Good morning, but today I'm going it's not working. I don't know. Yes. Yes. Okay today I'm going to discuss the relation between the entanglement entropy and the renormalization group flow. The idea is to show you that it's possible to prove C theorems in terms of entanglement entropy, okay, in two, three, and four dimensions. Okay, let's... No, this is not. Let's start defining C theorems. The basic idea is that the renormalization group gives you a systematic way to study changes in the physics when you change the energy scale or the distance scale. Perhaps the simplest way to think of this is if you put your system in a lattice and you want to see the changes in your theory when you change the lattice space, for example, okay. And, okay, this information at the end is encoded in the changes in the coupling constants of your theory. These are known as the beta functions. And then if you want to have a picture of the space of theories, perhaps the first step is to identify fixed points, okay, in this space of theories. In this fixed point, the theory looks the same at all scales. We say that these fixed points are scaling variance, okay, and then the renormalization group flow interpolates between fixed points, okay. But what is interesting is that, in fact, in the flow, not all critical points can be joined, okay, with each other. There are constraints provided, okay, by C theorems. So take this as a definition of what it is C theorem. This state that certain C charge decreases from the UV to the infrared fixed point, showing the irreversible character of the RG flow, okay. So here I have listed three conditions. This C function has to satisfy in order to have a C theorem, okay. The first one says that you need a quantity which is independent of the regularization you use, okay. This we usually say a universal quantity. The second requirement is that C has to be dimensionless and well-defined at the fixed points, finite at the fixed points. And the last condition is that C decreases along the renormalization group trajectories, okay. And okay, now let's see why we can say that any universal dimensionless decreasing function C will do the job will satisfy the three conditions there. If you write the first condition as an equation, this is what you get. This is telling you that C is independent of the regularization scheme you are using, okay. The total derivative of C with respect to tau, it has to be zero. The second condition C dimensionless can be written in this way. And now if you combine these two equations, what you get is this. That it says that changes in C when you change this here R, here is a characteristic length of your system, okay. For example, in the case of entanglement entropy for regions could be, I don't know, the length of your interval, okay, of the region. And what it says, this region is that changes in C, the way C change when you change the length of the system is proportional to the change in C when you change the coupling constants, okay. So if you find a quantity that is decreasing with the length of your system, you are done. You are sure you have these three conditions fulfilled, okay. So let's see how, yes, say it again. The function here is the chain rule.  You can write it in terms of these partial derivatives and this gives you a function. Yes, but the point is that here, what you have here is you prove that from condition one and two, the changes in C due to changes in the length, characteristic length of your system are equivalent to the changes in C, changes in the coupling constants. This is the only thing you need. I am showing this because what we are going to show and also happens in the zomological proof. What he proves is that he finds a function C that is decreasing with a length, a characteristic length of the system. And then you can ask yourself, okay, why something that is decreasing with the characteristic length of my system is decreasing along the normalization group trajectory. And this is why, because C is dimensionless and is independent of the regularization scheme you are using. Okay, this is the motivation for showing you this relation. Yes, it should say tau here.  So in general, of course, you are knowing, you cannot, you can, this is showing you that both things are related. Okay. Perhaps it's redundant, it's a redundant way of writing it. But this is just to show you that many times people ask why if you have something which is decreasing with the length of your system, you have something that is decreasing along the normalization group trajectories. That that's why I'm explicitly showing this, this relation. Okay. So the first C theorem that appeared in the literature was due to samological in 1986 for two dimensions. And what he proved is that the C function at the fixed point for in two dimensions corresponds to the Virasoro central charge. And he also found the C function in terms of these two point correlators. This is the trace of the stress tensor. And using reflection positivity, he showed this function is, the derivative of this function is negative. Okay. The idea is that of course this, the samological of C function at the fixed points, okay, takes, is finite and is given a Virasoro central charge corresponding to the conformal field theory at the fixed point. Okay. This in a way, try again. Let's skip this. Again. And now let me, let me go to the entanglement entropy side and let's see if we can give a new prove or an alternative prove of the same theorem, but in terms of the entanglement entropy. For that, I will use these two properties of the entanglement entropy. The first one is, tells you that the entanglement entropy given two sets, okay, with the same causal domain of dependence, you have the same entanglement entropy. Okay. This is easy to understand because what you are doing is tracing over the degrees of freedom that lives outside the region. And of course, the complementary region of A and A prime is the same as the global state is the same. Of course, you get exactly the same result. Okay. This is a way due to causality. Okay. And then we are going to use a strong subadditivity that I have already mentioned yesterday or the day before. So these are the two basic ingredients I'm going to use. Okay. Let me go back or forward. Let's see how the proof can be done in terms of entanglement entropy. So the basic construction, you have to take two intervals which are both to each other. Okay. And you put the boundary on the light cone. And the idea is to use the strong subadditivity to get some relevant constraints or information, okay, about this quantity here. So if you see the, why I'm saying I'm using the independence of the Cauchy surface because I can rewrite these are the two regions I'm considering. The entanglement entropy of this region here is equivalent to the entanglement entropy of X, Y. The entanglement entropy of B is equivalent to the entanglement entropy of Y and Z. Here we have the union and here we have the intersection. Okay. And now if you take the limit, this, this is big R and this is a small R in the limit. Okay. Big R going to small R. What you get is this equation here that has second derivatives of the entanglement entropy and first derivatives. From here you can read this function C here, which has first derivative, negative first derivative. And you say, okay, so this C function, remember the requirements I have listed before. We need three things. Okay. First, we need a dimensionless quantity. You need a regularization independent scheme quantity. And the third one, you need something which is decreasing along the normalization group trajectories. And in fact, this C function defined like this satisfies the three requirements I mentioned before. Okay. And yes. Yes. Well, here, what we need is Lorentz invariance and we are using Lorentz invariance and we are using, you are assuming unitarity, but well, you need causality, I mean, to have this independence of the Cauchy surfaces. And you need Lorentz invariance to express the entropy as a function of the length of the interval. Okay. Otherwise, it's not true. But these are the two things I'm using. I'm using Lorentz invariance and causality. Well, I'm not using, if you want, in the use of independence on the Cauchy surfaces, you are implicitly saying that your theory is unitary, but causality. But it's not, there's no step here where you need unitarity. Okay. Yes. And okay. Then if you want to generalize, okay. Let's compare the, so now we have two C functions in two dimensions. We have the the entropic C function and the samological C function. Both gives you a, are equivalent in the sense that, yes. What? S of r. F? S of r. Okay. S of r. Yes.  It's just the length here and bigger here, the union. And small r is this length here. So the size of a is just the square root of the product of both. Okay. So here you have the entropy twice the entropy. The same, you are taking a and b have the same length. So you have twice the entropy here. And this is the, the union. Well, this is the union and this is the intersection. Okay. And the infinitesimal limit, you get, you get this expression for, for big r close to small r. Okay. And from here, you can read this function satisfies as negative derivative. So, so far we have, we have two. Well, something which is interesting is that this entropic C function at the fixed point gives you, it's again proportional to the bidazotto central charge. Since you know how to write the entropy at the conformal point. So this is the expression of the entropy at the conformal point. If you evaluate your C function at the conformal point, what you get is something which is proportional to the bidazotto central charge as in the samologic of proof. Okay. And here it's the way it looks, the, the C function for a Dirac, a real scalar and a Mascherana field. And then you can ask once you have two, two different C functions, you can ask, which is the difference if, is there a best one, are they related to each other? If you can deduce one from the other one. And the answer is that the, the entropic C functions in fact are not related to the samologic of C function. In, in what sense? The idea is, I mean, when we were trying to, to answer these questions, we didn't know that Capelli, Friedman, Friedan and La Torre in 1991, they, they already answered the, the, these questions. They didn't know about the, these entropic C functions, but what they, they, they, they show in this, in this paper is that in fact, once you have one C function, you have an infinite number of C functions that can be built in terms of this spectral density rho here. Okay. And the, the way you can construct any C function is using, okay, a numerical function that satisfies these conditions. So any function, any C function has, that has this form satisfies the three requirements I mentioned in the beginning. And, okay. So, so you have a huge family of C functions in two dimensions. And you can say, okay, this entropic C function belongs to this family or not. And the answer is no. It's completely different because, and one way to, to deduce this is you know the relation in an example, I mean, you can show this is not true because you know the relation between these spectral densities for a scalar and a Dirac field. And this relation implies that any C function which is, which belongs to this family satisfies the relation here. So, as this is negative, what you have is that the C function for a scalar has to be always above the C function for a Dirac field. And for the samological C function, this is true. Let me see. The first two curves corresponds to the samological C function and these two to the entropic C function. And in one case, okay, you have for a real scalar and for a Dirac field, which is the example I am giving you here. And for the case of the samological C function, what you have is that this one here is for a real scalar and this one is for a Dirac field. And in the case of the entropic C function, you have exactly the opposite. It appears first for the Dirac field and then for a