I would like to start by reminding a little bit about the PQ-Webs as duality in type-2-V and what happens when you place these three brains in the mix. And then I will discuss in detail a billion mirror symmetry in three dimensions and a stepwise approach. And then, can you hear me now? And then an approach which is called stepwise dualization. And then if we have time, we will try to generalize to the non-Abelian case. So these are the brain setups I would like to talk about. Let me introduce, first of all, the standard Honeywitten brain setups. The main players are D3 brains, NS5 brains, and D5 brains. And usually you draw something like this. You have an S-brain, and then you have D3 stretching between an S-brain. So here I explained where the various brains are stretching. So all of the theories we are discussing will be three-dimensional. So all the brains stretch along the first three directions in type-2-V. So here will be X6, will be the direction where the D3 brains are going. Then there will be NS brains, will go vertically. So this will be X4, 5, and 6, 3, 4, 5. And then we can add the D5 brains, which will go along the remaining three directions. So these setups, if we just stop on the first three lines, we'll have N equal 4 supersymmetry. There will be an SO3 times SO3 symmetry acting on this coordinates, which is the SO4R symmetry of the N equal 4 supersymmetry in three dimensions. So what is known is that if you do S-duality in type-2-V, you replace NS5 brains with D5 brains, and D3 brains stay D3 brains, you will have a different gauge theory. And this is related to 3D mirror symmetry. And this part of the story with N equal 4 supersymmetry is quite well understood. What I would like to do is try to generalize to the case with half the number of supercharges. So one way to do is to rotate some of the brains. So we will have NS5 prime brains, where instead of stretching along 4 and 5, they will stretch along 8 and 9. And similarly for the D5 prime, instead of stretching along 8 and 9, they will stretch along 4 and 5. So once we do this, we have half of the supersymmetry. So the theories which live at this type of brain setups will have just N equal 2 supersymmetry in two dimensions. In this case, even drawing a generic brain setup with NS and S prime, D5, D5 prime, one does not know what is the gauge theory living on it. So what we would like to do is just take one example and try to work out the gauge theory. So one example where we know is the following. Instead of having just an S5, we put NS5 and then we put many D5 prime brain, one on top of each other. So this is called the PQ web. If we just do this, this is a five-dimensional theory, because if we take the NS and the D5 prime, you see that they have 0, 1, 2, 4, 5 in common. So they have five directions in common. So this is a five-dimensional gauge theory. In this case, it's an easy gauge theory. It's just free. But what we would like to do is to add a D3 brain going like this, transversely. So this would be now the sixth direction. So this is known how to do. Let me just do the case where we have two D3 brains arriving on the PQ web, which is what I drew here. And then we also add the two NS prime brains just to stop the D3 brains. So what is the gauge theory over here? We have an S brain, an S brain, and then we have D3 brain. So this will give us two U1 gauge theory if we just put one D3 brain. So I draw it in this way. The circle means gauge node in the theory. Then we will have, by fundamental matters, which will be something like this. These are massless strings, which have 0 length, so they will give rise to massless state, massless multiplets. So these will be chiral multiplets. I use arrows. There are two of them. And then I have to add the D5 prime. So if I add just the D5, this will give a fundamental field for this gauge group. If I add the D5 from this part, it will give a fundamental for this. But if I put the D5 prime on top, then I have many massless states going from D3 to D5, which will be fundamental. There will be some fundamental of this group and some fundamental of this group. Then the result is this. So we have K arrows going from one to this global symmetry group. So the square means it's a global symmetry group. So I have an SUK global symmetry, another SUK global symmetry. And they have all these type of lines. This was well known. This was known from the 90s. Now there is also super potential here, which is a cubic super potential. I just wrote it down. It's related to loops in the quiver. Now the question is what happens if I do NS duality? What happens is that instead of having a PQ web with one NS and many D5, I will have a PQ web with many NS brains and one D5. In this case, the answer is not known. What is the gauge theory living over here? It's probably going to be some billion gauge theory because I have just one D3 brain. But the answer was not known. So the purpose of the talk is to work this gauge theory out, and along the way we will find some interesting things involving monopole super potential, which means we have gauge theories where in the super potential there are monopole operators. These are the monopole operators which were discussed yesterday. In the case discussed yesterday it was n equal 4 supersymmetry and the super potential was never involving monopole operators. But with n equal 2 you can add the monopole operators to the super potential and you don't break the supersymmetry. So first of all let me review again 3D mirror symmetry. The simplest example is just one gauge group U1 with one flavor, one anti-flavor. And let me add also a singlet. So this is P and this is Q and then I add a super potential which is sigma PQ. So this is actually n equal 4 super young mills U1 with one flavor. And this is the super potential which ensures me that we have n equal 4 supersymmetry. The mirror here is just a free hyper. This is the simplest example of 3D mirror symmetry and this was given by Interligator and Cyberg I think back in 96.  When I do the S duality I get NS5. So this is the free hyper. These are the massless things that give the free hyper. And this is U1 with one flavor. So we can read off the duality very easily from the brain setup. What is important here is that what is the mapping of the operators. So here we have two free fields, let's call it P and Q, free chiral fields, n equal 2 notation. And what are the fields which are mapped over these two free fields? These are the monopole operators of this U1 with one flavor. So if we call them m plus and then minus, we have that this is mapped under the mirror symmetry in this way. We also have another gauge invariant operator which is sigma here. So where is sigma mapped? If you remember from the talk for yesterday, the sigma satisfies some quantum relation which is the following. Sigma is equal to m plus and minus. So sigma is mapped to the map to the product of P and Q. Okay, are there questions about this? Okay, so let's try to do, this is the very basic example. The next example would be U1 with n flavors. But then we can do it for n equal 4 and then we will have some generalization. We will have the sigma to the k equal to plus and minus. This is what was explained yesterday. Moreover, let me modify this duality a little bit to go to an n equal to dualities. What we do is that we can flip some field. What does it mean? Flipping a field. It means that let's say we have a gauge theory with some operator O. We couple this operator O to a new field sigma. And we get, so we have some theory with some super potential and some operator O. We change the super potential in this way. And we add a new field. So in this case I want to flip this operator sigma. So the super potential will be sigma PQ. This will go in sigma PQ plus sigma times, let's call the flipping field X. So in this case you can see that sigma and X become massive. So I can integrate them out. So I have to use the question of motion of sigma and X to integrate them out. What I get is that I get W equals 0. And I lost both of these fields. So I started from U1 with one flavor in n equal 4. I flipped this singlet and I just get U1 n equal 2 with one flavor and W equals 0. So basically I lost this singlet. What happens on this side? I have to flip sigma, but sigma is P times Q on this side. So the duality now, the mirror duality becomes a theory with three fields, which I can call sigma PQ and W is equal to sigma PQ. So this is an n equal 2 duality, which is the simplest one you can have. And this is just the equivalent to the n equal 4 duality. Just you can go from one to the other flipping at one field. This is called usually X, Y, D model. It's a Vestumino model. There is no gauge symmetry over here. But now it's in the duality between two interacting field theories, the simplest one. So now we can try to do something more general. We can go and do U1 with K flavors. So we start to get something similar to this. You see now here we have the U1 with K plus 1 flavors. So let's try to do U1 with K flavor. One way to do it is to use this duality in this direction, or the duality we had before in this direction. So we have P and Q, which are two free fields, and we can replace them with U1 with free fields and the superpotential. But now I want to do it for each flavor over here. So I will pick the first, let's call this small. I want to pick the pair P, I, Q, I for each I, and replace it with the U1 with the flavor and the sigma I. So once I do this, what happens over here? I have a U1. This is what I call stepwise dualization. This type of approach was advocated by Kapustin and Strassler, always in the 90s. We are now the superpotential. I replace every pair of fundamental fields with the U1 with one flavor. I do this K time, so I have K object like this. So now this theory is not the U1 theory anymore, it's the U1 to the K plus 1 gauge theory. And there will be a superpotential which has K terms, sigma I, P, I, Q, I. But now there is something missing in this picture, and it's the following that when I replace this fundamental field here, these fundamental fields become the monopole operators. So these fundamental fields were charged under the U1. So this means that the monopole operators of all these K gauge theories must be charged under this original U1. The way to do this is to add the BF couplings. So what is a BF coupling? This is like a Champ-Simon coupling. So a Champ-Simon coupling is usually for a billion theory, something like ADA. But if I use different gauge groups, gauge fields, then I will have something like ADB, or BDA, let me put it like this, BDA. But DA is usually called F, so this is a BF coupling. So I started from a theory which is U1 with K flavor. Now I have a theory with many U1s, the same number of charge multiplets. I add the K singlets, sigma I, and then I have to add many BF couplings in the Lagrangian. These are equivalent. I just use the basic mirror symmetry K times. But now something happens here. We see that this U1 doesn't have flavor anymore. This means that I can do exactly the pati integral over here. Once I do this, this pati integral gives me a delta function because this gauge field, I can exactly integrate over this gauge field U1. This will give me a delta function that tells me that a function of delta function, that the sum of all these field strands is zero. So I can think of this theory as the product of K U1 with one flavor, but then there is the relation that the sum of all the field strands must be zero. So a different presentation for this theory is something like this. Take a linear quiver. Instead of K gauge groups, I have to put K minus 1. And then I have many singlet fields, which are flipping to zero all these bifundamental fields. So this is the statement. This is the statement about 3D mirror symmetry for a billion gauge theories. U1 with K flavor is dual, is mirror to a linear quiver. What we did is just assumed that the original symmetry was correct, and then we proved this. So if you believe the first original duality, then this just follows. One way to see this through brains is the following. We can start from here that we have an s-brain, a d5, an s-prime brain, which is rotated. So we have n equal to 2. Then here we put many d5, and then we do the s-duality. What happens? The d5 become an s, and then here we have a d5 prime, and here we have a d5. So we see that also in this picture we have a linear quiver. So many U1s, one connected to the other. And then there is a flavor for the first one and the flavor for the last one, which is precisely this. So again, all this goes back to 97, I think. But this type of procedure is some kind of procedure that we can try to apply to this theory.  