, there's documentation, anything almost that you want to have, label information, product information, and I didn't put it in here, but there are some really cool apps out today. If you're kind of a weed and want to identify weeds and stuff, it's right there on your app. And so, again, these are things that really bring information to you, write to your fingertips and be utilized effectively in your program throughout the growing season, even in wintertime when you're thinking about what you need to be doing. So I just kind of want to end on this. You know, Mark, we come into the fields and typically if they got grass waterways, we spray around those grass waterways, right? We got to spray around them so we don't spray in them. But for zones. But for zones, and that would be in the yellow here. I make those yellow passes and I do a pass or two around the outside and then I start filling in, right? Too easy. But that's what we used to do and today, given that boundary, I load that boundary into the sprayer, okay? And now I don't have to go around those buffers anymore. You know, I don't have to make each one. Think about the efficiency and the time in the field that that reduces having to go from driving around each one of those just to make sure I'm doing the best job to where now I take the boundary, X out those areas I don't want to spray. In this case, the red, I go out there and this is what that sprayer can accomplish out there. More efficient, much better application than what we were doing, per se. So just some ideas here. We just really kind of ran through the technologies themselves. There's some real tangible savings. We talked about guidance, talked about section control, what it could prevent. We greatly improve our accuracy. And then I think from a verification standpoint, we get that as applied data and can be really a potential useful tool force, not only as a report, but even I have that as a spatial data layer if I need to and put that into some of my analysis. And again, I think the big thing is we minimize and eliminate application, potentially going back to where we started on this discussion about drift. I think the technologies can really help, spacing with some of the weather apps and things can really help us make sure we're out there at the right time, plus it's doing the right thing. Wind is gonna make a tremendous amount of difference. And the height that you talked about in this, things we haven't paid attention to in the past, we're gonna have to pay attention to them now. So, yeah. And this will help, and things are changing, but we have the tools that we depend on are changing too. And John, thank you so much for helping us understand this important technology. And we really hope that y'all watch all our precision ag videos. Thank you.


Hi, so I'm Norman. I'm Norman Yopoul. My son received the bike for Christmas. I decided to take him to the park I was on my phone I looked up to take a recording of him and he was literally 100 meters gone I start laughing because he was like dad hurry up hurry up hurry up as I was running literally I was only maybe five meters from where I started couldn't go further My shins my knees everything was hurting. I just couldn't carry on my son walked up to me Are we going home? And obviously my prior was this and he said why? I said because I'm not feeling well And for a kid that age, he shouldn't have a dad like that Two weeks later. I started my journey Waited 175 on that day a few weeks later The weight just started falling off I became more proactive for my baby It just started from there because of that conversation me and my son had the best part of this challenge So many things meeting new people starting and finishing and accomplishing the eight weeks challenge and not only that but just being here right now Would I recommend the EHP fit challenge definitely you just have to keep the faith and keep grinding man


Child malnutrition is a major public health issue in Sub-Saharan Africa, particularly in Ethiopia. This study found that about 67% of households are food insecure, which contributes to high levels of malnutrition among children. Factors such as female gender, older age of the child, having five or more siblings, not receiving zinc supplements, and lack of dietary diversity increase the risk of malnutrition. To address this issue, improved access to primary health care services related to zinc supplementation, growth monitoring and promotion, and infant and child feeding practices should be prioritized. This article was authored by Zellalum Tafis, Fekadu Retta, Buruk Mulu J, and others.


All right, so here's the story. You will not hear anywhere else.  But it turns out that there has been a scheme that has been promoted by certain environmentalists in alliance with certain investment banks to find ways to restructure the debt of developing countries, of what used to be called third world countries, in a way that commits those countries to environmental protection while reducing their debt load. It's called, and I didn't make this up, this is a headline in Bloomberg, it's called the debt for nature swap, debt for nature swap. And this is a new ESG qualifying, this is important, new ESG qualifying, money maker for the investment banks. It's a way for these third world governments to get reduced debt burden. And it's a way for a lot of the environmentalist groups to score a win. And I was reading this and I was going, wait a minute. I get a win-win-win, but there's no way a win-win-win can work here. Somebody has to be held with a bag.  There's a price to be paid here. All right, so I'm going to run through an example for you and we can together figure out who's paying the price and why they're willing to pay the price. And this is really, really important. Why are they willing to pay the price? And this has to do a lot with model high ground. It has to do a lot with feeling good about yourself. It has a lot to do with ESG qualifications. So here's how to work with Belize. Belize is the small country on the Caribbean in Central America. So the Nature Conservancy set up a Delaware-based subsidiary. So let's start off. Belize has this debt, $364 million. They're having real problems paying interest on it. They have people hold these bonds. So the bond, they actually have 553 million bond that the government holds, that it owes to investors. And it's struggling to pay this back. And Belize is a relatively poor country. But Belize is also an important country because it sits on beautiful coral reefs. It's got a lot of, I guess, tropical forests. It's considered environmentally, quote, important. All right, so here's what we do. The Nature Conservatory sets up a Delaware-based subsidiary, call it Belize Blue Investment Company, and raised $364 million from Credit Suisse. So the investment bank, Credit Suisse, gives this new entity Belize Blue Investment Company $364 million. This entity, we'll call it BBIC, the Belize Blue Investment Company. And Blue, by the way, is signifying green. But blue is green in the ocean, green in the sea, right? So BBIC takes this money and loans this to Belize. And Belize uses this money to pay back 553 million in debt at a 45% discount from the bondholders. Now, here's the first thing that you have to ask yourself. Why are bondholders willing to take a 45% discount? That's a big discount. That's a big discount. I mean, basically, these bondholders bought the bonds for $100, and now they're expected to sell them back for $55. Is Belize on the verge of bankruptcy? Is this really, you know, there's so much risk of bankruptcy? And maybe in bankruptcy, they'd get $10 on the 100 that they're willing to sell for $55? What's going on here? Why are they willing to write it down by so much? Now, part of it is that, yes, Belize is probably not the safest people to lend money to, and these bondholders are maybe happy to get some of their money rather than none of their money. But that's not the whole thing, because the probability of Belize actually going bankrupt is not that high. Not that high, I don't think. So what else is going on here? Well, the government has promised to use the savings that they got. So they're going to have to spend a lot less money on debt repayment, all those interest payments that they would have to spend. And they have saved 45% of the bond issuance that they will now not have to pay back. That's being written off. So they've committed to put that money away for environmental concerns. Let me just see. They are going to use it for conservation of the coral reef. They're going to use it for something about mangrove mangrove plants, whatever. They're going to use that money to beef up environmental protection and fragile mangroves and coral reefs in the Belize area. Now, why would investors care about this? Well, investors care because they get to say they're the good guys. They get to pat themselves on the shoulder. They get to declare to the world that they have been good citizens, that they have been moral, that they are willing. They've invested in green stuff. They probably get some ESG credits. Some of these investors, my guess is most of these investors are institutions. They're not individuals. And they get to put some kind of ESG gold star next to their name in the future. They get a lot of this good stuff attributed to them. And for that, instead of making a charitable contribution to some institution, they actually got to write down some debt instead, which some risk was associated with it. So they get, in a sense, a charitable contribution, which they write up in taxes. They get a gold star for being good environmentalists. And they get a little bit of cash from selling the bonds that might have been worth less than the cash that they raised. But probably not. They're probably worth more. So that's one half of the transaction. But now, Credit Suisse has $364 million. They have given a loan to Belize for $364 