So we want to discuss one loop amplitude at least for us. So we've completed, we discussed this, the major issue for closed-stream is outside. Let me quickly tell you about the similar combination for open-stream. So suppose we want to do a one loop amplitude for open-stream. That's this little string here that runs around in the loop. Okay? So the, the kind of stuff that we have is, is a cylinder. This side is identified as, it's a little string, the string is going in the loop. Okay? Now, we can ask, how do we mobilize the cylinder? Okay? This is the same as the number of zero-modes of the B operator that respect the boundary conditions of the cylinder. So why are the boundary conditions in the cylinder? The boundary conditions of the cylinder have been discussed in this direction. And at the edges, the boundary conditions we discussed before named it as B is equal to B. Okay? Now, on a torus, we had two zero-modes for the, for B and B to the left. Namely constant B and constant B. Okay? But then at the same time as zero-modes, it's going to be thought of as part of a torus. With the lovely trick it becomes, it becomes a torus. Okay? So we can have the same zero-modes except that billion people are not equal to zero-modes. Because B is equal to B to the left, B. Have the boundaries. Okay? Do you have the boundaries? I see lower and lower. No. Well, I mean, same line over here, it doesn't matter. But about other, I'm taking you with this little string, going around this string. But these are the end points of it. Of course, that's symmetric, right? You can think of it. I mean, that doesn't matter. That's not the way I think. Okay? So I'm thinking this is a sigma system. Okay? Fine. So there's one modulus in this situation. And what's that one modulus? The one modulus is very clear. It's the height of this. So suppose we always choose this to be zero pi, this is my direction. This direction is, let's say, tau. What is this? You probably want to call it t thanks to pi out of the table. And the modulus is simply the value of t. So that's the modulus of the game. What's the other angle? You see, the angle is fixed by boundary. You see, the boundary conditions we're putting are at the edges, there's a sigma of x is equal to 0. If you change the angle, then you'll have to put different boundary conditions. Okay? So this is this with less sigma x equal to 0. Okay? You can't change the angle. And if you change the angle, you change the boundary conditions. That's not a symmetry. So the modulus here is t. Okay? Now, once again, we want to calculate the measure of the boundary line space. So it's the same angle we had. You know, as we've seen last time, del g z z, if you remember, del g z z divided by del tau pi, I think it was, was equal to, what's proportional to 1 by d tau. And del g z pi z pi by del tau, because it was proportional to 1 by d. This is what we saw last time for the talks. Okay? Now, what are we doing here? What we're doing here is basically the same as a special case for the angular force. Okay? So in this particular case, we do more or less the same calculation, except we focus it at tau equals i time, and we're actually part of tau equal to i d. Okay? And because the tau inverse is rectangular, you know, because our metric always takes the form d s squared is equal to d sigma 1 squared plus tau squared times d sigma 2 squared. You know what happens? Basically, all we're changing is g y 1. But we change t. We put the necessary changes in g y y. And g y y has equal components of g z z and g z bar z bar. Okay? It doesn't look that way. The question we're asking is, suppose we have the w, the z coordinate, and we have g z g z bar is equal to, so the metric is equal to d s squared d z d z bar where sigma is equal to, belongs to the range 0 to pi, and tau belongs to, as we already formed it, in 0 to 2 pi. Now we're going to go to a new way, suppose, now, suppose we take d 2, so this is the general set. Now we go to the variable w such that d s squared is equal to d d z d z bar. Okay? And these ranges were signalized the same above, but tau belongs to 0 to 2 pi t plus n. And now we take this metric and rewrite it in terms of the metric, in terms of the variable z, where the periodicity is of z. Okay, let's, I'm sorry. To be consistent with the relation we used last time, we call this the z thing, but, okay. Like, okay? Whether we rewrite it in terms of the variable w, where the periodicity is of w, was that of 0 to tau, 0 to 2 pi t, without any effect. So what's the change that we have to do? The change that we have to do is, real is said is equal to real part of w, but the imaginary part of z, okay, is equal to the imaginary part of w, where the imaginary part of w reshapes, right. The imaginary part of z, so z where it goes to t times the t, so t plus delta t. So we take this metric, these definitions of the variables, yeah. Okay? And finally we look in terms of w and w, is this correct? Okay, it's the same exercise we did last time. Okay, thanks. So if we want to work it out, we will get d r e w total squared, because that hasn't changed. Plus t plus 2 delta t, okay, so just 1 plus 2 delta t by t for the first order, d in that thing. Because I can't substitute it. So the change in the metric is what? So delta g is, we have delta g imaginary imaginary is equal to delta t divided by t. That's correct. But now we can translate them to g z z and g z bar z bar. But g z z, you know, some linear combination of the real and the imaginary part. There's no change in the real part. So the change in both g z z and the change in z z bar are proportional groups. This is the single modulus in the game. What we have to do is to find where integral d to z or not, it doesn't matter. v times delta times d g z bar z bar by d t plus v bar by delta g z z by d t. In this insertion, only the zemo matters. On the zemo, v is equal to v bar. And each of them, each of them, and the whole thing, and the whole constants, v is equal to v bar the whole constants. So the whole thing can be written as the volume of this thing times, okay, so it's d to z times v of 0 times 1 by 2. Is this good? But this d to z is pi into t. It just adds some pi into t. So this thing is proportional to v of 0 without any factors of t. It's the volume of this thing. So the v insertions are just v of 0 with no factor of t. They're not the same as in the donors' view, if you raise that. Okay, two copies. Should be okay. However, what about the c insertions? We've got the same thing with the c insertions that we did last time. We have just one unfixed formula here in vector. It's the same thing that we said for v's, because there's double c in a c to the left, both constants, but now c is equal to c to the left. It's the volume of this thing. The one unfixed formula here in vector is translations along this section. And we could fix it in that one unfixed formula here in vector. Fixing the one unfixed formula here in vector is like choosing one boundary operator to be fixed. But because the insertion point of that c doesn't matter since the constant, zero model c is the constant, we can separate where we fix, where we put that c, and where we put the integration of the operator. And then integrate it over the vertex operator up to a division by the volume. Okay, so the next result is that instead of having the fixed vertex operator, we have all vertex operators integrated, but with an insertion of c, zero, divided by volume, and the volume is c. So the mind of conclusion is that we have dt divided by t, except they have to be value of b, zero, c, zero, time whatever, or time to integrate the vertex operator. You see where this one over t came from. Where this one over t came from, it's actually very intuitive. You see there was one gauge invariance that was left unfixed. The gauge invariance was translations along the strip line. So because the volume of this translation along the strip line action is out of bounds, we could forget about fixing it. That's what we're saying there. We're treating all vertex operators