When I do this, I will create many U1s. So we can already see that here we will have a theory which even if it looks like there are only, you know, the Dennis brains are all on top of each other. We will get a theory with many U1s, which is kind of strange. Anyways, let's first do the case k equal 1, because in the case k equal 1 you already know the results, and also we learn something. So the case k equal 1 we have from one side. We have this theory, U1, U1. There are six fields. And from the other side we know what is the theory, the theory here, because we have just one and s5. It's basically pretty much the same theory, but it's not gaged. So there are six fields, which you can see them as massless strings going from d brains to d brains. But there are no gaged fields, because there is just one and s brain. In order to have gaged fields you need two and s brains and these three that can slide upon them. And we have this type of super potential, the cubic super potential. So this would be s and s, d5, d5. And here we always have the same 1, 1, pq web, which upon s duality goes into itself. So this is the same on both sides. OK, so we can try to understand this duality, but one way to understand this duality, first we would like to prove it, usually always using the basic Abelian mirror symmetry. So all this talk is based on a paper that I wrote with Sara Pasquetti. Which is 16, 0, 5, 0, 2, 6, 7, 5. And in the paper we prove this duality. But along the way we found the third theory, which has just one gauge group. And so this duality actually becomes a reality. So one way to find a theory with one gauge group is to basically start from here. So let's put here k equal 3. So you see that the matter content is the same as this. We have a linear query 1 cross u1. The difference is that here we have three singlets with this type of super potential. Here we have zero singlets and a different super potential. So here the super potential is, if we call this p and q. The super potential is Apq plus At tilde, p tilde, q tilde. So what can we do is that we can try to modify these to arrive here. But we know that there is a mirror on this gauge, which is one with three flavors, without super potential. So let's try to add here, we can deform and add sigma i xi. So we have three singlet fields and we flip the sigma i. If we follow the map, the mirror map, the sigma i's where, so this is like pi qi, this was where like pi qi. So there are three sigmas and there are three mesons that I can write. So what it means is that here I should add a super potential, which is xi pi qi. So three times in the super potential. So I can write, let me write this differently in this way. So now I break the su3 global symmetry to u1 to some power. And here again I can integrate out sigma and x and I get w equals zero. So this is a different presentation of the basic duality, but this goes, now we are getting something similar to here. Now we have to add this type of super potential, Apq. So what was the map before? When we had u1 with k flavors, the map of the mesons, so we had pi qi is a matrix of mesons. So let me do, let's do the case of three mesons of three flavors. Then here I have p1 q1 p3 q3. And this is a non-trivial aspect, which is not discussed usually. So the diagonal one, they were going to see to the sigmas in the basic ability of middle symmetry. The off diagonal one, they're going to monopole operators. So for instance p1 q2 goes to the monopole operators which charge one and zero. So here I have two gauge groups. So when I say a monopole operator, so I have to assign the charge under both gauge group. Then I can have the monopole operators which charge one and one. And this goes, this is mapped to p1 q3. Then I have to charge zero and one. And this goes to the other one. On this half, on this triangle is the same, but with negative charges. So this is the map for the basic middle symmetry for u1 with three flavors, and it's possible to generalize. Here we also have mesons m with charge plus one. Here is mapped to the operator product of all the pis. And then with charge minus is mapped to the operator product of all the qis. So we have a linear quiver. We take the product of all the operators going in this direction. We get the gauge invariant. This gauge invariant is mapped to a monopole on the other one. On the other hand, here we have mesons, quadratic gauge invariant. These are mapped to a monopole on this. This is a generic feature of middle symmetry, which is mapping normal operators to monopole operators. So if you have some relations, which are satisfied by normal operators from one side, they will become quantum relations for monopoles on the other one. Okay, so here we want to add the apq to the story, which is the product of all the p in this direction. So we want to add the super potential. This is p1, p2, and p3. We want to add to the super potential p1, p2, p3, plus the other p1 tilde, p2 tilde, p3 tilde. So we get, now this theory, if we do this, becomes the theory describing the pq web. But we saw that what are these two terms mapped? These are mapped to the monopole. So here we have to add monopoles plus one, plus monopole minus one. So, say it again. This is a u1 cross u1 gauge theory with some super potential, which is precisely the one that we know describes this pq web. This is due to a u1 gauge theory with three flavors, three singlets, and monopole super potential, which is not obviously related to the brain picture. So this is a duality. Now it is also possible to show that this duality, one way to do is, I'm just going to sketch the discussion, one way to do is to think about this theory as u1 with two flavors. So we have two incoming arrows and two outgoing arrows, but then I gauge these two u1s together. So basically I take u1 with two flavors and find these flipping fields. Then I gauge and I get this theory. But if instead of starting from u1 with two flavors and the flipping field, I start from its mirror, which is just u1 with two flavors, I get some theory which if you inspect a little better, you see that actually it becomes... So from one side I have this, from the other side I have u1 with two flavors. This is the mirror symmetry for u1 with two flavors. Now I gauge something over here and I get that theory. So these are u1 cross u1 gauge theory. When I do the same gauging here, I get the product of two separated theories, which is u1 with one flavor, two times. But this again is equal using the xyd. This is equal to xyd model and this is equal to another xyd model using duality again. So I see that the product of two xyd model is equal to this theory. But this is exactly what we have here. We have six fields with two superpotential coupling, which are xyd. So basically what we found is that there is a reality here. This is one presentation, this is another, and this is obviously related to the brain system. This is another and this is related to the dual brain system. So what we want to do in the next half an hour is to generalize this reality in two different directions. One is to add more NS5, and the other is to just look at this. So one is to generalize this part of the reality and one is to generalize this part of the reality. Here we have u1 with three flavors and here we have just the vestumino model. So what we're going to do is that here we can replace u1 with three flavors, with u and c with an F flavor generically, add the monopoles and see what happens. There will be another dual. This will be a Aaroni cyber type of duality, but for the moment let's just try to generalize in this direction. Are there questions? Okay, so let's apply this stepwise dualization to this theory. So here I have many, I have the two u1s, then instead of taking A and A tilde, which are despite fundamental, let's replace it with the usual big A, big A tilde, and sigma A. Then instead of having PI, PI tilde, I replace it with u1.  So I have K of those. Same story from the other side. PF couplings, which are connecting me, but then I have a PF coupling like this. So I just use the 2K plus one times the basic a billion bill of symmetry on this case theory. And I get this strangely looking object. Now I can do the integral of the two u1s. I get two deltas now. When I implement the delta, I get a linear quiver exactly like the beginning. Then I get this u1 in the middle here. So these are A and A tilde. Here I have K minus one. And then I get another linear quiver from the other side. I have all the singlets. I'm not drawing the singlets, but there will be many singlets. 2K plus one. OK, so we see that what we are getting here is a theory with many u1s gauge groups, which should describe this brain system. We should be careful about the super potential because here we have all the singlets and all this type of super potential which will be sum of sigma i, pq, pi, qi, pip and so on. So we have all this type of flipping super potential, but then we also have the super potential coming from this cubic. So what is this going to become? It will become some monopole operator super potential. But the monopole operator here is not local on the quiver. So for instance, the terms p, i, q, i, a will be a monopole. So the super potential here will be this. Then we have sigma a, a, a tilde. Then we have something similar to this with the tilde, with the qs. But then we have a monopole. So the monopole will be something like all zeros, 1, 1, 1, all zeros. This will be one monopole term associated to p1, q1, a, p1 tilde, q1 tilde, a tilde. This is just the first half. Then we have the same with the minus, all zeros, minus 1, minus 1, minus 1 and so on. Then we can do p2, q2, a and this will be this object. 0, 0, 1, 1. Then we have 1 in the middle. So this notation is the charge. These are all the charges under all these ones. This one is the one in the middle. 