scalar. So, you are sure that the entropic C function doesn't belong to the same family. So, it's a different constraint even if all both at the fixed point looks the same, okay, gives you the same or are proportionate at least. So, nothing. This is just a comment because we were, for a long time, we were trying to relate both C functions and at the end we realized that it's not going to be possible, okay, because are completely different constraints. So, now let's go to three dimensions and what we have learned in two dimensions is that it's very useful to put the boundary of your regions on the light on the null cone. And we also have a hint in three dimensions, we knew we have to use circles. And why? Because from holographic C theorems, from the f, the conjecture of f theorems and also there was a proposal by Liu and Mesay for a renormalized entanglement entropy always considering circles, okay. The constant term of the entanglement entropy of a circle was the candidate proposed in three previous papers. In fact, in this paper here, it's not the constant term of the entanglement entropy for a circle, but the free energy. But at the end, you can show this is exactly equivalent proposal of the, I mean, you can show that the free energy, to calculate the free energy, it's equivalent to calculate the entanglement entropy for circles, okay. So, we were sure the circles were the good candidates and we want also to use strong sub-additivity because it works into dimensions. We know the boundaries had to be put on the light cone, but the problem is that now two sets are not enough and the reason I'm saying two sets is not enough because intersections of circles and unions of circles are not circles. So, and why you need the same kind of regions on both sides of the inequality because you need to cancel diversion terms.  So, the solution we thought is that instead of taking two, we can take an infinite number of circles. This is the planar construction, okay. You take circles, rotate it, an angle two pi k over n around a point, of course, different from the center and in the infinite and limit, the sets you get looks like circles, okay, centered at the same point. So, you say, okay, I can use, here I have written the strong sub-additivity inequality for three sets and, okay, it works in the sense that you have the same number of regions on both sides of the inequality, but the problem is that in this planar construction, you see this wiggle region has casps, okay, and we know that in three dimensions for circles, we don't have logarithmic contributions. So, in this part, the left hand side of the inequality, you don't have log contributions in the entropy, but you have log contributions to the entropy in the right hand side of the inequality, okay. So, it's not going to work because you cannot cancel the infinite on both sides of the inequality. So, the solution, go to the light cone, because as you approach the light cone, the angles, okay, go to pi and also the perimeters, even if at first sight you say you believe that in planar construction, this wiggle region has the same perimeter as a circle, it's not true. And, okay, you can prove that if you put your construction on the light cone, the limit, the infinite and limit is enough to, in this limit, the entropy of this wiggle region corresponds to the entropy of circles, okay, it has the good limit. And, okay, this is the expression you get for once you take the infinite and limit, and again, you take the infinitesimal limit, big R, go into small R, and you get this inequality now. You get a restriction for the second derivative of the entropy. This tells you the entropy is a concave function, okay. And again, from this inequality, you can read a C function, an interpolating function with, which is decreasing, okay, with first derivative negative. And, as you know, the expression of the entropy at fixed points, if you evaluate your interpolating function at the fixed point, what you get is exactly the constant term in the entropy. But now in, okay, remember we have three requirements, so we have already a decreasing dimensionless and decreasing function, but still you say, okay, this quantity at the fixed point is or not well defined. And the problem is that we know that the area term in the entanglement entropy is not universal, I mean, depends on the regularization you use. It's easy to see that if you change your definition of R in the lattice, for example, you can change the value of the constant term. And again, you can find a solution, you can find a solution introducing the mutual information, which is a well defined quantity in the quantum limit. And the idea is that you can define a kind of, I don't know, you can use this mutual information as a geometry regulator for the entanglement entropy. The idea is that you take these two regions and you take that in the limit when epsilon goes to zero, the mutual information is just twice the entanglement entropy of the circle, okay? Because, okay, the union is almost everything, so the entropy is zero and the entropy of A becomes equal to the entropy of B, okay? Here we are using that the entropy of the complementary region is equal to the entropy of the region if you start with a pure global state. So you have a way to define the entanglement entropy in terms of mutual information and then you are safe saying that you have a good definition of the quantity at the fixed points, okay? And, okay, now you say, okay, you can go to higher dimensions, you can go to four dimensions, just taking now spheres, okay? Boosted spheres and putting these spheres on the light cone. But before, which are the proposals done by other people, for higher dimensions, you have these the early result by Cardin in 1988. He proposed the coefficient of the Euler density term in the trace anomaly at the fixed point as a candidate for a C theorem, but just for even dimensions, in odd dimensions, you don't have such anomaly. Okay, for odd dimensions, you have these holographic C theorems that tells you these are very general because they have also not only a proposal for odd dimensions, but also for even dimensions. This is the same as Cardin's proposal. But for odd dimensions, what they say is the constant term of the sphere entanglement entropy, the good candidate for C theorems. And also we have the F theorem propose final term in the free energy, okay, of a three sphere decreases between fixed points on the renormalization group flow. And in fact, they show that in many cases that it works, but they didn't have the proof. So let's skip this part. And okay, let's go to four dimensions. Okay, if you try the natural generalization, as I said, is to take symmetric configurations of boosted spheres in the limit of a large number of spheres. And so you do exactly the same thing. You apply strong subadditivity. And what you get for any dimensions is this expression here. This is the general expression you get using this construction, okay? And okay, in any dimension, the only problem is that this is true only if you can replace the entropy of these wiggly spheres by spheres, okay? That in three dimensions was true, but you have to prove that in any dimensions this is true also, okay? So this if, in a way, means that you have to answer these questions here, okay? Does the inequality contain cutoff independent information? This means diversion terms cancel between the two sides of the inequality. The second question is whether the wiggly spheres entropy can be related to sphere entropies. And the last is, okay, suppose everything goes okay and you can replace entropies of wiggly spheres by entropies of spheres. Still, you have to make sure that the inequality teaches you something about central charges at the fixed point, in the sense that if the inequality is strong enough to reach the log coefficient in the entanglement entropy. Since we know that the strong subadditivity at most gives you second derivatives of the entanglement entropy. So you naively in four dimensions use this inequality and you evaluate for a fixed point, you know the expression for the entanglement entropy. What you get is that the inequality is incorrect, okay? You get the wrong sign. So, evidently, this replacement of entanglement entropy for wiggle spheres by entropies of a sphere was incorrect. We spend a lot of time trying to see if the angles in these in four dimensions gives you log contributions, okay? And geometrically, you can answer this problem and the answer is that there's no log contributions coming from the angles in four dimensions. It's hard to prove it, but still you can do it. So, the problem was not coming from the angles, but the answer is that the problem is that these wiggle spheres have gives you a finite contribution that is not canceled in the inequality. So, the solution for this is to use something called the Markov property. We are going to use the Markov property of the vacuum state and the statement is the following. The strong subadditivity for the vacuum state saturates when the boundary of your region lives on the null plane, okay? This is true for any quantum field theory and in particular, if you have conformal symmetries, this is true also in the light cone. So, what you can do at no cost is to insert in your inequality these zeros, okay? This relation, I mean, for the entanglement entropy, the strong subadditivity when it's applied in the UV is Markovian, okay? And then it's, you can introduce in your inequality these zeros and in order to define these new quantities. So, you are going to introduce this quantity that is just the entropy minus the entropy of the UV, okay? And you can do it, you can replace without changing anything else this quantity here in your inequality since the vacuum on the light cone is Markovian, okay? So, you are inserting zeros in your inequality and the good news is that now these new quantities have the good limit in the infinite end limit. So, these new quantities goes to, from wiggly regions to spherical regions, okay? Have the good limit. Then you can replace in your inequality here, it should say S for wiggly regions, but you can write S for spheres, okay? And, okay, this is the solution of the problem and what you get is this inequality here that tells you that the coefficient, the logarithmic coefficient in the infrared has to be smaller than the coefficient in the UV. So, this is what we know as the A theorem. In general, perhaps this is better to write this general expression here in terms of the entropy of the area and this tells you simply that the second derivative is negative. So, it tells you that this new quantity that has the entropy that has subtracted the entropy of the UV is a concave function and you can rewrite this expression in terms of the area and just gives you that the second derivative of this quantity is negative, okay? So, in this way, you put, if you want on the same footing the three proof, okay? For two dimensions, you get the C function in three dimensions, you get the F theorem in four dimensions, you get the A theorem, okay? And the three of them can be treated in the same way, just putting your sets on the light cone and applying strong sub-additivity. These are the ingredients we are using for proving the three theorems, okay? Then you can ask if we can go to six or five dimensions and the answer is no. And the problem is that, okay, everything works okay, but the strong sub-additivity is not strong enough. Second derivatives of the entanglement entropy are not enough to reach the log coefficient. So, it gives you an area theorem if you want. You think that the second derivative of the entropy in terms of the area is concave, you have two restrictions, okay? I mean, the slopes of the curve in the infrared has to be smaller than the slope of the curve in the UB. And you have also a restriction for the height of the tangent line at the infrared. It has to be positive. This means your curve is concave. And these two restrictions are not enough.  So, this is, we need more inequalities or or something is missing.