as integrated. But in forgetting about fixing it, we are treating gauge equivalent configurations as discrete. Now each gauge equivalent configuration gives us the same answer, but we get the volume of the gauge of it. But if we just treated that everybody's operator as integrated, and forgot about fixing it, then we would be overcounting by a factor of the volume of the unfixed gauge. That volume was t. So we did it right. That's the intuitive reason for this 1 by t. The intuitive reason for the 1 by t. Again, you need a b0 and c0 to make any sense, and this is the unfixed gauge intent. Is this clear? So remember this is the answer for the open strings, and the answer for the closed strip is d2 tau by d2 tau, and b0 is the bar 0, c0 is the mass int predictor. Now the rest of this class is to actually evaluate the closed strip partition function and the open strip partition function for the simple theories we can study, and then interpolate these objects. The candidates will show us some of the basic properties of string theory, as you bother. Then I sort of qualitatively move on. So we've done the closed strip thing before. But just quickly to remind you of our event and to remind you of the interrogation. So what do you have to put in here? We have to put in the partition function on the BC system with the partition function of the x conformity theory, and that's it. So now let's write down the partition function of the x conformity theory. The partition function of the x conformity theory with what? It was 1 by d tau to the power 26 by 2. So let me try to hold to the power of 26. Then we had 1 over q to the power minus minus 24 minus 1 by 24 1 minus q to the power 8 for the rest of the n of 1 over q to the power minus 1 by 24 product over 8 1 minus q to the power 8 where q to the power 8 should be negative. Okay, now somebody help me understand this expression. And that's the whole thing is raised to 26. Somebody help me understand where every girl in this partition function is. This is just z z matter on torus of modulite of modulite is equal to this. We're not integrating over any modules. This is the partition function of the matrix conformity theory on our torus modulus channel. Firstly, give me a Hamiltonian interpretation of this partition function. What? Hamiltonian interpretation of partition function on the torus is that of a trace over the spectrum of the conformity. Is this clear? Does everyone know this? We discussed this last night and this is the basic one in theory you should know. But somebody explain this to me. How do you compute the trace over a trace into the power minus beta h? You know the Euclidean path integral of what matter? The space for the circle and the size of the circle is beta. Okay? Is this clear? This is familiar. Suppose we have like 10 kilo atoms. We have like 10 kilo atoms. Okay? Then what would that the path integral so this is 0 to 2 pi this is 0 to 2 pi tau. Okay? What would the interpretation the trace interpretation of this of this path integral be? Same to of 2 to h over beta. Let's call this 2 pi t. That's tau. 2 to pi t as beta and it is living on a circle. Right. So let's say that the system has to be living on a circle of size 2 pi. So it would be trace of e to the power minus 2 pi e as h. How do we make this the strongest skew? How do you have a suggestion for a for a for a Hamiltonian derivative? So let's call this 3 t. You see, instead of just translating it to 9 you also translate it to space. So how do you get the skewness? You put a generator of translations at the last step of the bottleneck. You do a trace up to a generator of translations. Okay? So what is the generator of the translations? And leave it up by 2 pi times the real path. Okay? So you add e to the power 2 pi times the real path. And then I that's what generates. I'll go into it. And then the generator of translations. But h is L0 okay? So this was L0 not L0 and this was L0 minus L0 minus 0. So look at the terms of course which are the L0. So this is e to the power i times 2 pi times tau L0. You see? Times e to the power i to the power tau bar L0. So the Hamiltonian interpretation of the publishing function of the tallest of non-linear pattern of the tau is this. Okay? This is what we've chosen about q to the power 0. This is what we've done about q to the power 5. In this graph this is the thing we have to calculate. Now you understand by using these terms. Okay? So let's do the easy thing. What is this 1 minus e to the power L to the power 0? Exactly. So the oscillators. What is the spectrum of us is the L0 spectrum is the spectrum of oscillators frequency 1, 2, 3, 4, 5. Each oscillators frequency m as published in the publishing function 1 over 1 minus e to the power n. Because the occupation number of oscillators. So we've got all these oscillators and we have to take the product. Is this correct? The q bar was the same thing. Now what is this q to the power minus 1 to the power 0? L0 equals minus 1 to the power 0 by 0. Very good. And what about this intelligent power let's make the different number into 0. No, no. That came from the nature of it. You know just under the partition function of the bosonic sense. In just the partition function I would suggest the data is excited. I meant to you guys like let's say end of this is a chemical right. Okay, last week of October we have an exam all of consciously volume okay. And I'm going to be very careful. At least I know it's right. Yeah. That's what is the input? We've accounted for what? We've accounted for the oscillators. What is there at the moment there? It's a 0. 0 more is what? 0 more behaves like a heart. Remember there was 1 over 4 we have 1 over pi as alpha prime times back of 2 pi 6. Okay. There is this part of the Hamiltonian of the problem that we've not yet dealt with. Now in dealing with this part it's easier to barely use this form of the expressions of Hamiltonians than this form because 0 more not to both times 0 minus 0. So we have to calculate trace of A. So what's the spectrum so what's the Hamiltonian? The Hamiltonian is what comes from here is p squared alpha prime by 2 p squared by 2 n. This is exactly the grand deal for a non-electric particular mass n. Then it happens to be 1 by r. Is this clear? I'll write it down here p squared by 2 n. So this is spectrum. So what we have to do times 2 pi eta this is what we are going to do. Now what is this? Even if you take an expression of the stress if you take a d this is a constant exact. So this is we take a dp e to the power alpha prime squared p squared by 2 1 by eta because the stress we do in this is a fact that completes yes okay and now we are going to see the integral from having a 1 over square n. Now all the other factors that Wynchowski has we have been going to keep track of whether we have done them correctly we are not bothering you. So that is this paper for the glossary let's simultaneously put them together let's we write them for the objects let's make sure those things get back okay now we are going to ghost partition now some of the things we can say about this partition function immediately some of the things that we can say immediately about this partition function is that it is modular container that is z for instance realized that Or more generally, it's invariant as a full module. We discussed this module in a group. This SL2 is the same module in a group for last semester. That's right. But why is that? That is because this is a conformity. So the published function is invariant at the scaling. The basis of modular parameter tau is equal to geometry of the daughter's modular parameter minus 1 by tau, up to an overall scaling. And the published function is just invariant at the scaling. That's what we discussed. Great length, last semester. So why is that? Obviously, it's algebraic. We get a very interesting property in this function. So this published function that's defined by this in tau and power out, the product of q that's product of q bus, is invariant under tau goes to minus 1. This is something