million. What's Credit Suisse going to do with this loan? Credit Suisse, then, creates a special purpose vehicle in the Cayman Islands. And it issues $364 million in blue bonds to finance the deal. Remember, every time the bond has a blue next to it, it gets that gold star. And it probably gets that ESG stuff. And it gets all kind of social environmental credit for what it's doing, because blue is green, just applies to oceans, something like that. So then, the special purpose operation then sells these loans. Now, the loan is smaller. So Belize only has to pay now back a loan of $364 million instead of $553 million, because the investors had to write off. Now, Credit Suisse, who owns this loan, now has to sell bonds to make up the $364 million on its book. So it then basically then, once that happens, the Belize now has new bondholders that bought the bonds from Credit Suisse, from the special purpose entity in Credit Suisse, in order to finance all of this. So Belize now has to pay back a new smaller loan from BBIC. Remember, there's Belize Blue Investment Company. Over 19 years, with an interest rate starting at 3%, rising to 6% in 2026. It must set up a $24 million conservation endowment. So this is what Belize has to do. It sets up this conservation endowment. And it commits the spending $84 million on conservation and to protect 30% of the oceans. Now, here's an important part of it. It turns out that Credit Suisse is having trouble selling this new debt to investors. Because, hey, what's behind this debt and how do they know it's going to pay back? Is Belize really behind it? Is Belize capable of paying back? Nobody really wants to buy this debt, even though it's blue. There's a real challenge. So guess who steps in here? So in order to facilitate this final piece of selling the bonds to other investors in order to fund this whole chain, this whole transaction, and free up all this money for conservation, what is required is that the US International Development Finance Corporation, I don't even know that you knew that such an entity existed. But the US International Development Finance Corporation, it's not the IMF and not the World Bank. This is a US entity directly US, insured the BBIC loan. So it sold insurance. It basically didn't sell insurance, provided insurance over the BBIC loan. Basically, putting the US government on the hook, it believes can pay. So if Belize can pay, the bondholders will sit at the end of this. Belize now owns $364 million, really, to this credit suites entity, which owes this money to the people who bought its bonds. If that chain is broken, you, most of you, not all of you, the US taxpayer are now on the hook for it. So this is beautiful. Belize cures a $553 million deficit with a plan that saves its oceans. And this is amazing. It cut the country's debt by 12% of GDP. It reopened the country's access to financial markets. Redirected money from destined-for-found creditors into the local economy, primarily into local environmental protection. Belize then promised to fund $180 million over two decades to protect its oceans. And investors were glad to have backed a worthy cause. They got the goldstone. This is beautiful. A combination of public funds, public private enterprise, private funding, public initiatives, win, win, win, win, win, win, everybody wins, except. The initial bondholders lost. They took a big right off off the debt without going into bankruptcy, without seeing maybe they could get a much higher amount. They might have been able to get 80% of their money back. Instead, they only got 55%. We, the taxpayers, got hit with insuring something, probably is going to be OK. But imagine this on scale. We're talking about now taking this model from Belize and going out there and offering this scheme to countries in Africa, to countries in South America, to countries in Asia, all over the world. Sri Lanka wants to do this on billions worth of debt. Is the United States taxpayer going to be behind all of this? And if not the US taxpayers, the IMF is the US taxpayer in the end, or the World Bank, which is the US taxpayer in the end. And this is not global. This is not global sovereignty, governance. This is US governance. This is the US doing all of this. This is ultimately the US government providing insurance. There's no governance here. This is a multinational deal involving many countries. But there's no, the governance is all going to be local governance. There'll be, you know, the bonds are going to be under the laws of the Cayman Islands, the insurance is going to be provided by the US. That's not global governance. There's no global entity here. Indeed, the World Bank and IMF are global governance. The IMF and the World Bank do what the United States tells them to do. It's the number one shareholder. It is the dominant player. It provides them with all the funding. I mean, there's this fallacy that there's some kind of global governance going on in the world. There is no global governance. It's whatever the US wants. And in some cases, what the Chinese want. Nobody cares what most other countries want. They can vote on it all they want in the United Nations. Nobody pays attention to the United Nations. Doesn't actually do anything. World economic forum is not global governance. It's a gathering. It's a think tank. They advocate for global governance. They would like to see global governance. But there is no global governance. They have no direct, legally enforceable in any kind of sense. All they can do is advocate for ideas and try to influence people through ideas. They have no power, zero, zilch power. I know. Catastrophizing. Keep at it, guys. Keep catastrophizing the world. It really helped. Anyway, this is a scary scheme. Not so much because of beliefs, but because of the potential of this to escalate and to grow and to become huge. By the way, guess who makes money off of this? Guess who does very well in a scheme like this? They make money no matter what happens. No matter what happens, they make money. Credit Suisse. Yes, the investment banks. Investment banks are facilitating this. The investment banks are taking commissions left and right. Now the investment banks might be buying some of these bonds or selling some of these bonds. They might not be making a lot of money on that. But they are making huge amounts of money off of the consultants and the lawyers and the people who say, all the people that came in Ireland who set up these entities, who monitor these entities, the people, and of course, believes did well. A lot of people make a lot of money here. Indeed, this is very, very, very expensive to set up. One of the complaints against this is how expensive it is.  They view this as a sellout, a way to, yes, maybe it protects the environment, but it's a way of selling out. They're much easier, better, more direct ways to do this. Maybe believes could just default on the bonds and then take the savings and invest directly in it.  But I also want to emphasize here the power of this idea of getting a gold star. ESG is not without real implications to help people invest. But this idea that it's moral to sacrifice for the environment has a real impact on people and the way they invest and the way they allocate capital has a disastrous impact on allocation of capital. And this is an example where they feel good, they're willing to take a huge hit cut, they're willing to take a huge loss in order to pretend that they're better off. And there you have the power of moral persuasion. It's really quite amazing that this goes through and it's big and it's getting bigger. So this is a story, I think, from today or yesterday. I mean, no, actually late 2022, debt for nature swaps gained traction among developing countries. Green ESG, this is all under the Green ESG title, 58 of the world's developing countries, 58, most vulnerable to climate change, have almost 500 billion of debt servicing payment due in the next four years. 500 billion, imagine doing this at $500 billion and imagine if the United States actually, actually got guaranteed all this, 500 billion. Now that's the kind of news you're not gonna hear anyway and not gonna get critiqued. By the way, the subheading of this story, which was yesterday, this is so, Wall Street New HD Money Making Promises, Nature, Conservation Without a Catch, or With a Catch. The subtitle is, Belize is Home to a Threat and Call a Reef in Mountains of Sovereign Debt. It became a test case for a new kind of finance that mixes debt relief and environmental protection. The world is insane people, it's crazy. And this is just another headline, I don't have time to talk about this, this is another headline. Why fund managers started worrying about biodiversity? See that, you know, if I must realize that if they really wanna get an impact, have an impact on the world, they need to get the financial community behind them. That's the whole basis of ESG and here you get biodiversity, what's that gotta do with finance and it goes on and on and on. And these things get entrenched, you get whole institutions dedicated to these causes cause they make money off of them and it's almost impossible to fight at that point. Thank you for listening or watching the Iran book show. If you'd like to support the show, we make it as easy as possible for you to trade with me. You get value from listening, you get value from watching, show your appreciation. You can do that by going to iranbrookshow.com slash support, by going to Patreon, subscribe star locals and just making a appropriate contribution on any one of those channels. Also, if you'd like to see the Iran book show grow, please consider sharing our content and of course subscribe, press that little bell button right down there on YouTube so that you get an announcement when we go live and for those of you who are already subscribers and those of you who are already supporters of the show, thank you. I very much appreciate it.


