The strangest stories of World War II is the story of sneak craft attack, favored naval weapon of the have not nations. By swimmer, by human torpedo, by midget submarine, explosive boat and torpedo boat, the Axis powers strove with considerable success to whittle down the naval superiority of the Allies. The Allies learned vigilance the hard way to the tune of thousands of tons of warships and merchantmen sunk and damaged. In the Mediterranean alone, at Alexandria, at Suda Bay, Gibraltar and Algiers, Italian sneak craft accounted for 150,000 tons of Allied shipping. The simplest form of sneak attack is the swimmer. Using a tight fitting rubber suit to protect him from the cold and swim fins to increase his striking range, he could reach targets up to five miles. The breathing apparatus developed by the Italians showed great skill and design. The single oxygen bottle allowed the swimmer to work underwater for at least half an hour. Plenty of time to finish his deadly mission. For attacking shipping, their limpet mines and floating charges contained from four to 40 pounds of super explosive. They wrecked an Imagan bridge by guiding 1,500 pound charges down the river. And throughout the war, they successfully blew up locks along the inland waterways. In attacking ships, the swimmer almost always approached the targets on the surface, relying on his head net to camouflage his face from the lookouts. On reaching it, he put on his nose clip and his mouthpiece for underwater breathing, filled along with oxygen and submerged quietly to the bilge keel. The charge was pulled down after him and clamped to the side of the hull. The time fuse with its four-hour delay was started and the attack was done. Score for the swimmers, the Imagan bridge, many canal locks, but only a few allied ships. The most successful Italian sneak craft was their version of the human torpedo, the Celerolente Corso, the SLC. Popular opinion to the contrary, the SLC was not a suicide craft. It was a modification of a standard torpedo that carried two men and two heavy charges to the target. The two 280 pound warheads were in turn clamped on to the nose of the torpedo for delivery and were readily detachable at the scene of action. One of them was easily capable of breaking the back of a merchant ship. Together they could and did put a capital ship out of commission for a year. The craft was designed to put as little strain as possible on the operator during his long ordeal. Simple airplane type controls for the hydroplanes and rudder. Motor switch with four speeds forward and four reverse. Electric pumps to fill or empty the ballast tanks. The overall length of the SLC was 22 feet and it weighed a little over a ton and a half. The two high pressure bottles carried enough oxygen to last the torpedo men four from five to six hours of continuous use underwater. The captain of the craft sat in the forward position. He handled the controls and did the navigating. Cruising range was 15 miles at a cruising speed of two knots. In December 1941 four of these crafts scored a triumph roughly equivalent to a major sea victory. Slipping into Alexandria Harbor undetected they proved the craft's superior maneuverability and unusual striking power. Each pilot approached within 50 to 60 yards of his target with only his eyes above water. At night detection was almost impossible. Then he submerged and ran slowly and silently to his target. Each craft jockeyed to position under the bilge keel. While the captain held the craft there the number two man ran a line from one bilge keel to the other. Detached the warheads and placed the charges firmly in position directly under the keel. The time clocks were started and they drove away. In this manner two British battleships the Queen Elizabeth and the Valiant and an Allied tanker 80,000 tons of shipping were sunk in Alexandria Harbor in a single night. Later at Gibraltar they were able to bag nine British and American merchantmen. This constant threat of surprise attack was almost as much of a strain on the Allies as the 150,000 tons of shipping actually damaged or sunk. The Germans were inevitably attracted by these spectacular Italian successes and by the spring of 44 it organized a pic core of 10,000 officers and men. Their first successful craft was a one-man human torpedo. The real torpedo, the child, was slung below the mother which carried it to within close firing range of the target. Every detail of the design and operation of martyr was carried out with typical German thoroughness. A welded steel trailer assured rapid delivery at the launching point and camouflage nets preserved the secrecy of the operation. Here was a fairly effective weapon whose mobility was such that it could be quickly concentrated for mass attack. As originally designed the German one-man torpedo was purely a surface craft. Through inexperience the first ones beached harmlessly at Anzio Beach without firing their torpedoes. They were the subject of more curiosity than alarm. But later in the summer of 44 they carried out successful surprise attacks. The low silhouette of the craft running awash with only the dome visible made the run in on a dark night relatively easy. But once he had fired his torpedo and his presence was known he was quite helpless against counter-attack. The Germans could ill afford to sacrifice their trained men and the next craft were made able to dive. Martyr was found to be fully operable at depths up to 90 feet. It handled well and maintained an even course with a speed of a knot and a half is contrasted to a surface speed of somewhat over two knots. Her ability to dive thus immeasurably increased her effectiveness and the sturdy seagoing qualities of the craft underwater exceeded anticipations. The operators even found they could perform radical maneuvers without losing control. However the operator could not see underwater well enough to make an attack. His run into firing range was usually made awash. Even under these conditions visibility was something less than ideal making extremely close range necessary before the torpedo could be fired with any degree of accuracy. 50,000 tons of shipping were thus sunk or damaged in the last year of the war an amount out of all proportion to the martyr losses suffered by the Germans. The development of the midget submarine by the Germans is another chapter in the story of sneak craft attack. First in point of time was Mork, an all-electric one-man midget. She filled the essential requirement of ease and handling by truck to the point of launching and by truck or crane into the water. Mork was not very successful. Her range was a mere 75 miles and she was slow and cumbersome on the surface. Her batteries, which filled the whole forward part of the craft, could drive her at up to four knots. But the swells and anything but the commas seas battered her oversized hydroplanes unmercifully. Yet she had her good points underwater. These same hydroplanes gave the operator excellent control of his craft and she submerged and surfaced with fair success. Under actual operating conditions, she failed to measure up and after two 15-boat sorties in which all craft were lost, she was abandoned. Her successor was the streamlined Bieber, which sacrificed strength for speed. A gas engine was added for surface cruising and recharging the batteries. But her normal range was still restricted to approximately 75 miles. The concavities in the hull permitted the torpedoes to be carried outboard without greatly increasing the bulk of the craft. But they in turn weakened the hull to a considerable degree. Bieber, with her 30-foot overall length and six tons weight, was still small enough to be launched and maintained at quickly constructed strategic points. In her trials, she proved faster and more maneuverable than Mulk. But she was also tricky to handle, hard to navigate and afforded only restricted visibility to the operator. After Mulk was abandoned, Bieber was used constantly against shipping to the port of Antwerp. She had small success and suffered heavy losses. In 15 sorties, using 163 Bieber's, 53 of them, almost a third, failed to return. Bieber was being used as a stop gap until the new midget sub, Zehunt, was ready. Zehunt came into action in December of 44. The German engineers had at last found a small submersible that overcame the annoying limitations of the other craft. Zehunt had the great virtue of being mass produced. She was in essence a trimmed-down model of a full-size submarine and incorporated many of the best features of the British X-Craft, which carried out the raid against the Terpets in her Norwegian fjord the previous year. Her propeller was fitted with the cork nozzle type rudder, similar to that of full-size German submarines. The glass observer's dome on the hatch cover safely withstood water pressure to depths of 150 feet. Her diesel drove her at eight knots on the surface and she handled admirably. Here at last was the best midget submarine German engineering skill could produce. The captain called the orders to the engineer who handled all the controls. He kept her smoothly at periscope depth while he was coached into the target. He made ready for firing and diving. He fired the torpedoes at command and the fish slipped off the track on its run to the target. Tag her down and down they went as the captain took a last quick look through the periscope. Under water, her small size made it almost impossible for the warships to find her. Listening gear was incapable of detecting her propeller noise at slow speed and it was very difficult to ping on her small hull. About 70% of the Zehuins made attacks on allied shipping before the war ended. Though in many cases the crews missed their targets through lack of experience. Through the periscope, they swept the sky for aircraft before surfacing to recharge batteries and for a breath of fresh air. The morale-breaking loneliness of the one-man craft was gone. Zehuint, with her crew of two, could cruise almost 500 miles and stay at sea for a week. But Zehuint came too late and the German defeat prevented her from proving to the skeptical allies that