So, I'm going to talk about paper we wrote recently, it's 3D partition functions in Kivara Sora, which has been written together with Antoni Delin, who is doing his first post-doc in Milano, and with Fabriz and Yuri, who is doing his post-doc in Upsilon. So please, you know, unfortunately, I have to leave tomorrow to US, but please feel free to ask the many complicated questions and, you know, don't ask me, okay? Good. So, let me try to give you idea first, and then I will try to give more pedagogical talk because the subject is rather technical, so I will only outline the some technicalities, but I will concentrate on the idea, but the thing is the following. So, thank you. The idea is the following, that in principle, typically when we discuss, so we do localization, so for example, we discuss partition function for S3, I don't know, for land spaces, et cetera. So, for simplicity, I concentrate on 3D partition functions, and maybe toward then I will make some comments about 5D. So we calculate these partition functions, and typically, you know, there are functions of very few variables. So there may be functions to be of, I don't know, of rank of gauge group, there may be a level, maybe some kaoplan, phalaeolopoulos term, but it's a finite. So in a way, to a large extent, it's a number, and you know, it's a bit boring number, so it's a bit boring to study. Of course, some people concentrate on this number quite a lot, there is typically some matrix representation, and this guy depends from very few parameters. At the same time, it's not the only quantity we can calculate localization, we can also calculate typically some set of wilson loops in some, you know, representation. So in matrix model it corresponds to certain insertion, so in a while I will make it very precise. But typically in all discussions we talk about either partition function or we talk about wilson loops, et cetera, but what does make sense, it makes sense to put, to take these two objects together and put them into the generating function. So eventually my zeta t now will depends, of course, on some finite number of parameters which is related to the theory, but then typically it will depend on infinity many guys which people typically call times, it can maybe one set of times, it may be two set of times, et cetera. And then the claim is the following, that's what I will try to explain, that these guys in terms of this infinity many constraints, such as for infinity many, many PDEs, very complicated PDEs, but these PDEs, they have very clear geometric algebraic structure and they're related to cuverasaur. So this is idea and this is, this is general pattern in all other dimensions, again in some dimensions people just didn't study, but, you know, for example in 5D necrosse of partition function, it was a result by Pastein from December 15, you can do the same thing and it will satisfy infinity many algebraic PDEs. So in a way the idea is better not to study this or this object separately, put them together and then you write this. So that's what I will explain and the basically idea would be that this object has very clear interpretation in terms of CFT and this is BPS-CFT correspondence. So before I go there I assume that you guys don't know much so I will just outline your idea of what's verasaur constraints and then tell you some basic stuff about cuverasaur constraints, et cetera. So typically all these guys are matrix integrals with different measure. So when I'm giving you integral typically, right, so if I write for you the integral, so I have to calculate the number, okay. This is very cool, you know, you sit down, you calculate it by some means and typically for this integral what people typically write there is word identities, tts, which is basically an insertion of derivative under the integral. I mean it's a true statement but it's a useless statement because you cannot really calculate anything. So typically this is the whole idea here that instead of calculating this integral or calculating many integrals you can basically try to reduce the problem to generate a function. So namely for example I can, again, I'm here very few mathematicians because they ask me a lot about convergence so let's ignore these issues but I can basically park infinity by integrals in the following object, let's say t1, t2, et cetera and I will write something like this minus 1 over 2g x square plus n from 1 to infinity t and xn dx. So in principle if this is a reasonable function and there is not much analytical things so what I can basically translate this purely analytical problem to this, calculating this, then of course the question how do I understand this integral but typically the most natural thing to say that this is just Gaussian weight and then these guys expand formula and, you know, I can do the formula and write everything explicitly. So then there are two ways, I mean for this, this is very nice, for example, it's good for students to do but you can basically do this thing in two ways. So one way you can actually sit down and calculate this integral, for example, it's, it's, you know, the only thing to calculate this you need to know x and power 2p Gaussian what is equal and then you expand equally but you can do something else. So you can trade this guys for, you can write infinity many PDEs. So one of the things which I can try to insert, there it's a fallen operator. So as you can recognize it's almost verasora but the thing is I put this guy up inside. So of course this guy will satisfy the classical verasora. Then you take this guy, you put inside and then you get of course identity, very trivial identity e minus 1 over 2 g x square plus. So if you have questions please feel free to interrupt me, let me put k here. And this is dx equal to 0. Well now what you do, you just simply differentiate with respect to x everything and then whatever extra terms you have, you can generate them by taking tk derivatives and then what you eventually get if you, yeah, are you a mathematician? Then why do you ask? I warn you that, you know, I mean it's, the thing is of course it's convergent, depends how you understand this integral.  So you treat g as actually positive guys. So this is Gaussian weight and these guys you just expand formally. For example, this is one way of understanding integral. Yes? Yes? No I'm not there. This is, I mean, this is that level. I mean we come to three manifold, nothing to do with this. I'm trying to explain your idea.  But the idea is very trivial in a way. So instead of calculating integral, so I have integral, I have word identities. This is an empty statement. Now what I'm doing is I'm writing for instead of integral, I'm generating function for all integrals. Let's forget convergence, let's forget all this nasty mathematical questions, let's believe everything works. Okay, and then what I'm telling you that I can just tell you right, infinity many these guys. So for example, if I assume that n more than equal to minus one, then this guy is equal to zero. Now what I'm telling you that I can do this exercise, I can actually differentiate on the integral, I can write I will have only powers here of x, and then eventually what I will get out of this if you want it to be concrete, I will get some differential operators, ln written in t's and derivative of t's, acting on zeta of t equal to zero.  Again, this is extremely trivial exercise, but in a way so n plus one factorial t, tn minus g n plus two factorial dTn plus two plus, sorry I forgot here, I just decided for convenience because would he k factorial? Again, it's not of course important, so n plus s factorial, and then s minus one factorial ts s plus n something. And then you can write, let me not write it, you can write the same for l one, there is operator l minus one operator. So what I'm telling you is the following, that this generating function of infinity many variables, just killed by this first order differential operators, and of course next thing you can just check that these differential operators of course satisfy exactly the same algebra. So you can check that these operators satisfy the same algebra. Now what you can do again, the thing is why do you do it? Because as I told you, either you try to solve this PDE, so you can actually calculate integrals and model some analytical details, what you can get, you can just get this thing. So this is generating function for integrals in one variable. So this is called Bell polynomials related to Schur polynomials. Okay, so the whole thing is a following, you take this integral, either you calculate it, in this case you can calculate it, or you can prove, you can try to derive the value of this integral from verisoroconstraints, again, there is obviously verisoroconstraints not feel fixed normalizations, because this is PDEs, I mean, this does not fix the constant value of the integral. But this is idea of verisoroconstraints just in very simple example. Any questions? So the next level of complication, this is our favorite standard Hermitian matrix model. So Hermitian matrix model is the following, again, this is like 25 years old stuff, but so what I can do for you, I can write for the following model, again, I'm introducing, so I will do the integral over UN le algebra. So it's a vector space of, so this is a space of Hermitian matrices. So I'm writing Lebesgue measure here, and then I'm writing here minus sum over S0 to infinity, TS trace of MS. Again, if you're worried about convergence, you can put Gaussian factor, I mean, you can sort of make things, so you can in principle try to look at the algebraic things. So what is obvious is that, I mean, the Gaussian measure over le algebra will be invariant on that joint action. So if I sent my mu to U dagger mu U, and U now is in UN, so this is invariant. So there is very standard Texas side that you can just translate this integral to something like this. So this is again my infinite times, and then I will have here a product over Rn. So by any Hermitian matrix, by unitary matrix can be diagonalized. So I can basically diagonalize this measure, the only thing I have to keep track of things like Jacobi, et cetera. So I will have dn lambda, and then here I will have i minus j lambda i minus lambda j square, and then here I will have S from 0 to infinity TS, and then I replace here i from 1 to N lambda i S. Then again, here what you can do in this simple integral, you can try to repeat exactly the same game, and that's what people did. So it was one of the speaker who refused to come. I did the Russian one, so Morozov and Mironov, I mean, they did this version of the trick, but you can take this object, so you would like to calculate, and one of the things you will insert his operator, ln, which would be minus sum i from 1 to N, d d lambda i lambda i N plus 1. So obviously this is just classical verisor, so I have N variables, I just look at the sum of these guys, so you can easily, well, there's nothing to check. You know that ln, lm, N minus M, ln plus M, so this is classical verisor. Okay, now I'm not going to repeat the thing, but I wanna basically bring you the message, so this guy, this is matrix integral, it has nothing to do with conformal field theory. But then what you do, you do the following exercise, and that's what Mironov is Morozov did in 9091, so in principle you can put this operator here, you can actually differentiate, you will get some terms, you use some simple combinatorial identities, and eventually you will get that ln on zeta, t is equal to zero. Any questions? Okay, and then, so you do this exercise, and then you write this operators. So let me write for you this operators very explicitly. So now this is not first order operators, this