Hi everyone, Joe for jazby's casebreaks.com coming at you with our Second to last filler to unlock that jazby baseball is back repack But first let's do the blaster break itself then we'll re-randomize everybody's names to see who's gonna win their way in We've got overtime in Milwaukee. My Lakers in Milwaukee 112 left Tied it 111 apiece big thanks to this group for making it happen Appreciate you There are the teams right there. Let's roll it Let's randomize names and teams three and a three six the hard way one two three four five and six and Then six the hard way for the teams What a move Good bucket one two three four five and six Here's the first half of the list right there. No trade windows There's the second half right there And let's print and rib Lakers up by two on a nice hot room. We're a bucket 45 seconds left Yeah, Rex a Rex only cares about sweet 16 games starting three days later only because he's a Second I think in our jazby's bracket and they have to travel Rex come on There's traveling involved sometimes you're going to new locations for the sweet 16 Etc. Etc. And then you got to you got to give those those first two round teams Chance to catch their breath before they embark on another difficult round takes three days Rex said Rex hasn't I don't think Rex has traveled out of his state in a in a decade or so so Attracts There's a numbered Otani card to 199. It's a Riley Green new money card right there And there's a renowned rookies Sometimes they do during the regular season What we're talking about college, but those are like Millionaires playing for billionaire franchises. They've got a lot of money to hop on chartered planes whenever they want to and fly wherever All right, so there were there was your break right there Now let's see who's gonna win spots in the repack Unable to buy into the repack Anyone else having the same issue? I'm checking out here And it seems like I can go through the checkout process Yeah, and they're also kids. Yeah, sure. You're sure they're they can You know bounce back a lot more quickly than us, but it's only one of those kids only one or two teams that have actually might have a team player that could go to the NBA most of them are just pretty much fresh out of high school Yeah, adds to cart just fine All right, so let's go Roll it and randomize four or two six times top six after six we'll get into that repack one two three four five and six up Gilo what's going on and There's your top six right there. Congrats Tyler Tyler Ryan, Yohan Yohan Paul. You're in the repack now. Let me figure out what's going on with the check out Thanks, everybody. I'll see you next time for the next one. Bye. Bye


Hey, anybody who's operated at sea or shore knows that energy is absolutely critical to doing our job. By optimizing our energy use, we can increase our operational range, our endurance and payloads, turning energy into a force multiplier. Operational energy is important because it makes us a more effective fighting force. It makes us more lethal, able to prosecute more targets, able to stay on the battlefield longer so that we are more effective and a better mag tap to support the defense of the nation. Finding ways to conserve energy, afloat and ashore will enable more combat capabilities. We're using more efficient technology like the hybrid propulsion systems on board USS Macon Island and USS America and implementing additional shipboard energy saving measures. Let's all do our part. Hey, little things add up here. In Yucosca, sailors were able to reduce their energy consumption by 74 percent, almost three quarters simply by securing the lights and equipment when they weren't using them. We care about energy, but we don't care about energy because it's green. We care about energy because it makes us better at killing more bad guys and breaking their toys. With everyone's help and commitment to the cause, we can reduce dependence on fossil fuels while simultaneously enhancing our nation's energy security. Everybody pitch in here will make every kilowatt go farther, every gallon of fuel count, it will be a smarter name. Together we can make energy a force multiplier and achieve critical fuel conservation goals. We'll see you out in the fleet.


Hi everyone, Joe for jazby's casebreaks.com with a quick little random number block randomizer for the following teams here If you're not familiar with it, that's how it works But I think most people here are familiar with it Good luck. Here are the numbers right there. You get a block of numbers. Let's roll it randomize it three and a six nine times for names and numbers one two three four five six seven eight and Ninth and final time Got Nicholas down to Sean. Oh All right. Thanks Kyle. Thanks for hanging. We'll see you next time three and a six nine times for the numbers one two Three and ninth and final time after nine. We got nine down to four now remember as it says in the description Zero gets any and all redemptions including one of one redemptions One still gets live one of ones Nicholas you have nine Sean with one PJ with five Sean with two PJ with seven Nicholas with zero So any and all redemptions for those four teams down there Sean with six Dario with eight Nicholas with three and Sean oh with four. Let's order these numerically Coming up in a separate video will be that diamond icons break itself jazby's casebreaks.com. Bye


An opportunity to move into second place in Ligue 1 for Bradford City this afternoon, but a tough task ahead of them as they come up against the Rochdale side. They've won seven of their last nine games. So with Bolton not playing until tomorrow, a chance for Bradford to move into the top two. It's Rochdale coming forwards here. An opportunity for them perhaps, but a strong challenge comes in. Calvin Andrew, of course, for Rochdale this afternoon. Henderson as well. They are there. Main sources of goals. A chance here for them. Flash just wide. A real opening. Andrew Cannon couldn't take it. Will Rochdale carry this afternoon without Henderson. Or without Andrew. They've started well hit. Camps tussling on the edge of the area. And there's Lang to Camps. People towards the far post. Left side flag was up, but Sattelmeier didn't know that in the Bradford goal. Bradford to really click into gear so far in this game. Rochdale certainly been the brighter of the two sides. Marshall skips inside and looks to weave his way through the challenges. That has to be a yellow car for Canavan. Indeed, it is. Marshall's run abruptly brought to an end. A decent opportunity here to test Josh Lillis in the Rochdale goal. Effort comes in, but it's a comfortable save for the Rochdale keeper. Bradford, 3-8 from this corner. He forgets a punch only to the edge of the area. The strike comes in. Appeals for Handball. The strike from Nicky Law. Pressure starting to build as Bradford. Find a rhythm here this afternoon. Rochdale, of course, in fine form. As we mentioned, seven wins from their last nine. Bangerus, Paul in. Who wonder though, Bantakalvin, Andrew will affect them. Taking quickly. Hansen gives chase, but it was always asking a lot of him. It's a very poor clearance though. Bradford unable to capitalise. Was ever inside the Northern Commercial Stadium this afternoon. He was watched out too far to travel and for decent numbers as well. And to turn away there, Josh Cullen from the attentions of Andrew Cannon. And Bradford the free kick, Nicky Law. Beginning to grow from Bradford as we move towards half-time. 8-1-2 to Nicky Law. Sends in the cross off his left foot. Breaks for Clark. And Bradford take the lead. Sixth lead goal of the season for Billy Clark. And Bradford make the breakthrough just before half-time. Pressure had been building. Found his way across to Clark. Nillis went to his left, but he couldn't keep it out. Bradford themselves the lead. Pass played forwards. Marshall give chase over on the far side. He came out on top with defensive work for a second here before half-time. Took the traffic over on that far side. Effort comes in. Nillis tips it around the post, does he? Born as a Bradford. Born as sent in. And off clears the danger.  It's two. Bradford double le just before half-time. Rock style undone once more. Another ball into the box. And there was Timothy DeAnke with his second lead goal of the season. Got onto it early. A fine glancing header beyond Josh Nillis. Stuart McCall's side are in a very strong position. Way back into this game. He comes to the corner. The header comes in. Just have struck his own man in there. Can Bradford get it away? He law steps in. And he works out all right in the end for Bradford. Plays it forwards first time. Strong challenge. And he could be in real trouble here. Canavan has already been booked. And then Rochedale are going to play the final 32 minutes of this game. A man short. Josh Cullen turning away. Oh God. Marshall over this free kick. She sends it in. Kept out by Nillis. But there's Hanson reacting first to his own. Head up. Nillis got down low to keep it out. There was Hanson following it up. It's three for Bradford. And surely all three points. Rose Highest. He was the first to react as well. Three in two lead games for him now. He scored twice in the win against AFC Wimbledon a couple of weeks ago. He surely made short of the points here for Bradford. Chase on hit. And away by Nillis. Now Marshall had a decent afternoon on the right side of that Bradford midfield. Cullen taken down once more. Coming to be a real tricky customer. Josh Cullen growing reputation he carries. Marshall steps up and he makes it four. Fine free kick. Nillis rooted to the spot. And Marshall has had a fine, fine game for Bradford. He's rewarded with a goal. Just cleared the wall. And Nillis just turned to his left. And saw the ball strike the back of his net for a fourth time this afternoon. No doubt about it. Bradford heading into the top two on defeat for them. So far in the league this season. Coming away at Oxford in the middle of October to an end. Their best ever unbeaten start to a season. Inside the league wants to lose this season. Chance for a fifth. Nillis Hansen, challenge made by Mendes Lank. He's turning into a long 90 minutes now for Rochedale. A man short and four goals down to the game brightly. But that's just before half time which is going to cost them. Those goals for Clark and the end in the final four minutes of the half. Bradford in search of number five. Nillis pushes it away. Left it from the rice. Just looking to add further gloss to the score line. Now here's Cullen probing away on the edge of the area once more. Wasn't too far away. Got a wonderful afternoon. Time all but up here to find a way through. But there is the full-time whistle. Bradford putting Rochedale to the sword. Goals from Clark, Dieng, Hansen and Marshall. A fine afternoon for them. They're into second place in lead one. Bradford City four. Rochedale Nill.