Okay, what's the sound? Yeah, there's some, okay, what? Try to what? Yeah, I'm talking. It is on at this recording in progress, it says. Okay, so it's a pleasure to be here and give a talk for the birthday of Tom Rofka, the star whom I know for many years and know for even longer. So you can remember when I was a postdoc hearing a talk about the structure formula for Donaldson invariance by Komama Mofka, and then later I had to talk in the Albert Star, who was still as a postdoc about the new cyber-quitment invariance. And I've met him occasionally over the years.  And so, yeah, I wish you happy birthday. So this also reminds me of the times when people in gauge theory were still talking to me because I was doing things related to gauge theory, but now I do algebraic geometry. And so let me talk about computation in written invariance. Okay, so we talk about... I want to talk about modular spaces. So in algebraic geometry, we look, for instance, at the modular space of semi-stable bundles on an algebraic surface with an ample class. So modular space would be a space parameterizing some interesting objects and mathematics. And in differential topology, everyone could talk about the modular space of a mid Einstein matrix on a fixed complex bundle with, you know, with an opinion study metric. And then the Kobayashi-Hitching correspondence says that there's a homomorphism between these two. Usually one considers complications between these two spaces. In algebraic geometry, the modular space of semi-stable coherent sheaves is the rank R, Schrodinger class C1, C2. And in differential topology, or gauge theory, the Ulmberg complication by ideal instantons. And these have been used, for instance, to... Yeah, you can turn off the sound. Also bothers me. What? Oh, it was mute. No, no, no. It was mute. And so this allows us to compute Donaldson variance in algebraic geometry of algebraic surfaces. And now it doesn't want to. Okay. So now let's look at, in algebraic geometry, we take a project of algebraic surface with a hyperprint class. And I will assume during the talk that the first vector number is zero, or maybe even that it's simply connected. So the B plus, B2 plus of S should be bigger equal to three, which is equivalent in algebraic geometry to Pg being bigger than zero. So that means there's an everywhere... There is a non-bendishing holomorphic two-form on S. Then we want to look at the modular space of rank R semi-stable sheaves on S with given Schrodinger class C1, C2. I've written down what semi-stable means in algebraic geometry. It means that the sub-sheaves are not too big. They don't have too many sections. So a sheave you can think of if you don't know what it is as a vector bundle with some singularities. And now this modular space in algebraic geometry will usually be singular. It has something which is called expected dimension, which is this number I've written down here. And this BD, we don't know in the moment precisely where this number comes from. It's the expected dimension. It's the dimension that the modular space should have. Now we will have to understand what that means. Where does it go? Okay, so just... If I write the number like C2, I mean obviously the evaluation of C2 on the fundamental class of S and so on. So now, what I've written in advance, I will talk a bit more about them later, but I first give a first approximation. So for instance, in the original paper where I've often written, there was a conjecture formula for the generating function of the Euler numbers of the modular spaces of the rank two sheaves with given first-journ class and running second-journ class in terms of modular forms. So let me state this briefly. So for simplicity we assume there exists a smooth connected curve in the canonical linear system. That means there is a zero set of holomorphic two form which is smooth and connected. This is just for simplicity. And then again we have these intersection numbers. There's ks squared, which is the same as c1 of s squared and we have chi of 4s which can be expressed like that. The holomorphic Euler characters which can be expressed like that in terms of turn numbers. And in this case, the virtual dimension of the modular space is given by this formula that I wrote there. And then the conjecture of Waffa and Britten or the formula of Waffa and Britten is the following. We take this eta function which is a standard model of form of weight one-half and we take the theta function for the lattice z. So sum over x to the n squared and then we have the generating function for the Euler numbers of the modular spaces just in terms of this. So we write down this expression 1 over 2 eta of x squared to the 12 to the chi of 4s and the other term to the ks squared and we take the coefficient of x to the vd. The vd is the virtual dimension of the modular space I'm talking about in terms of the general class of c1, c2 that I've written on the other side. So this is the formula. Now there's... Well, you know, so on the same surface, you know, it depends for one thing, but yeah, so if you fix the surface, which is given by ks squared and chi of 4s, then the modular space of the same virtual dimension have the same order, I guess. So that's our only way to precisely like that. Yeah. But you know, okay, so this is the formula. But one should maybe be a little bit careful because it's not quite clear whether this is actually true. I mean, this is the Waffa-Witten formula, so this is actually... We now want to see in what sense this might be true. So this modular space will usually be in algebraic geometry quite singular and its dimension might be different from this virtual dimension. So in differential topology or geometry, one then usually takes the equation which defines the modular space, one deforms it and one looks at what one is given. Algebraic geometry, one doesn't do that. One keeps the modular space as is and adds some virtual structure and remembers what would happen if one wanted to deform it to something smooth. And so this extra structure is given by an obstruction theory of dimension BD. So I want to briefly say what that roughly is. And this obstruction theory then allows us to define virtual analogs of all the invariants of smooth varieties. So what is this thing? So at every point in the modular space which would correspond to a sheaf, we have the modular space as a tangent space which in this case is this vector space x1, ff, trace 3. So if f is locally free, this is just h1 of the enomorphisms of f, trace 3. And the obstruction space is the x2. Miemann-Roch will compute that the difference of these dimensions of these two vector spaces is the number VD. And the Quranishi tells us that there will be an analytic map, the Quranishi map from a germ, from a neighborhood of the tangent space from 0 in the tangent space of the modular space at f to the obstruction space such that an analytic neighborhood of our point f in the modular space is isomorphic to the inverse in which of 0. And so for instance, if the obstruction is 0 or this Quranishi map is a submersion, the modular space will be non-singular of the dimension of the virtual dimension, but otherwise it could be also very singular. And so now we want to capture this in some virtual sense. So a so-called perfect obstruction theory is a way to capture all the tangent and obstruction spaces at all points in the modular space at the same time. So it's a complex of two vector bundles of finite rank, holomorphic vector bundles on the modular space, such that for every point in the modular space, the tangent space at that point is the kernel and the obstruction space is the cooker. So, you know, as I said, it means we have kind of tied together the abstractions together via two vector bundles of finite rank, holomorphic vector bundles. And then we can define things. So we have the so-called virtual tangent bundle, which is just a formal difference of these two vector bundles. The virtual dimension is the difference of the ranks of these bundles. And the difficult part is that one construct the so-called virtual fundamental class, so a class in the homology corresponding to the top homology of a smooth, complex manifold of dimension, the virtual dimension, which behaves