we use when analyzing the open string spectrum in a little bit. So I just want to remind you of that. OK. Fine. Now let's return to the, let's return to the cost. OK. So what is the published function of the cost? Now I'm going to tell you the winner of the question, write down the answer, and I'll ask you to help me figure it out. This q to the minus 1, q bar to the power minus 1, q to the power minus, what is it? 26 by 24. And then product of n is equal to 1 infinity, 1 minus q to the power n squared, what is q bar? This published function was a b, b bar, c, c, y insertion, the cost part. The q to the power n is 0. So the spectrum of n is 0, so what? Where do we get this from? What are the modes of the c and b and c? Part of the links in here, and I'll get it straight as I said. This should be an enumerator. The b and c system has oscillators just at the x thing, starting from 0 to the n. But b and c keys were anti-communal. So the occupation number of each oscillator is either 0 or 1. I mean, because they're both. There's an extra minus sign because what are we computing? We're computing the partition function with periodic boundary conditions for billions. Okay? Why are we computing with periodic boundary conditions? Because they were of course for the homophisms, which have periodic boundary conditions. Well, the models have periodic boundary conditions. But the Hamiltonian interpretation of the boundary network with periodic boundary conditions for a field that is anti-communal, is traced with an extra factor of minus 1 to b. What we're computing is not tracing to the power minus beta h. We're computing trace of e to the power minus 1 to the x times e to the power minus beta h. Okay? So this is the vacuum. No oscillators. One oscillator excited. Since it has an opposite formula from this guy, it has one extra. One extra anti-community field excited. It comes into the minus sign. It's an enumerator that says that there are only two possible states. Occupation number 0, and occupation number 1. Is this correct? It's square into your z. Whatever we have to see here, I'll say, in the 0 mode sector, had we not had these extra insertions of v bar, cc bar, we would have got 0. Because the 0 mode sector has the slew state system with opposite formula number and the same energy. So trace of minus 1 to the x times e to the power minus beta h. But these insertions had specific altities. There's 1, 2 state system for left-overs, 1, 2 state system for right-overs. So there's a 4-fold degeneracy in the 0 mode sector. These insertions have become exactly one of those 1 states. Okay? And we don't get 0. There's no more acceleration. It's the state rate, which is obviously 0 on the side. It's 0. It's 0 state. We discussed this last year. It involves going the right scale up rather than the same. I won't get it wrong. Okay. So, fine. So we get this. Now what about the x bar? What about this q to the power minus 26 beta? Plus 26. I'm not a medium. I'm sorry people. I'm getting it wrong. So, I should have crown speed up q to the power, energy. Yeah. It's q to the power of energy. And energy. I should have had q to the power of energy. And so this was the new rate. I mean, sorry. This q was with minus 1 by 24 was the numerator. But down the stairs it was. I would have plus 1 by 24. Because the crown speed, then, was minus 24. Minus 1 by 24. In the latter sector. And we calculated q to the power of energy. Okay. So this q was the new rate. Sorry. Okay. Now here, people have. Here I can read that directly. But let me write it down. I'm sorry. Let me write this whole thing down. This would be q to the power of minus 1 by q to the power of plus 26 by 24. And product over n, 1 minus q to the power of n squared, 1 minus q to the power of q. Sorry. So this is the same cost. Now then, what does this factor? It's the same as this factor. Just explain the statement. It's a cost that is no other. There is no zero point in the problem. Right. Right. Every conformal theory has cascaded energy. You see. The vacuum, the identity operator, has dimensions here. So that 90 translates into the vacuum having energies. That statement is 90 because it doesn't adopt a conformal object. That means cascaded energy. And the correct version of that statement is that the energy of the state corresponding to the identity operator is minus c by 24. In this case, c was 1. So that's minus 1. L0 was 1. Minus 1 by 24. L0 by 24. Minus c by 24. L0 by 24. Minus c by 24. Minus c by 24. Everything is to the power of n, 6. Right. What is the conformal? What is the centrifuge of the bc system? It is minus 26. You know that because that's how we got the critical language, right? The full conformal theory of the centrifuge of 0, matter at charge at charge 26, bc system at charge minus 26. So this is the energy of the state corresponding to the identity operator minus c by 24, c is minus 26, minus n is plus 26. Is this clear? Finally, what is this? The word? It's 0. Okay. Yeah. So it's 0, but it's not. You know, this is not a miracle. It doesn't have the hugeness out of 0. When is the difference in this theory between the vacuum and the state corresponding to the identity operator? Do you remember the state corresponding to the identity operator was done the same as the vacuum of the bc? The vacuum of the theory, in fact, was c, was the state corresponding to the operator c. And since c has dimension minus 1, the vacuum has energy minus 1 compared to the state corresponding to the identity. That's this. All of the oscillators accounted about the vacuum, which would be right in the other energy of the vacuum. And we'd have that value. Minus 1. Minus c divided. That's the energy of the vacuum. It's much slower than I thought. Okay. All right. So now let's put all this together. We have to modernize this guy and this guy. Okay. So these oscillator factors of 26, 2 of them both. Okay. What about these other factors? You see, this and this can. But this remains. And this is exactly enough to be a q to the power plus 1 by 24 in the denominator for each of these factors. Okay. So let me write down what it means. What it means is 1 by 24 times 1 by q to the power of 1 by 24 product over n, 1 minus q to the power of n, product of q to the power, say, product of, okay, 1 minus q to the power of n times square root of q to the power of 24. Exactly. This is a partition function of this. This very powerful. In the life of the worker, there's a zero motion. You know what 26 is. Apart from in, down factors. This is what we were talking about. Okay. Yes. But if you actually do this extra in, down, it's exactly. And then we combine this together with the measure of a modernized space he has in the course. That was d to the power over n product. So that becomes d to the power over n product. And then square times wherever that's in the bracket. This is our final expression for the partition function over the darkness. And we were very happy with this expression, if you remember, because we wanted this expression to be modulated variant. And we checked that d to the power of n times square root of modulated variant. And, of course, this is modulated. That would just happen. Because whether it's the power of 26 or 24, it's modulated. The same thing that we have there, but the power of 24. Yeah. It's the partition function of 24. Bohr's answer to the problem is there, isn't it? Yeah. So we've got a very nice, we have this very nice body there in town, sir, for the partition function of your strength and the darkness. Okay. Now. Okay. This is very nice. Now, the thing that we want to do is basically get this. Okay. So, what is the partition function in strength theory? Well, in field theory, suppose you calculate the partition function. Okay. Suppose you calculate the partition function with no insertions of vertex operators. What are you getting? This is a correction to vacuum. Don't think that, well, in this problem, we know what the correction to vacuum energy might be. It must be. If the moles of the shear strength are done by field theory. That's