What happens when my passport expires? Can I renew my KataID? Is my passport expires? Can I renew my KataID with an expired passport? Tune in to this video, this makesharma TV the only channel Na kwa, niha mwen PHII, shu baki hnda nga na nga uchataidu nga. Igni si kuha, na kwiko na kwa nga illitha kwa kataidu uchataidi nga uchataidi nga uchataidi. meza niha kwa uchataidi nga uchataidi kwa kataidi. kwa uchataidi nga uchataidi nga uchataidi. You are in the hospital section, you are in the facility management, facility management section, you are technician, domestic worker, you cleaner, in any category that you are working in is that you need to be aware of this. To some companies they will never renew your Kata ID in case you want to continue with that company for a given period of time. Unless your passport has a validity date of six months, that is actually the period that your passport is held. So look at a situation whereby your passport has expired and your Kata ID has expired and you wish to renew. What do I have to do? This is from my own point of view and this is from my own experience. I will tell you what to do. First of all before you think about even of renewing your Kata ID, make sure your passport has a validity date of six months. If it is for example it is expired and you are within the country, let's say for example you are working in Kata, you are working in Saudi Arabia, you are working Bahrain, you are working anywhere. But in this case I will talk about a situation in Kata here. What you need to do is you need to first renew your passport first, you need to first get a new passport first. How do you get a new passport? It's just you need to go to a embassy, the embassy of your country in Kata that can help you renew your passport. To some countries they are so lucky that the embassies can process the passports within the country, within Kata itself. That is being so lucky. That's what I'm talking about, that's the opportunity that we need to share at the time. So if your country has that kind of service within Kata, then probably do it very fast before you can think of renewing your Kata ID. Because I do not think even the company will accept to renew your ID, they will not accept to renew your ID unless that passport has that validity date of six months. So to some countries they are unlucky, the embassies cannot process the passports from here. The only option they have to give you is that they will give you a recommendation later to go back to your country. And all of you, all of you know what has been happening, we've been having with the pandemic, the pandemic from 2019. With its trust trust effects, you know what has been happening. So what does it mean is that you need to look away, you need to look for a way forward how you can renew the passport before you can think of renewing the Kata ID. But let us look at a situation now, let us just look at a situation right now whereby you have got a new passport either from your embassy or from wherever you have to process it from.  You present that to your company, old can be the human resource department in case if your company is going to do it for you. Because to some people they must be freelancers somewhere, some might have their own visas, some must be a family-sponsored visa in one or the other. So what you do, you get the old passport, the new passport plus Kata ID. That is what is supposed to be submitted to the Minister of Interior for upgrade. Normally in Kata what they do or what they will do, they will get the old passport details, transfer them to the new passport. Because what I know is that old passport and the new passport will have different passport numbers at the same time. So they will transfer your visa sticker from the old passport to the new passport. And they will transfer your Kata ID detail of your passport number from the old passport to your new passport. So meaning that once the two passports, the old and the new passports are submitted to the Kata ID, you will have a new print out of the ID that bears the passport number of the new passport. It normally takes a little bit, not more than 3 to 5 days it can be done depending on the company that is holding it. Or depending on your company how it does, the work or how it will definitely follow up in any way or the other. So it anyway in the world, you don't need to get worried about that. That can be done within days, then you can have your passport or you can have your Kata ID back. Or in the same situation, if you get your new passport then that means your company can definitely renew for you your Kata ID. If you feel really want to add or you really need to continue with that company at one way or the other. So I think it is well answered but the main part of it all is how have you renew the passport from where. If you have the embassy then that is good enough, you are lucky enough that you have the embassy. They can definitely try to do that for you and you will get the passport within a given period of time that is allocated for that. Then you will have to submit the passport that will have to transport your sticker visa from the old passport to the new passport. Remember, they can give you an E visa or not even an E visa that can be given to you if your passport does not have validity period of 6 months. I think that is the mandatory period that each one is supposed to have. I hope you have learnt something and hope you can. So it is no big hassle to some companies. Human resource may be a little bit lazy and they may not do it well but it takes a little bit of 3 to 5 days.  Thank you so much for subscribing to my channel. If you feel the information is very important and grateful, please subscribe to this channel and comment in the sub section. Always be grateful to get back to you. By the way, don't forget to watch my other videos, educational videos. Always be grateful for the comments. Stay from the next creation TV. Thank you so much. See you again. Make sure don't forget to subscribe to this channel. The only channel that will give you the true information. Thank you so much.


Water can be your best friend, it can also be very deadly. We've had a few pretty bad samples come up and once those kind of hit the news then people were like, yeah we should probably sample our water, you know. There's concern though, I mean, their livelihood is at stake. Our dugouts are near empty or they are empty and they do have water in that we've got water quality issues as far as sulfates, high TDS. We know that livestock water quality can be impacted by drought, especially our surface waters. As those surface waters evaporate, the salts in those waters become more concentrated, specifically the total dissolved salts and sulfates, which can be potentially toxic to livestock when they reach different thresholds. NDSU Extension agents have been screening water sources across the state and helping producers determine if they're potentially toxic. We do have a couple of different water testing devices, we've got sulfate testing strips that we can just show the producer a little bit of what they're dealing with. Check the water quality, see how murky it is, if there's possibly any blue-green algae there and then work with the producer. If I do notice something that's amiss or if something doesn't look right, to work with that producer to figure out a good plan. I guess a lot of the testing too has been preventative. They're doing it before they're putting livestock out there. So they want to know ahead of time what do I need to be planning for, and I'm hoping they'll continue to call me and have me come out here out this summer and I told them we should be doing this at least once a month, especially if you get really hot and dry, that way we know for sure and if they need to get cattle out, they can. Extension agents have helped monitor or evaluate over 700 livestock water sources. Of those sources, 48 have had elevated levels of totals as all solids and 72 have had elevated levels of sulfates. What's really interesting is if you look at the maps for these levels and correlate it to projects funded through the State Water Commission, a lot of the projects funded are in areas where extension agents have been sampling and screening water samples. Dealing with people, you know, telling producers, for example, that they can't put cows out on a certain pasture and it might be the only pasture they have, isn't exactly the easiest thing to do. Give the straight information with maybe a little bit of optimism and sometimes people just want to talk. This is why call your local extension agent. We're sympathetic. We understand and we want to help you any way we can. We're not miracle workers. We can't make it rain, but we'll do what we can.