like the fundamental class in some way of a smooth manifold. And so this is actually the difficult part, but anyway, one can do that. And then one can define a virtual version of the order number, which is just the integral or the evaluation on the virtual fundamental class of the top general class of the virtual tangent bundle. And then our conjecture, which has been confirmed in many cases, is that the rougher-witten formula will hold if we replace the actual order number of the modernized space by the virtual order. Okay, so we have this. So this is kind of the first approximation to the rougher-witten statement, but rougher-witten actually look at something more general, which I just gloss over very fast because I don't even know precisely what the symbols mean that are here now, because you are the experts, and I'm just the amateur. But anyway, we have, say we have a Riemann Romanian manifold, the 4-manifold with the SUR bundle on it. Then rougher-witten in the original paper asked us to count the solutions to a pair of PDEs for a connection on E and two fields B, a self-dual 2 form in the joint bundle of E and gamma 0 form in the joint bundle of E, which is given by this formula. So this bracket with the point is somehow the lead bracket together with the contraction. So if you look at this, it's what does it mean to count solutions to such a thing, this B and gamma both are completely unbounded, so it seems to be impossible to make sense of saying we want to count the solutions of this. Now Tanagan and Thomas have found a way to translate this. So if you have a scalar surface, this becomes, if you can reformulate this as a statement about a vector bundle and an endomorphism of the vector bundles with values in the holomorphic two forms on S, and so then they define an algebraic geometry, the analog, so let S H be a projective surface with an ample divisor. A Higgs pair on S is a pair, E phi of a torsion-free sheave on S and a homomorphism from E to E tensor KS. KS is the bundle of holomorphic two forms, which is trace-free. And there is a modular space of stable such sheave where the stability condition is similar to the one we had before. And then, so we have this modular space and this modular space also admits a perfect obstruction theory which is what is called symmetric which means that at every point the tangent space is dual to the obstruction space. So that means that the expected dimension of the modular space is zero. So kind of virtually this is a finite set of points. And so we should define the Waffa-Wittnien variant as the virtual count which is the integral over the virtual fundamental class of this thing of one. Now there's a problem with that obviously because we still have no compactness. Now we have this parameterizes pair of a vector bundle and this this Higgs field so homomorphism from E to E tensor KS which can be rescaled arbitrarily so it's not compact so there's no virtual fundamental class. So then one uses a trick. So if this thing was compact one could compute in a different way by the bot residue formula. So you just integrate over the so you have there is a C star action on this modelized space by just rescaling the Higgs field. And so then the bot residue formula would say that you can instead integrate over the fixed points of this action one over the Euler class. Now there's a virtual version of this where one does everything virtually. So one there's a virtual fundamental class induced on the fixed point locus and this has a virtual normal bundle which is the part of the tension the virtual tension bundle on which the action is of this C star is non-trivial and then we just formally write down the bot residue formula and we define this to be the integral over one on the modelized space. And so this is then the definition of the buffer written invariance. Now if I want to study this one has to see what this fixed point locus can look like. So I claim now that this fixed point locus has a decomposition parameterized by the partitions of the rank of the bundle. And this is as follows to a partition lambda we get the part where the E splits as a direct sum of sheaves of rank lambda i and the now equivalent map which you know C star equivalent map phi, if we have a fixed point has the will then be, has to be in such a way that it's just always maps E i to E i minus one, tens of K s. And obviously then the last map has to map, has to be the zero map. And so we have in particular two special components. One is a so-called horizontal component where the partition just consists of the trivial partitions where it's just E and the map phi is the zero map. And so that means this modelized space is nothing else than the modelized space of sheaves of rank r with Stern-class C1 C2. And we have the vertical component where this splits into sheaves of rank 1. Now, so there are all these wonderful numbers we have defined so we can put them in a generating function.  And so that means this modelized space of the Waffen-Witten has virtual dimension zero. And so we look at this generating function and then according to what we said we can write it as a sum of such functions one for every partition of the rank r. No, it's just that lambda will parameterize the contribution of the fixed part corresponding to the partition lambda. Okay. So let's look a little bit at the so-called horizontal part so where the partition is trivial. So as I said, the modelized space of sheaves has a perfect obstruction theory of virtual dimension vd and we have this virtual Euler number and then Tanaka and Thomas show that this virtual Euler number is up to sine just equal to the contribution to the Waffen-Witten invariance corresponding to the to the horizontal part and so we see that this generating function this part of the partition function corresponding to the horizontal partitions is just the generating function for the Euler numbers of the modelized space. So in particular the Waffen-Witten partition function contains the generating function for the virtual Euler numbers as part of it. And so the formula that I mentioned in the beginning comes from that. Now there is something called S-duality which is the origin for the fact that there should be modular forms in this and so this predicts the behavior of this generating function under modular transformations. So you should have SL2z somehow acting on this generating function and something nice should happen. So that means we write Q as the I tau where tau is from the complex upper half plane and then you have the two operations which generate SL2z is tau goes to tau plus 1 which sends Q to itself so this doesn't change the generating function but the other one is tau goes to minus 1 over tau so the non-trivial element and something should happen there and kind of be the and so this has to do with looking at the so-called the partition function for the Langnitz-Duell of SUR so we sum over all cosets of H2 of SZ minus R times H2 of SZ with a sine ER as a R-thruit of unity we take the generating function the SUR partition function for C1 equal to this W so it only depends on C1 modulo R times H2 and so we take this generating function and the statement is of W for Witten also is that if we replace or I mean our version of it that if we replace tau by minus 1 over tau so the non-trivial element in SL2z so when Q is equal to E to the pi out tau then up to sine and the simple transformation factor we just get that the SUR partition so our partition W for Witten partition function from before translates into that for the Langnitz-Duell and so it is not completely evident but if one works out what this means in concrete cases one finds that this operation will interchange the contributions of the horizontal and the vertical path and it is known by Thomas that if the rank is a prime number then the contribution for partition will only be non-zero if the partition is either the trivial partition R or it is 1 to the R and so the whole partition function consists only of these two parts and they get interchanged by this S2 additive transformation so using if we believe in S2 additive as a prime number then if we know the vertical partition function we know all the Waffen Witten invariance so this is our motivation