here was a weapon to be reckoned with. In sharp contrast to the successful underwater craft the motorboat story was extremely disappointing to the enemy. The Italians designed a 20-foot torpedo boat, the MTSM, to attack ships either at sea or in the harbors. The propellers were retractable, so the crew of two could easer over a sagging harbor defense net to attack the shipping inside. Two Alpha Romeo engines, one on either side of the single torpedo tube, gave her a top speed of 32 knots. The torpedo was fired by aiming the boat directly at the target. And after firing, the boat was turned sharply away from the following torpedo. This was fine theory that seldom worked out in practice, for the ship's gun crews were able to shoot most of the boats out of the water or drive off the attacks before damage was done. The German version of the torpedo boat was the Wendell boat, a lean, streamlined craft with a single, non-retractable prop. Two torpedoes were shot from the stern and so arranged that one was fired on the run-in and the other was fired during the retreat. In addition, her armament boasted two rocket launchers, one on either side of the pilot house. Like the other sneak craft, she required comparatively calm seas for operations. Her high speed of 33 knots and the two rockets were supposed to disrupt enemy gun crews, so she had a better chance to get within proper torpedo range. The Wendell boat made fine propaganda pictures for the Nazi newsreels, but her performance as an offensive weapon was no more impressive than her Italian counterpart. The explosive boat was a simpler method of delivering a charge to the target. The Italians used it successfully in the last war and continued to experiment during the 1920s and 30s. They developed a hull that planed beautifully into an Alpha Romeo engine that gave speeds up to 30 knots. The combined propeller rudder could be swiveled at will so that with a trained operator at the wheel, the usual type of torpedo net defense could be hurtled with surprising ease. Although in actual operations, the boat was sneaked over the nets as quietly as possible under cover of darkness. In the early years of the war, the Mediterranean was alive with these craft. They swarmed into Malta and Suda Bay in mass attacks, but the ease with which they were spotted and their extreme vulnerability to gunfire placed them in the category of nuisance craft rather than effective offensive ones. Nevertheless, because it was a cheap way of delivering a massive 800-pound charge to its target, the Germans copied the Italian explosive boat. Trailer drawn and usually launched directly from the trailer, the German craft, Linzer, was a much cheaper mass-produced boat with a Ford V8-type engine, non-retractable prop, and indifferent sea-worthiness. In the dying days of the war, the Germans played up Linzer to bolster morale at home. Spectacular pictures of this secret weapon and fake shots of the damage it could do were intended by the Goebbels machine to whip the starving Germans into a frenzy of enthusiasm. The driver aimed his boat like a gun, locked his controls on a collision course, and at the last possible moment jumped. The 800-pound charge detonating on contact supposedly did the rest. Near the end of the war, the Nazis formed a new combat unit to manned radio-controlled explosive boats. The radio-controlled man in the pilot boat steered the other craft and could regulate the speed. Three boats made up a combat team. A pilot boat and two explosive boats. A pilot drove each explosive boat until an attack was started. Then he jumped overboard, and to quote the Germans, he was nearly always rescued, either before or after the operation. Radio control made little difference. It saved the lives of a few Nazi boatmen, but the guns of the escort ships still blasted the boats out of the water with almost 100% success. Against an alert enemy, the motorboat idea in any form was a dismal failure. Too late for this war, but almost ready for operation, were two new craft, one German and one Italian. This is the German High, an attempt at a super one-man human torpedo. Its increased length doubled its battery capacity, which could be used for increased range, faster speed, or both. But its great length, over 40 feet, made it extraordinarily clumsy and an ever-present potential death trap for the operator. High failed, and the German unconditional surrender stopped further experiments. Directly opposite to the German High was the Italian SSB, which was also caught by the war's ending before she could get into action. Except for the midget submarine, Zehun, she was probably the finest sneak craft to come out of the war. Her two enormous warheads total nearly 900 pounds of high explosive. The crew of two rides inside a cockpit, which protects them from the water pressure and helps streamline the craft. The face masks and breathing gear are the same as on the older two-man torpedo and can be put on even after the men are underwater. SSB is 26 feet long, weighs a little over two tons, and has a top speed of six knots. Whether turning, diving, or running, the control is positive and rapid. Look at the ease with which the pilot dives and climbs underwater. The SSB is fast and powerful enough to overcome many of the tides and currents that prevented the other two-man and one-man torpedoes from operating successfully. And her cruising range of 45 miles is three times as great as that of the older model. Watch the fast, sharp turn to the left as she surfaces. Shipping is attacked in the same manner as with the older two-man torpedo. For operative technique, the whole operation is shown on the surface beside a ship. After coming alongside submerged and in a real operation, sinking to the bilge keel, the number two man gets out of the craft with his clamps and fastens them to the bilge keel. As this is a merchant ship of 6,000 tons, only one warhead is needed to blow a tremendous hole, break her back, and sink her. The clamp holding the first section of the head is loosened. While this is being done, the captain holds his craft in position under the bilge keel in a real operation alongside the ship in this demonstration. When the head is loose, a twist or two by the man underwater frees it from the craft. As it has only two pounds of positive buoyancy, it is easy to pull it under and fasten it to the hull. The number two man then climbs back aboard his craft. With the second section of the warhead still in place, the SSB can attack another ship, making it possible for two men to sink two ships in one operation. This was the array of sneak craft pitted against the Allies, and the Allies learned by hard lessons that the best defense against them was constant vigilance and a full dress harbor defense. Attacking a harbor, the sneak craft could easily evade the long range surface search radar or deep water magnetic loops at the harbor mouth. Even the line of sonoboys on the surface or hydrophones on the bottom could seldom pick up their weak propeller beats, and then only if the craft were operating at high speed. The long range heralds set up on either side of the harbor will not detect sneak craft. They are for the full size submarines and surface vessels. One possible means of detection is the multi-turn loop, which in some cases will record the passage of the midget craft. Another detection possibility is the short pulse herald. This device can ping on a very small object, but requires constant alertness, the most expert of operators, and ideal sound and hydrographic conditions. The surface of this water is swept by super sensitive radar that picks up objects as small as a periscope or a perspex dome or a swimmer's head. Radio in the harbor entrance control post directs the cutters to the attack. Torpedo nets are the last line of fixed defense. The latest and best stopped torpedoes, one-man human torpedoes, midget subs, and with specially rigged surface elements, they stop motorboats. The two-man torpedoes and the swimmers were the only ones who could make their way past the net defenses, using net cutters or slipping through openings near the shore. The harbor patrol boats armed with search lights, machine guns, and depth charges were constantly searching for the sneak attackers who were able to penetrate these defenses. At slow speeds, these underwater craft made little or no noise with their propellers or engines, sometimes at a very close range and under the very best of listening conditions, a skillful operator might faintly hear the propeller beats. Of course, if the craft makes a maneuver such as this crash dive of the Zehuint, the experienced sound operator could quite easily hear it. However, exhaustive tests have proved that under sneak attack conditions, it is next to impossible to hear any of these midget craft. The electric torpedo is by no means silent. True, the sound operator hears it the instant it is fired, but then it is much too late. The latest detection devices developed at the end of the war but not yet installed in our harbors were the multi-turn loop and the short pulse herald. The multi-turn loop in 60 feet of water is the most sensitive of magnetic detection instruments. However, a sneak craft built of non-magnetic material should be able to cross such a loop without detection. The short pulse herald promised to be one of the most effective detection devices in use. Tests revealed that up to 400 yards, this device with skillful operation could detect sneak craft under average condition. These and the radar were the newest weapons for harbor defense. The end of the war found the sneak craft that had been so crudely and hastily built for defense about to become important secret weapons of offense. It needs but little imagination to see what these craft could do to even our largest shore installations, should they be equipped with new atomic weapons. To be secure is to keep well-abressed of all future improvements in sneak weapons and to press vigorously the development of more dependable detection equipment and countermeasures so that we may not be caught by this form of the opening gun of modern warfare, the sneak attack.