the answer to what we would get by summing over the vacuum energy graphs of all the particles of free stream. Okay. So that's the exercise we're having. Okay. So, suppose we have a particle of mass m, a scalar particle of mass m, and we want to calculate its contribution to the, to, we want to calculate its contribution to this vacuum energy business. You know, we want to calculate its contribution to the vacuum energy. We want to calculate its contribution to the vacuum energy of this area. Okay. So, what do we get? What we want is to integrate BGP at a log of K squared per cent. Right. Because the easiest way to say this is this graph. And that graph represents just that, that logarithmic development. But a more physical way to say it would be, okay, I'm just going to, can we move forward from here? This, if you were to accept this graph, this graph is just a lot more. We have factors of all, depending on the stream of the, A will be the number of degrees of freedom. Okay. Suppose you were doing just a scalar particle, it would be exactly this. And if we had additional, you know, let's say vector particle would be multiplied with effective number of degrees of freedom. Okay. That's always how it works in a 1, 2. Yeah. So, we're going to get this ninth here. That's a true statement. So, there may be this ninth here just to sum over all the effective degrees of freedom. Okay. So, this calculation is correct just for scalar particles. But it's true actually, but over every kind of particle, if you multiply by effective number of degrees of freedom. The state would have been. This, sir, this effective vacuum energy graph. Okay. Can be treated in a sort of pretty okay, that helps us to make contact with what we have in the stream of freedom. Okay. And that way is to rewrite this in the following way. To rewrite this as dT by T times exponential of minus T and for fun, you put it in 2 years at the level at which we're working in learning factors at this time. DT by T exponential of minus T by T You see that suppose you didn't have this T here. Then this also could be proportional to 1 over square root of T by T times 1 over T by T okay. Now, integrate both sides with respect to T by T okay. And that will be 1 over T here okay. And there's another way of saying it actually the state is a bit a bit careless because this integral is not really very defined. You have to define it with respect to a subtractor. People have cut off here. Lowest part of epsilon. Another way of saying it is the formulae. Another way of saying it is that if you look at the formally this object is independent of k squared by x k squared plus x squared by T depends on the speed times k squared plus x squared this measure is invariant formally this object is not dependent on k squared okay. But the reason it actually does is that there's a cut off here. There's a divergence at smaller things.  That cut off state is very small. The better than the cut off state we don't have to think. And when you make this change your value you change that cut off by this factor of k squared that's k squared and that's the option at the small term. So that's the second way of saying this thing. You know you get another way of repeating that. Without this T the fact that this is one of the k squared plus x squared is my initial analysis. And the same my initial analysis that makes it a log limit as well as the equivalent of this. Okay. Now this is a very useful reference.  Let's just forget about all those things which we can read. Okay. So now two representation and it has an interesting interpretation. Suppose we're interested in looking at the theory in first one language. Okay. Then this is sum over all particles parts. T is the modulus of that surface the length of that part. DT by T is a sort of measure that you would have calculated by the other of all the processes that we've been dealing with for the strict theory. And this is simply the fact that you're computing the trace of the Hamiltonian weighted with the effective temperature of this quantum mechanical system So from the point of your first quantum language this is very natural. Okay. And that makes it clear that this is the right expression to use in comparing with the strict theory with a strict theory. Because again, it's clear that it's the right expression to use because because because it's strictly working effectively first. So now let's see. So what would we expect from this whole view the vacuum energy of our string theory to give us what we expect is that we would have a minus 3 by 2 into k squared plus m i squared with some i over all the particles state. We should sum up the particles weighted by effective degrees for you. So bear in the same we should sum up over all the states of the physical states of the deformity. Each of those gives you some polarisation of the item. Okay. Then it deals with the orientation. Okay. Now how do you relate m i squared to something important? Well, remember our Marshall formula. Our Marshall formula was that alpha prime a squared by 4 was equal to L0 minus 1. But that was also equal to L0 bar minus 1. Right? This is alpha prime X squared by 2 is equal to L0 minus 1 plus L0 bar minus 1 by L0 now it's pure opposite we take it out of 0. Okay. Remember that twice alpha prime X squared by 4 is equal to this. You see every oscillator state of L0 that corresponds to particle in the state there. The Marshall is given by this formula. But that corresponds to particle only but the arbitrary oscillators of the left and of the right but some gets in an error machine. L0 is strictly weighted by the house that you have with you. So the first thing they do is to replace P by a tau variable. So P is all alpha prime tau. So that's not the problem. Okay. So we get integral of these tau by tau that hasn't changed then exponential of minus tau alpha prime T squared by 2 that will be out. Now exponential minus tau alpha prime means squared by 2. Okay. Further down to some for independent organization. But that some now will be replaced by trace over the World Sheet Hamiltonian and it will replace alpha prime squared by 2 by exponential of minus tau minus 1 plus L0 power 1. Okay. Now we I'll call this T again. It's useful for me to have a T. It's tau but we've got x things. So this is getting DT by T. Okay. L0 and L0 power will now be implemented later than actually. So now what's important should say L0 is equal to L0. The ideal is that L0 and L0 power are integers. For example, representation of the delta function with integers over all space integers. We multiply this by d theta integral over theta to the left of 0 to the right and multiply exponential of i theta into L0 power 1. That's the next function that says L0 to L0 power and enforces that. Now it's imagine your variable tau is equal to theta plus i times t. That this gives us q to the power L0 q bar power L0 bar. Okay. We have q, q bar bar to the power minus 1. That's the minus 1 stat.  Okay. And then we do the integral of a k and get our in tau it was t, t was in tau to the power 1 and 13 by d to tau. It's d real tau that's the actual one. Now this was imaginary part of tau so we recover exactly what we want to do. Exactly what we want to do. Exactly what we want to do is what we want to change. We have d to tau by in tau now this in tau this is in about 13. So this is square and then we put 12 in there. So 1 by square in tau times q to the 1 by 24 q bar to the 1 by 24 and this is proper. 