is second order, so they will be tk dtk plus second derivative over t0, and then finally this term ln k from zero to N, second derivative of tk dtN minus k, so this is the second term, et cetera. So this comes just from word identities, so this matrix integral. So typically you'll put these guys, it's very obvious why you put here this condition for these powers and more than equal minus one because you don't wanna mess up this convergence, for example. So now, if you stare for these guys, whoever did a free boson and stare for these guys for a while, then you would realize the following thing. You basically will realize that what you have there, it's a free boson representation. So if I look at my Heisenberg algebra, and I can, for Heisenberg algebra, I can pick up some representation and the most obvious representation to pick up. Again, in my discussions, I'm a bit ignoring zero modes, et cetera. So basically what I can do, I can choose these guys to be something like square root of N tN. So introduce infinity many variables. So this is my creator operators. So my N is positive. I'm sorry to confuse you, but this N has nothing to do with that, okay? And then my creator operators, this is guys which would be just proportional to derivative, something like this. So this is the representation of Heisenberg. Now if you pick up these representations up to some numeric, stare at these formulas, what you realize is the following, that this is nothing else. So what you have there, it's the following formula. It's one over two M from minus infinity to infinity of normal ordering of A M minus M A M. So basically this is free boson. Again, at the time it was not that obvious. So this, I mean, this integral, you take a integral, you know, just got integral over the algebra and eventually this integral, the very sort of constraints related to free boson. So if you now try to think a bit more what you have, so this is what I'm telling you, this is pretty standard thing. I'm just, I will do it more and more complicated in a while, okay? So basically one of the way of looking at this integral is the following. So I introduce my free boson. And then basically I would like to construct some guys so I can think about these guys as an element, element in a folk space. For example, I pick up this representation. So for example, you know, I can construct all my states, polynomials, et cetera. So all this, you know, theory of symmetric functions, I mean, can be recast it. I mean, it's related to representation of Heisenberg. So it's in this folks space. And then I basically have to construct your state which would be annihilated by these guys, et cetera. So in a way, this problem already, it's related in somehow to singular vector fields. But the very canonical way of doing it is the following. I basically can introduce for you a screening current which up to the fire of lambda. And the thing is that these guys with these guys behave in very concrete ways. So it's typically ln is s of lambda. This is some derivative of some operator. So it means that if I integrate this guy, so if I do integral of a correct contour so that derivative vanish, then this is zero. So this is typically called screening current. So this is current, this is screening charge. And then what you can think about zeta t. So zeta t for Hermitian matrix model can be thought as a following, that you just take your object, which let me denote, this is let me denote q. So I just take a qn and act on the vacuum. So in this representation, vacuum is just identity. And of course, this is by definition, we'll satisfy Verasorra constraints because Verasorra heat in this, they commute the heat to vacuum, then he later this is zero. And in a way, the matrix model, if you will just try this integral of this, you have to do the normal ordering. And exactly when you will do the normal ordering of these guys. Sorry. Where here? Right. Yes, exactly. I mean, it's a representation, right? So what I'm saying to you, for you, for example, it's obvious that I can, what I'm saying is as a following that I can write for you a minus one, a minus two. This is the same as a polynomial t one, t two, right? That's the sort of statement. It's a representation. It's true in a concrete representation, I choose for Heisenberg, okay? So this is in a way, one of the way of looking at Hermitian matrix model. And the thing is that whatever matrix model we get, you just have to modify the story somehow and make it more exotic. But this is the idea of Verasorra constraints. Any questions? Just final comment is that when you order these guys, so when you do normal ordering, what you will get, you will get exponent of a sum i not equal to j log of lambda i minus lambda j. This is standard calculation in the CFT, which is of course the same as a wonder month. Okay, I mean, right now when I'm presenting it, it's very obvious. 25 years ago it was not obvious. So now what you can do, so our goal is the following that our goal eventually to reproduce some measure. So this is where it's canonical, simple measure. In, for example, in localization, we have more and more complicated measures. So the idea, I will first explain one basic example and then I will spend time explaining the main result of the paper. But one of the things is the following that we'd like here to get a different function, something more complicated. And one of the way of doing this is basically try to deform Verasorra. So you look at different deformations of Verasorra. So let me write this down explicitly. So I will now start to talk about Queverasorra or Sorra. I'm not going to give you any general theory, I'm just, and mainly I concentrated on a free field realization, free realization. But the whole idea, we keep this philosophy from Hermitian matrix model, but we deform Heisenberg, we deform guys, we deform these guys so they become, now not quadratic, they become something complicated, but they still satisfy some algebra and then you get eventually the same thing. So these things still will be true and you will get something annihilated by these operators. So let me talk about Heisenberg. So now I will deform it by some complex numbers, which I will tell you in a moment. Let me be, so PQ and just this is zero mode, I guess it's what, and then so in general Q and T can be complex numbers and there are the following relations. So it depends which numbers you discuss more fundamental. So P is equal Q, T minus one, and quite often you say that T is equal in power Q beta. So either I pick up Q beta or I pick up QT or I pick up, et cetera, QP. This is just standard things. Okay, again the whole idea is now if I try to form my guy like this, so just think if I take this formula and I deform my Heisenberg, I start to calculate something like this. Again there may be some, I mean modifications, but roughly speaking, I automatically will not get this measure. It will be more complicated. Okay, so let me tell you about free-filtralization of Q verasaur and what's how it's related to verasaur. This is just zero modes. It's a momentum Q, so I have to have A zero. So the formula which I wrote here, this is for N and M in integers minus zero. So typically we have to keep a zero mode, so we, I mean for zero modes we have separate guys. This is some technicality if you wish. Right, so now, Hi, Q verasaur. So this I just take, I postulate and then what I can do, I can do to write for you the following. So what is Q verasaur? So this is basically deforming verasaur not within the algebras, but within associative algebras. So this has been done around 95, group of Japanese a lot at all. So let me write the thing and then tell you in what sense it's a verasaur. Oh, deformation of the verasaur. So you can write this algebra. So I fairly some structure constant, so they come from expansion of concrete functions. But the thing is that you can fix this function by associativity, okay? So this is fixed, fixed by associativity. And then if you now take your Q and try to say EH bar and try to expand this in a up to quadratic order, then you can see that sort of only, so if I write for you the formula, TN, it will be two, some constant term plus H bar square beta, ln plus Q beta square over four, delta N zero plus terms of all the H four. So Q beta is just some variation. So what I'm telling you is the following that you can write this algebra sansats, you can fix it by associativity. But another requirement is that you would like in quadratic order in H bar, these guys will be actual verasaur. So this is called verasaur. So you deform verasaur using associative algebras. This is basically a W algebra, okay? So of course you can ask the following question, how to write these guys. So you can write concrete sansats for these things. And so this is L plus of zeta plus L minus of zeta.  So this is free field realization. So again, it's a computation which has been done by Avat at all that if you take this Heisenberg, you know, you write these guys, you take these guys, of course you expand them over sum over TN zeta minus N. You can see that TN satisfies this relation. Of course, this relation can be written in many different forms. And I'm not writing for it, but this is a coefficient of expansion of very concrete function. Okay, it's a quverasaur. Then next thing you can mimic in Hermitian matrix model, you can write also the analog of a screening current. So screen current is given by the following formula. So just one comment for you right away that you realize. If I wanna now look at these guys as a differential operator, so all of this Heisenberg is deformed, I still have a canonical representation of Heisenberg.  I may say that I'm not deformed in Heisenberg. I can put all these coefficients inside of this A N and then my complications will pop up here. So I mean, it's a folk space. It's the same folk space. I just have an action of totally different object there. But up to these factors, which you can put in definition, I can still write A N for positive N as a derivative in T and this is just a multiplying with negative N as a multiplying T. So now if you look now at these guys and you put here your operator, so you put your representation in derivatives, et cetera, you can see that the operator is horrible, but of course it's well-defined. But in principle, it's exponent of differential operator. So these guys in the representation of Heisenberg is up only quadratic guys. This becomes now a very complicated operator, but it's totally well-defined. There is ordering problem solved, et cetera. So now I'm writing for your screen in charge. So again, it's some expression. Beta Q, W, beta. The whole thing is done because I would like to mimic exactly what I had before. So if you do the calculation, then the thing is that T and this SW is equal to, now it's a difference operator. So I'm not specifying this. This is always a sum operator, but this is almost, it's a Q derivative. So you can calculate this, so we don't care. Important thing that if I take a correct contour, sorry, W, so if I take a correct contour, so what is very obvious is the following, that if I take a correct contour for integration, then of course this is zero. Simply in this integral I can change instead of QW, I multiply here, I change variables in this integral. So this is the same integrals. Again, the thing is that you have to think about the contour, but let's say we take a contour, which is, so it means that if I integrate these guys, so if I integrate these guys of appropriate contour, then I will get that this is equal to zero. So from this point of view, I can repeat exactly the same game I did before. There is some subtlety, zero modes, et cetera. I'm not going to discuss them, but