What does all this have to do with scalar geometry? What we want is to fit our problem of studying scalar Einstein metrics or similar things into this kind of general framework. And that can be done in two closely related ways. One is infodimensional and one by taking the limit of fine dimensional pictures. But so the infodimensional approach, the relevant group is the G, it's the symplectic diffeomorphism group. So we have a scalar manifold, X, but we can just forget about the complex structure and just think about the symplectic manifold and all the symplectic forms under consideration will be equivalent as symplectic forms so it doesn't matter which one we choose. Probably more precisely we should call it the Hamiltonian diffeomorphism group or something, but that's not going to be important. And we can think of this as acting, so A will be the set of almost complex structures, compatible almost complex structures. We fix this symplectic form and then we can look at this thing and you can write down in a formal way, these are infodimensional spaces, but you can write down in a formal way the structure that we had, a symplectic form and metric, an infodimensional scalar structure on this and so forth. Then the moment map is just given by the scalar curvature. So mu of J is essentially the scalar curvature of the metric determined by a complex structure and the symplectic form. Again, this is a slight distortion of the truth, but it's true for our purposes. Actually minus the average value of the scalar curvature. Just subtract off a constant. So this is a function which is essentially in the dual of the Lie algebra. The Lie algebra of this is the function, so this is the right kind of thing to be, the dual of the Lie algebra. So the things that we are looking for, the things that we expect to meet in this general picture are just the constant scalar curvature metrics. I'm saying a zero at the moment map will be something with constant scalar curvature where the scalar curvature is equal to its average value. So in fact, I don't have an almost complex structure, but we're always just going to restrict to the subset of integrable complex structures. In fact, we're going to really restrict to a single orbit in our discussion most of the time, so you can worry about that. So you can write down a lot of what we had. What you can't really write down is the complexified group because that doesn't exist in any genuine sense as a group, but you can still make enough sense of it to carry through essentially everything we've said. In particular, we can interpret the quotient space Gc over G as the space of scalar metrics. If we fix one complex structure, we can interpret this by thinking of this as an orbit or the quotient by G of an orbit in the almost complex structures. We can think of this as a familiar space of all scalar metrics in a given class, i as a sort of omega naught plus i d bar d5 for some fixed scalar class. So the symmetric space structure we expect on this does more or less make sense. It corresponds to writing down a Romanian metric introduced by Mabucci, which is just that if we take a tangent vector, we're at a given point, we take a tangent vector is just given by a change in phi, so we want to say what the norm of delta phi is, but it's just the obvious thing. We take the, let's call this thing omega phi, we take the L2 norm with respect to the usual measure determined by this metric. So the only interesting thing which is happening is that this metric measure is varying as we vary over our space. So let's call this d mu phi. We want to make sense of the geodesics in this space in some form, and these are functions of phi t, geodesic. If you can write it all out, what you find is that these correspond to solutions of the degenerate, the homogeneous Bonjour-Jampere equation on a larger space. So if you think of taking x times s1 times an interval, if our t is in our interval, when we think of this as a scalar potential on this space, but the circle acting trivially, then we just corresponds to a form which is null. So solving the geodesic equation just corresponds to solving a, so this homogeneous, this is essentially d, if I think of phi as the function of two variables corresponding to this one parameter family, essentially we're looking at the equation d bar d of phi to the m plus 1 is equal to zero. And we can write down what this functional is corresponding to the norm. So it's called, again, goes back to Mabuchi, Mabuchi functional, which is, again, essentially we define, what we define is its derivative. So you need to see that this actually, so we're really defining a one form on our space. You need to see it's a closed one form, so up to a constant defines a function, but that's the case. So the formula, again, is that the change in n, infinitesimally as we change by phi, we just take this scalar curvature minus the average value of the scalar curvature. D mu of phi. Does this notation make sense to you? So as we see, the critical points, I'll just say the scalar curvature is constant, as we say. And then there are other things. Another basic important functional that comes in is just defined by, would I, is just defined by taking the integral of delta phi. So this is kind of a formal setup for understanding the constant scalar curvature equation on the scalar manifold. In fact, if we're working in the right topological setting, if we're working in, if the scalar class is the first-gen class of the manifold, then any constant scalar curvature metric will be scalar Einstein. So I have a certain identity. So we can think of this as a way of understanding the scalar Einstein equations also. But in fact, there's a, that's a rather, since it's embedding a problem in a harder problem in a sense, it's embedding a second-order equation, a fourth-order equation. There's a more direct, but to me, more mysterious way of setting up the scalar Einstein equations as functional by this, it's called the ding functional. Well, let's see, no. Another functional one can define, which is equal to, we take this, this I, and then we take minus the logarithm of the integral of, which is omega phi, so it works. So this isn't the case when the line bundle we're considering over our manifold is equal to the dual of the canonical bundle. So if we have a metric, so phi is to giving us a metric on the line bundle in a more invariant sense. So if we have a metric on this, it just corresponds to a volume form. And that's what this is. So, more of an incoordinance, this is essentially e to the phi, up to a constant factor. So this is something we can only define in the scalar Einstein setting, but again, the critical points are the scalar Einstein metrics. And remarkably, this is a result of Bo Vanson. This is also convex along gd6. I don't, there's no way that's true, but it's a fact, this is also convex. All three of these are convex? All three of these are convex. Well, this is linear in fact on gd6. This is convex by the general theory more or less. This is convex by a hard calculation. I don't know, kind of a... And that's something that actually comes into the story in an important way, at a technical level later. In the sense that this geodesic equation is not an elliptic equation. One can try to understand it in a certain sense, but solutions will generally have singularities. So if you have singularities along your... If you're trying to understand these functions along a geodesic and you have singularities, it's not quite clear how it's going to work, because what does the scalar curvature mean if you have a very singular thing? But this thing is much... Of course it doesn't depend upon semi-derivatives. So Bo is the expert side, but roughly one can easily produce kind of weak solutions of this equation. And the advantage of this being functional is it's still defined along such... You don't really care about the singularities. Okay, so this is something about the kind of inferred-dimensional picture. So because it's inferred-dimensional, hard work is required often to actually make the kind of formal properties work. It gives a context for thinking about things. So another approach is by taking the asymptotics of fine-dimensional set-up. So here we just consider... We just think of varieties in projected... Some fixed-projective space. So think of this as a projected space with its fixed Froobini-Study metric. We think of, speaking of the set of all varieties of a given numerical invariance of, let's say, the chow variety of such a thing. And then we have... Our group G would be SUn plus one. That's on the chow variety. And also the complexification, just so that this is just... And in fact, this chow variety can be embedded in some big projected space. So we can reduce to the standard picture if one likes. Any case, there's an actual metric and a line bundle and so forth on this chow variety. And what you find is that the moment nap of some variety V is just given by... So this should be a skewer joint matrix. And the layout of it here is just given by taking the integral over V. We take this formula. So I'm thinking of Z-alpha, the standard coordinates on our projected space. If I make this combination, it's homogeneous. So it's a well-defined function of projected space. This just means we take the trace-free part when we project out to get to them. This is a momentum after the action on the chow variety. That's the momentum after the action. Another way of saying that is if we take a fixed... Let's focus on a given one parameter subgroup defined by some A, then mu of V, A is equal to the integral over V of HA where this HA is the standard Hamiltonian on projected space for the corresponding action on projected space for the one parameter subgroup. I'm probably... You put some I's in somewhere to make this work. So it's a very natural thing. So let's... We want to understand this numerical invariant. When we have something fixed by one parameter subgroup, we look at the weight of the action on the fiber. That's just given by... Well, essentially by this formula. But let's... When we take account of this projection to the algebra, what we can write down is the following formula that we call the chow invariant. So supposing V is fixed by X, A, T the one parameter subgroup, then the chow invariant is going to be... We'll write this with the trace of A over the dimension, which is N plus one, minus one over the volume of V times the integral of HA. So this is essentially the same formula all we've done has been normalized it If A is a multiple of the identity, this vanishes. It's just a normalized function. That's this numerical invariant that we wrote down. The weight of the action. The thing we call the I of X lambda. Something like that. We go to the fixed point and we write down this weight of the action. This