for looking at the vertical Waffen Witten invariance now so again write down a few model of forms there is the eta function there is delta which is the most standard model of form eta to the 24 and I also look at the teta function of the ER lattice so is that to the R intersection matrix given by the ER matrix so we have the 2's on the diagonal 1's on the diagonal things next to the diagonal and then we maybe minus or anyway okay and so and we also introduced this delta AB which is just saying if we have two numbers in the second comology we say delta AB is equal to 1 if A is congruent B model if A is H2 and 0 otherwise so we always and then there is this theorem kind of structure theorem for this vertical partition function so there are some universal power series which do not depend which only depend on the rank R so they are independent of anything of the surface or whatever we are interested in C0 and Cij for one smaller equal to i smaller j equal to r minus 1 such that for all polarized surface and all C1 we have this generating function is given like this we have something with the delta function to the holomorphic Euler characteristic we have this teta function so this with the 0 is the same as the one without the 0 divided by eta to the minus KS squared and then we have this universal power series C0 to the KS squared and then the sum over all r minus 1 triples of classes beta i and then the contribution is only non-zero if C1 is congruent to the sum of the i times beta i and then we have the product over the Ziber-Gritten invariance of beta i times Cij to the beta i times beta j so this is the formula and we have only these unknown power series that the Ziber-Gritten invariance I use the algebraic geometry convention so the Ziber-Gritten of Bi is what you would call the Ziber-Gritten invariant of 2 beta i minus KS so that it becomes a characteristic homology class and to simplify what I say later if the canonical linear system contains a smooth connected curve then there are only two non-trivial Ziber-Gritten invariance so which are not zero the Ziber-Gritten invariant of 0 is 1 and the Ziber-Gritten invariant of KS is minus 1 to the KiO4S all other ones are 0 so that then the formula would become a bit simpler but that's a method if it's called theorem it's a theorem if it's a physics theorem it's called conjecture no I mean that's yeah I mean okay but you know so now so we take the non-trivial part of this thing so everything in the lower line so everything which we don't know explicitly and we put it as a new generating function so if we know this phi we know all the the vertical we want to compute them so now we compute them we are able to compute them at least to get a concrete conjecture up to rank r equal 5 and again for simplicity to make the formulas look simpler as we turn out to be more than complicated enough we assume that KS contains a smooth connected curve so that we don't have to sum over Ziber-Gritten class and so so I put some notations so we take a quotient of two such theta functions for the AR lattice one is the one we had before and now one shifted by some class in the AR lattice and we call this TAR and so it's a quotient of two modular forms of weight one of a certain weight and so it of the same weight and so it's a modular function kind of invariant under the action of the modular group and then again I recall this definition of the delta AB and then with this which we have the following so we can first look at the rank 2 case so in that case the conjecture of afferent Witten that I said before if we take the s duality relating the Euler number to the vertical invariance and then put this together with this translate into this formula so that this phi is just delta so it's it's one if c1 is equal to zero the first part and then if c1 is equal to ks then it's minus one the chi of s of this quotient of theta functions so this is this and then this is the rank 2 case rank 3 case is a little bit more complicated but not much so we have contributions only if c1 is equal to zero ks or minus and we still have these theta functions now for the e2 lattice not for the a1 lattice but in addition we have this x plus and x minus which are the roots of a second order equation so we take kind of in so we know that this ta one is a modular function so modular functions are filled so these are again modular functions in some kind of extension field and so we have this and then now I will very quickly go to rank 4 and 5 because it gets more and more complicated and basically incomprehensible but you know just to see that there are explicit functions and that one can work them out and that the problem is not simple there's not a simple answer there's a complicated answer which we don't completely understand and in particular it's not so clear how one goes to get so much more complicated time so this is the conjecture for rank 4 so we see the structure the general structure is the same we have contributions when the first term class is zero order 2 ks or minus ks or plus ks and we have again these quotients of theta functions for the a3 lattice play a role but we also in addition have this continued fraction of Ramanujan which is the simpler which is a nice modular form which also has this product function in terms of theta functions and then finally we again cannot just take kind of the ready made modular forms but we have modular functions but we again have to solve this quadratic equation in modular forms to get this addition to Z so but anyway you can see it's a very complicated it looks very complicated but you know it is completely explicit so we know all the if all the of written invariance if we have this this formula yeah yeah yeah well I mean no we haven't really figured that out I mean it's somehow also not maybe enough cases I mean it's obviously you have you know it's some extension of gamma zero and but it's even bigger than that and so I mean all the group is even smaller so I mean we don't know precisely I mean obviously that would be very important to figure out but I mean in some sense as we can only do one at the time I mean we haven't even kind of tried to figure out where precisely these modular functions live maybe that would be a reasonable exercise you know I mean obviously you can work it out there but and then I very quickly flashed to you the rank 5 one so there this is done in terms of the Rajas or just Ramanujan continued fraction which is maybe one of the most well-known continued fractions and formulas of of Ramanujan so you have this continued fraction which can also be written as this infinite product and then we get this amazingly complicated formula but you know at least we can see the structure is the same so we have a contribution if C1 is 0 KS minus KS 2KS minus 2KS for all the the cosets of you know of multiples of KS mind modular 5 times KS and then we have some so we have this in addition I which are certain expressions in this Ramanujan functions and finally we have these theta functions now for the A4 lattice it's always AR minus one and then we now have to add to this thing the solutions of three quadratic equations in modular functions and so this is the most complicated formula that I want to present and but you know I just the point is there is a formula which is completely explicit unfortunately it's not the formula of the kind which one would think are I know these ones so okay then it's obvious for 6, 7 and 8 it must be this because there's a clear pattern at least in my mind there's no clear pattern okay and now we want to go to the whole Wafawit-Ninven it's not just a vertical one so we conjecture a similar structure formula to the one of La Raca for the horizontal Wafawit-Ninven now which is the same as the generating function for the order numbers of the modular spaces of sheaves and so in this case everything is kind of dual we replace the AR lattice by the dual of the AR lattice so the intersection form is replaced by the dual matrix and we take a similar quotient of theta function for this dual lattice and then the conjecture is very similar to the one before so we have some trivial pre-factor then we have a certain expression so eta 1 over q to the 1 over r to the 1 half to the square for s