now what I'm telling you that I can take my integrals, roughly speaking, so in power n, put on the vacuum and get something, okay? So I get something and then I'm saying that this something, if I call it zeta, so this something you'll be annihilated automatically by this positive. So let's ask what is this, so you can actually calculate. So this is, I'm going to write for you the thing explicitly. So my zeta of t looks as follows. And that's when three manifolds and gauge theory will enter in a moment. So this is just some complicated, but straightforward calculation. So what I have, I have some contour integral over a region. I from one to n dwi two pi iwi then I have here and from zero to infinity. Okay, let me write this in these notations and then w, so i not equal to j, w i divided by w j q infinity, w i divided by w j t q infinity and then here I will have my t k, k rounded from one to infinity, i from one to n w i k. So how do you get this integral? What you do, you write your screening charges. So this comes from the measure, so this guy is identified is exactly with my screening charges in power n acting on the vacuum. So this comes from normal ordering and this is just my generating function. This is creator operators in my conventions. So you still have them there. So I mean, these guys still act on the vacuum. I mean, this is a generating function and this comes from the normal ordering. So is everything clear? The symbols are all just clear. Do I have to define them? Everybody understand what's written here, right? Let's assume so. Okay, good, but now the thing is that when you stare at these guys, what you realize is the following, that this is in fact a partition function for u n theory for n equal to u n theory plus a joint chiral with mass on the following geometry. So t, so it's a disk, which is you currently rotate. So it's a two disk time circle. And the parameter t, it's roughly exponent of the mass. So this is, so in a way what one can say right away, then if you know, again, it's identification, but the statement is the following. If I would turn things around, if I will put Wilson loops along s one circle and put them all in generating functions here, then I will get a sum object which would satisfy infinity many constraints. So there's a lot of relation to McDonald's polynomials, it's, I'm not discussing it here. Okay, what is important here, it's identification of this object with this object. Again, when I'm saying partition function, I might actually mean a generating function. Okay, so now let me explain the main result here and that's what I'm doing. So I'm interested in a compact manifold. So let me start with s three. So for s three, if I take the theory, so I'm taking n equal to u n theory plus adjoint karel of mass m. So it's generalizable to marginal theories, I'm just looking at simple examples. So my partition function would look as follows, it's i r m and I will have a d n x and then I will have here i not equal to j. Then there is this double sign. So my s is squashed. So what I'm thinking about my guy is omega one of zeta one square plus omega two, sorry, omega two zeta two square equal to one. So xi minus xj w one w two. Then there is s two m plus xi minus xj omega one of omega two. And then typically here, so let me be more pedantic and try to do it explicitly. Yeah, nothing special. The thing is you do what you can do. So this is a thing. I mean, I'm going to, so unfortunately, you know, there is, if you want to go to concrete things, if just let me make comments. So the results were explicitly has been calculated. There is closed form, it's s three, it's a land space, it's s two times s one. So this is on the market exists concrete formulas and you can take them. And the statement is that I will tell you that all this generating function will be killed by two copies of commuting, whereas our constraints is appropriate way of identifying parameters. Now what is up to the catch? And this is for any postdoc speech students or even senior staff. I mean, n equal to theorists exist on Cyford. So it's a result by Fistucci, Demetrescu and others. So you can put n equal to on Cyford, but there are no formulas here explicit. Because one thing that you have a supersymmetry, another thing is to calculate a matrix integral, take into account all flat connections. So in principle, we would believe that we should be able to do something here, but you know, nobody. So s three is because people calculate it. We can sit down, there is concrete formulas and do it. But in principle, I mean, this is up to catch. I mean, one should be able to produce formulas for Cyford up to some orbit fold. I mean, it's locally free, you on action. Absolutely. So this is huge class of manifolds and people prove that it is identical to supersymmetry, but nobody dared to write the concrete matrix integrals, well, maybe exception, Simons. But again, there is a lot of issues here, et cetera. So, no, they're much better than Rouschi-Tichin to arrive. So this is all the stories secretly related to complex Chin Simons. So this is, I mean, this is some upgrade. And but again, this type of theory is not yet well defined. It's up under discussion, but secretly it's related to complex Chin Simons. Absolutely, yeah. So I don't want to discuss the subject because it's outside of my scope, but secretly sort of adding the mass, you know, having U.N., this is somehow should be identified with the complex Chin Simons, et cetera. So there is this discussion in the literature, but it's not very conclusive. I mean, there is no clear cut answer. So is that equal to? Absolutely, yeah, it's specified. So the rank of this guy tells me how many integrals I have. So then if I take another, you know, theory than I have integrals. So this is like this. And then what I wanted to write, I still have at least to have time to explain your result. But, and here of course, what you will have, for example, you will have standard this terms, minus i pi k2 of omega one, omega two, x i square plus two pi i k one, omega one over omega two, x j. So this guy's Chin Simons level, this is Philly and Lopoulos, for example. So now what we want to do with you, we would like to put Wilson loops, but we have to think how to put Wilson loops because we would like to put a supersymmetric Wilson loops. So it's important in this logic that I'm choosing my omegas to be generic. So there is, we'll be lot of algebraic degeneration when they're rational, et cetera, et cetera. So I choose them generic. If I choose them generic, there is only two supersymmetric Wilson loops I can put. One Wilson loops when zeta one equal to zero, and it will have this periodicity. And another Wilson loop here, it will have this periodicity. What I'm saying is it's not true if omegas are rational. I can have torus nodes, for example. But if I choose them generic, then that's what I will have. And then it means that for example, if I wanna put a Wilson loop, then I have to insert in the integral correspondingly the following guys. I have to insert, for example, trace in some representation of my exponent of two pi i x over omega two, for example. No, no, well, it's basically, if I think about S3, S1 vibration, it's only two loops which sits over north and south polo S2, right? So this is the only thing. But this is what supersymmetry is telling me. So either I put this guy or I put another guy. And I would like to write the generating functions for both of them. So either I put these guys or I put, so this is representation one, I could equally put in another representation two pi i x over omega two. And of course, these guys is nothing as a short polynomials in dependent from the exponent. R1, R2. So if I wanna get a Wilson loop, I just put a short polynomial here. And then there is this standard formals which I'm going to use it. If I have a sum of all source, let me call them S, I think this is more canonical. So if I write this at T hat S Rw, this is equal to exponent of n more than one Tnj Wjn while these Tn's are related by formal change of Tk hat n over n, sorry, T like this. So that's what I'm doing. Now what I would like for you to introduce a generating function. So my generating function will depends on two set of times T and T prime. So how I define this? I define this as a sum over two set of representations. And then I will have S of R1 of T hat S of R2, T hat prime. And then I will have my integral which I had before with insertion of, so we'll have d and x, I will have my measure. So this guy is exactly this measure constructed out of double signs. Then I have my key exponent, okay. And then I have corresponded the Wilson loop R1, e to pi i x of omega one. And then I have S of R. So I would like to have a generating function for Wilson loops, supersymmetric Wilson loops. So if I do it and I use this formula then eventually what I will get I will get the following integral. So my measure, my e w x j. And then here I will have correspondently exponents of n more than zero Tn. Then I will have j from one to n e to pi i x j of omega one. And then I have tn prime. Now j from one to n e to pi i x of omega two. So I have to have two times if I wanna have keep track of all these loops. So this is my object. So let me now tell you the answer, the main result of this object. So let me for simplicity choose my chance simons level equal to zero. It just was simplicity result looks simpler. So in principle one can generalize it appropriately. So now I told you that I can write for you these operators as I wrote before in some representations for t and t, t prime. So I will have to free field realization for quiveras or I'm now looking that these guys is more than equals zero. So these guys by construction are commuting because this is used different times. The statement is the following that these two guys, tn will kill this function. So this is a priority. Let me also put here prime. This is different operator. So again, I'm repeating that this guy, there is no really obviously symmetry because this enters with this periodicity, this enters with another periodicity. Now it is important that this is not identical algebras. I mean they have a different parameters. So let me write for you the parameters. So if I'm writing for you the thing, so I have two copies. Copy one and copy two of my verasaur. And in gauge theory I have the following parameters. I have my squashing parameter for this here. I have a mass, et cetera. So then correspondingly copy one, this q one will be the following. It's a e two pi i omega of omega one. So omega is just omega one plus omega two. And t is equal t one is equal to q one and power b and it's equal to two pi two pi i capital M of omega one. And then q two is equal to two pi i omega omega over omega two. t two is equal to q two beta two pi i M over omega two. So this is your glutuk verasaur and this is the following relation of guys. Again I'm repeating what is quite unique here. This is just one integral. It's not two integrals. I mean the statement will be obvious if there will be two integrals. So if I took my result from before, when I got verasaur then it will be, the thing is here the trig works because these parameters are gluten very, very particular way. So if you start to think geometrically, so if you think that q one is equal to two pi i tau, so tau is just here, it's a ratio of omega over omega one. Then my q two is just equal to the following things. It's a minus two pi i tau, tau one minus tau. So this is a sum element of s l to zeta. And this is exactly element which you will use when you will glue s three out of solitary. For example, if I will, I mean, the same statement will be true. The measures will be different. The integral is different. But the same things, for example, true for land spaces. For land spaces you will put here r, et cetera. Now what is important, the trick that these two commuting guys lives together nicely, it doesn't work. So I cannot really take two results and reduce two integrals to one integral, et cetera. So the whole trick, it works nicely only when the parameters of verasaur of two q verasaur glued by s l to zeta. Otherwise it doesn't work. So I have no time to explain for you the details, but this is the idea. So this is the main result. And of course I skipped for you a lot of technicalities. And what I would like to stress at the moment that it may appear trivial result, but it's not trivial result. And the thing is because of screening charges. So when you prove it, of course, you will start to prove it by basically by gluing two free bosons and thinking that if I take one free filterization, I take another free filterization, everything works. So I can basically repeat for your story. I can take TN. I will write for your screening charge. One, I will take another TN prime. I will write a screening charge two. And then somehow what is obvious is that you would like, for example, now to construct S1 tensor S2. But don't forget they would depend from the same guy. So when I will act this by TN, so of course TN will act on this. So I will get D of S1. So this is my Q difference operator. Q difference operator. TN tensor S2. On S2 it does not act. I will use totally different free bosons for representation of this guy. But the thing is this is not good because I cannot put on the integral because this is not equal to D on S1 times S2.  