It was 2007 when Carly Ryan fell head over heels for her boyfriend, Brandon Cain. Investigators say that the two had everything in common, but Brandon had a few dark secrets that Carly was blissfully unaware of. Detectives would learn that Carly and Brandon had been dating for several months leading up to the crime, and everything was going well for the two. But one day in February of 2007, things would take a dark turn when Carly failed to return home from a night out with her friends. She'd been acting somewhat strange in the moments before leaving that day, repeatedly asking her mother for hugs. It seems almost like she knew something was wrong, but she was powerless to stop it. Carly's mother certainly felt that something was a bit off that evening, but she could have never imagined just how terrifying things were about to become. Carly Ryan was born in January of 1992 in Stirling, South Australia. She was raised by her mother, Sonya, for most of her childhood, but there's never been any mention about what happened to her father, so I suppose it can be assumed that he was simply out of the picture. The thing about Carly is that she was growing up in the midst of a social media hurricane. By the time she was a teenager, it seemed like there was a new social media platform coming out every other day of the week, and this was long before Facebook was the goliath that it is today. Most of this case takes place back in 2006 and 2007, so we're talking about the days of Myspace, Zanga, Tumblr, and the countless other online messengers that were around. It was an incredibly interesting time to be on the internet, but it was also a remarkably dangerous time because many of the safeguards that are in place today simply didn't exist back then. Considering Carly was just a teenager at this time, her mother, Sonya, was pretty critical about what Carly got up to online. Carly and Sonya were remarkably close, meaning Sonya knew pretty much every detail of Carly's life. She'd often walk by the computer and take a peek at what Carly was doing, but knowing that her teenage daughter was a smart girl, she trusted that Carly was being safe and cautious. Sonya says that she feels like she knew everything that was going on in Carly's life. She knew all of her friends, kept tabs on what was going on at school, and was an ever-present force in all that Carly did. Not in a helicopter-parent kind of way, but in a pretty healthy mother-daughter relationship kind of way. You've got to remember it was just the two of them, so they were understandably super close. But the main issue here is that at this point in history, the internet was wild to put it lightly. Carly was known to spend a lot of time on a website called RateMyBody.com. For those of you that aren't familiar with this site, it's pretty much exactly what you would think. People post photos of themselves and anonymous users rate that person's body. The big problem with this website is that, as we've already established, there were virtually no safeguards in place. The website prided itself on anonymity, and that means that there was no way of knowing if the images you were looking at even belonged to the person who uploaded them. Worse yet, considering this website was often visited by teenagers, well, I think you'd get the picture I'm painting here. This was not a safe website, and it was a major hotspot for older men who had some rather nefarious intentions. Thankfully, this website has since been shut down. But Carly was often described as a scene girl. This is a bit of a vague term that's most often used when referring to teens or young adults who are super interested in the gothic punk lifestyle. These would have been the kids listening to bands like Blackville Brides, making Alexandria escape the fate, all while reading Twilight or something similar, wearing all black from head to toe, black hoodies, black headphones, so on and so forth. And don't think I'm saying this in a judgey or joke kind of way, I was one of those kids too. Heck, I'd still listen to all of those bands, dying is your latest fashion, one of the greatest punk albums of all time. For Carly, this was a group of people and a lifestyle that gave her a sense of purpose, a sense of belonging. She was known for being pretty active on websites like VampireFreaks.com, which is another goth or emo website in store.  Her profile was pretty much everything you would imagine it to be. It was full of gothic selfies, heaps of makeup, links to all of her favorite online forums, quotes from her favorite books, typical MySpace stuff. By sharing her interest in this genre of entertainment, Carly was able to make dozens of online friends. But there was one friend in particular who really caught Carly's interest, an 18-year-old named Brandon Kane. Brandon was a young musician who was born in Texas but had recently moved to Brisbane, Australia, the total opposite side of the country from Carly. The two immediately became friends as soon as they met. They liked all the same bands, had all the same interests. It was almost like they were meant to be. Before too long, their relationship grew into something more. Carly began to share stories of her new online friend with her real-life friends. It wasn't too long after this that Carly stopped referring to him as simply a friend. He was now considered her boyfriend. All of Carly's closest friends knew about Brandon and Sonia knew about him too. It seems that in the early days of their relationship, Sonia was happy that her daughter had met someone that she could be so open with. Even though Brandon was a few years older, Sonia didn't find this too concerning. She mentioned that she would look over Carly's shoulder from time to time to see what the two were chatting about, but she never noticed anything suspicious or anything that concerned her in any way. Before long, the two started video chatting with one another. And by all means, Brandon appeared to be the guy that he claimed to be. Carly couldn't have been happier. Even though her boyfriend lived over 20 hours away, she was just ecstatic to have someone that she could be close with. But it didn't take long before things started to get, well, a bit unusual. Brandon was quickly becoming the main focus of Carly's life. Whatever the two were up to, the other person was immediately informed about it. They shared everything with one another. What I found particularly fascinating is that, as we all know, most teenage relationships don't last too terribly long, especially online relationships. But Carly and Brandon managed to keep their relationship going for more than 18 months, even though they'd never even met in person. After they'd been chatting for about a year or so, Brandon wanted to introduce Carly to his father, Shane, and he did this over a video call. As time rolled on, Carly started talking more and more about Shane. In fact, it didn't take long before Carly was talking about Shane just as much as she was talking about Brandon. This is when Sonia started to get a little bit concerned. She asked Carly why she suddenly had such an interest in Shane, and she explained that Brandon and Shane were incredibly close, much like Sonia and Carly were. Sonia reminded Carly to be careful, and Carly made it very clear that if anything started to get weird or uncomfortable, she would tell her mother right away, and for Sonia, this was enough to calm her fears, so she dropped it and let it be. Sonia would later learn that Shane had a job as a security guard, and this job caused him to travel for work events every so often. In February of 2007, he was traveling across Australia for one of these events, and on his way back home to Brisbane, he offered to stop by Carly and Sonia's home to drop off a few birthday gifts that he and Brandon had purchased for Carly the previous month. At first, Sonia thought this was a little bit strange, but when Shane showed up at the family's home, he was wearing his security guard outfit, so the story seemed to check out. Shane seemed to be exactly the man that he claimed to be. He was clean-cut, professional, and nothing seemed unusual about him. In fact, Carly and Sonia felt so safe around him that they offered to let him spend the night at their home, inviting him to Carly's birthday party the following day. But while Shane was in town, he offered to take Carly shopping. Now, this, in my book, is definitely a bit strange. What would a 50-year-old man be doing taking a teenage girl shopping? Even if he was the father of her boyfriend, this seems a bit strange, considering the two had only just met, and there's been no indication that Carly's mother was even present during their trip. But the following day, at Carly's birthday party, that's when things started to get really bizarre. When Shane showed up at Carly's birthday party, it was immediately clear that something strange was happening. When Carly's friends and family members started showing up, Shane started to get visibly uncomfortable. There wasn't any particular moment where you could point to and say, see that? That's weird. But Sonya started to notice that Shane, for lack of a better word, seemed possessive over Carly. It seemed almost as if Shane and Carly were glued at the hip. He didn't let her wander off too terribly far, and he hung around Carly throughout the entire party, rarely ever speaking to anyone other than her for more than a few simple sentences. But the following morning, that's when things really started to get weird. As soon as Sonya passed by Carly's bedroom, she noticed Shane and Carly were lying on Carly's bed. In one report, it was claimed that Shane was actually lying on top of Carly, and Carly was visibly uncomfortable. Sonya immediately sprang into action and told Shane that he needed to leave immediately. It doesn't seem like he put up too much of a fight either. He knew he'd been caught. He grabbed his things and left. As soon as he was gone, Carly revealed that he'd made a few passes at her and that she had repeatedly rejected his advances, insisting that she was in love with his son, not him. Carly then told her mother about the birthday presents that Shane had shown up with. Now, because of YouTube's terms of service, I can't really explain the full extent of these gifts, but let me just say, one of them was an outfit that no 50-year-old man had any business gifting to the girlfriend of his son. This was the moment that Sonya truly understood what was happening here. She made all the right moves in the coming days, taking away Carly's access to social media, banning her from using her cell phone, keeping a much closer eye on her online activity, and calling Shane and telling him that he was never allowed to speak to her daughter again or she'd report him to the police. Mind you, this all may sound a bit harsh, but this wasn't done as a way to punish Carly in any way. This was all done in a bid to keep Carly safe, and based on Sonya's statements since then, it seems like she likely did a good job explaining