24 because we're doing this is like like like like physical spectrum and then happy post we have exactly the same expression that we had before except for one change we never tell you about that one changes the changes are the original integral integration in string theory you integrate tau over all equivalent tau and you remember from last semester that was tau from minus half in the real axis times the exterior of the human circle so the region of which we integrate is this the fundamental domain of the torus the set of all equivalent torus set of torus are not equal to each other up to a modulator in the string theory combination here in the string theory combination here what you get is the integral over the whole upper upstream because theta 0 to 2 pi if you rescale theta by 2 pi 0 to 1 minus half that's the same method and T remember remember T that's the source difference so apart from this change in integration domain apart from this change in integration domain we got in the same this change in integration domain is actually very important it's actually very important to the following case you remember from our theory calculation the part of the calculation that was sensitive to UV divergences was large k now large k transits to small t why is that because we have this e to the power minus t that's k squared so the only way the large k is very small otherwise large k is exponential suppressed so the part of the diagram that corresponds to UV divergences to field theory was small t as present in the integration that field theory seems to give us but it's absent in the integration according to the rule of the string you are thinking this is a bit of a thing because I happen to choose this particular modular modular domain I have chosen this in that case we would have had a small damage and a potential divergences but you see all those things are the same so let's try some what they say what is this point under the modular problem the modular transformation that takes a familiar years tells us about better so this point part is infinity again so what you are saying problem what you got there so what about the problem and then at large at large t the only values of k that contribute are very small values of k so this is one of the great things about string theory you see if you have problem at large t it means that then must have been in field theory language a problem at very small a value of k or restated if there was no problem at very small values of k as long as this is big day there cannot be a problem at large t so now what I am saying is that string theory links good i of a here to good u v u v v let's see this in multi-day oh we have to run this thing yeah let me just one minute let's see this in multi-day you see let's look at this partition function let's look at this partition function at very large values of t okay at very large values of t only in the ground state problem the ground state in this problem particularly in a problem has negative energy okay so what I am saying is that you take this partition function expand it and the power series expansion I mean the power series is equal to power k and as we get e to the power 2 t that's the ground state plus 1 that's the 0 the the the contribution of muscle particles plus extra energy dispersion and we have to do the integral d to so let's create a theta action just the t action so d t over t squared and if you remember we have t to the power 30 okay just in the square of 20 so d t over t now this guy here he's just wrong he blowed up extra energy at last so we you know in the basically if you got a state of negative energy effectively okay that's going to give you the energy now why it's because it's because you're trying to do a path integral of path integral of e to the power plus m squared i squared minus k squared i squared so k is smaller than m these moles these suppression these moles the amplitude for the moles k is smaller than m want to grow rather than you know if the path integral is maximized by these amplitude both will be very large all will be very small and that gives you the divergence that's the divergence basically we see the fact that if you take any negative path particle and try to do perturbation there okay you'll get a divergent contribution there it's from k is smaller than it's an infrared divergence so we are closely telling does have this infrared divergence because it has a vacuum that we knew however in the absence of the tachyon suppose we managed to make a stream there where there was no day in the past state in the probabilities no vacuum then this onwards is final this is a stream theory which has no pattern so we want to have to make this apology about the infrared divergence the ultraviolet range can always view the path in no way so that the ultraviolet region is just not there all the possible problems are infrared and if we know that the theory is a stream theory stream theory for this particular question of energy that's something very smart it cuts off effectively high-moving technologies you see because one last thing I said and that says you might think that well that's sort of easy we just put some cutoff in momentum space somehow for you and we get some sense I want to emphasize that's not true that's not true because one thing I want to emphasize is that and the tau goes to 1 by tau you see these points are invariant and the tau goes to 1 by that boundary of what's linked by tau and a point here is back to the point here the boundary is but actually this edge this thing is the same as this thing so it's a cylinder and this part is the same as this part so you see it's like a cylinder whose edges it's back okay and infinity every point and infinity should be thought of as the same point you know where this can be so what this is is like a sphere the topology is like atmosphere and this from the very beginning here it's a compact matter that's really important because you may remember from last semester that all our our our no-ghost sphere was the fact that you know BRST equivalent amplitudes BRST equivalent operators gave us the same amplitudes and relying on there being no total derivatives and module amplitudes you know BRST equivalent operators are amplitudes up to total derivatives and module amplitudes if there are bounds of these two materialized places it's total amplitudes but we can't do it if BRST equivalent objects give you different amplitudes you have made non-states interfering and your theory breaks you down okay and this is the problem that is played every previous attempt to quantize you try to do a cut-off by hand it's very hard to do that way that's not great if you're bothered and therefore it introduces negative non-states okay strict theory has a very clever way of putting this cup off in a way that preserves you in an area if you violate it in this nanny way if you try to integrate it over some other part of the fundamental domain you will introduce negative non-states in your theory and the theory who makes this it's a very particular way of cutting off the theory that manages to make sense this is a very important okay and this starts the open string also


From Boston, Massachusetts, it's theCUBE. Covering LiveWorks 18, brought to you by PTC. Welcome back to the seaport in Boston, everybody. This is day one of the LiveWorks show. PTC's big IOT user conference, but it's much, much more than that. My name's Dave Vellante, Stu Miniman. You're watching theCUBE, the leader in live tech coverage. It's really our pleasure to have Devin Cleary here as the director of events at PTC. Dave, thanks so much for coming on theCUBE and thanks for putting together such a great show. Oh, thank you so much for having me. This is great. You're welcome. So, you know, I say it's a user conference, but it's so much more. I mean, talk about what your intent was and what you've created you and your team at LiveWorks. Absolutely. So for us, we take a step back in corporate events and we're really trying to bring sort of a unique flair to the corporate events world. You know, in a nutshell, we at PTC have a 25 year legacy of doing really powerful user events and it was really an inspiration two years ago to kind of shake the mold and again, no pun intended, be disruptive in the marketplace. So for us, we sort of coined a new term or strategy that we call industry inclusiveness and this is something where we wanted to sort of break down the four walls of the company and invite industry influencers, individuals who are leading the charge inclusive of actual competitors because for us, it's better together and the whole story