Well, it works, but I cannot put this under the one integral. Of course, if I will have here X, here Y and integrate, then there is no problem. It's really a copy. But I would like to do one integral. And because of this property, it's not good. But the magic is the following, that if the parameters of this theory are just in such a way that this D acts trivially here, then this becomes true. And this exactly happens when it will be glued by SL2Z transformations, OK? So I have to finish, but let me just say a few things. So it can be generalized to these cases, LR, and some two versions of S2 times S1. Why we don't do other manifolds? Because there are no explicit formulas for this. So for example, we can maybe come up with some ways of gluing currents, et cetera. But we have no measure to compare. So it's simply there are no gauge theory results. So this is one comment. Second comment, you can generalize everything. So in fact, the theories which one can do, one does not have to do your own theories. If the theory is which is extensively considered, it's there are 3D closings considered by passed on by Nikrasov. It's a skewer type theories. So in principle, you can have a UN node, and then you have a marker. The only thing we always have to decorate our UN theory by some adjoint to have an M. And this is responsible for T parameter. In principle, you can go to the limit when T goes to 1. So there is rounds here, a lot of things that will correspond to certain degenerations of the algebra. Some of them studied, some of them not studied. So for example, one can generalize this to ABG mode. The only thing is if you would like to see full algebraic structure, you have to take two nodes. So you will have these guys by fundamentals. But they also have to decorate by adjoint. If I don't want this adjoint, there is certain value of M which I can do it. But in principle, so they will be this diagram, your diagram. So Peston constructed for this diagram, the w-algebra. So there will be these two copies. So if I construct this default ABGM for general values for scores here, some partition function, generating function will be annihilated by two computing copies of this clear w-algebra, which was constructed by Peston, et cetera. For all the theories, it works. It's first generalization, second generalization. Of course, everything, all the theories can go on to all these three type of manifolds. You can include, of course, Chen-Simon's level, which corresponds to insertion of some vertex operators. So the rest of our constraint becomes a bit more complicated. OK? So I have to finish. But basically what we see now here in details is some remains of 5D picture. So in principle, the screening charges which I wrote, it's the same screening charges which were used by Peston in his December paper. So in principle, one can write a 5D microsoft partition function for this keyword type theories, roughly speaking, as ejection integrals. So this is symbolic things as ejection integrals of infinity-many copies acting on the vacuum. So that's a Peston result. So this is a representation. The thing is that in principle, what you do now, you talk about generating functions, and it will be annihilated by infinity-many constraints. So of course, this is an R4 times S1. So this is the result with the Peston at December 2015. So for example, one would expect here that you can glue some similar things. We sort of, it's under consideration. We don't know. But one can also, I mean, for the compact manifolds, you will glue things there also. The only thing that apparently, if you think for a while the correct notion of modulo double for q-verasora, it should not involve not acyl-2-zeta. It should involve acyl-3-zeta. And the thing is, because verasora, q-verasora automatically has a symmetry over q and t. So it means if you take this picture and you impose symmetry about qt, you have to generate full acyl-3-zeta. And that's exactly how you, in general, five manifolds you glue partition functions, et cetera. But again, it's something very speculative and remains to be understood, et cetera. But for example, the result, which is sort of obvious for Peston, that a partition function on S5, a generating function, will be annihilated by three commuting copies of q-verasora with the parameters which you can read from geometry. So I have to stop here. Thank you very much.


Hi, this is Pastor David Osales of Calvary Chapel of the Chino Valley, California. In the late sixties and early seventies, people were amazed at a new phenomenon that was shaking the younger generation. Young people were coming to faith in Jesus Christ in great numbers. And the press quickly referred to us as the Jesus people. This was not something that the unsaved world would have expected, because there was a great turning away from the Christian underpinnings of our nation. And there was a creeping worldliness that was settling in and transforming American culture. Interestingly, on April 8, 1966, Time Magazine ran a cover headline with the question, Is God Dead? Then on June 21, 1971, the same magazine had a picture of Jesus on the front cover under the banner, The Jesus Revolution. Now how did this happen? How did this youth revival begin? As we look at our day with the violence, fear, and uncertainty, we can believe it is the worst time that this nation has ever had. But this obviously isn't true. The simple fact is, in the sixties, America was in turmoil. The decade was filled with turbulence, anger, and revolution. It was during that time that the U.S. committed itself to policing a small Southeast Asian country named Vietnam. In the sixties, President John F. Kennedy was assassinated in Dallas, Texas. And Jack Ruby killed Kennedy's assassin, J. Harvey Oswald, on TV before a live audience. Civil riots broke out in Watts, Boston, Washington, D.C., Newark, Detroit. And at the Democratic National Convention in Chicago, raised fists and cries of burn baby burn rang out in America. The sixties was a time of chaos, anger, and protest. During the sixties, Martin Luther King Jr. courageously led marches for racial justice and his reward for such concern was being gunned down in Memphis in 1968. Later John F. Kennedy's younger brother Bobby was assassinated. UC Berkeley, Harvard, San Francisco State, and other institutions of higher learning were invaded by students and occupied in protest against the war in Vietnam. Four university students were gunned down by National Guardsmen at Kent State. Later, at law enforcement, was high and young people began to cry, kill the pigs. We had the Cuban Missile Crisis, the Berlin Wall, and in the midst of this turmoil, hippies came into existence, invading San Francisco's Haight-Ashbury District. Drugs, alcohol, lovins, and free sex became the lifestyle of many of the younger generation. Psychologist Guru Timothy Leary encouraged youth everywhere to begin to take acid. Our mottos became tune in, turn on, drop out, and if it feels good, do it as long as it doesn't harm anyone else. This new philosophy of life found a way to make its way into the mainstream and was normalized through a revolution in music. The British invasion led by the Beatles, the Rolling Stones, the animals, the who invaded America, sweeping the youth into counterculture lifestyles and anti-Christ philosophies. I can still recall when John Lennon stated, the Beatles are more popular than Jesus Christ. Though it caused outrage, at that time, I agreed with him. We had rock music, folk music, protest music, soul music, psychedelic music. We had rock musicals, every kind of music that you could imagine. It became a time when singer-songwriters openly espoused politics, believing that it was their social responsibility to do so. Thousands of young people gathered at Yazger's Farm in Woodstock, New York, and became the Woodstock Nation, which inspired folk singer Joni Mitchell to write the song Woodstock, which was popularized by Crosby, Stills, Nash, and Jung. Contrary to our selective memory and revisionist historians, the 60s were anything but happy. We were rightly described by singer Don McLean as a generation lost in space. The Apostle Paul describes it better in Ephesians 4, 16, and 17. We were darkened in our understanding, separated from the life of God because of our ignorance in us. By the hardening of our hearts, we lost all sensitivity, and we gave ourselves over to sensuality, indulging in every kind of impurity with a continual lust for more. Again, the words of Crosby, Stills, Nash, and Jung are correct. We were helplessly hopeless. In the midst of those days, in spite of the moral darkness, God began to move powerfully. Many hippies began to see in Jesus the ultimate hippie, the preeminent revolutionary. His message of love, community, faith, and forgiveness began reaching my generation. Multitudes of hippies started to come to faith in Jesus and it amazed America.  