this to Carly. It's awful that Carly lost so many of her freedoms because of this guy, but when it comes to the safety of your child, all bets are off, you do what you have to do. But the problem is that, well, we've all been teenagers at some point. We all know that regardless of what your parents tell you to do, if you want to do something, you'll find a way to do it, and Carly wasn't willing to let Brandon go. She admitted that what happened with Shane was pretty insane, but Brandon wasn't to blame for this. No sooner than her mother forbade her from speaking with Brandon, Carly was right back up to her old antics, speaking to Brandon every chance she could get. Only this time, she was keeping it a secret and her mother had no idea. A few weeks passed by, and it was February 19th, 2007, when Carly told her mother that she was going to be spending a night out with a group of her friends. She got dressed up in her best outfit then headed for the front door. But strangely, Sonya says that it was at this moment that Carly's behavior began to change. She turned to her mother and asked her for a hug, then another, then another, and another. It was almost as if she was afraid to leave. Her demeanor had changed without any rhyme or reason. Sonya didn't really know what this was all about, but what kind of mother would turn away hugs from her daughter? Carly's last words to her mother before she left were simply, love you mom. The door closed and Carly was never seen again. Carly never returned home from her outing with her friends that evening. When she still hadn't shown up by the following morning, Sonya knew something had gone terribly wrong and that's when she called the police to report her daughter missing, every parent's worst nightmare. But for Sonya, her nightmare was about to get far, far worse. Sonya would be subjected to something that no parent should ever have to face. As she was pacing around her home, pleading for some sort of news about her daughter, she heard a knock at the door, followed by two police officers with sullen expressions. As we all know, this never means anything good. Carly had been found, but not the way her mother had hoped. Investigators revealed that early that morning, detectives had come across a victim who'd been floating in Horseshoe Bay. That victim was identified as Carly Ryan. When she was taken in for further forensic analysis, it was determined that Carly had endured at least 19 injuries before she lost her life, each of which was more haunting, heartbreaking and heinous than the last. Security cameras and witness reports would soon reveal that Carly was last seen on the beach in the Horseshoe Bay area at around 9.30 the previous evening. She was in the company of what appeared to be two men, but it would later come to light that this had been one man and a teenage boy. They had arrived in the area in a blue vehicle, and it was this vehicle description that was used to track them down later on. As it would turn out, the two males who were seen in the CCTV security footage were none other than Shane and Brandon. Except that's not entirely true. See, that's because Shane and Brandon, they didn't exist. 11 days after Carly was discovered in Horseshoe Bay, police closed in on Gary Francis Newman, as well as his teenage son. His teenage son has never been named due to laws in Australia that prevent the names of young offenders from being revealed. It would quickly become clear though that Gary was in fact both Shane and Brandon. He'd created an alter ego online to lure teenage girls and cause them to fall in love with him, faking interest in everything they loved and stalking them both online and in the real world. What makes this situation so much worse is that Gary had either convinced or forced his teenage son to play a part in the scheme as well. Considering there's virtually zero information available about Gary's son, we don't know if he was a willing accomplice or just as much a victim as Carly was. Basically, Gary was the one who was chatting with Carly for more than a year online, but anytime he needed to schedule a video call with Carly, he would ask his son to step in to make things more realistic. All the photos that have been shared between the two were also of his own son. When Shane or Gary was forced to leave Carly's home after being caught lying in her bed, he was understandably upset. After all, he'd been concocting this plan for more than a year and a half and in the blink of an eye, it was all over. But he couldn't let this be the end. He needed to see Carly one final time and this time he would bring his teenage son along to help finish the job. Carly was lured out of her home that evening under the promise of finally being able to meet her online boyfriend in person for the first time. She lied to her mother and explained that she would be going out with friends, but in reality, she was due to hang out with her boyfriend, or so she thought. The thing is, Carly knew that something was fishy about this situation. She had seen all the red flags, her mother had warned her about both Shane and Brandon, but she chose to risk it all anyway. We know that Carly knew about the potential dangers because of how apprehensive she was to leave her home that evening. Her mother knew something was a bit off too, but considering Carly lied about her intentions that evening, there was little her mother could do. As she was blissfully unaware of the level of danger her daughter was about to place herself in. Now, don't think for one second that I'm blaming this on Carly. She was never anything more than a victim of this awful, heartless monster. I merely bring up the fact that she ignored all the obvious signs of danger as a warning to parents or teenagers that when your gut tells you something's unsafe, it's probably because it's unsafe. If you smell smoke, there's probably a fire. We've been given the gift of gut feelings for a reason and you should pretty much always trust them. But if you could imagine, this story is about to get a whole lot worse. If you remember, it was nearly two weeks after Carly was found in Horseshoe Bay that Gary's home was finally raided by the police. When detectives showed up at his home, Gary was actually in the middle of chatting up another teenage girl online. When his home was searched and investigators combed through every square inch of his place, they found a notebook that had documented at least 200 different aliases that Gary had been using online. From what I can tell, he used this notebook to help keep his story straight so that his victims wouldn't see right through his charade. Brandon and Shane had been just two of the names, less than 1% of his total list of characters. In his notebook, investigators found names, ages, occupations, interests, everything that related to each and every one of these characters that he'd created. If you consider that Gary used two aliases when speaking with Carly, that means that he could have had another 100 victims, assuming he pulled the whole father's son card for each of them. In reality, this number of victims could be substantially higher. There's just no way to know for sure. This notebook was also a goldmine for investigators because it even documented user names and passwords for each of his fake online profiles, giving them every last piece of evidence that they needed to get this man behind bars. But we have to remember that putting someone behind bars does little to help calm the pain of the family who are now left with one less person at the dinner table each night. Whereas yet, in Sonia's case, she's now left with no one at her dinner table each night. Sonia's world ended the day that she lost her daughter. Her purpose, her goals, her ambitions, they're gone and she can never get them back. Thankfully, Gary was sentenced to life in prison. Unfortunately though, he still will be eligible for parole after 29 years, but considering he was 50 when this crime took place, the man will likely be 80 before he ever has the slightest chance of seeing natural sunlight again, though we can all hope that this day never comes for Gary. In the wake of Gary sentencing, Gary's ex-wife came out and explained why the two had gotten divorced many years before this. She explained that Gary had been shockingly aggressive towards her, assaulting her multiple times, forcing her against her will on many occasions. When he then started turning his attention towards their own teenage daughter, that's when she knew that she needed to get herself and their three children out of there. Unfortunately, this wasn't even a wake-up call for Gary. He would later adopt a son of his own, the one that he used in his online schemes and he simply repeated the cycle. After all was said and done, Gary's son was cleared of all charges which pretty much secures the idea that his son was likely just as much a victim as Carly was. In the aftermath of such a tragedy, Sonia felt that she needed to do something, anything to help parents whose children may end up in similar situations. This led her to form the Carly Ryan Foundation, a foundation that offers certified online safety programs and conducts regular seminars to help educate children and parents about the dangers of online predators. If this wasn't enough, Sonia was also able to establish Carly's law, an Australian law that allows prosecutors to both charge and convict online predators before they ever lay a hand on a child. They can do this by establishing intent based on chat logs as well as convict an adult who misrepresents their age to a minor. This law has already saved so many lives and Sonia was the driving force behind this law every step of the way. If not for her, there's no telling how many other children may have ended up just like Carly. If you're a parent or even if you're a teenager, I would strongly urge you to visit CarlyRyanFoundation.com to better understand everything that the foundation has to offer. The resources page has heaps of valuable information that's been updated for modern times to help keep kids safe on more modern platforms such as Roblox, Fortnite, and the various other social media or gaming platforms that are predominantly aimed towards children. There's nothing that any of us can do to bring Carly back. But if Sonia has it her way, every child across the globe will become better educated about internet safety so that stories like this will one day be a thing of the past. No one should ever have to go through what Carly and Sonia dealt with. And it's our job, you and me. It's our job to keep these kids safe. Thank you guys for tuning in to another episode of True Crime Stories. If you enjoyed this video, check out this other interesting case I covered and don't forget to subscribe. It's totally free and keeps you up to date with all of my future videos. You can also click that join button below to support the channel and see new videos long before everyone else does. But my name is Ty Knots and I'll catch you guys in the next video.