0 and the same with the minus. And the last one will be m with all 1 all the way. So we have many monopole operators, 2k monopole operators, half with the plus sign, half with minus sign. But they will involve groups which are not attached to each other. So this is not the local in the quiver. Usually everything was, when you have a quiver with an equal force supersymmetry, every node will just talk with the nearest neighbor. This is a little bit more complicated. Another thing we can do, we can use the result from before to replace this one with three flavors in the middle with the square. So before we remember, if you remember, we had this duality. So we can apply this duality inside here and we get a theory with one less gauge group because this is one gauge group, this is zero. And we have six fields. So this is a presentation which in the case k equal one reduces to what we know. The other one didn't reduce. So we have four different theories. We have this theory, then we have this one, which would be the dual of here. And then we can also use this duality inside both to change the presentation a little bit. If we use this presentation, we'll use this term, the sigma tilde a tilde, but we get, if we call this is p1 q1 p1 tilde q1 tilde. This is xx tilde. We have a cubic term, px p1 q1 plus x tilde p1 tilde q1 tilde. And here we lose the one in the middle and it's just like this. So again, we have many super potential operators. We have the cubic terms and then we have flipping terms. So this will be the result for this question mark that I drew before. And the interesting thing is that there are many ones more than you would get if you spread this k NS5 brains because we have k NS5 brains. So in n equal 4 you would expect k minus 1 u1, but here we get 2k minus 1, so almost twice as much. And then we have all these monopole super potentials. So this is the result. So I think one thing one can do is to map the chiral rings from here to here. This is not easy. We just mapped the generators of the chiral ring because it's easy to study the mesons. It's not easy to study the whole set of monopole operators. So for instance here we have many mesons which are mapped into many monopole operators that you can construct here. And then we have a few monopoles, just the one you can construct out of these two u1s. And these are mapped to many mesons of many type of normal meson operator you can find over here. But you can check that at least at the level of the generators of the chiral ring there is a perfect matching between the two sides. OK, if there are no questions, I will go back to this duality again. So let me write it again. So from one side we have u1 with three-flavor and the super potential is, let's call it this Pi, Pi tilde. The super potential is sigma. There are three flipping terms, sigma i, Pi, Pi tilde. And then there is the monopole with charge plus one and the monopole of charge minus one. This is this side of the duality. From the other side you just have six fields, A, B, C, A tilde, B tilde, C tilde, and the super potential is A, B, C, plus A tilde, B tilde, C tilde. So this presentation of the duality is not SU3 invariant. So what we can do is to get rid of all these of the three singlets in such a way that we have SU3 times SU3 global symmetry. So what we have to do here is to add the sigma i, xi. Now we have to look at the map. So here we will be introducing some more cubic terms because the sigma i are mapped to quadratic operators over here. The end result is the following. We have u1 with three flavors and just a simple monopole m plus one plus m minus one is dual to this object. So what is this? This is xij. This is a bifundamental matrix of SU3 times SU3. So there are nine fields. We started from six fields. We added three fields. And the super potential is just the determinant of x as a matrix, as a three by three matrix. So there are nine terms in the super potential. In this way you can see immediately that the SU3 times SU3 global symmetry here is preserved on this side. One thing is that the duality, this duality we discussed at the level of the field theory, but if you put the field theory on S3, so this is what in the previous talk we heard about, these S3 partition functions for N equal 2 on S3. You will find some partition function on both sides. And this will be something like dx. And then we will have three times. We have Sb of x plus Mi, Sb of minus x plus Mi tilde. So this will be a U1 gauge theory with three flavors and three anti-flavors. And from this side you will see that there is just a product of nine singlets. So basically you are projecting down the duality from the level of the full gauge theory to the level of a three partition function. You will find some identity. This is the identity. It doesn't really matter. But this identity was already present in the literature. So for instance already in 2002 there was a paper that was discussing this identity. Of course they didn't know about the relation with gauge theories and this was called ultimate integral identity because apparently for their purposes which was some integrable system story this was a very basic identity. Otherwise it was also known as a new pentagon identity. Okay, so what we did in a paper which we didn't publish yet with Francesco Benin and Sara Pasquetti is to try to generalize this story to the case where you have UNC with an F label. So I just tell you the result. The result is you have NC, then we have NF flavors and the superpotential here is just M plus plus M minus. So these are the two basic monopole in UNC with charge. So M plus is the following. The charges are if we go on the carton of UNC there will be plus one and all zeros. This is M plus and minus will be something like all zeros and minus one. So these are two different monopole operators we have to add both of them to the Lagrangian. And once we do this we are left with the global symmetry which is SU and F square because the monopole operators if you don't have the Lagrangian here you have SU and F square but then you have a u1 topological symmetry and then u1 axial symmetry. But these M plus and the minus are both charged under both of these two you want symmetries with different charges so you're breaking both of them. And the dual is okay let me write U and F minus NC minus two is the two end flavors the NF flavor sorry and the superpotential is the usual cyber superpotential so sum i and j M ij Q i Q j so this is very similar to the Aroni duality but the Aroni duality doesn't have the minus two. And then here we have the other superpotential is again M plus plus and minus where this M plus and the minus are the monopole operators of the dual gauge group and here is another different the Aroni duality there is a flipping of the two monopoles here we don't have any flipping but they both appear in the superpotential and again here the global symmetry is SU and F square so one way to argue for the symmetry one can check that this duality makes sense for instance one can compute the modular space of acqua on both sides and it matches another way to argue for the symmetry which also provides a ultraviolet completion for the theory is that because the one question you can ask here is whether starting from just UNC with NF flavor and adding this superpotential is relevant so generically if NF is too big the superpotential is not relevant the boundary case is NF equal to NC plus one anyway but we can start from a duality in four dimension so this is a 3D N equal to duality we can start from a duality in four dimension which is a USP duality USP 2 and C with NF flavors usually it's called 2 and F with the 2 and F flavors so this is not anomalous in the four dimension and there is a dual which is the interligator pull-out dual which is USP 2 and F minus 2 and C minus 2 with 2 and F flavors and here there is a superpotential which is MQQ this is very similar to can you read here ok so basically you are this is like the cyber duality for USP gauge groups if you take NC equal to one USP 2 is SU 2 and so this is the notation I'm using so this you can reduce to three dimension you find the same duality except that when you reduce to three dimension you are turning on a monopole superpotential so in 3D let's just go directly to 3D you have this duality but now the superpotential here is the monopole which is there is just one monopole for USP and again here we have the monopole now there is a way so this theory is SU 2 and F global symmetry there is a way to turn on real masses in such a way that the USP is broken down to U and C and 2 and F is broken down half of the flavors become massless make up massive half of the flavor but now the superpotential gets doing this again you are going you are giving some expectation value and giving some expectation value so this is the mechanism which was discussed by Bollywood back in the 70s generates monopole superpot can generate a monopole superpotential in the infrared so here we get monopole plus plus monopole minus so we get precisely this and if we do the same on the mirror on the dual we get precisely this dual so this is another generalization of this reality I was discussing at the beginning one nice thing is that if you plug F equal 2 and C plus 2 which is the in some sense the self-dual point where there are charges for instance of the basic fields will be exactly one half so if you are familiar with the cyber duality in four dimension if you have SU N with two end flavors it's a similar situation this theory lives at the S duality wall of a four dimensional gauge theory which is SU N with N equal 2 with two NF flavors so this is N equal 2 in 4D so this theory can have a duality wall this was discussed by LeFloch and he found some sort of duality like this but he didn't show that there is a monopole superpotential so some things are not really working well so anyway so last comment I want to make is that if you start from this S duality wall you have a co-dimension one you have a wall in four dimension on the wall there is a three dimensional theory which is precisely this type of theory with the monopoles so this is another example where going from higher dimension to lower dimension you generate monopole superpotential the other example was when you compactify on S1 you generate one monopole superpotential and also here I think I can stop you


Have you been perplexed by the lack of consistency at the plate? Um, perplexed, no. Frustrated, yes. Um, but it is what it is. Turn the page and show up tomorrow, or actually off day tomorrow. Um, Thursday, Friday. Hmm, show up Friday. In Baltimore, where'd you go? Have you ever, have you been able to put your finger on anything as to maybe why you're not being able to go through big stretches being consistent? Um, I'm just, just not consistent. Um, and I know that's vague, but with my timing, um, it just, just hasn't been consistent. So, uh, just keep working at it. That's the biggest thing. Keep getting in the cage with the guys and keep going. When that's happening, cage work, anything else you can do to try to spark something? I mean, keep going. It's frustrating.  So, um, just gotta keep going. That's the biggest thing.  I would encourage you right now, um, that I'm on a great team and we're right where we need to be, um, and, and I've been through it before, really. Um, it's no fun going out and, and not performing, but, um, you just gotta keep going in anything, in life. Um, and kind of that, that's kind of what I fall back on always. Um, keep working, keep going, keep trying to figure it out and, and keep having fun really. Uh, keep playing the game. That's it. Play the game.


Question. When a man constantly talks about his ex, does that mean he is not healed? Oh, yeah! People that ramble on about their past relationships going on and on and on and on and on and on and on. Yeah, they have residue.  It gets boring, but it gets exhausting. It gets exhausting. So choose people that have healed or at least are healing from their past relationships. Thank you so much for that question, Lenny. I appreciate it.