A youth movement hit the United States and the press quickly called us Jesus people. In 1967, Ed Plowman, the assistant editor of Christianity Today, wrote the book The Jesus Movement in America. In his book, Plowman attempted to describe what had begun sweeping through the United States. He followed the Jesus people from Haydashbury to New York City, chronicling the movement, and in his introduction Plowman wrote, I just couldn't believe it was the real thing, hippies reading the Bible and praying, yet there they were. In the storefront coffee house, some ministers had opened near the intersection of Haydashbury in San Francisco. What I saw and heard distalled my doubts about these wild-looking young people and the sincerity of their belief. Drugs didn't seem to matter anymore. They said Jesus Christ had given them a better high. They spoke freely of their new love for God. They loved the Bible. They loved each other. And in the electric atmosphere of vibrant unselfishness, I had a strange feeling they loved me. What was true then is still true today because Jesus broke through those barriers. At that time, the Christian band Love Song wrote the song Little Country Church, which included the lyrics, long hairs, short hairs, some coats and ties, people finally coming around, looking past the hair and straight into the eyes, people finally coming around. And it's very plain to see it's not the way it used to be. Out of this movement and moment in history came Calvary Chapel Ministries. Of course there were other groups of believers celebrating Jesus, but I got involved with Calvary Chapel as a 20-year-old young man, and I've been following Jesus now for almost 48 years. With all of this said, I just wanted to remind you that God is still on the throne. I wanted to remind you that it isn't over yet, and God still has much to do. I wanted to encourage you to trust God's Word, to be filled with the power of His Holy Spirit, to seek Him daily, to fellowship with Him in prayer, and to not forsake relationships with like-minded believers. I wanted to remind you that when it seems to be the darkest, God's light shines the brightest. I also wanted to remind you that with God all things are possible and that God still loves the world and desires all to come to Him in salvation through His Son Jesus Christ. Sometimes it can seem that there is no hope and that we should just give up. This isn't true. We need to remember that if God is for us then who can be against us? We need to remember that we are more than conquerors through Him who loved us. Hold fast to God, trust His promises, don't give up on sharing your faith with family and friends, with your neighbors, and when given opportunity, share your faith with strangers. A.W. Tozer once pointed out that when the world has been in its darkest times, God has moved mightily and though things are difficult in our day, it is time for the church to be the church to wake up out of sleep and to do the work of ministry. It's not too late, hold fast, trust God, and be still. We shall see the salvation of the Lord. This is Pastor David Rosales of Calvary Chapel of the Chino Valley, California.


In this presentation, we will talk about how to set up and record a petty cash fund. Setting up a petty cash fund seems like an easy thing to do to have a minimal amount of cash that we can have expenditures for small purchases for. However, it can be a little bit tricky to set up the petty cash fund and there is kind of a shortcut to recording transactions for the petty cash fund. So we'll go over the process of setting up the petty cash fund, recording the initial investment in the petty cash fund, and then recording the activity from the petty cash fund. Now the objective of course in this will be to have not just the checking account where we need authorization in order to take money out of the checking account, we would typically want anything going out of the checking account to be by electronic fund transfer or by check so that we have a clear paper trail of what is going on. The petty cash however if we just have some small items that we need to


heard of SDs. You've heard of vessels. You've heard of ours. You've heard of SRs and SPs and S pluses and S minuses, but have you heard of an SD mine? Oh, I forgot, S deltas. So, but have you heard of an SD minus? I'll tell you what it is. It's really simple. It's just a discriminative stimulus for punishment. That's it. It's just a stimulus that signals that under this condition that when this is present that a behavior is gonna be punished. So, that's really it. Like an SD minus, on our channel, yeah, an SD minus, on our channel we might have referred to that as an STP before. I've seen them written several ways. STPs make sense. Or an SD minus. Take your pick. Signals punishment. That's it.


Hey Virgo! This is Kelly from House of Virgo. This is going to be your next 24 hours love reading for all Virgos, Virgo Sun, Moon Rising, and Venus. Some of the messages may or may not resonate. Just take what fits, leave the rest. If you'd like to get a personal reading from me, there's a link in the description box below this video. You can just click on that link and that will take you directly to my booking site for a one-hour phone call reading. Okay, so if you're new, welcome to my channel. Please, if you like this video, please do hit like, share, and subscribe on your way out. Okay Virgo, let's take a look at the past position with the person you may have on your mind at this time. Present and the future. Alright Virgo, I'm going to do my best here to give you the best reading that I can. Let's see what the love message is here for the past. What was the love messages? I see definitely you were trying to cut through and get some clarity about a situation in your past that left you feeling kind of confused with someone. There's definitely chemistry and a desire to take a relationship to the next level with someone from your past. I see you being quite stable in a lot of ways. Making your money, working hard, being routine, making sure your cabinets were filled and very focused on work as well. The moon energy can represent Pisces. So let's see, I just want to get a couple cards here for the present and the future. Okay, so there may have been some deception in the past and an energy of like problems that just could not be brought to light, full clarity, somebody you're needing to trust your intuition on things more than having actual clarity. Okay, a lot of confusion. I just see you sitting here a vergo in the past in between what's not seen and what the truth, trying to come to the truth about something. Now let's take a look. What was this deception? Okay, so the two of pentacles here, maybe there was some juggling. There may have been a decision or some choices or somebody was weighing their options and really just trying to balance things out and make a decision about, you know, a relationship or a connection with you or even to go into a higher level of commitment. Okay, let's take a look at you here. It's Queen of Pentacles, Queen of Wands. Okay, there might have been a decision between two people, you and a fire sign, Aries, Leo, Sagittarius or a Taurus Virgo Capricorn. Okay, but seems as if there was some potential truth that came to light in the past with the Ace of Swords. Okay, there might have been some new conflict or some things that needed to be overcome. And I feel like your person, it seems as if something was communicated to you from them, some truth was given to you from this person in the past. Okay, let's take a look. Now, some of you here could also be a Virgo on the cusp of Leo. Okay, so that could represent you. And if it wasn't two people, it may have just been that this person might have had like, might have had some emotional things or they were moody and trying to balance their moods or they may have thought that was thought that about you, that maybe you were a little rollercoastery with your emotions at times. When maybe sometimes you could be really fiery and passionate and other times you could be really stable and reserved.  But I do see there was a very strong attraction to you from this person. And I definitely feel like this person was in a position where in the past, in their heart, in their mind, higher level of commitment was on the table and they did want something there with you. Yeah, look, the lovers now either they told you that they loved you in the past. If they did, it was truthful. They meant it. Or they told you that they wanted to try to work on this partnership with you in some ways could also have been a truth that they were looking or they were looking to find someone whom they felt that match with.  Or for others, it could have been you telling them you're looking for your other half. Okay, and maybe you were undecided. I kind of feel like both of you wound up in this position where you were both undecided about each other in the past. Okay, it's like the love was there, but there was some things just there's a sense of uncertainty in back then and not being sure about if maybe it could work. I feel like you both were sure there was chemistry and that opportunity to ascend to a higher level of commitment with each other was definitely on the table there. But there was a little bit of like that to a pentacles kind of makes me feel like him and Han like maybe maybe not maybe maybe not could have been you doing this or your person doing this or both of you reacting to each other where it was a lot of like up and downs between the two of you. So the present energy. Love yourself first and forgiving and learning. Okay, so you're in a position right now, Virgo probably of loving yourself at this time like respecting yourself, putting yourself first, making yourself a priority. And there might be an energy here of you releasing and healing your past in some particular way so that you can receive more love in the present. Now what's going on in the present here. So I feel like the three of wands is here. You know, Virgo, I have to tell you, I feel as if your person, whether you're in communication with them or not, I feel like your person presently has no intention of letting you go.  Because I feel like you're kind of maybe you let them go. Like maybe you just finished you just ended this thing with them. And there was a lot of wish you washiness in the past. Or maybe you both just went your separate ways. But I feel like here, it just seems like what the three of the threes are about communication. And it makes me feel like your person is is like waiting for you or waiting to see what what could happen going forward. The night of wands is here. So this is a very lusty, passionate, free spirited energy. So it could be waiting for someone to visit or waiting for someone to show up or waiting for you to arrive or to send some kind of message or something. Maybe you put something out there and you're waiting to hear back or they put something out there and and they're waiting for you or waiting to hear back from you. Let's take a look deeper at this three of wands. Oh, the ace of sorts is here again. So now your person, there's some truth. Hmm.  I feel like they may be waiting or hoping that you will forgive them for something that they've done or something from the past.  And it's like as soon as you reach out, I feel like they'll come towards you that night of wands that passionate, lusty, fiery thing because I feel like your person like still has that for you but it might be dormant at this time. Let me take a look maybe because there hasn't been or there isn't any communication really but I do feel like they have a truth and as soon as as soon as they get the opportunity to talk to you, I feel like they would could have something to do with travel. They might say that they're blocked from traveling or blocked from connecting with you in the present. See what the name of one says. Okay, death card. Wow. Okay, so we have Scorpio and Gemini energy here. Also, so that this death card. Wow, it just feels like to me. As soon as you say this word, say the word to them, they will transform, help to transform this relationship. I feel Virgo that you're kind of just like, you know what, I'm loving myself right now. I'm doing what I need to do for myself. I forgive you know, everybody from A to Z so I can heal my past so I can have more love in the present but it feels like that might be very attractive to this person.  