we have something to the ks squared and then we have again unknown power series d0 to the ks squared and di j to the product of cyberquitten classes and then we have some over r minus 1 tuples of cyberquitten classes the product of an rth root of unity to the i times beta i times the first churn class we are talking about so in this case the formula does not only depend on the rank and the surface but also on the first churn class in this form and then the product of the cyberquitten classes of these beta i's so this is this formula where these d0 and di j are universal power series which only depend on the rank what is di j well I don't know in general what I mean I haven't thought about if one puts q equal 1 I don't know whether I mean it's not clear to me why I mean so okay you have a model of formula so you could go to the cusps and see what happens there okay so that's maybe an interesting question but obviously you could go to other cusps in some sense you can see that we see in a moment that setting tau to minus 1 over tau replaces the di j by the c i j so one thing is that if you go to one other cusp you replace horizontal by vertical and vice versa so in that sense there is this thing I mean if you are near so not just go to the cusp but the neighborhood of the cusp so if that's maybe not your question but let me just say it so so S2LET translates into relation between the di j and the d0 and the c i j so this one can actually kind of see that this is reformulation and so and it's a very simple relation if I put q equal to 2 pi i tau tau is in the upper half place then d0 of tau is c0 of minus 1 over tau and di j of tau is c i j of minus 1 over tau so the simplest possible relation so the value of a certain cusp of the di j is equal to the one of c i j at another cusp and also the development in the neighborhood of a cusp of one is equal to the development of the neighborhood of another cusp so in that sense I mean don't know where that helps your question and so thus conjecturally we know all the rough of it in variance in ranks up to 5 so in particular we know the Euler numbers of the modular spaces and in fact one can easily work out what this means we have explicit expression in terms of modular forms or modular functions of the what d0 and di j are and so c0 and c i j are so we can also the things with explicit formulas for the d0 and di j up to rank 5 okay I don't know how much what is the time so I have still a few minutes no so then I can say a couple of words about why one should believe in all these conjectures you know what kind of work we actually did instead of just sitting and having some interesting dreams about numbers so and so I want to briefly say how one can check these conjectures and find them so so let me talk about the horizontal of a written no the vertical of a written invariance so this the part the vertical part of the modular space as we had seen parameterizes pairs e phi phi is the Higgs field where e is a direct sum of rank 1 sheaves the map phi always sends e i to e i minus 1 so in a chain like that so if I have a sheaf of rank 1 on a surface it is the ideal sheaf of a zero-dimensional scheme so basically finite set of points tensorized by a line bundle and so the zero-dimensional schemes are of length n so corresponding to second Schrodinger class equal to n are parameterized by the Hilbert scheme of points and the we had this phi is a homomorphism from e i to e i minus 1 tensor ks so that means that if e i is equal to i z tensor l i then l i minus 1 tensor l i dual tensor ks must be effective so there must be a holomorphic section of this okay so we are in this situation and so we can work so therefore our thing is given by the ideal sheaves of r sub schemes so points in the r-fold product of the Hilbert scheme of points on the surface and so if we fix these bi so these the first-journ class or whatever or just a line bundle l i minus 1 tensor l i tensor ks for i from 1 to r minus 1 then this fixes a component of this fixed-point locus corresponding to 11111 where these line bundles are these and this component by forgetting the line bundle projects down to the product of Hilbert schemes of points so if we take the generating function this is subjective so we get the whole we get all the Hilbert schemes of points like this if we do this and we have the restriction of the virtual class on them on this of a written fixed component and we have can restrict it to this thing corresponding to beta and we can push it forward to the product of Hilbert schemes and one can explicitly say what it is so it will be a product of these cyber-gritten invariance of these bi where these bi say are the first-journ class of these line bundles that are called bi multiplied by some class gamma which depends on this beta cap product to or whatever with the fundamental class of the product of these Hilbert schemes and so if you want to where this gamma of beta is an expression in certain classes of certain universal sheeps on the Hilbert scheme there are kind of two kinds of universal sheeps so which I have written down here one is the basically the ideal sheeps kind of globalized over the Hilbert scheme we can tenserize them by line bundles and the other one is structure sheeps of the sub-schemes I mean globalized okay so we have these universal sheeps and so we have this expression which is explicit in these things and then there is an old result with Elling student-learn that if you just have one just on the Hilbert scheme of points you take any integral or evaluate any expression then this can be universally expressed so independent of the surface just in terms of the holomorphic Euler characteristic as a polynomial in the holomorphic Euler characteristic of the surface ks squared ks times this line bundle to which you make the universal sheaf and see one of the line bundles squared now we globalize this over the product of the Hilbert schemes and then we get this expression that these universal power series c0 and cij of q depend only on the vector of these intersection numbers I wrote here on the surface namely ks squared bi of ks, bi times ks and bi bj so they only depend on this tuple of numbers and so we can compute what they are in general by looking at as many examples we just need to look at as many examples as we have as there are elements in this vector which are such that the corresponding vector of numbers is linearly vectors of numbers are linearly independent then what we compute for them will determine c0 of q and cij and therefore the invariance for all surfaces so now in this case we can just take linearly independent tuples we can take our surface just to be p2 or p1 times p1 and then vary the bi, these line bundles so on p2 or p1 times p1 we obviously have an action of c star times c star with finally many fixed points and we choose line bundles to which this action lifts so equivariant line bundles to this thing so so then one can show that in this case the action on the surface will lift to an action on the Hilbert's scheme of points which still has finally many fixed points and these fixed points are parametrized by tuples of partitions of n if we take the Hilbert's scheme of n points and so therefore we can now use localization so what residue formula what localization to compute c0 of q and ci of q in terms of the combinatorics of partitions now as we are not smart enough we don't find a nice closed formula in terms of whatever symmetric functions and so on but we just put it on the computer we compute up to a very high degree in q and we know the first whatever 20 coefficients of this power series and these are enough to to guess and check that the formulas or the formulas I told you are will be should be the right ones and then I should also say that we have this relation between the horizontal and the vertical invariance so the horizontal invariance can be treated in a similar way there is a so called Mochizuki formula which computes virtual intersection numbers on the on model space of sheaves to other more complicated intersection numbers of river schemes of points which however can again be related to intersection numbers of universal sheaves and so then we can use the same method to compute them and we see