ḣāgā vice dui oshe goudhīmā ḣāgā vice dui ôlo hqodhīmā  caution no Music He said to me on that day not qualify his greatness ʻĀdā bāi du ʻāo jīma ʻa'če le kīma ki ʻĀng ʻōwai chō nū li kanū le yā ʻūla hīnū ʻōchō jīma ʻāgabai du ʻbefia wā ka'u la hā ʻāwai dē mai li Āgā dī zō ʻōwai chō wītā gāgā ʻōchē nū fia chē nū You are the girl that's in comparison ʻājō wūwke būw tō mahabou ʻOwes apān a tāiṋ longa go ʻāi fe lā vi siĕ ʻu rā wāis man ʻi seczu mī on that day ʻgā nūt qualify his greatness ʻĀjā ʻĀgabai du


Hi, thank you for tuning in. I am Sunita Moth. I work as a director of AI model systems at NeaMap. Today, we are going to talk about a peculiar kind of crime scene investigation. This is QCSI and how focus is who killed my part exactly who has done it. Every intriguing investigation begins with a disaster and ours is no different. It started off by QCtrl applied my pixie dust magical app which is we thought is well tested in local environment and bare metal and as soon as we deployed all hell broke loose. We started to see a container being killed left and right with OM kill as a reason and error code exit code 137 and this is then going into crash loop back which is of your joy to look at when you are getting things out into production. So then that sparked a massive hunt for what exactly happened and who killed the part. So let's start with the investigation mode. We have a particular container process that's being killed repeatedly potentially because it's being a memory hogger.  So it's either somebody in somebody with more power has killed the process without the desired wishes and it's a runtime error then. Okay so we know some context and let's look at the details for how the containers run on a host machine and then who are all in charge of in making the container process lifecycle run on a host. So we obviously have a host the bare metal or the instance or virtual and then on top we have the container runtime and container runtime is comprised of two different levels the lower level runtime and higher level and time the lower level deals with interacting with systems host using system calls and making use of kernel and OS features container D which is the higher level runtime then deals with the higher level APIs that interfaces users and deals with image management etc aspects. So then we have the runtime that's broken down into two levels low level and high level runcy and container D are two very popular examples of these runtimes obviously there are many different other runtimes. So now we have container runtime and then your process that we call container then runs on top of it and the layer underneath the runtime and the host then guarantees the isolation for your container process so they are kind of not stepping on to each other's toes. So this is what happens on the host level. Now when we put Kubernetes in the mix that is a container orchestrator not just on one host on many hosts then we need another process who is responsible for managing container processes on the host on its own way and also managing across all the other servers which is essentially what Kubernetes is a part of it I should say has become very big. So that process that we're talking about that deals the management at the host level is called tubelet that is a system D process that manages your process running and the way it does it is by implicitly talking to your container runtime that's provisioned on your node. Now that then talks to image registry and deals with the container process lifecycle. Now CAdvisor is a way to grab container resources utilization and stacks about it which is a part of a tubelet. So tubelet then talks to the container runtime to facilitate the lifecycle of container processes and it also has CAdvisor's parametric collection. Now there are other parts in that figure that I'm not going to touch upon very much because that's kind of not the focus of the discussion. Now in current version all the way up to K20 the way tubelet talks to container runtime is via a thin layer called docker shim which is a means to mitigate the communication or overhead with talking to docker. This is all going to change a lot in K20 and 22 but for what we're talking about it's not so much relevant. Okay so coming back to our actual investigation then we know that our containers are being forcefully killed but it's not through manual intervention then based on what we have discussed it's either the tubelet who is in charge of managing the process running from a cube viewpoint or an OS kernel then who is in charge of running processes on the host. One of the tools are killing the process there. It doesn't look like there could be other suspects that we would have to deal with. So let's talk about what container processes and the isolation how that's guaranteed at the OS level. Namespace and cgroup these are the two important aspects that allow for the isolation of the container process. Now namespace is responsible for isolations from a file system networking in other aspects. Cgroup on the other hand is a feature of kernel that allows for hierarchical management of resource and resource requirements and cgroup memory and other features or resources can be used to manage via cgroup. Now to elaborate more on that I think a bit of a demo would help and that's what we would now look at. Okay so what I'm going to do now is start a container process and the container process that I'm going to start is essentially iPython on our container from numpydev and all I'm doing here is essentially saying give me iPython as a process from the image numpydev and run it and now what I want to do is I want to look at the stats for how much footprint this container is is running with and as you can see it's telling here that it's using 35 meg of memory and some GPU and now what I'm going to do is start the same container again under different name with 40 meg as memory requirements. Now if you see I have two processes running they have been running for a little bit now let's talk cgroup here. So cgroup is managed through a file system in a way like this and you can see all the kind of resources that cgroup then would manage. Now if I look into sorry look into memory I would see these are the kind of aspects of memory that's then managed by cgroup. What's of interest is kernel memory and also memory in limits and in few other aspects. Okay so if you look closely here you would see a folder here called docker. Yeah it's there. So under memory then we have docker and you can see there are two these IDs that corresponds to the container that we have run just now 4 4 3 7 4 4 3 7 and 6 5 c 6 c 6 c so this is a short ID and this is the full ID of the container now let's have a bit of a look into what the memory limits from the containers are and I'm just going to cat the memory limit type and all I'm doing here is say give me full full ID of my container that's 40 meg limit and you can see when I do this I am getting about 40 mag as a process. Now if I just go in here and make this I would see a really large number this is actually the maximum in 64 container by the multiple of 4 kb for page size which is the Linux page size so it's a way of saying that this container is running without a memory limit that is unlimited memory. Now let's do another thing let's bring up another container with a with the 20 mag memory and this is obviously not enough memory that we needed to run with and then we started the container now if we look at what happened we see that actually the 20 mag container was just killed. Now what we want to do is look at the inspect this container and all I'm doing doing is saying do I inspect on this container and I want to only look at the state measure and you can see it's saying this process was actually omkilled with an exit code of 137 and we could do the same thing with 40 mag container and we would see then it's not omkilled it's still running etc so we just simulated the omkill scenario in our local environment. Now I want to show you something interesting and this is about the swap error that we were getting earlier here it was saying that your container doesn't support swap capabilities and memory limited without swap so that means if I asked for container to have only 20 mag memory my container is only going to get limited to 20 mag because the swap which is a capability of systems to go beyond what's available in physical RAM and extend use a little bit more than what the capacity is and that aspect is disabled now so we we can't really use more than what we have but this is my mac now and I would run the same to come on like before so I'm running limited limitless kcsi and 20 mag kcsi and now you would see that when I run this actually the 20 mag container is actually still running it hasn't been killed and I could see local stacks on this and I would say it's still using 90 mag but it's actually making use of the swap for for the extra that it needs. Now let's do a differently let's give it a little let's make it swap list and I do that by explicitly specifying the same memory as swap and thereby disabling the swap and the moment I do that you would see that my container the strict one is killed which is exactly for the same reason and we could inspect on this and you could see that it's actually only killed for the same reason okay so we were talking about docker here like this um and if we are in a cube context as in if uh if the node is a member of a cube cluster then we would also see here cube pod at the same level as docker now we can see here in this example that there is actually one pod running in here in a and in the same way as we had a docker container running and if we look into that pod we would see that we have now two containers running inside this pod okay so presumably one is the POS container which is the container that first gets created to create the networking in the right new space and environments and then the actual process container is created so everything is set up beforehand but if we if the if this pod had two containers in it then we would see here three um three entries for three different containers including one for POS so that was about um there was about cube pod now quickly want to touch on the process and if we do okay so let's just so we said a container is a Linux process how do I know what is the process ID for my container and to do that is essentially this what we say is we say docker inspect and I want to inspect the process ID for this container with an ID that is that belongs to this particular limitless KCSI container so in a way of saying is give me we ask for the process ID by doing a docker inspect using the container ID and then we do a process tax and you can see that 3505 is the process ID on the host level as in the host C is that there's this 3505 ID and this is pointy 295 process now there's an interesting sudo file system based on fee for that Linux manages and this is basically under proc so proc is for process and we could say 3505 and then we would see all these properties of the process I guess some of them are some of them are the the stream processes are pipe processes that other systems use this to communicate then on now want to particularly talk about the limits here and you could and you can see all the limits are mentioned here in terms of various kinds of limits now particularly want to talk about O and score and this is basically this is how the system manages what is the score for OM for this process and in the event of a memory crunch the scores are used to decide which process should get killed there are actually three files on proc for OM one is the score which actually is used to manage the score or record the score the other are two adjustment files as in how much you want to offset the score and there's two for different Linux versions but that's not so much relevant for what we're talking about so we had to look at how C group works and allows for container processes isolation and we also look through how OM scores are managed and how container knows which process to then kill okay slightly changing the gear and talking more about how do we ensure the how do we ensure the quality of service and resource requirements so when a pod is running on a Kubernetes it allows users to specify the resource requirements and it does this in three different fashion one is you basically don't specify any limits and in that case the quality of service becomes the best effort and then the other one is best able where you give it a range and based on the range the queue will try to best place it these kind of pod give a quality of service as possible now the third one is guaranteed if you give the same if you give the same memory requirement as limit then the container the process is called guaranteed quality of service from the point we point and the guaranteed ones are the best kind of parts they are least likely to get killed in the event of OM and they're also good part in a way that it's easier for cube to manage in placing them there is no variability or fuzziness in what kind of resource requirement that would give us and in saying that the best effort parts are then the most likely to get killed because they are the most unpredictable from resource management we point so we talked about resource requirement and quality of service and how