Some of you might be in no contact at all. Like, you know, doing that right now. And they're like waiting to hear from you. And it feels like if if you were to reach out like they're waiting for you to reach out to them, you might not be wanting to Virgo, you might just be like not not wanting to initiate and I feel like they want you to initiate but something in here with you is like for you like I feel like your person would come rushing because they don't want this thing to end whatever it is whatever this I don't know what's going on. Let's see the four pentacles. Yep. Here you go six of swords. So overcoming their fears one of this person's fears is that they're very heavily blocked like they guard their heart. And it seems like with the six of swords here, this is just an energy of basically overcoming your fears, you know, taking that risk, getting out of this tumultuous water energy here, you know, and just you know, going into a calmer, peaceful place just kind of feels like a transition that needs to happen and and this person would be willing to relocate and move but I feel like for some of you they may think that if you've blocked them, that you're moving on, you're moving on or you're just maybe you're not like physically moving on. Some of you might be actually physically moving, but there is an energy here of like kind of like you may not be really leaving this person, but you may be leaving them where they are waiting for them to initiate something with you. Okay, and I feel like they're waiting for you to initiate something with them. What a mess. What a mess. I'm not sure what happened there in the past. Let me pull a card for the lovers. Okay, somebody wanted change. Wanted things to change and get into like, you know, a loving relationship. Was it you? Or maybe it was your person or maybe somebody moved on from that idea. Well, I don't know. I'm not sure. I have all these positive cards about that. The ace of wands. I feel like you and your person truly did love each other, but there was just way too much. I don't know. You guys just was really hard for you both to get into balance. To get on the you know, like on the seesaw to be balanced. You know, you both one was up and the other was down and then one was down. The other was up. There was a lot of like up and down. It feels like. So, let's take a look at the future. Separation and release your ex. Virgo, it looks like you're done. I don't think I don't see you reaching out to this person and I don't see them initiating anything with you. It almost feels like you're letting this thing go and this person, look at them here. Four of cups, three of swords, five of cups, heartbreak, regret, remorse. I don't even know that you're you know, intentionally trying to hurt anybody here. I just feel like you're you're healing something. You're loving yourself, respecting yourself. You're you're telling yourself, you know, I can release this and because I feel like I deserve better. I think you might maybe you worry this person's going to come back in and then the cycle will keep repeating and maybe you just don't have the energy to keep doing that anymore. That same dynamic. Would you take this person and and meet them halfway and have that love with them again if it were played if it's playing out differently in a more healthier way than yes. But Virgo, it just kind of feels to me like takes two to tango and I feel like you want to very much be around someone who's going to appreciate you and and you know, acknowledge you and love you and be consistent and someone that you can be in a relationship that you feel safe and secure with and rightly so, you know, so I feel it's like I feel like it's separation for you and this person but I also feel since this is their reading, the ear person may have had a connection with someone that was difficult that they couldn't let go of. For some of you that might have had something to do with what was going on up here in the past where there was like some, you know, either two choices or your person had a phantom X that they still couldn't get that energy out and it looks like they very well may be releasing that person while you're releasing them.  They're clearing out that energy of a past X or someone that hurt them and at the same time you are clearing out the energy of your person which sometimes can be good because further down the line you both release your need for this person to come into alignment with you and their need to compare you with their last X and not be able to let go. There was still some kind of third party and the third party very well just could have been memories or trauma. Let's take a look. I'll get more clarity. This four of cups here is really just a sense of feeling unfulfilled. Your person is not someone who they have a hard time getting their emotional needs met. Look, three of cups. So there they are. They're either out there socializing with others or dating others. It might feel sad or indifferent to the fact that maybe you are trying to socialize more and live your life but they also might not be finding their emotional needs are getting met with other people they may be talking to or if they're dating other people going forward. They're indifferent. If you're dealing with a man who's interested in women, your person is showing up here like doesn't want love from those other people. They're indifferent to it. All right. I just lost that card so we're done with it anyway. So why is the three of swords here? Oh my goodness and it showed up when I pulled it. It was in reverse. So three of swords again. Healing heartbreak. Wow and the three of swords reverse reduces to the two and the two of swords is always about making compromise. It's time to compromise. Make a decision and it's also recovery. It's apologies. It's recovering after a loss and a physical healing. So it could be you know if you decide that you're done this person and they're you're letting them go. They're letting their past go and this person now I feel like is going through some kind of healing process in the future. Some grieving with that five of cups here. There's an energy of like loss and regret and some grief and just maybe even feeling abandoned or unloved if you decide that you know you're not going to initiate. It's not that you don't love them at all. It's just that you don't feel loved by them. Maybe at one time you did feel that way. It was strong. Look the ace of cups. Didn't we almost have it all? Your person listen let them go through this process whatever they're grieving or whatever trying to figure out about your relationship right. I feel like your main thing right now and for both of you is to forgive past people or to let go of the past and any kind of hurt you both might have felt from other people from each other and to love yourselves make yourselves a priority and grieve these losses from the past. Both of you I see that happening because I feel like this is both of you. See releasing your exes this card speaks about it being time to clear your energy. That energy of the ex okay not so much like for some of you it can be the physical releasing like no more but in the energetic state whatever the residual where you still think about that person you know when enough time goes by and the heartbreak and you heal you don't think about the person anymore to the depth that you used to and so I feel like this energy is playing out for both of you but I also feel like this grieving is a blessing here this sense of feeling those emotions for both of you is a blessing because the ace of cups then comes out and this is like a new spring beginning happens here that's why I was saying that in the future this kind of feels like a good I like a good thing okay it does it feels positive it's all about the journey right and you you and your person um I don't know if the timing just wasn't right are you both were on some kind of journey separately and then you kind of like bumped into each other on your journeys but you still had a path to walk and they still had a path to walk but something happened where there was a spark a magnetic attraction and and it became difficult for you both to let each other go yet you knew that maybe it just wasn't going to be the right timing or things wouldn't work out I lost myself for a little while your person this relationship deserves a second chance you know I know some of you on your like third and your fourth just take it as a resonates you know it deserves another chance okay I know that I crossed the line with you okay I feel like there might be some regret or remorse about something that your person might have said or done that just really crossed the line for you and and did something to you or to this relationship that maybe cemented it in the fact that it's done yep interference an external party is intruding on this relationship now for some of you it could have been somebody else person place thing or you know seeing being an energetic thing um but your true love is already part of your life okay so I feel like this is your true love um I'm not telling you of course to sit back and wait at all I feel like you should continue to live your life and be as happy as you can and if somebody else comes into your life or go that you know I mean you never know how things are going to go and things could heal with you and your person you just don't know but the the thing here right now is you need to stay in a place of being respecting yourself because that will attract romantic love to you whether it's your person or somebody new okay this person I know I messed up everything they got some heavy guilt or grief or something going on within them they don't want to lose you but they're not initiating partially because they feel like maybe you're not going to accept or you don't want to or they don't know if they deserve you after some past stuff but this is your soulmate and they do love and accept you so you should know that I don't feel like you really did anything wrong Virgo um I just feel like you knew you both loved each other and you both wanted things to change but there was a lot of unknown and you wanted to have a turning point both of you but it was really hard for you both to get on the same page in the past but they do feel you were the best thing in my life so let's get one more card for you Virgo to see what your advice is here more advice for Virgo going forward okay page of fire so enthusiastic be enthusiastic about your life be open and optimistic creative be impatient with your life Virgo don't sit around and wait for things to happen okay there is news of exciting opportunities embrace them when they come allow any creativity that you have within you to soar do things that fuel your passion and finish what you start so whatever is going on in your life at this time do not let that set you back if you have a setback get right back up on the horse and keep moving forward okay that's your advice at this time I hope that you enjoy this reading and I will see you guys tomorrow take care