that we can also compute it's a bit more complicated so it takes also more effort to the computer but we can compute something and this gives us shows us that this s duality holds up to a high level and for instance that the relation between the d ij and the c ij is true up to the level we can compute and so we are confident it's true okay so this was all I wanted to say yeah they involved no so I mean the thing is the Waffen-Witt makes some assumptions like for instance they this is some I don't know whether it's precisely this assumption so for instance they might make the assumption that the canonical that there is a that the canonical contains a smooth connected curve or otherwise they have an expression when they have a more general formula they have an expression in terms of the connected component of the canonical curve and now one can translate that you know once one knows what cyber grid invariance are then this formula this expression in terms of the connected components of the canonical curve is precisely in terms of cyber grid invariance so the connected components of the I mean essentially the connected components of the of the canonical divisor are the cyber grid classes I mean in this algebraic formulation so in that sense it's just I mean the cyber grid invariance are in some sense in their formula only it's before they invented them yeah so you'll say one shouldn't expect new invariance from these formulas no I mean the the whole yeah so this whole thing somehow shows that I mean I mean everything that I've ever computed with these modular spaces always can be expressed in terms of of cyber grid invariance plus some universal power series so it appears that these modular spaces at least if one computes invariance like this do not seem to contain any more information than the cyber grid invariance that's true so if one is interested in finding invariance to classify for many folds it's kind of nonsense to to do this but I'm more interested in the structure of the formula


Good day, fellow investors. As said in the previous video about my 2018 strategies, one strategy that you need to have as a hedge for whatever happens, especially if financial turmoil hits the global economy, is to own gold hedges. You can own gold in a physical way, however I prefer to own gold miners. Much more leverage, much lower necessary investment to get the benefits if gold prices increase. So let's see how can you approach gold miners for an all-weather portfolio perspective, how much should be allocated to such investments and what are the risk and rewards. This is the gold price since 1973, since gold has been de-packed from the dollar and you can see that in that time there are long periods where gold prices don't go anywhere or even decline, but there are also times like in the end of 1970s, 1980s where gold prices spike even 10 times or in the 2000s when that also happened. When investing in gold you have to also be expecting what happened from the 1980s, where gold prices went nowhere for 20 years. This is again something that can happen. However, if you own gold miners, even if in 20 years they explode, which they probably will, you will make 10, 20, 30, 50 times your money as it has been the case for those who invested, let's say, gold miners in 2001, 2002 or in 1975. So from a risk reward hedging perspective, it is extremely important to own gold miners because by selling them in case of financial turmoil you can buy whatever is left in the crisis later, rebalance accordingly. Nevertheless, you have to expect a lot of volatility. New month mining increased fivefold during the 2000s but also decreased 90% after 2011 and as gold prices fell. So you have to see how much can you weather, so you have to see what you own. Okay, if a gold miner that I own decreases 90%, what is the hit that will be for my portfolio? If you have 5% of your portfolio in gold miners and they fall 90%, you will lose 4%, 5% of it. So really have a similar relocation towards what can happen. And let's dig deeper into what can happen, what kind of gold miners there are so that you can better allocate your investments. When investing in gold miners, what they own under the ground is sometimes more important than what they own above the ground. Because you're buying the gold, you're buying the future now as a hedge. So Barrick Gold likes to see itself as the company with the largest gold reserves in the world. So they have 85 million ounces, which at current prices is much more than 100 billion. Given the 20 billion market capitalization, there is a lot of potential in such a company. However, when you look at gold miners and their presentations, they will always say what's best and what's working for them and omit some things. It's not lying, it's just omitting. For example, Barrick Gold here says that it has the highest reserves in the world, but it doesn't mention Polyus Gold. Polyus Gold is a company that has the highest life of mine, but also is the second largest gold reserve base company. Barrick you can see here is close to Polyus, but they don't mention Polyus. So this is another interesting company. Now it's again a bit expensive, but if you wait, if you're a patient, you can really buy those miners in the cheap. You don't have to invest now. You can invest over the next 10 years when those companies are cheap, so you invest a little bit now. If they become cheaper, you invest more. We have to always think that investing is not about what happens in the next three months. Investing is about building wealth over the next 40 years, because that is a sustainable way of investing, and that will make you well off. So really see about, okay, this is my portfolio location, be patient, things change a lot in the long term. If you just look at what happens every five years, then you will see that the volatility is huge. If you look at what happens in the next three months, it's very difficult and a lot of energy is spent for nothing. So really look at these gold mining investments from a long term perspective. From the net debt to EBITDA, Harmony Gold is the lowest one with the highest EBITDA. However, Harmony Gold has very high mining costs, which are again something to watch. So if the company has a lot of debt, then it's much more risky, especially if gold prices go down. If they don't have a lot of debt, then they can weather whatever happens. However, apart from that, it is very important to look at mining costs. And you can see here the mining cost curve, the cheapest producer are Polyus Gold, some Turkish miners. Then we have higher and higher cost producers up till the price of gold. Of course, if your producing costs are higher than the price of gold, you simply don't produce. Nevertheless, the higher the cost, the higher is the leverage, the minor the stock price will have the gold prices. The lower the producing costs, there will probably be a dividend. So there is more yield, immediate yield, there is more profit and there is more safety.   If you are more leveraged, if your portfolio is more oriented to really growth stocks, to really quickly gaining some returns, tech stocks or something like that, and you want to balance your portfolio accordingly, then you can buy high leveraged, high cost miners. If gold prices spike, you will get the same result and immediate protection to whatever happens in the other environment. Another thing to look at is low political risk or you don't want to see gold prices higher and then some government, I don't know, in Africa or in Greece or in Turkey or in Canada say, oh, we're going to raise gold taxes or we're going to confiscate your mine. So that's also something important to look at and something to be very well diversified. How much to allocate to gold miners? Three, four, five percent maximum, maximum 10 percent of your portfolio if you can weather that risk and rebalance accordingly. So I have described what can happen, what are the risk rewards, and now it's up to you to look at the other videos that we will discuss commodities and other sectors and see how that fits your old weather portfolio. It's all about your risk and reward. Looking forward to your comments, click like, don't forget to subscribe, and I'll see you in the next video.