and talk track around LiveWorks is collaboration accelerates innovation. So for us, we want to make sure we embrace a lot of different people, walks of life and diversity and the intent is to create a one time a week a year successful program that focuses and profiles nine of the most disruptive technologies on the planet. So this is everything from robotics to AI to IoT to AR, blockchain and so much more. And for us, this is really the essence of what LiveWorks has become. Which again, for us, we want everyone to know that this event is sort of the world's most respected digital transformation conference. So a couple things I want to point out. Well, it's over 6,000 people here. The kickoff was in the theater of the round. I've only seen that we do over 100 events every year. I've only seen it done twice and it's worked both times. I think it's a home run when you do the theater and around. The intro was, I tweeted out this morning, it was like an Olympic opening ceremony. I mean, really, where do you get your inspiration from that? So you know what, for us, I have a really amazing team that works with me and collaboratively and for us, we really want to sort of challenge the status quo. So we always look for things actually outside of the tech bubble, if you will. We look at music, we look at fashion, we look at art, we look at a lot of pop culture sort of references and that sort of stems our ideas of how we sort of nurture and create what we call the apex or live works or what you saw this morning. And for us, I'm all about what I call delight moments. So these are moments that, frankly, are sort of above and beyond the core content of what the conference offers and just making people have a great time. Showmanship and entertainment is just as much important as the core again content that we offer at LiveWorks. Yeah, Deb, you've got a big tent here with a lot of different topics. There's a show I go to, we talk about the random collision of unusual suspects, which this reminded me of. Can you talk a little bit about how in these diverse communities yet, we should see some overlap and some bumping together? Yeah, absolutely. So again, with LiveWorks and sort of again, profiling these nine to 10 most disruptive technologies out there, we're always trying to recruit people that are very diverse from various backgrounds. One specific goal that we have, just from a geographic perspective, is making sure that over half our audience is from international markets outside of the United States. So again, when your bumping shoulders are walking in the halls of everywhere around us, you're guaranteed to hear someone that comes from a different walk of life, a different experience, a different educational background, and that adds a lot of value to the overall conference. Now again, we target everyone from administrators to engineers, developers and more because really this show runs the gamut on everything from product design and sort of the ideas of what you want to do all the way through service, manufacturing. It is a full scope of Industry 4.0. So to your point, there's a lot of intersection and a lot of overlapping because every company, every person, every individual wants to experience and learn how to embrace what we call disruptive tech.  First of all, thank you for that. So this today has been all about thought leadership. It reminds, Stu and I were saying, it reminds us of some of the stuff we do with MIT. We have professors, you have thought leaders talking about not, kind of frankly, some boring products. And it's not a sales pitch. Right, it's not a sales pitch. But why that decision and what's your vision for where you want to take this thing? Yeah, so again, I would say that a lot of conferences, and this is no offense to my brothers and my sisters in the events world out there, but people are so sick and tired of going to the standard trade show. The days of pipe and drape and aisles of just being pitched to and receiving free stress balls and hiring staff that might not even be employed by the company, but they just frankly look good, those days are completely over. And our audience, the technologists who really matter in this world who are doing a lot of great work, they want that substance and that core content. So for us, it's really a vision about that's embraced and sort of evolved into give back and let the content lead your success. And that is going to help amplify the voice and further the mission. We look at live works as a catalyst well beyond the company that employs me and the people that work for just these companies. We have a vision to make Boston an epicenter, a headquarters, a world renowned attraction for technologists worldwide, knowing this city for IoT and for AR. And for us, we embrace the innovation district as that pallet, that backdrop, that environment to allow us to really accomplish that. So live works is growing exponentially. We experienced double digit growth this year, which is amazing. Starting where I was only with this company two years ago at less than 2,500 attendees and we're at 6,100 right now live on the show floor at live works. So the future is really bright for us and we're embracing this notion of the convention center is only going to be constricting for so long. It's time that we also implode those four walls and we embrace the outside. And what our plans are going forward, which I'm really excited to sort of announce, is we're going to be now becoming more of an industrial innovation week in Boston and taking our plans mainstream. So that means taking the content that we focus on and the partners that we work with and the industry thought leaders and now you start to actually replicate these events throughout the entire seaport. So think of it and again, most of you know South by Southwest. I'm a big fan and an avid follower. Think of it South by Southwest meets industrial and that is the future of this show. Love it and you know, we're thrilled to be part of it and it's palpable. You actually see now in the seaport, you know, we were talking off Kimberley, you can't compete with Silicon Valley in terms of what Silicon Valley does. You shouldn't even try. We're by Coastal. We have an office in Palo Alto. We know it well. It's a unique vortex. But I certainly IoT, you know, blockchain, VR there really is some clear innovation going on here. And so if you can focus on that, you can actually really blossom an ecosystem and that's really what you're doing. Oh, absolutely. And you know, again, PTC has been headquartered here for over 25 years. They're a leader in industrial innovation. They are a company that believes in giving back. We have curated and nurtured through partnerships with Harvard Business School with MIT Innovation Lab, et cetera. We've cultivated some of the greatest startups of our time right now who are creating groundbreaking technology in IoT, in AR that is changing the world. We're even actually doing work right now in our backyard with Boston Children's Hospital, for example, doing incredible work with our before year product and AR that's helping actually find a cure for Alzheimer's. So again, the possibilities are endless and the innovation is limitless. Well, you're the hot company right now. Obviously, you know, growing very rapidly. You're kind of like the comeback kid. You're clearly punching above your weight. The Scott Kirstner article in the Globe was unbelievable. Thank you. I know we're very, shout out to Scott. You got to be thrilled with that. And so, but what's interesting to me, Dev, is you're not, you could ride that wave and just pump up PTC, but you're doing things that will allow you to sustain this as a community member, paying it forward, you know, it's kind of a cliche, but that's what I see. Thoughts? 