is it. So the condition that the chow... So what branches is the condition of the stability, the chow stability, it would be called, would be that this chow is positive. So what we're saying is that we start with some... Maybe we've got a class of notation. Let's call it V naught, say, fixed V naught. We start with some V. We want to understand if it's chow stable. What that means is that we take any one parameter subgroup and we flow it until we flow it into something fixed. So we get some V naught. And we want to say, in a stable situation, if this chow applied to the fixed thing is positive. That's quite a natural meaning. What that's saying is that to the trace of... This is just the average value of H on projected space. This is the average value of H on V naught. So the stability condition is when we flow downwards, which is going to be very complexified, we're taking the gradient flow of H. When we flow under the gradient flow of H downwards, the average value in the limit should be less than the average value on the ambient space. So you sort of feel... Unless it gets hung up in some bizarre way, that should be true. What's that saying? The integral of H... What's that, the integral over? So this thing is the average value of H... Of the projected space. The next integral is V naught. This is V naught. So this is the average value of a V naught. So this is something we could write down for a general... In Iranian context, we say we're looking at sub-manifolds that when you flow down, the average value in the limit is less than the average value on the ambient space. So this is a notion of Chao stability for something in a fixed projected space, which is quite a natural thing or something we can understand. But we want to think about the asymptotics of that. So now we're going to... The notation's going a bit weird. So now going back to the picture of an X with an L, for each K, we can embed X in some... If K is sufficiently large, we can embed by the linear system of sections of this thing, the projected space. And then we can apply this picture. On the other hand, if I have a... Supposing V naught is... Supposing we take K equals 1 and V naught appears there, then we can take the sections of... We can re-imbed it in a bigger space by taking the powers of the sections. So we can get the same V naught. We can also have this line bundler L on it. So rather than having a single... So now we would like AK to be the generator of the action on H naught of V naught L to the K. Changing my notation. Yep. So we have a V naught, this line bundle over it. This automorphism acts on all these spaces. And so we get this. And so we can write down this expression not for all possible Ks. So we can... Trace AK over... This is NK, we're calling it NK plus 1. Minus... We'll take the same... This... This sort of hammer... This integral actually won't vary with K. We normalize up to some normalization. This is independent of K. Integral. So maybe I should put a K. I put a K in here to make it exactly right. V zero is going to depend on K, right? If V zero is going to depend on K, because the chal variety you're going to be in is going to depend on K. What I'm doing is I'm slightly switching between everything. Once we've got a V zero, we've got a line bundle over it. Now we can take the powers of the line bundle to get a whole... We can bet it in a different projector space. If you're looking at chal varieties for different projector space... Then it'll be in a different... Yeah, that's right. It's like all the different V zero in some sense. It's the same V zero, but we're embedding it in bigger and bigger projector spaces. Yeah, that's right. So I'm slightly... Yeah. So we can write down this thing. But these... At least when K is large, these things have... These are given by Hilbert polynomials. These are polynomial functions. And where we've normalized it, this thing will have a limit as K tends to infinity just by general... This will be a polynomial of degree n plus 1 in K, and this will be a polynomial of degree n in K. So we've got the... And... Um... Yeah. For the way we've set it up, the top terms cancel, so the next term is a constant, and this is the futaki invariant of... Well... Maybe we could call it V naught a, or e to the a t, or something. V naught with this action, essentially. So might it happen that the quantity in the parentheses is negative for some low values of K in some of the states? Oh, yes. Yeah, we don't... This could jump her up. Yeah. So, and in fact, when we go to these asymptotics, there's some subtleties. So things that ought to be the same at first sight actually could be a bit different, but... But anyway, this is a correct... This is a formula that defines a certain numerical invariant. And that's what we're going to use to define stability of having... So in a sense, we could have cut out the last 40 minutes and just written down the definition. The last 40 minutes is being given. So why are we defining it in the way we're defining it? We need another lecture then, I think. I think we need another lecture. We're going to get one more. What time? What time is it going to be? Tomorrow. Tomorrow. We'll see. I mean, it could be at 12 or something like that. We can discuss what time. But you're right, I'm not going to... I think it's worth explaining that rather than just writing down that. Anyway, so now we're going to define the definition of case stability. So when we're talking about we start, we take a v and we move it by one prime of the subgroup to get a v0. That's actually the same as talking about... that's equivalent of talking about a family over c. Which is called a flat family or something like that. So I'm going to change my notation. So this is supposed to be c star equivariant. So as the c star acts on c in the usual way, we're supposed to have a lift of the action but we're supposed to have pi minus 1 of t is isomorphic to x for non-zero t. But pi minus 1 of 0, we should think of as being something different, x0. We're going back to about x's rather than v's. The same thing. And we also have line bundles on top of everything, but let's not write that down. The the futarkian variant, changing notation of this gadget is just the futarkian variant of x0 with the action. The c star action gives an action on the fiber over 0. Anything we define there. So this is a good algebra geometric definition because it doesn't really matter if this makes sense even if this is a scheme or whatever. We already just know that these things are given by Hilbert polynomials to get a good definition. What does it have to do with our other picture, our kind of input dimensional picture, the differential geometry that at least if if x0 is let's say smooth initially or not too angular then we can write down a formula essentially what we've written down before. It's given by taking the Hamiltonian for the action and pairing it with the scalar curvature minus the average value. So this is essentially a version of the Riemann-Roch theorem in a sense. There are a kind of Riemann-Roch formulae for this that expresses this in terms of carmology and you write that in terms of differential forms and you get such a formula. So this is if x is sufficiently smooth. H is the Hamiltonian for the induced action on this central fiber. A is the action on the Yeah, exactly. It's what we call H. I think I don't understand it. You had this C star action but over here you had like an ambient projector space. So you had this ambient unitary group but here we just have a sort of abstract family of varieties. Do you put them all in some big projector space or something? Yeah, you can pass between the two pictures. When you have this you take the direct image of the H naught of L to the K and you trivialize that here and then you put them all in a big projector space. One parameter group sits in the GLA and then you're over in the other picture. Yeah. Essentially, yeah, certainly. So yesterday you You need to understand equivariant bundles, vector bundles over C but you do. So as you say this is the definite. So the K stability, let's not write it as we've written, it says that if we have a given X you should have a fixed line bundle as well, is stable if any time you fit it into a family like this, generation test configuration, it's called this futaki invariant is positive. With some some extra few words to cover borderline cases but that's the point. It's the case to build an X and we can put X in this family. Then that should be positive. But there is a kind of infidimensional words, the related infidimensional discussion, in which you can translate these one parameter subgroups into geodesic rays that's what you should expect. It's an infidimensional notion where you say you look at geodesic rays and you want you can define the futaki invariant that way essentially from the limit of the derivative of this babuchi functionalism. What does geodesic rays correspond to points at infinity? You can compact it by a symmetric space? Well that's the kind of thing one right but that to a certain extent people have made sense of this and proved that if you have this algebra-geometric picture you can get in a sort of a weak sense of a geodesic ray. So roughly we should think of all these algebraic degenerations as you say as points at infinity in this space. Impacted by symmetric spaces by looking at equivalence classes of geodesic rays? Right. But I doubt the end of that works on the nose because it's all but it at least works enough to see that you have this is the right definition to be working with. So this is essentially what we're writing down is very close to what was defined by Tiar in the 1990s. At a technical level you get different definitions depending on just what kind of singularities you allow in your x-naughts. So let me just mention that in fact we can set things up we can set the definitions up a bit differently in a way that we don't need this c-star action. And at the end of the day you get the same concept. So let me just explain how they're supposing you just know you have a family x over say over a disc, say, no with pi-1 of T isomorphic to x or fixed x for a non-zero T. Then rather than thinking about the weights of this action and so forth what we've been doing, you can also think about there's a certain both for the Chow and for the Futaki story, they correspond to certain lines that you can functionally correspond to a variety. There's a certain way you have a variety, you write down a line associated to it. So if you believe that then given this family we get a line bundle over the disc not very interesting, but this isomorphism means that the line bundle is trivialized away from zero. So we have a relative germ class in variant and a line bundle on delta trivialized over delta star simplifies