In this presentation, we'll work a few problems related to the disposal of property plant and equipment. We'll start off with the most simple kind of disposal and then we'll add some components and some complexity as we move forward. We will enter the data into this blue area. This is where the journal entry will be. We'll then post it not to the general ledger out just to this worksheet. So we're going to post it to the center column, which will give us a quick view of the effect on the assets, the liabilities, the equity, the fact that we're still in balance and net income. So a worksheet like this is perfect when we just have a few journal entries. So let's see what we have. Equipment is fully depreciated and no cash is received. So in this case, we're going to dispose of this equipment and it has been fully depreciated. The nicest thing to be able to have when working a problem like this is to have the trial balance in front of you. Now when you work problems in book problems, they often won't have that. They'll have to give you the information in some way. But if you can see the actual trial balance, it's best because you can see here's the equipment has a debit balance. Here's the accumulated depreciation. It has a credit balance in this scenario. All we're doing is saying it's been fully depreciated and now we're getting rid of it. We're actually disposing of it in some way and therefore need to take it off the books. Be aware that one, it's not necessarily the case that if it's fully depreciated meaning it has a book value of zero, the value of the equipment minus the accumulated depreciation is zero. That doesn't mean that the company's not still using it. We still may have it. We still may use it and therefore we shouldn't take it off the books unless we do use it. And two, note that there's no salvage value here. We can tell that because we took it down to the full amount here. We didn't leave any scrap metal. So we're not going to be collecting anything on it and we took it down to zero in terms of the calculation for depreciation. Also recognize that in this problem, we're just going to say this is the only piece of equipment. It's $110,000 piece of equipment. We're going to put it on the books, take it off the books. In a real life situation, we would typically have one equipment account which would have be representing multiple pieces of equipment and then go to a sub ledger to remove the piece of equipment we are particularly looking at. Here we want to be able to see it and I want to see it directly, this one piece of equipment being represented in this account to be taken off the books, but just be aware of that the process would be the same. However, we would have a sub ledger that would list out all the components of property plants and equipment and then we would just take out the components related to the piece of equipment we're talking here. We are going to here say that this is the one piece of equipment we're going to be removing from the books which cost $110,000 had accumulated depreciation of $110,000. So we got to remove this from the books, the equipment's on the books with an asset and a debit balance. We need to make it go off the books so we're going to do the opposite thing to it which is a credit. So I'm just going to copy the equipment account, right click and copy. I'm going to put it on the bottom so it's going to be our journal entry. I'm going to put it on the bottom in B6 and right click and paste 123. Then the amount's going to be a credit. I'm going to make that a negative for our journal entry, $110,000. Then we're going to need a debit of the same amount. I'm going to put that in a formula context here by saying negative of this number. We could just type it in there, but I'm going to say negative of that number flipping the sign. And then the other side of course will be accumulated depreciation. So here's accumulated depreciation has a credit balance. We need to take it off the books because the account it relates to equipment has been removed. So it has a credit. We're going to do the opposite which is a debit. So we're going to copy that, put that in B5, right click and paste 123. So here's our journal entry for the removal, the disposal, the most straightforward type of journal entry. If we're disposed of it, we're not getting any cash for it and it's been fully depreciated down to zero. Let's post this out and see what happens. If we go to the accumulated depreciation in H8, we will say equals and then point to the accumulated depreciation in C5 and it'll take the credit balance of $110,000 down in the debit direction by $110,000 zero. Of course, we're out of bounds by $110,000. Now we're going to post the other side to equipment in H7. So within H7, we're going to say equals and point to the $110,000 credit bringing the balance down from $110,000 by $110,000 to zero. So it's achieved our goal of bringing us down to zero, this representing that one piece of equipment that's been fully depreciated. Note what didn't happen, no effect on net income. Net income being revenue minus expenses. We don't have any revenue expense accounts here because we had already expensed the equipment in depreciation and it's fully depreciated at this point in time. So we've already allocated the cost to the periods to allocate them to. We can't allocate any more costs because it's already fully depreciated, already at zero. So let's take a look at another scenario down here.


So, here's an overview of what we're going to cover in this webinar. You're going to have a very brief introduction to the Big Data Network, Phase 2, and the Urban Big Data Centre, and then Mark and Shiva are going to talk about the integrated multimedia city data that they've been collecting. So this consists of a number of data strands, a survey, GPS and life-logging devices, image analysis, textual media data and multimedia data, and at the end there's going to be time for questions. So just to say that all attendees are muted so we can't hear you, if you do have a question then you can type it in the question box at any point in the webinar. If you can't see what box I'm talking about, if you look to the top right of your screen you should see an arrow, a red arrow, and if you click on that arrow you should be able to see where to type your questions in. So there's going to be no time to answer the questions actually during the webinar. The talk's going to be about 30 minutes long but then there'll be plenty of time for questions at the end. Okay, so this is the third of three research webinars that have been given by researchers from the Big Data Network, Phase 2. So what is this Big Data Network, Phase 2? The ESRC has invested in three business and local government data research centres. The BLG which is based at the University of Essex, the CDRC, Consumer Data Research Centre at Leeds and UCL, and the Urban Big Data Centre and our speakers today are from the UBDC. So the three research centres aim to make data that's routinely collected by business and local government organisations accessible for research purposes and this is to benefit both the data owners and society as well as researchers and in such a way that individuals identities are safeguarded. And Big Data Network supports the UK data services funded by the ESRC to support and coordinate activities between these three centres. So our aim is to unify data discovery across the three data collections to encourage sharing of information and expertise across the centres and to coordinate user training and capacity building for researchers using their data. Okay, so that's all from me. I'm now going to hand over to Mark who's going to start the main part of the presentation. Okay, thank you Sarah. So hopefully you can all see my screen now. Okay, just a start with, let me just introduce my co-presenter, Siwa Naviska, who's the research fellow here at Siwa. Hello. Okay, so I'm going to batter on because we've got quite a lot to cover. And just, what I want to do is just say a little bit, very briefly about the Urban Big Data Centre. Some extent some of that's already been said by Sarah, but essentially our centre which is funded for a five years period is, the aim of the centre is to bring together and link data from our wide variety of sources. Local government and business data particularly is the aim, although we've got wider sets of data than that. And the idea of bringing these data together and linking them together is that we provide new and innovative data sets for a wide range of people, not just academics but also policy makers, but as much as possible to the general public as well. But not only are we sort of bringing these data together and creating these data sets for other people to use, we do a number of other things like we do a lot of education work around big data, about working with big data, and we have a remit in that way. We also hope to facilitate people in terms of new methods, and we hope to be at the cutting edge of new methodologies as well, and we hope to facilitate others in those areas. Okay, so let me just talk a little bit about the integrated multimedia city data projects as it's called, or IMCD as I'll refer to it from now on, or as a colleague of ours calls it the IMACD project. This is a project that was funded by the ESRC as a way of kickstarting the data held by the Urban Big Data Centre. It's always been run slightly separate from the Urban Big Data Centre, and I'll come on and tell you a little bit about that in a second. It's a collaboration across the university, but not just our university, but other universities. There are colleagues in Newcastle and Sheffield who work with us, but within the university we've got people who are working in urban studies, in transport in particular. We have two teams in computer science who work with us, the information retrieval teams, and then we have a team from education who have a specific learning remix. So we've collaborated quite widely across the university. The Urban Big Data Centre has wider collaborations in that and includes other people as well. Okay, so let's get to the meat of the IMCD. The main thing I would say is there are five real main strands of the IMCD data, but they tend to hang around the household survey. The core part of this was a random representative survey of people in the wider Glasgow area. And by that I mean the urban metropolitan area of Glasgow. It's commonly known as the Glasgow Clyde Valley Planning Area. As I say, it's a random representative household survey. It includes all the adults in the household, and it's unique in that it's got a unique combination of modules, but really the uniqueness of the project is more in the combination of these five data strands. So as part of this project, we've collected data from a sample of the household survey which included carrying GPS sensors and life-logging sensors. I won't go into that too much today because she was going to talk about that in more detail. Just to say life-loggers are wearable cameras, really, although they collect wider information than that. The other main parts of the survey are we have a textual media data retrieval project, and essentially they crawl the website, downloading data about Glasgow from a number of websites. We're talking over a hundred websites, websites like social media websites like Twitter, Foursquare, and other social media, but also news websites, BBC, but also papers, what we collect data on weather, and a number of other things. And then we also collect from similar websites, we collect multimedia data, mostly images, again, downloading and connecting information from Glasgow. And finally, and a little bit tangentially, we have also essentially bought a mixture of satellite data and LiDAR data. Satellite data, we bought stereo pairs to allow us to build 3D models that can be used for other research purposes. For those who don't know, LiDAR data is essentially very similar to 3D data. It's created by airplanes, essentially passing backwards and forth across an area, bouncing lasers off the ground and building up a 3D pattern, a very, very accurate 3D pattern of the city. Okay, so I'm going to talk a little bit, move on, I'm going to talk a little bit about the survey and then I'll hand over to Shiba to talk about the other parts of the project. As I said, this is a household survey. We targeted a, or wanted 1,500 households, and what we expected to get somewhere between a, from those 1,500 households, we expected to get around about 1,700 to 2,000, 3,000 people. So, that's a range of 60 to 100 percent, so we weren't expecting to get 100 percent, probably closer to the 60 percent, if we're honest. The coverage, as I have said before, is the Glasgow Clyde Valley planning area. So the survey has main modules on travel and transport. It also, we also collect data on sustainability, so we collect