Oh, okay, now somebody called the attack helicopter, man. Oh, yeah, and did anyone notice that's a Maze Bank tower from GTA? What is up, everyone? And today we're gonna be reacting to some spider animations. Let's begin. Okay, this is Bonteep meets Chuchucharls by entity. You're gonna drag yourself, bro? I see you got some feet. Okay, I already know this is gonna be scary just by the look of it. Oh, it's a mini Chuchucharls. Like a little toy. Pocket for the poses. Charles is coming down the trails.  He doesn't even know it. Dude, look behind you. Turn.  Oh, so the toy is pretty much a trap for people to play with it. And then Charles comes and beats off of you. Oh, I was broding out here like the cranky. So lit up. He's dead, dead. Okay, what is gonna happen, man? This is like so intense.  All right, I'll wrap you in my man's, the Bonteep. Damn, this is by Fifushka Big Big Spider invasion next level. I guess there's like some backwards. What happened here? I do not know. In spider. That's not a guy spider.   Oh no, there's a lot of black widows. Yo, get the flame thrower. Okay, oh, give me the chills. Okay, no, that is not good, bro. You need to start running. Hide in the house, go on the roof. Yo, he's dead, no way he survived this. Why is there so many spiders? So they keep getting bigger. Oh, heck no, man. That's all I got to say. This is the Spider-Man by Simon Doolan. It's literally Spider-Man, by the way. Oh, you passed the F-Alio.  I mean, this is literally a Spider-Man. Imagine if Spider-Man was actually like this, like he actually kills the villains or bad guys. Oh, nice save. Oh, never mind, take that back. He's supposed to be helping, bro, what? Even the constix is crazy. Dude, that was literally the Spider-Man. I'd never seen anything like this and it's pretty crazy. Oh, look at his eyeball. Oh, there's people caught on the web. Oh, there's webs everywhere, holy. Simon Doolan, 2021. Yo, that was crazy. They literally took Spider-Man to a whole other level. Now, by a niric flow VR, we got Giant Spiders Attack, CGI animation. Oh, no, spiders turn around. Do not come towards the camera. Why are they walking towards us? Turned. Okay, we're dead.  Okay, no, 3, 2, 1. We're dead. No. Okay, now we're dead for sure. This is coming to right at us. 3, 2, 1. We're dead. Okay, safe to say we're alive. Frypops animated Attack Spider. Apparently it's a Halloween prop from what it says on the title. But this thing looks so freaking disturbing. Like a lie, it's kind of scary. Oh, he's jumping at me, bro. I don't like this. I don't like the sound effects.  Yo, you need to chill out. Before I go and get my big old boot and stomp you with it, man. This is also by Fifu Shkachichi, Charles' final boss, new video. Found footage. That was a long title. Wait, where the heck is this guy? Bro, he's like in the desert and there's a train. The heck? Never seen anything like this. It almost seems like a dream. Okay, now why did it go down the creepy tunnel? Oh, I see Charles. He was right outside that door to the right. What the? All right, ladies and gentlemen, well, there we have it, some spider animations. Hey, shout out to you guys. Those there are scared of spiders. You guys are brave. If you made it to the end of this video, comment, I hate spiders. Just so I can know, you know? Just so I can know if you're a real one or not. Well, yeah, thank you all for watching and I'll see you guys in the next one. Peace.


My name is Kaisa Ekisi Ekman. I'm a Swedish author and journalist and I've written about issues such as trafficking, surrogacy, capitalist crisis and the euro crisis. And I am going to participate tonight in a seminar called Time to Get Serious, How to Crush Capitalism and the Far Right with One Blow. The media discussion on why the far right is rising and the function of the far right is erroneous because the media and also the dominant parties have been focusing on this as a kind of ideological populist movement, even explaining it with psychological reasons, whereas from a Marxist perspective, as I have, the function of the far right is to maintain the dominance of capital. And this is true for Sweden because if you see, the big debate we've had in the recent years is the privatization of healthcare and welfare systems where we have one of the most neoliberal systems in the world, even more than Chile right now, where schools, for example, can be run by private equity companies. And this was about to be abolished. This could have been abolished if it wasn't for the far right that came into parliament, taking basically the voters of the old Social Democrats, the crass of left-wing, even of right-wing, and were very lobbied by capitalist organizations into accepting private companies in welfare state, meaning that because of their presence, they were able to keep this, which basically nobody in Sweden wants. So I think in part it's the same idea as in the 30s where you have basically capital speaking new language, speaking a populist language, speaking with a voice of the people. Even you can see this in the case of Donald Trump. But really the point is to maintain the dominance of capital over workers. And also one basic function that the far right has in my country, Sweden, is to pit workers against each other. Newly arrived workers against workers who have been here for a longer time or who are born here. So we don't unite against the capitalist class. The left should become populist in my idea. The left should not be so troubled as it is now. I think the basic ideas, the politics of the left are good. They're not bad as such, but the problem is the left appears every day more and more troubled and has a lot of the time gone into cultural struggles instead of focusing on the main challenges that every country faces. In Sweden, the main challenges right now are of course housing because we have a big housing problem that nobody's taking care of. There's shortage of housing. There is the debt bubble that's growing every day. There is unemployment that we used to have 1% in the 80s stabilizing now at 8%. There is segregation. There is crime and all that needs to be dealt with. And the only way you can deal with that is using the welfare state and taking control again of society, which has been left to neoliberal forces. But I think that the death of the left is starting to get into all these cultural questions and trying to approach the extreme right in the way of ideas, speaking of ideas, because that will never work. You need to get down to basic to what unites people. And what unites most people is that we're all wage earners. Most of us, 90% of Swedes are wage earners. So we need to focus on those questions and have a progressive politics in the cultural questions, but not talk about them so much. You know, rhetoric needs to be focused on main important issues, otherwise you're never going to get all these people back.


Cellular senescence is a state of irreversible replicative arrest and apoptosis resistance that leads to tissue destruction through a pro-inflammatory secretory phenotype, SASP. Senescent cells accumulate with aging and contribute to various age-related diseases. Discovering pro-survival senescent cell anti-apoptotic pathways, SCAPs, has led to the development of senolytic agents, drugs that eliminate senescent cells, which are showing promise in pre-clinical models and are being translated into clinical interventions. This article was authored by James L. Kirkland and Tamara Tkonia.