to green. And that's the same as the other thing that we defined. It can be formed from those or from this this Deline construction of a way of pushing down line bundles. It's not various ways of writing it. Okay, so finally I think we can get on to the his metrics with cone singularities. So it'll fit in best the way things are turning out to postpone any kind of analysis. I was going to talk about the linear elliptic theory on these a bit, but let's postpone that to the next lecture. Let's just see how we can fit into this sort of futaki invariant storing. So what we're considering of course is the model cone with angle beta is given by this metric in polar coordinates like a cone angle 2 pi beta. So we're going to say something more precise about this, we're going to consider some D in X more precisely in the linear system minus mu times K for some fixed mu positive mu and we're going to consider calometrics which have got a singularity modelled on this transverse to D. But let's not go into any kind of more detail, but let's just say that we can think in a certain natural sense which could be made rigorous, we can think of the such a metric the curvature, for example the scalar curvature having a delta function contribution along D. This cone you can think of in the two-dimensional picture is having Gauss curvature a delta function at the origin. So now we want to define a modified phutarchian variant. In fact, we can modify the whole story of all this stuff to put these divisor in, but the crucial thing is the phutarchian variant of change notation, I seem to have got let's call it, let's suppose we can change to fit in what we're going to do later, let's take Z rather than X and delta rather than D the phutarchian variant with this parameter beta of this pair when we have a C star action on this setup preserving so what we can let's write down the formula, this is the ordinary phutarchian variant as we defined before plus plus a correction term essentially is the integral of the Hamiltonian over delta but we'll put some of the normalizing factor in as well so this is a definition and again this we can also express this algebra geometrically if we want in terms of by writing these as the leading term in Hilbert polynomials why is this for good definition if we take our previous formula for the phutarchian variant but now we substitute in the, so we compute in the scalar curvature but now the scalar curve should have this delta function term on D but now that's precisely this or minus this so we're just subtracting off the delta function term so this is equal to let's write as the integral over z minus delta to emphasize of s minus s hat I the scalar curvature not including the delta function contribution this is what I'm inviting this integral so this has precisely got the property that this vanishes if we have a metric of constant scalar curvature with this delta function singularity this thing will be zero so I can let's go back now finally to discuss the strategy as I as I pretty much repeat what I said at the end of my talk on Friday but now we have more background to understand it so this is we for reasons I won't go into there is a scalar Einstein for small beta there is a there is one of these scalar Einstein metrics for some values of beta doing a small and also the set of the set where you have a solution is open so you can deform things so what we want to know if it's starting from some small value where we have this metric with a cone singularity we want to deform it all the way up to beta equals 1 so so the crucial thing is the closeness see we want to say if we have some sequence beta i increasing to a limit beta infinity and we have solutions x actually x i will be x but it's more of the integral x i solutions what we want to do we want to be able to say we can do for these singular metrics just what we did for the ordinary metrics in the first talk yesterday so we want to have some limit we want to have a Gromov-Hausdorff limit which has actually got an algebraic metric structure and we're going to have carrier on we have these d i's as well in the natural way we said done sir i said the words we want to have a limit which is an algebraic metric take an algebraic variety super kind secondly we want to fit one of these c star equivariant families such that such that the central fiber is z but of course we'll have the divisor is what we're going to have the family with the original d and the divisor deltas in the obvious way and secondly we want to be able to say that the futaki invariant for this beta infinity of x is 0 that's what I'm going to say but those are the three things we want to establish about that because if we've done that then we've proved our theorem essentially because this futaki invariant of beta is just linear we didn't write it down it just varies linearly with beta so by the easy directions normally called in this theory when you do have a solution the thing was stable so the futaki invariant back here was positive there are various ways of proving that various proofs in the literature it was 0 here so when we went out to 1 which is when it's the ordinary futaki invariant it has to be negative of course there's a special case when beta infinity is 1 and then you have to get the idea that's a good place to stop more or less I haven't got past I hope I've explained these are actually technical things to do if you're not coming tomorrow you should believe this is a variant it needs more work but it's a variant of what we did before it's the same idea this is this requires some technical words and quite a lot of technical work but it's not too hard to believe formally you'd expect this because we're also going to have a limit of our metrics in some sense here which is going to have a singularity along delta in some sense and if everything was sufficiently smooth then the formula we wrote this would be a constant scalar curvature metric so if we could apply the differential geometry formula this thing would be true so what the work involves again involves deep work but what it involves is saying that the singularities are not too bad that the differential geometry still works interesting


The Eboni State Governorship Election Petition Tribunal sitting in Abuja has dismissed the petition filed by the All Progressive Grand Alliance, ABGA, and its candidate, Bernard O'Do, against the victory of Governor Francis Muifru of the All Progressive Congress APC for lacking in merit. In a unanimous judgment, a three-member panel headed by Justice Lecombe O'Goumoyer dismissed the petition for lacking in merit. The tribunal held that the petitioners failed to prove that the second respondent, that is Muifru, was at the time of the election not qualified to contest the governorship election. The tribunal held that there is substantial material evidence before it which shows that Governor Muifru duly resigned his membership of the People's Democratic Party in PDP. The tribunal held that the petitioners failed to approach the proper court to entertain the issue of membership for a political party. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Well, welcome back. Okay, so now that we have our base rigidbody class in place Let's go and create the drone controller now, and we'll start to see how all this stuff is, you know, hooked together All right, so let's get going. Alrighty. Let's go and get the drone controller So what I would need to do is I need to remove the Rigidbody in the base rigidbody.  So I'm going to go and say remove component What it's going to do it's going to tell me you can't remove the component because this base rigidbody Has said that it requires that Rigidbody. All right So that just really helps you make sure that all the components that you need are attached to your game object. Okay So the way to get rid of all this is we need to delete the base rigidbody first So we're going to go and say remove component And then we can remove the Rigidbody because there's no dependencies now. Okay, so let's remove that All right, so let's go over into the scripts folder here and go and say create new C sharp script And we're going to call this IP drone controller Yeah All right, there we go And I'm going to go and change the icon in the sky. So let's get the indie pixel icon And click off of it to assign it There we go. So now we're all official. Let's go and Double-click it before we assign it to our drone model or game object and let's take care of some code first So we're going to say namespace is indie pixel All right again just to protect the code Keep it all compartmentalized And what we want to do in here for our required components. We want to make sure that we in fact do have a Drone input script. So I'm going to say require Components and we're gonna say type of All right, so we're using type of there. Here we go So type of and we're gonna say IP drone Inputs I just want to make sure that that particular script is in place. Remember the drone inputs Also, make sure that we have a player input. So we're kind of creating this cascading, you know set of dependencies All right, so that really just helps you Set up a new drone really quickly Even if you know, you have someone who's setting up the drones who hasn't done all the code They they won't miss any of the components or anything like that All right, so Now we come down to the class and what we're doing was we're currently inheriting from money behavior is that base class in unity, right? That gives us access to You know all the functions that we use over and over like start and update, right? Well, the base rigid body inherits from money behavior So and we want to include all of this code that we just wrote All right, I want to write this inside the drone controller. All right, that would be redundant So let's go and just inherit from our base rigid body So now we get all of money behavior and we get all of our custom code, right? And then we also have access to this virtual function right here that we can override So pretty cool way to go about setting all this stuff up. They call it object-oriented oriented programming Okay, so that's kind of your first step into that. So we're just inheriting from another class So we get all that functionality All right, so let's go and create a new region and these can be my variables again You can always set up your templates if you want And in this case, we are just going to type them again because it doesn't take that long honestly All right, we don't need update because remember now that we're inheriting from the base rigid body class We already have a fixed date update running. What we want to do is just write our own implementation of handle physics Okay, so I'm going to come into drone controller and we'll do our region we'll say custom methods down here and Region and