likely a pod is likely to get killed now in terms of resource there's two broad kind of resources compressible and incompressible compressible means if you breach your limits you are likely to get throttle but it won't be a deadly event incompressible on the other hand says that if you breach your limits cgroup or something would kill your process my memory is an incompressible resource and cpu then is is a compressible resource so based on what we have discussed I think the question here is can cube overcome it or can cube allow to overcome it and how about linux kernel and this is a very important question and it's not we are posing now it's been asked for many years from a kernel viewpoint and the common view is that it's a feature not a bug but there are contrary opinions as well around overcome it is a bug so can cube overcome it absolutely if we are allowing pods to run with a limit and it's possible that there are two pods running with a big range of limits and collectively together they breach the total available resources and mind you the swap spaces are disabled on communities for for the right reason so we cube can overcome it but it when it over commits it basically over commits without a backing to go further now sure same thing applies to cpu as well you can cube can overcome it from cpu and and a memory viewpoint and the os are configured to overcome it as well by default but they do have a swap space to fall back on to to kind of use a little bit more space when when the physical memory is is reached okay so going back to our actual crime scene when we profiled locally we never really saw the resource requirement to go beyond six gig it was kind of always in the 16th landscape landscape so we tried many different combinations of quality of service and trying to just mitigate the issue while we investigate how to fix it and finally we settled on to this really crazy 31 gig as a memory requirement for the container leading to the as an end of the systems to run and but we would still see omk we would still see the guaranteed parts being killed even though we don't really notice any spikes or a case where the limits have been breached and at no point the node was found to be underduous it had enough memory left from the monitoring viewpoint that it was never really reaching its own to the limit so just reviewing our board back we know that container behaves kind of reasonably we are still getting a kill the quality of service is configured to the best capacity still there is a kill it is likely to be an overcome at a related issue and we know that the suspect is now either the kernel or cubelite okay so we had a bit of a lucky draw we found a critical events where we noticed a particular spike in the in the memory usage and this would go about all the way to a little over 28 gig still within the limits of 31 gig and it was a lot less frequent than actual events and like I said in the bounds of memory limit but we still don't know why the containers were getting killed but we do have an indication that sometimes our processes are spiking up memory usage based on some unknown reason okay so we talked about om scores before what happens how does the om workflow gets triggered so linux manages this k message kernel messaging stream where all these events are then put in now k message kernel messaging parser then parses it and translates it into events through event hardware now the two events that we are interested in is om event and om kill event om event kind of indicating hey memory surge is happening there is there is actually an om situation and the other one is okay we have an om we just need to do a recovery let's start the killing which is the om kill and then there are watchers which would watch to these events and take appropriate action so we would have watched tubelet would have the watch implemented and so would be the some some processing in linux kernel okay so there is nothing in application log that would indicate any problem with memory search but we know there is a search very rarely we don't see any event of any kind of om on cube system parts cube system processes or in any of the event log as far as cube is concerned the node is all healthy and it's all Hapuna Matata okay coming back to again so then based on that we conclude that it's not actually tubelet who is killing the process so let's look at kernel logs then and this is where we landed up then this is an excerpt from our kernel log and we can see that actually om kill was invoked and it was invoked because cgroup ran out of memory and you can see here in here that it's actually om kill invoked and then cube part this is the application part was killed as a result of memory limit and the actual usage was 31455 or 31.4 gig to 31.45 gig again there is a difference of about 1.5 thousand kb that it's still kind of short of the reaching memory limit but it's almost reaching and you can see that swap usage is still zero and on the os level the swap is unlimited so like you know memory usage is still unlimited from from a system you find kernel is using a little bit of memory but it's it's it's not the application usage so much and it has its own limit as you were seeing earlier okay so talking about the some of the metrics of cgroup here now RSS is the resident set size which is a portion of the memory occupied by the process that's held in in RAM and it's it's represents the anonymous memory and the subspace memory now RSS huge on the other hand is actually the anonymous transparent memory that corresponds to the huge pages which is which is when four kb page size is not enough for for for the sort of requirement you have if you're using large memory allocation and in that case a page size will become a lot bigger than four kb and in that case your resident set size huge would indicate the anonymous huge page memory okay and then we also know that anonymous memory often abbreviated as anon is is a memory mapped with no device or file backing and then it also indicates the memory that's on heap and stack so coming back to the second part of the log as you can see here we are saying that the part with usage the actual usage is this and then within that part there are two containers one is the post container which is really using very little memory so not so much the focus right now but this is the application part and you can see it is actually using an active anonymous memory of 31.38 gig and cache is a little bit the RSS memory is also then 31.38 gig and the huge page memory is 29.9 gig so all in all there is only very little memory that's being used that's not on the huge pages and but we are still very much within the limit of container which was 31.45 as it was said so so this is where we are we are almost the process is almost reaching the limit and it's getting killed the OM is getting invoked and it is getting killed there is still enough memory available on the nodes the node is not under due risk and if you look at this total VM we could see that we have a really ridiculous amount of virtual memory that's being allocated 62.59 meg is being allocated and it does look like we have some kind of unused memory allocation that's that's going on but coming back to like you know why the process was killed we know that it was because it was reaching the the memory limit it was just a little bit shy I to be honest I'm not sure why it was still getting killed when it was just a shy of the requirements but it is getting killed just being on the shy of requirements and yeah I must mention if you haven't seen Ian Lewis blog on almighty container and if you're I want to know more about what past container is I highly recommend reading through that blog so then as I mentioned we were quite confused why the process is getting killed despite being shy of the limit but given it's only a few few kb shy we're just going to accept that it is getting killed there now the problem we have is when we get over and kill the behaviors are exactly like that it's a runtime error you can't recover from it gracefully and you can't even fail safely and this is exactly not what we want so what we want is we want a safe recovery and handle more in a predictable fashion so we look that disabling the overcome it and save it failing more at an application level rather than abruptly being killed and there's two settings on VM level where you could say overcome it or memory is disabled too far disabled here they are too far disabled and then there's another ratio aspect which which is only used when you disable the overcome it and it's a way of saying that I don't want my system to overcome it and only commit to their total allowed memory up until cube 18 this there was no way to provide this setting if you provide this by a user data script on your node provisioning side it would essentially get overwritten in cube 18 onwards the system parameters property that now kops allows that you can use to configure your cube clusters but even in that the overcommitter setting explicitly overcome it memory is equal to two is actually disabled there is no way to systematically provide this setting and make sure your nodes are actually disabling the overcome it so really the only choice we have here is to to on the fly update the nodes after they have come up and they've joined the cube cluster to override this overcommitter setting so we kind of follow the script to to update all the nodes with this overcommitter setting we obviously there's probably a reason why it's disabled but we don't know the details and that's why we selectively apply only for a particular fleet of nodes where this particular process goes in so just reviewing our board we know who are who who the killer was it was always kernel and we also know that actually our well behaved application was not truly well behaving but disabling the overcommitter definitely mitigated the issue we can see that the process has been running for about nine hours without any interruption when the case would happen at least 15 20 minutes so so frequently so this was a good mitigation but obviously it is not a solution we have an application that's hogging more memory than it should and then we reviewed the application and bought the memory footprint download that mode chunking option to again help ameliorate this problem so all in all in summary we have a container that was killed because it was reaching its memory limit and it was killed by OS kernel and disabling the whole committer was mitigating the issue and but the actual fixes to reduce the memory footprint and guarantee the resource quality of service and resource requirements of the part to have more reliable experience on given days and that's all I had thank you very much I hope this was an interesting listening in to our experience and it was there was some learning for you in it if there are any questions I'm happy to thank you


Patriot Prime Reviews is a channel for adult collectors and may not be suitable for children under 13 years of age. Viewer discretion is advised. Hey, what's going on guys? Patriot Prime here once again with another video. But before I get started with the subject of this video, I want to give a huge shout out to my sponsor toyhacks.com. Toyhacks is a company that provides upgrade decals for modern transformer figures along with reproduction decals for the vintage ones. While visiting Toyhacks, make sure and check out the Toyhacks Armory to see their line of Transformers weaponry in multiple collars. And toy stages for awesome display backdrops. Each purchase from Toyhacks earns you Robocents that you can use for future purchases. You can check your balance anytime in your cart. Toyhacks is a company run by collectors for collectors. So make sure and check out toyhacks.com and tell them Patriot Prime sent you. Now, on to the review. Now before I get into the featured part of this video, I want to give a huge shout out to biglick.com. Dilla and I went to Roanoke, Virginia over the weekend to check them out. Oh my gosh, did we have a good time? And it was so cool to see the excitement through Dilla's eyes as we entered that convention center with all the displays and vendors and super cool cosplay costumes.  You want to see an impersonation of me with Dilla in the Comic-Con? It was this. I was like, what is he? I mean, he was everywhere and that boy came home with some swag. He had two swag bags loaded. He had been saving up since November plus mama hooked him up with some funds. So he's got a lot of stuff that he's going to go over on his channel. I for one really didn't see anything that popped out at me. So all my money pretty much went to Dylan as well. But I didn't leave empty handed because I ran into comic book artist Michael Watkins. And I found out he's been a huge fan of mine and a subscriber since the beginning. So I was absolutely honored to meet him for the fact, you know, comic book artist and he was a subscriber. It was so cool. And he even had a print ready for me that he autographed so I could bring home. So Michael, your art will now be featured in every Patriot Prime Reviews video because it is framed and hanging up right there above my generation one combiner. So Michael, thank you so much.  