Thank you very much for coming. So today we're going to talk about sidechains and Layer 2. And the talk is about how they're different, yet very similar in some ways. My name is Georgios. I do consulting and research on off-chain protocols. And my main focus on interoperability and scalability. So the big question is, why do we want to interoperate? And this is the answer. There's a lot of currencies. They all want to talk with each other. If the multi-chain thesis is to survive in the long term, we have to figure something out. Why do we want to scale? So I just learned that there is a talk by Joe Lubin happening right now. Like, when one million is devs, who cares about the devs? What about the users? So there is no way to get the users without being able to scale with quick confirmation and quick low fees. So let's go back to where it all started. So blockchain released this paper. And I think it's the first time that sidechains was mentioned in the term. Turns out I'm wrong. Like, this never happened. The first mention of sidechains was by Satoshi in 2010, which he mentioned on Bitcoin Talk. As usual, like, that sidechains to do interoperability. However, what he actually was talking about was merge mining, which is a completely different technique. Three years later, we have Greg Maxwell, a very prominent Bitcoin core contributor who described this game called Coin Witness, which was very similar, which is very similar to what people call today, ZK Rollup. And then we have this guy called Killer Storm, who actually described the first sidechain construction by utilizing certain types of proofs. So the two-way peg, as described in the blockchain paper, and by Killer Storm, describes a mechanism by which somebody locks some money in an escrow, and then via peg-in transaction, you create the same amount of money on another chain, and that is a sidechain. And in that sidechain, you may have a different rule set, like, maybe the chain progresses faster, maybe it has smart contracts.  And there's multiple ways that you can implement that. So, like, let's dive into it. The main problem that we're trying to solve is, like, how we can observe another chain state and convince ourselves that this chain that we're being shown is legit. In Bitcoin, that's very easy. Work. Hashes are very easy to reason about. They're quantifiable. You can do some math and you can figure out exactly how hard it is to attack. The trick here is that, however, if the proof-of-work algorithm is very expensive, like, you need to be able to verify it. And doing it with any fancier, like, proof-of-work algorithm, it's very hard, and you cannot verify a script, for example, on EVM. And the way that you do this is via, I think, all the SPV proofs, the way that most light clients work, and there's a very close interaction between sidechains and light clients that I will get to very soon. So, instead of providing the full chain, you provide the chain of headers, along with Merkel proofs of your transactions. And what you're trying to convince is that the chain that you're giving is actually the longest chain. This is too expensive. This is too long. It's linear. I need to provide you, like, so that you're guaranteed that I'm giving you the best chain, like, without ever having any trusted checkpoint.  That's way too expensive. So, there's some techniques called NipoPause, the one technique called Superblocks NipoPause by Dionysus Zindros, and Flyclient by Benedict Boons, who should be around this area, so you should talk to them about that. Snarks, which Barry, like, alluded to earlier, and stateless SPVs. So, stateless SPVs are another technique by James Prestage, who's also around, and you should talk to him about it. The problem here is that all work is not equal. If I have the Bitcoin chain with a bunch of hash rate and a bunch of physics and the Ethereum chain with the GPUs and, like, a different hash rate, having an asset on the one chain and on the other chain, even if it represents the same, like, kind of, like, collateral, it's not actually the same. And I have developed this mental model where I want to think of cross-chain assets as alloys. So, it's similar to how in chemistry, like, you can combine one metal with another and get some different properties. I think that, like, moving a Bitcoin from the Bitcoin chain to some other proof-of-word chain, perhaps, like, tokenizing Bitcoin on Litecoin, for example, for faster confirmation times is an option. But, however, like, due to the difference in the hash rate, you're no longer as secure as you were before. So, you can call that BTC30. And what about the BTCX, where X can be TBTC, WBTC, you pick it. Some derivative off of the Bitcoin, which tries to peg, like, the price to it. And it's going to be used in the DeFi space, for example. However, the assumption here changes from, like, the honest majority of the miners to the honest federation. For example, if you're doing a federated peg or, like, to the whole mechanism around it working. So, you have technical risk arising. So, each solution has a different, like, trade-off space. There's no for lunch. What about proof-of-stake side-chains? So, proof-of-stake side-chains, like, don't exist. What about proof-of-stake like-lines? Which, the argument is that it's equivalent. This is a proof-of-work block. Many proof-of-work chains. Many proof-of-work blocks. And you accept a proof-of-work block only if the hash of the block header plus some nonce that you change is less than a number. So, let's take this and switch this in the proof-of-stake situation. You replace the nonce with signatures, and you accept, like, the block only if the blocks that you have received have signed, like, more than two-thirds of stake. So, how does this look like? How am I going to do a proof-of-proof-of-stake? I will pick some blocks, like, every some amount of time. I will check that each time the validator set would have changed in this proof-of-stake side-chain, I would verify that they signed on the latest block. This means that also, of course, it's linear because I have to give you still linear to the size of the chain blocks. And, but also, the side-chain smart contract or the light client must always be aware of the latest stake distribution. Because how will I know that who is the two-thirds that I'm receiving the money from? The signature from. There's an attack here, which I want to call the cross-chain nothing-it-stake attack, which basically says, usually, in proof-of-stake change, you have the nothing-it-stake problem where validators, like, start building on two chains. And basically, if you can take the data from one chain and put it on the other, you can slash them, like, for equivocating, for double-signing. However, what if I have a chain, like, I'm a validator, I have a chain that I'm building on, and then I'm just having a hidden chain that I'm also building on, but I'm not sending it to anybody except light clients. The light client must be able to take the signatures that I gave them off, out of band, and put them on the main chain. I'm not aware of any chain currently that has this mechanism implemented. Tendermint, right now, has a few documentation, has some documentation exploring this.  The issue, also, with this is the long-range attack, because what if, how, like, you need to, in order to incentive align this mechanism, you need to slash. How do you slash if the person that fed you with the signatures is now unbunded? It's complicated. So, like, the rule that you must say is that, like, you will only accept proofs, like, signatures, from people that are still bonded. You reject from unbunded validators. How do you know which validators are unbunded? I don't know. Like, currently the dominant approach is having a trusted checkpoint via, like, so that you always know what is the latest, like, bonded set of validators. This is an open problem. There's many solutions. There's many other solutions we can take, but they all, again, they all, like, tend to some subjectivity, which does not exist in proof of work. Everything so far, we assume that each chain is individually secure. If we're both, like, if both chains are secure, then sure, you can do, you can make them communicate with each other. Security and, like, requires that you have something that is high-cost. Something that is high-cost is not scalable. That has high-cost is not scalable. So, side-chain is constantly harmful. What if the side-chain, like, mechanism, if you try to use it for scalability, and if you try to use it for scalability inherently, it will be less secure, does not want you to get out. So, what if the liquid side-chain suddenly becomes the devil and, like, they say, no, like, your money's gone, you're done? So, we don't want that. The kind of taxonomy that we have for side-chains then means that we have the federated side-chain, which is the multisig liquid, the proof-of-work side-chain, which is with nipo-pause for logarithmic SPV proofs, and summary organization proofs, because, as we all know, I hope, when you have a proof-of-work chain that forks, like, you want to be able to punish for that fork, and you have proof-of-stake side-chains, where you have, basically, a multisig, which gets rotated each time the stake changes during elections, or, and you also add some equivocation. And the thing is that you trade always security for scalability if you want to use it that way. There is a great paper list, like, last week, actually, by, like, say, and friends on communication on course distributed ledger. Right now, they're doing a workshop on it, which was very unfortunate because it conflicts with us. Talk, so make sure you read this paper. To, like, elaborate on, to conclude on my point about side-chains and interoperability solution, it's not a scalability solution. You need an independent security model. And the moment that you have independent security model, my argument is that you're not in the layer two, domain space. It's a layer one that talks with other layer ones. It's, like, on the same level. How do we scale them? What's gonna happen? Off the chain. So Paddy McCurry is around here, like, everything that's working on, like, off-chain scalability requires that you have a layer