what we'll do is we're going to say protected override And then if you hit space the IntelliSense will tell you that well because we're you know inheriting from base for your body You have one option here and that's that handle physics. So you can just double-click that And there we go. So now we're overriding it and we're calling the base base dot handle physics It means it's going to call whatever code we might have written in the base implementation in this case There's nothing so we don't need to actually call the base. There are times when you would have to do that though All right, so what do we want to do here? So in our handle physics We want to go and call a couple things. So we're gonna, you know be controlling some Engines and we're also going to be controlling the actual Controls for this like pitch and roll and and yaw. So we need two functions here. We're gonna say handle Engines like so and we're gonna do handle controls And then we need to actually write this implementation. So we're gonna do Void and actually let's make these protected virtual as well We might want to make other types of drones. All right, so to do that We're gonna do a virtual this allows us again to override whatever we write In here inside of this particular function in another implementation of a drone controller Okay, so hopefully that makes sense. We'll call this handle engines There we go, and then we'll do another protected virtual Void handle controls like so Awesome All righty now remember also just to reiterate, you know, how cool inheritance is This handle physics won't run if there is no rigid body So if we go the you know base implementation here in the base rigid body class Nothing will run if a rigid body is not detected. All right, so This is it's really nicely, you know, organized so that we reduce the amount of errors we can we will create Cool. All right. So the next thing we need some variables up here So what I'm gonna do is I'm going to create a new header up here. We'll call this some engine properties like so and What I want to do is I want to create a list of engines, but we actually don't have that class yet So I am going to change this to Drone properties. How about our control properties? Let's see even better. All right, so let's start here. We're gonna say private Float and we want to do the min max pitch All right. We're gonna initialize that the 30 and then we want another one. We'll say private Float min max roll. All right, so this is the the rolling and we'll initialize that the 30 as well And then we want to do a private float yaw power Now these are just names that I had come up with earlier You're more than welcome to you know name them whatever you want You know, you'll get more of an idea of what you want to name them once we get through more of the Physics and stuff. These are just names I came up with All right, so we're also going to need another private variable and this needs to be the inputs, right? So the IP drone inputs and I'm just going to call this input for the variable name All right, so what we should do because we're requiring the component We know we're going to have one there So let's populate this variable with the actual component. All right, so we're going to say input is equal to get component all right and We want to look for the IP drone inputs Like so Cool. All right, so that basically will grab the instance The drone inputs now will give us access to the properties that we made Earlier on. All right, so then we could get the values using these properties Okay, cool. So next thing we need to do I think that's actually pretty much it. Oh You know what we need to do. We need to make sure these show up in the editor or in the inspector So we need to do a serialized field on all these guys. Oops Let's copy those and paste those guys down like so very cool and Let's do something with Let's just prove Physics in general. How about that? So let's prove that, you know, we're actually inheriting from This particular class All right, and that our weight is actually working and assigning it properly to the mass So how do we actually make something? How do we actually make an object to sit or hover in the air? Basically counteracting the force of gravity. Well, the equation for that would be mass times gravity, right? so if we take the current mass of our particular object and we multiply it by the the magnitude of gravity, right? In which case Instead of unity if we go to our project settings and we go to physics it's set up for earth gravity All right, so it's negative 9.81. Okay, but if we take the magnitude of that, it's going to be a positive number So it'll be 9.81. All right So if we do mass times gravity or the magnitude of gravity and multiply an up force So vector 3 dot up and we apply that as a force to our particular model or our object The object won't go anywhere because we're literally Counteracting the force of gravity with the exact same amount of force. All right, so let's take a look at this. All right So I'm going to do RV and it looks like where's my base rigid body over here Aha, so let's make the rigid body protected not private. There we go. I didn't have access to it because It was private right even though we are inheriting from the base rigid body because this variable is private It's localized to just the base rigid body class now that I made it protected any class that inherits from base rigid body We'll now have access to it. So now I can say RB. Yep, there we go. So it's add force All right, so we're gonna add a force. So in this case, let's just do vector 3 Dot up. All right, and we want to multiply that by Our RV dot mass so the mass times the gravity or the magnitude of the gravity, right? So we say physics Dot gravity dot Magnitude Like that. All right, so if everything's hooked up, right? And I just kind of positioned the drone anywhere in space It's not on the ground the drone won't go anywhere All right, because we are applying an equal and opposite force to the force of gravity All right, so we're counteracting gravity and this is how we make things hover right and this is just a basic example here But there's a great way to just prove that all that stuff is working. So Let's go back into unity over here and go back to the inspector over here And let's drag and drop our drone controller on to our drone game object and look at that. We have a rigid body We have our drag an angular drag. So the start drag and the start angular drag are gonna get their values from here Okay, and our weight and pounds is one so one pound and now let's go and Lift this up in the air a little bit and get a better shots here. They're angle on this I think that's cool. And then let's just hit play and look at that Even though on the ridge about it. We saw gravity turned on right? We're not going anywhere because we're creating a force that is counteracting the force of gravity Cool All right, and we are on our way. So I'm gonna close the lecture there and move on to the next


Okay good afternoon everybody you're very welcome to this edition of the ESB lecture series lecture entitled smart networks for the energy transition I'm Fergal Vaknamara and I'm going to try to chair this session today and I'm really delighted to welcome to the Institute Professor Nikos Hatzeguru, Nikos you're very welcome. Nikos is the chair of the European Technology Platform for smart networks the energy transition he's also the chairman of HEDNO which is the Greek distribution system operator and equivalent of our ESB networks and he's also a professor at the National Technical University of Athens. From ESB's perspective this is part of the ESB lecture series and we're delighted to be associated with the Institute and delighted to be involved with this lecture series which I hope you found useful those of you that have been attending the series. What we're going to do today is is the usual format the speaker will present for 30 minutes or so and that will be on the record it'll be filmed and afterwards the Q&A session will be under the Chatham House Rule which as you know you may use the material in the Q&A but you may not attribute it to this house or to any person who's here in the room. I try to finish up two o'clock or just very shortly afterwards and can I please ask you to put your mobile phones on silent and those of you that wish to tweet the tag is at IIEA. So I suppose about the energy transition it goes it's very important to us to understand the transition and when we talk about the transition it's always important to know where the destination is and you and EITP SNET have contributed this piece of work and vision for 2050 involving 200 stakeholders in Brussels over what two three years and you built on the 2020 vision that that also was produced by the same platform. I've looked at the vision and I've counted up seven or eight adjectives in this and some concepts around circular economy and some concepts around Europe being a continuing leader in the world energy industry so we'd be very interested to hear your talk and you're most welcome to the answer to this. Thank you very much for allowing me to stand because being Greek I think I'd like to do my hands more. So thank you very much. I'd like to thank the Institute for its invitation. I'm very glad to be in Dublin and speak to you. I wanted to speak with you. So what I'm going to present is the vision of the EITP SNET for 2050 and just to make things into context let me summarize what happened in the EITP and a certain innovation in energy sciences. So 2008 the same plan was announced of the strategic energy technology plan that has set these famous very big goals for 20% in our gas emissions, 20% in energy in private production and 20% in energy efficiency. And then in 2014 we were able to create a roadmap that spoke about individual technologies and then put in a higher target of 40% of our gas emissions, 27% in energy efficiency and that also provides several policy challenges. And kind of we have the famous energy union priorities, what is called the winter packets that also puts new packets as new regulations that there is no discussion about. And just in 2016 the EITP SNET was formed. It is then the European Energy Innovation platform of Smart Networks for Energy Transition. And in fact this was a result of a unification of previous fragmented initiatives for the advisory bodies and initiatives from Europe. Basically there were two groups, it was the Smart Grid, the European Energy Platform, the Electric Networks and then the EGR which was the effort of the TSOs and TSOs to show the way that you had the commission for the energy transition regarding networks. So these activities were unified by the EITP SNET in 2016 and the EITP now have a new focus on innovation implementation and mainly on sector coupling, so