And if you didn't see that, just click the link above now on to the figure. So my brother who lives in Ohio always hits the flea markets, the pawn shops, the clearance bins, looking for toys and goodies, both for his collection. He's a big GI Joe collector and he's always looking out for me. So he sent me some goodies home via my parents who are visiting him over the weekend. So Michael found me, my brother Michael found me a rat trap on clearance. I never saw rat trap here. We got Cheetor Prime Megatron, never rat trap. So he found one in the clearance bin that he sent me also sent me a G1 wild rider. And what I thought was a generation two cliff jumper.  And I went to transforming and I was like, no, that is not cliff jumper's face. So I did some research and found out this is a G2 hubcap. I had no idea that hubcap was in generation two. I mean, I knew of Prime and Starscream and Ramjet, Bumblebee, the Dinobots, Constructicons did not know hubcap was part of that line. So I did some research and he was released in 1993 along with Bumblebee and I think they colored him red. So he would, you know, be a good contrast with Bumblebee, but they didn't use the cliff jumper mold because they didn't have it or something. So they used hubcap and colored him red. So I thought that was just fascinating because that's something I never knew.  So now without further ado, let's take a look at this awesome 1990s generation two figure and welcome to Patriot Prime Reviews. We'll start things off by looking at hubcap in his vehicle mode, which is a penny racer style Porsche 924 Turbo. And I can only imagine how good looking this car was back in the day. I love that shiny red chrome look he has. But unfortunately, mine is showing his age. He's faded in spots. There are chips. But still, he's not too bad looking. I mean, the tires, which are rubber, are in perfect shape. And those are usually the things that go first. Now, as I said earlier, I thought this was cliff jumper, but the big difference between the hubcap mold and cliff jumper here is the lack of spoiler in vehicle mode. I should have noticed that first off, but I'm really not that familiar with hubcap. Alas, I don't have a hubcap in my generation one collection. So I'm taking a closer look at the figure. He's got the black windows here, the wheels, the rims. I'm really surprised how good those look or how good a shape they are. I mean, look at cliff jumpers here. That side's not too bad, but they're a little dry. I actually saw on Facebook where some collectors put armor all on their rubber tires. I think we'll try that out. Lots of nice details on the front. You can see the lights there, all kinds of chips. And I wish there was a way to restore this guy. I love the looks of these. I don't have any G2 minibots, and I know they were all this glorious chrome. But man, he looks so sharp and rolls really, really good. And I just noticed when I flipped over, he's got that Telltale G2 insignia right there. They always had some kind of marking that said either Autobot Decepticon or they even had their name. And he's not really bad, chipped on the bottom. A lot of the mini vehicles, well, neither is my cliff jumper. So yeah, mine are actually in fairly decent shape. Let's say I brought Bumblebee out. Yeah, none of these are rough looking. I've seen a lot of these where the paint really scratches off this little section right here. So all in all, nice vehicle mode. Let's go ahead and get it transformed. Super simple.  Then you're going to bring these sections out, which are the arms. There we go. You're going to pull the front out. Now sometimes you want to be careful doing this. You grab by the toes, you can pull the feet right off. So you lock those legs in place, bend the feet up. And there we have Hubcap in robot mode. Once again, looks really good. I love these vintage figures. And he's got a great head sculpt. That's one issue I always had with G1, G2. I hate when the whole face is painted one color. So let's bring in Cliffjumper here. Get him transformed real quick. So we can compare the two. And as you can see, Cliffjumper has the spoiler. Hubcap does not. And they've got the different head sculpts. Other than that, these molds are exactly the same. Now articulation is a G1. The arms can do a complete 360. The toes can move up and down. And I guess his head can look up and down as well. And that's it. Now I am thrilled to have this guy in my collection. Because like I said earlier, I don't have a G1 Hubcap. I was hunting one down when the Generation Selects Hubcap came out. But I don't know why I never got one. I got sidetracked with other new figures. So I still may have to hunt one down now that I have this G2 version. But I really like this figure. And I'm so thankful my brother found him for me. And now for some quick size comparisons. Here is 1993's Generation 2 Hubcap with Generation 1 Optimus Prime. Generation 1 Cliffjumper. And Generation Selects Hubcap. 1993's Generation 2 Hubcap is a surprising reuse of the Generation 1 mold. This one took me completely out of left field. As I said, I had no idea Hubcap was in G2. I love the looks of this guy, especially with that red chrome. I'm going to have to do some googling to find out if there's any way I can restore this guy to his former glory. Because I can only imagine how good he looked back in the days fresh out of the packaging. So there you go guys, 1993's Generation 2 Hubcap. Now if you enjoyed the video, don't forget to like, don't forget to subscribe, and don't forget to click that bell icon to get notified when I upload new videos. Also, if you're in any position to help out the channel, I do offer channel memberships here on YouTube. I have to give a huge shout out to all my current channel members, because it's support like yours that helps keep this channel growing. Once again guys, this is Patriot Prime, signing out. Hula!


This is how you calculate the travel time to one of your stations. We'll stick with station 21418, that's our example station. So we picked the arrival time at 70.26. So we just need to subtract the origin time of the earthquake, which we've already calculated. And here is the answer we get when we subtract these numbers, 0.0195. And remember this is in days. But we want to convert this to hours because later we're going to calculate the velocity of the tsunami. And we want that to be in kilometers per hour. So if we multiply by 24 hours in a day, then we can make this number be hours. And when we do that, we get 0.468. So that is the number of hours it took the tsunami to get from the earthquake to where the station is, a little less than half an hour.


Hello and welcome to the session. In this session, we will study about measures of variation. Now measures of variation are used to describe distribution of the data and it also tells us about stretch of the data. Now we shall study inter-partial range and mean absolute deviation. First of all, let us discuss inter-partial range. Now suppose this data is given to us and here we have represented the data in the shape of a box. Now we know that medium divides the data in two halves. So here this vertical line in the middle of the data represents the medium since it is dividing the data in two equal halves. Now these halves are again divided into halves. Now here this vertical line in the middle of the low half of the given data divides the lower half of the given data in two halves. So this is called the lower quartile of the given data. Similarly this vertical line in the middle of upper half of the given data is called the upper quartile of the given data. Now here the lower quartile is denoted by q1, the medium or middle quartile is denoted by q2 and the upper quartile is denoted by q3. So quartiles divide the whole data set into four equal parts. This means here each part contains 25% of the data. Now here inter-partial range is the range of middle half of the data which means here inter-partial range starts from q1 to q3. So inter-partial range is equal to upper quartile minus lower quartile. This means inter-partial range is equal to q3 minus q1. Now if the inter-partial range is small then there is less variability and if inter-partial range is large then there is a greater variability. Now let us see one example for this and here for this data set we have to find the inter-partial range. Now let us start with this solution. First of all we will arrange the given data from the least to the greatest. So arranging we have 2, 2, 3, 3, 4, 5, 5, 6, 7, 9. Now here the number of terms in the given data is 10 which is even. Now for finding the inter-partial range first of all we have to find the median for the given data and then we will find the lower quartile and upper quartile of this data. Now here number of terms is even so median q2 is equal to the mean of middle two terms which is 4 plus 5 whole upon 2 which is equal to 9 upon 2 and this is 4.5. Now this median will lie in between 4 and 5. Now this is the lower half of the given data and this is the upper half of the given data. Now the median of lower half of the given data set is called the lower quartile and here the median of lower half is 3 so this is q1 and the median of upper half of data set is called the upper quartile. So here 6 is upper quartile. Now here inter-quartile range is equal to upper quartile q3 minus lower quartile q1 so this is equal to 6 minus 3 which is equal to 3. Now let us study what is mean absolute deviation. Now mean absolute deviation is equal to sum of absolute deviations from the mean upon number of terms in the data. This means it is the average of absolute values of the difference between the mean and each value in the data set and the difference between the values and mean is called deviations. And absolute deviation is the absolute value of the deviation which means it is the absolute value of the difference between mean each value in the data set. Now mean absolute deviation tells us about the spread of the data and if it is small then there is less variability and if it is large then there is a greater variability. Now let us discuss an example for this in which we have to find the mean absolute deviation of this data. First of all let us find the mean of the given data which is equal to the sum of the observations whole upon the number of observations which is 5. So this is equal to 15 upon 5 which is equal to 3. Now let us draw a table in which we will write these values and we will find the absolute deviation. So here we have drawn a table in the first column we have written the items in the second column we will find the deviations and in the third column we will find the absolute deviations. Now let us denote the items by x so deviations will be x minus mean and absolute deviations will be absolute value of x minus mean. Now mean is equal to 3. Now here when x is equal to 2 then deviation will be 2 minus 3 which is equal to minus 1 or x is equal to 2 again deviation will be minus 1. Then for x is equal to 3 deviation will be 3 minus 3 which is 0 then for 4 it will be 1 and again for 4 deviation will be 1.  Similarly we have got these absolute deviations now on adding these absolute deviations this is equal to 4. We know that mean absolute deviation is equal to sum of absolute deviations from mean upon number of terms in data. So here mean absolute deviation is equal to sum of absolute deviations from the mean which is 4 upon number of terms which is 5 so this is equal to 0.8. So here mean absolute deviation is 0.8 which is small it means the variation is less. Now let us discuss the effect of outlier. Now any striking deviation from the overall pattern means effects of outliers on mean and variance. Now outlier is a value in the data set which is either very large or small from all other values in the data set. Now let us see an example for this in which this data is given to us. First of all let us find the mean of the data which is equal to 16 upon 5 which is equal to 12. Now we have got mean is equal to 12 but no value in the data is anywhere near 12. Also when we calculate the mean absolute deviation for this data then that is equal to 14.8 which is very high. It means there is a greater variability but you can see that these values in the data do not vary much. So this high value of mean and mean absolute deviation is due to a very large value 39. It means 49 is the outlier for the given data. So from this example you can see the effect of an outlier. Now let us see how you can check an outlier in any given data. Now here consider this given data. Here you can see that number of terms is 7. So median will be the middle term and the lower quartile is 4 and upper quartile is 6. So here interquartile range is equal to 2. Now to check an outlier first of all we will multiply 1.5 with the interquartile range. So this is equal to 1.5 into 2 which is equal to 3. Then in the next step we will add this value to the upper quartile. So this is equal to 9 and we will subtract this value from the lower quartile. So this is 1. Now any value in the given data which is less than 1 or greater than 9 will be an outlier. Now in the data you can see that no numbers are less than 1 and 36 is greater than 9 so 36 is the outlier of the given data. And in this way we can represent this data in a box and with a plot. So in this session we have learnt about the measures of variation. And this completes our session. Hope you all have enjoyed this session.