data on green behavior and green attitudes. We also collect information about ICT use, and we also have a large module on education and learning. And one of the unusual things about the educational and learning part is that we collect information about knowledge. So with every single part of the survey, we tried to collect data, that was data on attitudes to that area. We tried to look at behaviors in the area and also look at knowledge. So we could look at people, what people reported attitudes were, what were their behaviors and what do they look like and compare to their attitudes, but also knowledge. So we asked a number of very innovative questions that look at people's understanding of the area. Okay. Also in the survey, so that was the core of the survey, but also quite a large number of the questions are more typical survey questions that you get in surveys like the Scottish Household Survey and a number of national surveys. So we had large demographic sections. We've got asked questions about people's neighborhood and their communities. We asked some questions about where they lived before. They moved to the area they're in now. We had a small module on health questions. We asked information about people's employment and previous employment. We have quite a significant amount on income. And we have a small section really about people's cultural and civil engagement. Just to give you, these are two of the more unusual questions that we have. So this first one is really an example of one of the knowledge questions, one of the questions designed to try and get to understanding. So essentially it's a calculation. So people are asked a question and then asked to give an answer, but it requires them actually to work out the answer. And another example of a rather unusual question was does your household have any pet dogs? And the reason for asking this, we were requested, could be put this in the survey, is because there are a number of researchers in public health think that the ownership of a pet dog might be a contributor to a better health. So we included this in our questions. Just very briefly to finish, we were in the field, the survey was in the field from the 15th of April to the 21st of November in 2015. We actually achieved 1,508 households. I asked 51% of the people who were approached accepted, but a 30% of households, of those samples refused to take part. But of those that did agree, of the households that agreed to take part, we got 2,095 people who took part, excuse the spelling mistake. So 74% of eligible adults. So that's about 1.4 adults per household compared to the 1.9 adults per household in the census. And the data is at local authority level and that should be available quite widely. So should be able to get that data fairly soon. Okay, and now I'm going to hand over to Shira. So hello. So one of the strands from IMCD project was the central survey. And in the central survey as Mark said, we asked people to carry tiny GPS devices and wearable cameras. GPS device collects information about your location every five seconds, and the wearable camera, it takes photos every five seconds, but not only photos. It can also take information about how fast you accelerate, about it can detect light, it can detect brightness, and a few other things. So before we started the sensor survey, we had to first choose a proper device. And as we wanted to make it really easy for people, we didn't want them to spend much time on charging the device and learning how to deal with it. Therefore, we chose the device that was not only cheap for us, but also the best for the potential users to use it. Also with the sensor project, apart from the GPS device and the sensor the GPS device and the life logger, we asked people for some ground truth data. So we needed something to verify what sort of data was collected via GPS device and life progress. We asked people to fill the activity diary where they told us what they did on the first day of their survey. So to be able to proceed with the data collection, we needed first to design systems and hire researchers who would deliver trackers to all the people who agreed to take part in it. So we had a system in which we were able to manage when and where people are getting the devices. And once we collected the devices from the people, we could put all the data into our life log memory server where we could visualize the data and see what we have there. So some statistics. So from this 295 people who took part in the survey, we got 90%, so almost 20% of people who decided to carry either one or two devices for us. And we thought it was a fantastic achievement according to previous studies. Here you can see how the differences between male and female and people who were carrying both devices and one. And the very important thing is also that the average age of respondents for the sensor survey was a little bit lower than the average age for the household survey. So as we may think younger people are more into technology and were more willing to help us with it. So having the data from GPS trajectories and life loggers, we were able to combine it. So not only to see where the individuals were going, but also what these people saw. So to be able to enrich this information in some more, this data in some more information, we had to first process GPS data.  At one point it's in Glasgow, the next one will be in Iceland if you lose the GPS signal. Then we had to segment trajectories. So we had to divide them into a homogeneous segment, so movement and non-movement. From this point, we identified stops. So we knew where the person stopped. Knowing where the person stopped, we could add additional information to this. So we could try to identify where is the home of a pool, the work, dentists, etc. So having all this information and classified data, as you can see on the map here, we covered quite a lot of Glasgow with the detailed movement patterns of all our participants. And then imagine that from all these people, so it was 402 people who carried GPS device, 265 of them carried also life logger, that what gave us an opportunity to create not only something like Google it with Street View, that we can see what's going on on the streets, but also like a street view inside of your house, inside of your office. So we can analyze what was going on constantly and like everywhere, not only on the street. So because as you could see on this data, we could see on the data that GPS is quite, it could be quite intrusive, the data that you get from it could be quite intrusive, but it could easily give us information about all your locations. I was wondering whether, I was wondering whether you know what techniques could be used to protect privacy with GPS. And I would like to show you now a movie that we have animation that Glasgow's Kulowart prepared for us showing movement of men and women in Glasgow within one week, sorry for the colors, it's blue for boys or for men and pink for women. And to answer what you said, that you can blur the data, you can obstacles, star and end point, restrict access to the data or leave out of the street names on the map, we can do all of it. So in our data set, we first, what we did, we obscure, start and end point on the map, but we can blur the data. There are various methods to analyze trajectories to protect individuals, individuals privacy. And the data sets you can see here, we can distinguish different patterns of women and men during the week, and you can see it on Sunday women spend quite a lot of time on shopping in the city center. So the next part, the next strand of the data, the next strand of the IMCD is the textual media data and multimedia data retrieval. These slides, we got from our colleagues from Terrier Dream, so thank you to them for these, and I will try to tell you as much as possible on it, even though I haven't done it. So I won't be talking about all the data they collected, but I will focus on three main types, and we'll show you later the analysis that are possible with this data. So we collected Twitter data, and we've collected more than 65 million tweets in between July 2014 and November 2015. Within this number, we also collected some geo-located tweets, and tweets that were created by certain users like BBC, West Scotland, Police Scotland, Glasgow City Council, etc., and also tweets from certain, for certain topics, like certain hashtags, so like Glasgow, Glasgow 2014, Glasgow 2015, Glasgow, Buchanan Street, etc., and I, and here you can see just the tweets marked in Glasgow taken from Eric Fisher map, so these are all geotag tweets in Glasgow, and I was wondering whether you know what is the percentage of tweets in our sample that are geotagged? There are a few people who had it right, quite many of you said that it's 10%, so we had less than 1%. Less than 1% of all the tweets were geotagged, so still from 665 million, it's still quite a lot to analyze. Another tiny strand of data within the Terrier Team project was the weather data, so we are getting information on Glasgow weather, so there's hourly information about temperature, humidity, precipitation, wind direction, etc., and this data is collected at the same, it covers the similar time as Twitter and the survey. Next strand was connected with transportation data, so we got some static data about cycle routes from Glasgow City Council, we have also railway stops and railway stop names, locations, and identifiers from NOCTAN database, and also to make it more real-time, we have a daily data fit on timings of passenger trains, so it's a real-time feed about the train delays. So the Terrier Team, to allow people to analyze these different difficult sometimes to get an individual's data set, they created something called Euroban Data Dashboard, and this data dashboard is restricted by IP address, so you have to apply to UBDC to be able to get access, and then you have to do it for a particular research project, so then it can be validated whether you can get the access or not. But what they did, they created a few data services inside, so social media, where you can analyze different terms and different tweets and try to detect different events on Twitter. Also, there is part that allows you on analyzing transportation and do-ever. So I'll focus quickly on the transportation data, so we can get the information about the different times, different train delays according to different days. You can also visualize your own GPS trace, it can be also classified, so you know, excuse me, where the person was walking, driving, taking the bus, etc., so you can analyze all this data, then we can try to combine the information from train delays and all the transportation analysis with Twitter data to find out what people thought about all these things. So from the data we've collected, we know that there was a huge peak in delays on the 1st of July, and then we analyzed the Twitter for the unhappiness about the Twitter, about public transport and commuting, and we still got the same peak on the 1st. So we thought, hmm, there must be some like weird correlation in it. Do I have the weather? Sorry. Oh, I think I lost one slide, but there was a third one saying, showing the weather in, weather in Glasgow, and on the same day, on the 1st of July, it was the only warm day in Glasgow, it was 26 degrees, therefore people were showing their comments on that it's hot, people can't stand standing in the trains, that the Scotswick can't cope with the weather, etc., etc. So what I wanted to show via this slide is that you can do proper analysis and proper investigation by combining these different data strands. And I think that's it. I hope you enjoyed it. Thank you very much for your attention.