it's not only now the Electric Networks but in all kinds of networks, also gas and liquid fuels, thermally and so it's beyond smart electricity grids, speak about the home and the system. The mission of EITP SNET is to set out the vision for the sector of innovation for smart networks and then get stakeholders to this vision to prepare and update the strategic system of innovation roadmap to report on the activities at European, national and industrial levels and regarding SET plan to provide input to the SET plan Action 4 which is related to energy networks and mainly the flexibility of energy networks so how the system can work with very high penetration in your premises. Identifying innovation barriers, developing knowledge-saving mechanisms to help bring results to the employment and the last point is perhaps the unique feature of EITP SNET is to provide a consolidated stakeholder view. So that's important because EITP SNET, for the first time, consolidates the views of all stakeholders and the energy. And these are TSOs, TSOs, these are TSOs, national employees, so we have also members of the ZNU, various nationals from Europe to the academy, storage, both technology and service providers, consumers, aggregated in terms of individual organizations. Thermal generation, here we speak about flexible generation so this is how to help the system operate with very high penetration. We are interested in the last thermal units, but in the thermal generation it is flexible to help the system operate. Renewable social generation, again, how renewable tools can provide flexibility by being controlled or provided services. ICP, both medical and social providers, equipment manufacturers, suppliers, the big manufacturers, and data-fetched energy carriers that you also have somewhere from regulators. So everybody is in this organization and what is important is that we try to provide consolidated views and it's very difficult to provide a meaningful view that has been agreed by all of these factors. There's a lot of discussions, a lot of exchanges and concessions. How it is organized, there is a governing board that is also the European Commission, is there a voice? It's 30 members, plus representing all these stakeholders. We have an executive committee of nine members and then we have a national stakeholders' coordination. So national stakeholders, not all nations of European Union participate but there are some representative members, persons. And then we have an expert coordination via five permanent working groups and all of this is assisted by the ETIPS Nets Secretariat which is funded by the Intensives for Review Project, which is a European project that funds the administration, secretarial support of all these organizations. But the actual work is done in the five working groups that are working group one, speak about reliable economic and efficient market systems about the real system, the system. And then, working group two, speak about storage technologies and several interfaces. Working group three, about flexible generation, both thermal and renewable. Working group four, about the stylization of customers. And working group five, about innovation, implementation. So how it can bring the outcomes, the main outcomes of research to industry, to business environment. There's a group that coordinates the national stakeholders. So in a few words, this is perhaps an important work group that sets the priorities, the requirements of the system. So that's mainly chaired by TSOs or DSOs. And then we have these three flexibility resources which is storage, flexible generation, and active consumers participated by the stylization. We have this working group that tries to bring research outcomes to the product environment. We have the national stakeholders group that provides what is done with national funding, so this is coordinated. So in fact, where we are at the moment, as I said, we were born in 2016. Now we are, in June 2018, we have published the vision. So this is what we're going to talk about today. Then at the moment we work on the 10-year roadmap because this is just a vision. You won't get many answers to just, we see a vision. But then you must see what steps you have to take to realize the vision. So this is done now next through the European, through the 10-year roadmap, the implementation plan that is divided back into three-year periods. And all this will be provided as input to Horizon Europe. And in fact Horizon Europe is very heavily influenced by the recommendation of this group. So if you look at Horizon, the previous working program usually had a lot of influence from the European platforms, like Greece. Now we believe, we think that that would be the main input of what should be done regarding such innovation in Horizon Europe. So the goals are what we always have set for many years, which is affordable energy for market-based mechanisms, security, resiliency, reliable supply and environment. So the three main pillars, they remain the same also in this current vision. And in fact, what is the main idea from the current system that you have little renewable inputs, mainly fossil fuels and raw materials, low circularity, low cycling, small scale CO2 capture, in efficient conversion, so the result is high CO2 emissions, high waste generation, to come into an integrated industrialized energy system, efficient system with renewable sources of input, almost full circularity, little waste, little CO2 emissions, recycled materials and CO2 capture and use. That's the dream. And let me come to the vision. So when we speak about the low carbon, secure, reliable, resilient, accessible, cost efficient, market-based, pan-European, decrepit energy system, supplying the economy for a fully CO2 neutral, circular economy by 2050. And that's perhaps new. So what's more or less discussed before, maintaining and extending the global European cost-efficiency energy systems. So also, we need to see how Europe maintains its leadership currently in whatever it has or also expanding its leadership, and also during this transition. Okay, this is the pictorian that summarizes really all this vision. Very convenient that it looks like W. Here's the port and the airport and everything in the right place. It's inspired by W. So in all these small boxes, there are elements of this vision. I know we can't read them, but just let me describe them. So in fact, to speak about the system with a variety of additional sources, both centralized and decentralized, so both large thermal, large stations and also distributed sources, and these are fully or large circular. So what you see here is nine energy numbers to very large energy numbers. You see no coal, no gas. There is a little nuclear, and that was a lot of discussions about nuclear. It should be clear now. It's not our vision, but several countries insist that by 2050, nuclear will not be without energy. So it's necessary even that nuclear will be here. And even liquid fuels will have been replaced by synthetic fuels or fuels generated by renewable energy. So you will have a fully or largely circular production system. Where the customer will be fully engaged. So if you see it here, you see zero energy buildings, smart cities, renewable communities, peer-to-peer energy trading, heat pumps, solar thermal generation, rooftop solar, energy communities, all the various resources, distributed resources. Many forms of storage, not only electrical storage through batteries and through university hydros, but also storage in gas networks, storage in liquid fuels, all forms of storage. And this is a particular emphasis on storage in this region. So that's for instance how today the electricity market works. We have dispensable non-renewable, we have dispensable renewable and variable renewables, which is which or etc. in demand. In the future you have an automated value-based storage conversion where of course the pigs are covered by stored energy and from your service you store the energy etc. So you have a more efficient system. And you have convergent technologies, widely used, all forms of convergent technologies, power to gas, gas to power and heat through these technologies. You have power to liquid, power to heat, that's of course common today. So you have all forms of convergent technologies. So you have a system, you have networks that exploit all the flexibility provided by the other networks, fully integrated networks. Electricity, heating and cooling, gas and data and a lot of digitalization. To make all this system work, you need of course digitalization, you need exchange of data, you need exploitation of the data in all forms to provide logistics that help the system operate efficiently. And again all forms of wireless communication, wireless communication, all technologies are clouded. So, now let's look at the building blocks of the vision. In all this activity, customers are supposed to be in the center. They have the central role of how the system will operate. So there are three basic principles that can be identified. One is markets and markets will enable price-based coordination. So, based on a various forms of development generation with no substance anymore, you will allow system that is efficient exploiting the new rules with market rules. You will have an optimal use of new rules. Whether demand across Europe, so it will enable diverse use of resources, buy more synthetic gas, will enable and use value for industrial products and also for houses, also for aviation and for shipping and non-business tracking. And as I said, storage will be also taken full advantage from seasonal to hourly variations. Digitalization and communication is the second important ingredient. You will have information with technology like Internet of Things that will exploit the wide installation of smart meters and sensors to the network that will provide data for real-time monitoring and control for the information needed but only from sensors but also from other activities that they have in our society. You will have analytics for the mining, you will have all the information of the data from the network and massive connectivity and massive exchange through machine to machine and all these widely connected machines in the system. And finally you will have the integration and the collaboration with the customer and the physical system and by that I mean between TSOs and DSOs because as you know now flexibility is very important so you need flexibility not only from the connected network electricity, gas and heat and buildings, etc. but you also need to have a cross-collaboration between TSOs and DSOs and in fact as system developed and more and more new the flexibility is displaced, a thermal generator at the transmission level that is displaced gradually by the new generation which