Okay. Okay, good.  We should be live on the homepage. I'm going to give everyone just a second to get over here. I apologize. We were supposed to be live on a different stream, but it didn't seem to work. So we thought we'd just want to get it to you guys here as fast as we could. So I'm just trying to send all this out to everybody. So that everyone good. We are, we are fine. We should be live. Okay, sorry about that. Everyone. My apologies. Welcome to ESL 001 pre. The review. This is part two of our unit two review. If you haven't seen the other ones, feel free to go check them out later. And we'll put links in the descriptions below, but we've wasted enough time. I'll just hand it over. And so we can just get this started. Hey, welcome everyone to ESL 001 pre-reading and predicting this week. I'm happy to be able to work with you guys and get you going on that. So what is pre-reading? I remember this presentation is reflective of what we have in that wonderful course at Sailor. So if you haven't already joined, you may want to. And basically we learned that one way to learn from a reading is to make predictions. So we're going to start out by talking a little bit about what our prediction and that's basically making a guess as to what will happen in the reading. You start to read something and you're thinking about, okay, what, what is it that I'm going to be reading about? You start to ask those questions. You start to think about, you know, what you think it might be. And that starts to get you focused and ready for what comes next. So you're going to use the title. You're going to use subtitles and pictures. And then you can sort of get an idea of what the author is trying to present to you prior to the reading. Okay, then as you read, you see if you're right. And why would you do this? This is a way for you to become a better reader. Sometimes when we read something quickly and we're not paying attention or we're not practicing some of these strategies, we don't get as much out of the reading as we could. Take a look at the image entitled below. What do you think may be happening and why? So we have the title one car circles back. And of course we have the image here to take a moment and just think about what your first impression is or what may be happening should be actually thinking about is what the title might mean. And then we have, of course, the car here. We have the phrase one car, the title one car circles back. And we see the circles on the car. We see that it looks like an older car. It looks like a taxi. And then we start to put it together and ask the questions like, what does that mean? Is it about a taxi? Is it about, you know, the whole process of picking people up and going back and where is it something else? Is there something else happening here? So in the course we learned that there are some additional strategies summarizing where you identify the most important information in sentences. That's where you're reading a paragraph or a short article and you start to understand what it is that they're trying to tell you. And remember, writing is meant to give a message and have a purpose in most of the cases. And then you're going to be asking yourself, you know, what are the main points? You know, what are some of the things that we can pull out of that reading and use to better understand? So summarizing is taking that basic information and processing it to, you know, pull out the main points. The next thing that you should be thinking about is question generating. And that's where you ask questions about the information provided. That really helps you become an active reader. And some questions include, I wonder why? Does this mean? What about? So as you're kind of going through and reading each section or whatever it is that you will be reading, start to ask those questions. Because that's going to help you become more familiar with the material and help you dig a little bit deeper to better understand it. You want to also practice clarifying where you identify things in the text like vocabulary that you don't know and other difficult concepts, maybe phrases, maybe some of the questions in the text, things like that can help you. If you start to identify those, help you start to break it down so that you're able to process it better. You want to try to reread and restore meaning. And so you want to make sure that if you're unclear about something, you go back and you take another look at it. One of the things that I know we all experience as readers is when we read something quickly and we don't fully understand it, because maybe we skimmed it, maybe we didn't read every word. And sometimes we need to do that in order to fully understand and not get the wrong understanding or get a misconception or not fully understand what it is that the reading is trying to tell us. So examples of clarifying, maybe it's trying to say that or the author is trying to make us see that. So think about clarifying also as if you were explaining what you have read to a friend. And the friend says, I don't understand what you're telling me. What is it that the author was trying to say? And then you go and you clarify it by giving your friend that breakdown, those details that really help to show what the author was trying to do. And it's kind of like when you know something if you can explain it fully to someone, that's what you're trying to be able to do. So you're trying to pull out those important parts in order to be able to effectively communicate that idea to one way to make sure that you are understanding. So here's an example we'll take a look at. Review the following paragraph using pre-reading strategies. So this short paragraph, which is the two sentences, I'm going to ask you to think about the main point. Try to share or respond to the paragraph is about question generating, what about? So as you're reading it, what are you thinking in terms of what are some other questions that you feel you would like to have answered? And also clarifying the author is trying to make us see that. So we look first, of course, at the title, A Rumble in New Jersey. And it's about New Jersey because that's where I live. But take a look at the rest of the paragraph, just do the best that you can in summarizing generating questions and clarifying. And we'll just discuss that in just a moment or two. Okay. We'll start to just take a quick look at this and see what you guys are thinking about as you're reading through this. And remember, this is just an exercise to get you familiar with some of the strategies you can use when you're reading something new and unsure of, you know, what it may mean. So we start with the title, A Rumble in New Jersey. Now that can mean a number of things. Rumble can be something like the sound of thunder in the sky or it could be, you know, the occasion where there may be, you know, people fighting in the streets or it could mean simple, the sound of something that sounds like the earth is moving. Right? So you have a lot of different ways of kind of approaching or looking at a rumble in New Jersey. So the first question is, what does rumble mean? Right? So that's something to ask. And then when we read the actual paragraph, this is an interesting paragraph in that if you don't read it closely, you may miss what's happening. So it tells you one day in August in 2011, residents in half of New Jersey felt a trembling and rocking under their feet. In many towns, the residents went out in front of their homes. Many carried children and stood on the sidewalk. The rumbling continued for quite some time. So if we're not sure what rumbling means, we can start to ask the questions like, does it mean that something was happening in the earth? Does it mean that there was something happening in the streets? We can start to ask those kinds of questions. And then we have, further on in the paragraph, by the end of the day, there had been some damage to buildings and many roads. We remain blocked by rocks and huge traffic jams. So that sounds like there's something happening within nature itself. And then we look at, if we read back just one sentence, people driving recorded, there was a lot of commotion on the roads as people pulled over and waited for the earth to stop moving. So that gives us some of the key things for summarizing it. It gives us those details to better understand it. So we know just from reading that sentence closely that it's about, of course, an earthquake, right? Mike, do we have any questions posted or any students who wanted to share something in response to this quick example? I'll let you know. I'm keeping my eye on the chat, unfortunately, because our technical difficulties are, our delay is a bit longer than we'd like, but I'll let you know when stuff comes through. Feel free to leave stuff down in the chat there, anyone watching, we will see it. All right, so predicting. This is when students hypothesize, and that's kind of a big word, but hypothesize or guess what will happen next by focusing on the background knowledge they have already. So each one of us can start to say, I think I know what happens next because of our own experiences, because of our knowledge, because of our education. And what's great about that is even if you're wrong, you're going to find out as you go through and be able to adjust to that. So in other words, when you start to predict, know that you're taking clues, you're applying those clues, you're seeing that those clues fit. So it gives you a reason to confirm or disprove your ideas. Sometimes in order to do this effectively, you need to look closely at headings, subheadings, and questions. So some examples of predicting, this might be about, I think that what will happen is, and when you start to do this, you get a little bit deeper into the reading and can sort of start to pull out those details that help you better analyze the reading. What happens sometimes is when we read something and we get frustrated or we don't immediately understand, we may not participate in predicting or we may not start to think about, well, what clues are in the title or subtitle? And then we lease out, right? Because we kind of shut down and then we don't really get that information. So know that this is a way to get you over that hump just in case you start to read something and you're not sure what it means. So let's say you're going to practice a little bit of this, read this title and try to answer the questions below. So the title is, Great White Shark Circling New Jersey Beaches, A Rare Phenomenon. So try to answer these questions briefly. This is just kind of a quick predicting challenge to get you familiar with this process and how it can help you. And then we'll talk about this in just a few moments. Okay, so let's just take a quick look here. Hopefully some of you are able to pull out the information from the title and start to do a little bit of this predicting. So Great White Shark Circling New Jersey Beaches, A Rare Phenomenon. What information does it give you? It's a very brief amount of information. It's a very, it's a title. So it's not going to give you a lot of information. But we know for the first thing that it's about a shark, okay? A very special type of shark, the Great White Shark. And then we are given the information that this is rare. So it's something that doesn't happen all the time, right? So we know that this is something that stands out and is newsworthy because of it. So if you have something similar to that or if you have other information that you wrote down that actually helps us better understand that, then of course that would be something to please share in the chat. But the second part, what questions do you have about the title? You might have questions like, why is it a rare phenomenon? Why was there a Great White Shark Circling New Jersey Beaches? How did they see them? Was there, was the shark scaring people? Was there a time when the beaches had to be cleared or evacuated? So those are all questions that now prepare you to read the rest of the article. As you ask, you can then become more familiar with what it is that you're going to actually be focusing on. And then you have, what questions do you think this reading will answer? So some of the things that you may consider are, what exactly happened? What are some of the things that scientists are saying about the Great White Shark? What are some of the things that the people who live by the beach think about the Great White Shark? And what is the town trying to do to deal with this Great White Shark that's actually circling the New Jersey beaches? So if you had something similar to that, you're on the right track, you may have even come up with some more original ideas.  