100%. And you know, again, the way that we sort of frame live works is, I want you to think of PTC as the presenting sponsor. They are an investor in the vision that this team has to carry forward the community and the movement all around industrial innovation. And again, we feel that Boston, being in sort of our headquarters and our backyard, it's important that we're giving back and again, furthering that opportunity to further solidify our right, as a rightful heir of IoT and AR as a city, as a community, and as a state of Massachusetts. Dev, wondering if you can give our audience that didn't come to this event. Quick flavor of what's going on.  You know, my friends from the West Coast are like, this isn't warm, but for Boston, it hits summer. But give us a quick tour around what PTC is. Yeah, so we're all about an immersive experience at LiveWorks. You know, again, you're going to have sort of the checklist of what you absolutely need to have at an event to sustain someone's expectations. So the content, the networking, the value. But again, we like to take it a step further and things that I call delight moments. So for example, this year in Extropolis, and Extropolis for those of you at home, that is our sort of expectations shattering, groundbreaking playground for adults in technology. So every corner, every ounce, every inch of this show floor has something to engage, ignite the five senses and tell our story. And one example specifically I love to highlight this year is I've actually created the vision with a whole slew of individuals from PTC and partners and whatnot, something we call the X Factory. Manufacturing is one of the biggest industries and business in the world. Mostly every company at an enterprise level has some sort of manufacturing component to it. And what we wanted to do this year is create the factory of the future. Meaning working with the leaders like McKinsey and again, HeroTech and global brands in Germany who are defining manufacturing and who founded manufacturing in our history, we have partnered with them to say, what does that factory of the future look like? What are companies going to be doing five, 10, 15 years from now? And what can we expect? You're getting that first at LiveWorks, which is awesome. And the whole process is let's not have a standard kiosk. Let's not do a laptop with a video. Let's actually build out a 20,000 square foot industrial factory with multiple stations from digital engineering to service to again, AR induced digital twins and everything else in between. And let's actually have every single attendee create design and manufacture a smart connected product. We're working with our partner, Bell and Howell from a shipping and service and supply chain perspective. And again, we are blowing the roof off this show on that one activation and there's over a hundred in total throughout this entire show this week. So that's a little bit of a flavor of LiveWorks. And beyond that, we do things from everything from a puppy daycare hour to sort of do a high tech, low touch feel. We do incredible food presentations and we're going to be ending with a big bang tomorrow with our closing party called the Mix at Six, which is one of my favorite programs the entire week. And that is actually a superhero themed event where we're actually having a guest host and a personal friend, Paul Rudd, who is the ant man for Marvel. He'll be hosting our event. And the whole notion around superheroes is that we tell everyone this week, unleash your inner superhero. Take advantage of the technology that is on display and realize how it can enable and empower you to now have superhuman powers. So everything from AR giving you the power to see the invisible to IoT helping you give the power to predict the future. Everything is possible and everything is creative at LiveWorks. Well, it's obviously working. And so I'm sure your execs are seeing this going, great, good job, way to go. We got some momentum, let's double down. But back up two years ago, how did you sell this to the folks because we see a lot of guys like, how many leads are we going to get out of? How much revenue are we going to drive? How did you get through that knothole? So let's put it in this perspective. There's a lot of intrinsic and intangible ways to measure the success of a show and the value and the impact brought to a company. One thing I would actually say, I've worked in the tech industry for over six years now. I've been in the events business for over a decade. I've worked for some of the most incredible and impressive and media driven startups in the world right now. PTC though is a very interesting ecosystem. Their executives actually embrace the notion of what I presented first and foremost about again, industry inclusiveness as we call that term. And for us, we have a vision at PTC to be disruptive, to be groundbreaking. If we do not embrace that ourselves as our culture and our business model, how do we hope someone else to believe in the products and the vision and the mission that we set forth in the marketplace? And from that, you got a response if you have, let's do it. So again, am I going to be 100% honest and transparent? Was everyone embracing that 100%? No, but again, I think the proof is in the pudding and I think again, it's a leap of faith in saying, listen, take a chance, be disruptive and see what the product of our fruits of our labor could be. And again, here you have it three years later, triple the size of the audience, tripling the size of the success, seeing multiple customers, multiple partners, multiple industry leaders now attaching themselves to this brand. So for us, LiveWorks is nothing greater than a record-breaking success this year and I'm so excited for the rest of you at home to experience on the live stream. Or again, check out 2019, June 10th through the 13th. June 10th right here, right? Right here again. Dev, well, first of all, thanks so much for having theCUBE here and making us a part of this awesome event and look forward to working with you in the future. Congratulations on all your success. Thank you so much. You're very welcome. Okay, and by the way, check out thecube.net, that's where all the videos here will be, check out siliconangle.com, all the editorial coverage, wikibon.com is where the research is. We're a wrap here from LiveWorks day one, Dave Vellante for Stu Miniman. Thanks so much for watching. We'll see you next time.


Residents of Magogel phase 2 in Lagos stand guard against possible demolition of buildings in the area after a siege of, suppose, hoodlums and a bulldozer. Also on the breakfast, Nigeria's economy is in the spotlight after passing off a 17.1-2 trillion-dollar budget by the National Assembly. What prospects are there for the economy in 2022? And as always, we take a look at the papers this morning for a quick review of the biggest stories making headlines. Always great to have you on the breakfast here on PLOS TV Africa. I am Osaugie Ogbonwang. And I am Mesib Ogbonwang. It's good to see you. Merry Christmas. Yes, same to you. And of course, we had to completely get into the Christmas spirit with our very, very interesting hats this morning. Of course. Yours looks pretty interesting. As well as yours. Good morning. Thanks for joining us. We're sitting off, as always, with our top trending stories. And this morning we're going to Kanu State where the chairman of the, you know, commander of Kanu Hisba has made headlines because he has made statements concerning the, you know, Miss Nigeria pageant, which was won for the first time by a hijabi. Her name, of course, is Shatu Garko. And of course, the Kanu Hisba has threatened to question the parents of Miss Garko for allowing their daughter to participate in the Miss Nigeria pageant. This, of course, has created a lot of, you know, conversations across social media and, of course, across the country, you know, asking why this is necessary. They are saying, according to the Kanu Hisba, that the Miss Nigeria pageant is no different from the Big Brother Niger show, a reality TV show. And the parents should not have let their daughter, who is from Kanu State, to participate in the pageant. Now shortly after she won that, you know, contest, the arguments were on both sides. Now you have some persons who are saying, oh, yes, it's good to see decency win. And I would always say that that's not the only criteria for measuring. Most times it's not about the outfits. They also put out questions there where they ask you. And if you're able to answer some of those questions and come up, you know, with some level of creativity, all of this is some of the measures, you know, that have been used mostly in some beauty pageant. I'm sure that it wouldn't be different from the Miss Nigeria. So not necessarily, you know, the outfit, because a lot of persons made the buzz about having to dress, you know, very decently and all covered.  