did more flexibility and naturally in place of bigger source now exist more and more a distribution network for you have the most distributed generation connected you have more active customers connected electric base, etc. these are flexibility sources and it's an ongoing discussion how this will be exploited by TSOs, DSOs and several models that can help both balances and also congestion dealing with congestion in the system subsidiary is another important concept which means that systems must exploit must rely as much as possible to the local optimization of the system and the problem in the higher levels when they cannot deal with it locally so again the ideas of microgrids, the ideas of globalized communities all this is thought of taking an important role in the future and final automation I mean you see now the system highly automated not of course manual but more automation and automatic services and remote control, etc will be installed in the system as well as equipment now that are more based on flexibility provided by power electronics by fax systems and all these mutilations so that's another picture of how the future grid systems will look like so you have here a generation that is provided mainly by renewable electricity also new electricity and heat new electric cooling the renewable gas, the renewable fuel and you see here the consumption which is noted by two way arrows which means the concept of consumer who not only consumes but also produces electricity everywhere in households in the industry, in agriculture and you see a much more wide amount of electricity for the development of ground transport, marine aviation so you have this new change also in the energy consumption in the middle are the networks so you have the gas networks, the thermal networks and the liquid fuel networks that are interconnected through local compression technologies you have gas storage, heating and cooling storage and the main electricity storage the batteries as high as you have all the interconnector the combustion source gas to heat, gas to power or to heat or to gas or to heat etc so that's how the system will look like and the electricity network is the backbone of this system it's the most important vessel type type of network and it's made for the system of air so the first network is the backbone of the grid system and you see all these other energy networks being interlinked and supporting each other regarding the flexibility of the system so the framework of the radar is as I mentioned before you can see the world economy already Europeans are quite advanced in some aspects for instance in standards there are some good there is some leadership in standards there is some leadership in other fields so this is to be strengthened and expanded all these protocols will bring economic disruption and so creation to see how new business will be formed how education will be transformed how it will create new specialities, how the university will adapt to these new challenges we need to think again about the governance and financial processes there is the feeling that at the moment the business is not done perhaps optimally there needs to be more important how to bring the sets into product to make more use of what is created in the European projects and it is important also to the last message I said that we need to up to date we need to bring stakeholders together we need to get parts, make platforms stakeholders, communities with benefits because if we don't do it today the time is passing very fast and Europe will be there behind and so that's my talk thank you very much for that


Lemongrass, Symbopagin citratus, from the Posi family is a widely used plant in pharmacological activities due to its antiseptic, antibacterial, antifungal, and anti-inflammatory properties. It has been primarily used for food preservation, therapeutic applications, cosmetics, and agriculture, but this review also covers lemongrass as a source of cellulosic matter for adsorbent use and biocomposite production, with recent studies on emergent types of lemongrass fibres being reviewed. This article was authored by Zatilhafila Kamaroudin, Ritwanda Maidin, Modsilkhafli Selamat, and others.


This is stock number AT430A, we are here at Summit Automotive in Fond du Lac, Wisconsin, your new and used heavy-duty truck headquarters. Today we are checking out this super clean 2008 Ram 3500 quad cab long box dual rear wheel. This truck has a 6.7 liter Cummins diesel and from this HD video you will be able to tell that for the age and miles on this truck. It is in really nice shape, brilliant black crystal pearl is the color we shoot all of our videos in 1080p. So if you have HD capabilities on your computer, tablet, or smartphone device, turn them on right now because it's like you're right here looking at the truck with me and definitely your best way to check out the vehicle before seeing it in person. Comes with the steel wheels with the chrome covers, Firestone TransForce LT 23580R17 tires, with I'd say probably about 80% of the tread left, frame and underbody looks like it's in really nice condition, front fenders in really nice shape, I didn't see any dents or dings on the front bumper, very nice condition, passenger side fender is in nice shape as well, no major dents or dings on that, and the passenger side rim, no scuffs or scrapes on that. As you go down this side of the truck you can see just how clean the body is, how reflective and mirror like that paint is. We take these HD videos so if you're far away or even if you're close by and just cannot make the trip down, you can still see the truck, hear the truck and have confidence in the vehicle that you're looking at before you even get here. Cab is in excellent shape, passenger side doors, I didn't see any dents or dings on those, the Dooley tub looks like it's in nice shape as well, frame and underbody, really nice shape for an 08, it has been DPF deleted and it has MBRP exhaust on it, the back tires are general Ameritrax and they have probably about a little over 50% of the tread left on them, you can see the box rails are in really nice shape, I'm talking about these guys right here, those are usually what goes out first as far as a corrosion standpoint, but they're in really nice condition, got the chrome tipped exhaust as we come around to the back of the vehicle, full towing package which includes a 7 pin wiring and a receiver hitch there, tailgate is in really nice shape as well, it has an access soft tonneau cover, no major rips or tears on that, does have a ding at the top of the tailgate, unless you're really looking for it you can't see it, has a spray and bed liner toolbox up there and fifth wheel bed rails, you also have a 7 pin wiring in the bed, really clean back here, there's a dent I was talking about on top of the tailgate, but we want to give you the most accurate representation so that when you get here there's absolutely no surprises and down this side of the truck, really nice and clean as well, it really tubs in nice shape and this back rim is in nice condition too, down the rest of this side of the truck I didn't see any major dents, has the heated pulled out tow mirrors, they fold out like so, they also fold in, inside the ST package gives you the gray cloth interior, seats are in really nice condition, didn't see any rips or tears, factory floor mats throughout, windows power locks and power mirrors and as you hop inside the truck here you can see that this one has only 53,124 miles, you get the white faced instrument cluster, the steering wheel is in nice shape as well, no major scuffs or scrapes on that and you do get cruise controls on that steering wheel, you get the six speed automatic transmission with the optional tap shift AM FM CD player, climate control down there, aftermarket brake controller, this one has never been smoked in, cigarette letters never been used and you do get the 4x4 shifter on the floor, passenger floor mat and seat are in nice condition as well, no rips or tears and the headliner is in excellent shape in this truck, you get a compass temperature and mileage display and we'll take a quick look at the back seats and then we will check out under the hood, back seats are just as clean as the front seats, no major rips or tears back here, it does have the latch child safety system for your car seats, factory floor mats and carpeting is in nice shape back here as well, that will take a quick look under the hood, I'd personally like to thank you for checking out the video today, hopefully from this HD video, you'll have been able to tell just how clean this truck is all the way around inside and out, under the hood we have the 6.7 liter Cummins diesel engine bay is very clean, runs very smooth, this truck has been fully safe and inspected by our service shop as a fresh oil and filter change, all the fluids have been checked and topped off, truck has been gone through mechanically 100% and is 100% ready to go, to see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, wranglers, halftons, recorder tons, one tons, you know we got to go to our website www.summitauto.com, full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you'd like to check out more HD videos you can go to youtube.com slash summit auto, remember to like, subscribe and share on this video and all the videos that you see there, in fact in a second you will see a link to subscribe to our YouTube channel on your left, a link to more heavy duty truck videos like this one on your right, if you have not been to our website on the bottom link to this vehicle on our website click those check us out and we really look forward to helping you with this super clean 2008 Dodge Ram 3500 quad cab long box dual rear wheel Cummins diesel, thanks again.


So my whole thesis is built around Disney and Disney, I mean, he founded the studio in the 30s, his model's been staring everyone in the face and nobody's replicated it since the 1930s and it went like this. Disney understood one thing that every studio has ignored for whatever reason and that was every piece of content that he put out had to be feeding into a brand ethos. So everything is about the magic of childhood, about good triumphing over evil. So if I say to you I'm going to go see a Sony movie or Warner Brothers movie, you don't know anything about it. Right, no I don't have any sort of, oh well if it's a Sony movie it's going to go this way. But if I say I'm going to go see a Disney movie. Right, yeah, you're right. You already know something. I've got a preconceived notion of what it's going to be about and that I can probably bring my kids that I don't have. Yeah. Exactly. Possibly going to be animated. Right, so our thing is if Disney's the most magical place on earth can we make the most empowering place on earth?