Were other states affected? Things like that, those are all the different types of questions that you might ask to better understand what it is that you're reading. Here's more information. This is the first paragraph, basically. And we have in New Jersey, many people at the beaches report seeing a huge shark swimming in the waters near the beaches. It is easy to see the shark spin, and when the shark is spotted, the lifeguard makes everyone leave the water. There have been several attacks, and this makes everyone uncomfortable. So some of the questions that we were initially asking, you know, did they have to evacuate or leave the water? And we have that answered here. We have it described who was seeing the shark. Okay.  So we, like in the slide before, we talked about those questions, and now we're getting some of those questions answered. So we're actively engaging with the reading. Okay. So it's active reading right now. So understand that these are just some of the strategies to kind of help you pull out those important bits of information that make up the whole. And what should you look at first to understand the reading? And we talked about that. We talked about the different things that you should be looking at. Just as a quick check, based on, of course, of course, material and what we've been talking about, using context clues, what does phenomenon mean? See if anyone can come up. So I guess we could narrow it down by taking a look at, we have the word rare in front of it. We just see phenomenon in the title. Okay. So by reading it, we get the idea that this was an incident. This was an occurrence. This was something that happened one day. So we might get the understanding from reading the paragraph and then looking at the title. That phenomenon means, you know, rare event or rare occurrence. Something that, you know, doesn't normally, normally happen. So based on this short paragraph, what do you predict will happen next? We have people at the beach who see this, the shark, and there's lifeguard sees it and says, everyone out of the world, we have a rare event. So based on this short paragraph, what do you predict will happen next? We have people at the beach who see this, the shark, and the lifeguard sees it and says, everyone out of the water, everyone has to leave the beach. There's been several attacks on several beaches and it's making everyone uncomfortable. What do you think happens next? What can we kind of judge or not judge, but what can we kind of say might happen next? Krista, we have a comment down here about a phenomenon meaning a situation. So I think maybe a little more context of how a phenomenon is more than just a regular situation. Right, thank you. Based on the context. Yeah, that's a very good breakdown. It does reflect like a situation, but phenomenons used to describe a very special situation, something that's not normally seen. Otherwise we would say like a rare event, a rare happening, something unexplainable is usually how we describe phenomenon in English. You know, like UFO phenomenon or things like that where we don't really understand what it might be. And so the question of course is perhaps, you know, the title gives the impression that the great white shark is something more than it actually is. And maybe it's being used to generate that interest and that intrigue in that title. So thanks, Mike. No problem.  I wasn't there. This is a news report. What am I supposed to do with this? But if you're predicting, if you're saying like, I wonder, you know, if they had to send scientists out to try to determine why the great white shark was there. I wonder if they were able to chase the shark away from the beaches. I wonder if everyone's okay that may have been attacked by the shark. So those are all things that would help you kind of go down that path of what's happening next. And remember, it's not meant to make you imagine things, you know, without any sort of reason. It's meant to help you think about, okay, where's the author going next? And let's find out. So in this case, in this predicting challenge, you're being asked to answer the question, what can you predict the lifeguard will do if the shark swims near the shore all day? So I'm kind of following up in, you know, what we were just talking about. What do you think will happen? And this helps you read on to find out if that is what happens. It helps you start to ask the questions, you know, what do you think happened and why. So we've kind of answered this, I think, but basically what we're saying is the lifeguard, if we know that he's already made people leave the water, if the shark is there by the beach all day, he's not going to allow people in the water. So at some point, he's just going to have to say the beach has to be closed and no one can go in the water. So what I'd like you to take a look at as we are exploring this topic is read the passage and answer the questions below. So we have a short paragraph here. Well, I'd like you to think about what could be a title for this paragraph, right? So you're going to try to create your own title for this. What do you think infiltrating means? What do you think or predict will happen next? Give me just a few minutes to take a look at this and we'll talk about it. I will have to give a shout out to my favorite answer we've received on any of these so far from Anne. I don't think it's correct, but I love it. The lifeguard might have to kill the shark if it attacks people. Not usually what lifeguards do, but I like the jaws of it all. Very good. Yeah. I wonder if they could. That's an interesting question if they're able to. That would actually solve a good answer. When I was a lifeguard, they didn't pay me enough to go fight a shark. If you went through this, you should have picked up on some of the clues here. It's talking about high school teachers and college professors and students and spelling and grammar. So basically you have high school teachers and college professors are saying that many students do not follow spelling and grammar rules when they communicate. And we see this like texting language where we use numbers instead of actual letters or words to make their shortcuts. And then we read more over many teachers and professors lament that the misspelling and bad grammar in social networking communication are infiltrating and negatively affecting students writing. So I'm asking you to think about what could be a title for this paragraph. Some titles might be things like teachers see change in communication, teachers see students writing changing, teachers are concerned about students communication habits, things like that because we're going to take the teachers or the professors, we're going to use students and we're going to talk about, of course, the grammar or spelling. So any of those into a title would be helpful because that's kind of encompassing everything we're seeing in that paragraph. And then I ask you what infiltrating means. So we have to look at the clues. I remember we talked about that before where we look at the word in the sentence and we look at words around it and try to come to some understanding of what it could mean. Mike, does anyone have any ideas about infiltrating? I haven't seen one yet, but the chat also has to catch up sometimes. If you're thinking about what it could mean, it's kind of meaning it's impacting. Students are finding it and using bad grammar and the spelling. So it's kind of becoming a part or being used by, so infiltrating in this case, being used by, being a part of, because we can see that in the next part, negatively affecting students writing it's full, so we know it's become a part of their writing. And now what do you predict will happen next? So we know that the professors and teachers are very happy with the spelling of grammar, you know, changing in the communication that students do and that they blame social networking. So if they were to try to do something, they might address how not to write like you're writing on social networking or how to use different tools to check your writing so that you're not making these mistakes. My prediction would be that, you know, the professors and the teachers are irritated or angry that students are making these mistakes and will want to make a change. And so hopefully you guys have a better understanding of how to make some predictions, how to use summarizing and clarifying to help develop your ideas and understanding of what it is that you're reading. And of course, that you'll be able to do things like predict and pull information from titles and subtitles so that you can better understand what it is that you're reading. And I'd be happy to take any questions or, you know, go over anything that I've discussed today if anyone would like me to, you know, revisit some of the things that we talked about. Remember too that all of this information is found in the ESL course and that you can go in and complete the assignment, participate in the discussion and be a part of the course overall. Yeah, well, we'll give people a second if anyone has any questions they want to type in the chat. But yes, as you said, of course, go check out the ESL course at Sailor Academy. It's on sailor.org. You can also go to continue the conversations on our discourse discussion forums. All of that will be linked in the chats below. And of course, we'll be here we'll be back here next week to continue our review of ESL-001. And yeah, with that, thank you everyone for joining us. Sorry about the technical difficulties at the beginning. But we'll get those ironed out. And good to thank you again as always. Thank you everyone for joining us. Good job with your answers today. And we'll see you next week. Thank you guys.