one, a layer two, and some mechanism to make them communicate. You need to put the minimum amount of data on chain because the chain has a finite amount of space. And if you're going to support one million F devs, you're not going to be able to hold all that capacity. And maybe a theorem two is gonna do it, but what if it doesn't? So, what's layer two? So I call it a delayed settlement protocol with layer one guarantees. So you have a protocol where you log some money on the layer one, then you perform some off-chain operations, and then you have guarantees that are, like, equivalent to your layer one security model that you'll be able to get your money out. And there's two, like, dominant approaches right now, which is the commit-chains approach, which is, like, what Plasma is, roll-ups, no-coast, and they have, like, some certain different trade-offs, whether they can do smart contracts or not, and there's channels. And the dominant channel approach is the lightning for Bitcoin. And as far as I can tell, there is some state-channels initiative, which, like, everything merged and coulders to them because it was a very hard task. So, and they have, like, different properties, but we're not gonna talk about channels in this talk. So let's dive into the commit-chains. So firstly, we had Plasma, like, 2017 with Dalek Joseph, they published this paper, nothing in the paper worked, and it describes, basically, a mechanism where you have an operator that takes hashes of the side-chain and it puts them on the layer one. But, and the security of the commit-chain or the Plasma, like, it comes under the assumption that you're able that any time that, like, something bad happens, you can take some fraud-proof from the Plasma-Chain state, put it on the layer one, compare it to the hash that was committed earlier, and you can get your money out, like, within some time. And it has some security assumption that, like, you must be able, like, to get your money, to get the fraud-proof vein within a week's time or two weeks' time. So this is, like, a security assumption that very security-oriented folks will argue against, but, again, that's not the topic of the talk. The problem with the Plasma construction is that the operator, it's that there's sole discretion to give you the data. So what if they don't? Like, you have some state, they create a mercenary of the state or of the latest UTXO set, they commit it, but they don't give you the data. You have a problem then, because, in certain, they can commit, they can create an invalid state transition, and this invalid state transition will never be revealed, and, like, you will never know that you no longer have your money. So there have been, like, changes to, lately, to the Plasma-like protocols to fix that. And it turns out that maybe, yes, maybe Plasma was a premature optimization. Maybe, like, many people might have raised money on Plasma or something that might be broken. What can we do? That's how technology will move forward. So how are we going to solve the data availability problem? We cannot. So what are we gonna do instead of having off-chain data fraud-proofs? We'll put data on-chain with fraud-proofs, and that's what we call optimistic roll-up. And this is what the, currently, the Crypto-economics lab and the Plasma group teams are working on, which is basically that you take all the data that is off-chain, you create a smart, like, encoding of them, and you dump it on the cold data of the layer one. And that's kind of cheap, because the data is not part of the chain, it's just part of the database, like here. And the other people that are working on this, like, another, like, independently, like, thought of construction was called Merge's Consensus by Mikaela and John Adler, which basically says what I just said. You have, you commit, like, all the, like, the Merkle route, and also you put an encoding of the transactions. And you use, basically, the layer one as a data availability oracle.  Like, and I'm saying this, like, just so that we can get over the word salad and, like, understand, like, the bits and pieces that make a mechanism. ZK roll-up means that you have the commit, the new Merkle route or the latest state or the transaction that happened, you take a zero-knowledge proof, which attests that this state transition is valid, and you put it on chain. The smart contract verifies that the state transition was valid with MoonMath. The problem with this is that maybe you need a trusted setup, as we saw in snark, September, where, like, five new snarks were, like, released. Maybe we can remove the trusted setup, but I wouldn't build a cryptography that is released on 2019. And they can be expensive, like, proving times are expensive, verifiers are also expensive, and they can be slow. So, again, no free lunch. And note on the on-chain data availability, because it has been, like, pumped as an idea that, like, is gonna solve all our problems. I'm not a fan, because the blockchain is supposed to be the verification layer. The blockchain is not a file storage, like, and FileCo and another chains that are going to do that do not exist yet, so we know that, like, this is a hard problem and maybe won't get solved. The solution, solving the data availability problem, like, will give us the ability to do, like, DeFi and all the other, like, use cases that we're trying to figure out for this industry on the layer two, cheap and fast, but, like, on-chain data availability reduces your scalability benefits. You cannot have, like, infinite throughput, like, with the other layer twos, because, again, you're bounded by the layer one's capacity, so it's really a constant size improvement. And also, it's parasitic, in my view, by parasitic, I mean that, like, the moment that you start utilizing the change so heavily, what about the other apps that are not on your layer two, your roll-up, or whatever you call it? Are they all going to come to your roll-up? Like, I think that's too, like, ambitious. And there is a post by Vitalik recently, where he, like, elaborates on this, and he's a fan about this idea, which, yeah. Some takeaways from this talk is that we know how to do both proof of work and proof of stake side-chains. It's hard to implement them. You need them to both be individually secure in having an honest majority assumption for more than one layer one is hard, as we have seen for multiple 51% attacks on smaller, like, chains. Layer two inherits security from layer one, and, like, I have a small taxonomy of, like, what goes where. I'm a fan of the, like, direction. This is, like, the current direction that we're going, it seems, but we should be, like, very skeptic about how much, like, we're just dumping on the layer one, because nobody can sing in Ethereum full node, and this is not gonna help with it. The conclusion is side-chains are for interoperability. Layer two is for scalability. Side-chains are not layer two. Thank you very much, and I'll be happy to take some questions for three minutes. And also, yeah, I should have changed this. You can find the thought at scaling, at side-chains2019.pdf. There's a microphone if anybody wants to do a question, we'll have three minutes. Hi, thank you very much for the talk. So you gave, I think, very detailed criticisms of both layer two and side-chain solutions without highlighting too much of their positive aspects. What solutions are you actually fond of? I'm fond of the plasma construction for simple state transition for payments, because this industry solves payments, and I'm happy, like, if I can get a construction that can do multi-sig time locks, like, and that's it. And plasma does that fine right now. So plasma for? Plasma for simple payments. I do not care much about smart contracts like smart contracts. Multi-sig time locks are sufficient. Okay, thank you. Thanks for the breakdown. One thing that you didn't talk about, which I thought would be interesting to hear your perspective on, is hybrid approaches for roll-ups. So where we use, you know, proofs of work from other chains to make the data availability there, but do the fraud proofs on another chain. Right, so with, it's a question that I have a roll-up where I don't post all the data on chain, only for specific state transition. So it's using availability from something other than the L1 that you're bringing? No, I do not think that's good. Because your security model changes wildly. The security model that I want is, I have the layer one, I know exactly how secure it is. I know that I have the Bitcoin chain, it has this much censorship resistance, this much capacity, I can dump all this data. The moment that I'm going to use Bitcoin Cash as a data availability layer, which is what you're talking about, means that I have to trust Bitcoin Cash is miners. And do you know how easy it is to censor Bitcoin Cash? Very easy, like 10% of Bitcoin Cash rate. So no, like one chain for, if you're gonna dump data somewhere, dump it on one chain in my view. Okay, okay, thank you so much.


Lagos State Governor Mr. Baba Jidesan Olu on Wednesday signed the bills for the establishment of additional two universities in the state. They are the Lagos State University of Education last week and Lagos State University of Science and Technology. They are centred to the bills transmitting Lagos State Polytechnic in Ikorudu, Isolo and Surulera campuses to the University of Science and Technology. The Deniro-Gusanya Colleges of Education, Ijani King and Michael Otedola College of Primary Education will now be Lagos State University of Education. The signing ceremony took place at the Lagos House, Marina. It was witnessed by the special advisor to the Governor on Education, Mr. Tokumbwa Wahab, Commissioner for Justice and Attorney General, Mr. Moyesore Onibangjo-SAN, members of the governing councils and management staff of the tertiary institutions, among others. The Chairman, Governor Kansu of the Lagos State Polytechnic, now to be known as Lagos State University of Science and Technology. Elsewhere, right top Polytechnic, the Elsewhere Chairman of the Colleges of Education, Ijani King, now to be known as Lagos State College, Lagos State University of Education. 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.