So there were some persons who said, oh, yes, it's a good thing to see decency win. It's not all the time that you have to put out your body there. Well, of course, we know what beauty pageant's about. And on the other hand, now on some cross, a cross section from the Muslim saying, oh, as a core Muslim, she's not a Muslim. And if she is a Muslim, she would not participate, you know, in this contest because it goes contrary to what, you know, that religion believes or what they believe in and all of that. But I really still continue to ask myself the freedom to associate, freedom of association has been guaranteed by the Constitution. I mean, we're allowed to, you know, choose which religion or association we want to belong without being co-heised and being forced. And I really do not know how she participating. I don't know what, so I don't begin to, you know, offend some persons, but I don't know what the laws for heaps by is. I don't know why they would be asking. She's an adult and I'm sure that she's responsible for taking her decision. So calling the parents and questioning them, I really don't know how that would pan out and why that should be done. So for me, you know, it really depends on what any person describes as indecent. I've never looked at the Miss Nigeria page pageant and seen anything or, you know, in my head thought of anything indecent. It's really just about, you know, personalities and Nigerians deciding to throw words, you know, here and there. And so I don't even know where that, you know, conversation is coming from about, you know, being indecent to win.  But for me personally, you know, I really just see this as, you know, another moment where you would expect that we would be celebrating the fact that, you know, in 44 years, the first time, you know, a person wearing a hijab is winning, you know, the Miss Nigeria pageant. It's something that we should really be focused on and, you know, getting people to understand that, you know, everybody is welcome, you know, to these pageants and everybody is welcome to, you know, 2021, 2022 very soon to be able to participate.  You know, a person in Nigeria is free to do what they choose to do. And so I thought that that is something that we should, you know, a lot of people should be focused on and be celebrating.   And that's simply what, you know, this means to me.   These, you know, thinking, this thinking is not very different from those who are against Western education, you know, in my opinion. It is not different from it. It is simply, you know, a group of persons who have decided that they would not grow. They would not move forward. They would not be forward thinking.  They would not in any way try to be better, try to be developed, try to be, you know, to be, you know, to move into the 21st century. They want to remain in the 18th century, maybe in the 17th century, and that's where their mentality chooses to remain. Another thing is, it really just tells you that the concern of Northern Nigeria is not insecurity. A lot of people in the north, I remember we spoke about this on Tuesday. Yeah, you just took that out of my mouth. Yeah, I mean, we spoke about this on Tuesday, and I was saying that that's one of the reasons why a lot of people see the East protests about North is bleeding. And they just, you know, throw their face the other way. Because when you hear stories like this, you get to maybe tell yourself that these people are not really concerned. They are priorities, you know, currently in Northern Nigeria and of course across the country. They are priorities for themselves. And not about security and getting a better life for themselves and getting proper government and getting education, healthcare, infrastructure and some of all those things. That's not their business. They are looking for more ways that they can strangle, you know, the growth and the forward-thinkingness of Nigeria and us moving forward. And Nigeria is a country. If we are being serious about moving forward, because it currently doesn't even seem like we are serious about it. If we are being serious about moving forward, we should kick. We should use broom to flog. We should drive. We should chase away every single character in every office, in every space that still has this type of thinking and still wants to take us back into, you know, the time when Noah's Ark just landed. And that's honestly what we should be doing. Anybody who's still thinking in this manner, who still holds on this tight to whatever religious practice or beliefs that they have should be completely chased away, you know, with brooms. But you know that that's not going to happen. That's because we're very big on religion as a country. And that will constantly... If we're still that big on religion, that isn't taking us anywhere in any way. And sadly, like you have talked about, one would think that the Heaps Bar Police would be very proactive with the insecurity issues that the nothing region is actually going through. I mean, all of that.  They live with us. Do you know these persons?  So your friend, the next door neighbor. So how come we don't have all of these, I mean, buddies, these persons showing concern, trying to help the effort of the police and all of that in ensuring that... They're not necessarily a security agency. No, no, it's more like, you know, it's like you have the Amotecu to this other part of the South East. Well, I don't think that's what it's about. I think Heaps Bar mostly, you know, are really just, you know, police, it does anything like that.  You know, but I still believe, you know, that we don't even necessarily... And this is me thinking that we don't even necessarily need to have... It's fine to have Heaps Bar. No, no, my point is this, if, you know, it's like saying you have the vigilante groups and you have all of this... They're not necessarily security bodies or agencies or what have you, but of course they perform these functions before... Because prior to this time, prior to the time, Nigeria became together.  We had administering our affairs in, you know, the way we could.  You know, trying to please the community and all of that. So it is still, I'm still saying that they still play that role of, you know, security. I mean, if you're going about arresting and saying, well, this one is not doing this or this one, this person should be flogged. So how come they're not also being proactive in terms of security and looking out for these elements who are committing these crimes and trying to, you know, work in hand with the police? That's my point. Once again, you know, they are not that body.  So the issue, no, so what does their religion say about mother?  So if they say control religion, no, I'm listening. If you watch, you know, and if you followed when you hear his bad did this, his bad did that, it's not anything concerning security.  They are destroying bottles of alcohol. They are banning people from... So he doesn't say anything about killing? I don't think that's really what their concern is. And once again, that's what I said. So that's also the pattern of, you know, the religion is not concerned about mother and killing. That's my point. That's what I'm saying. Okay. Well, anyway, congratulations to Chattu Garco. And I hope that once again Nigeria learns that, you know, our focus should not be on some of all these things. You know, we should really be focused on moving forward. And some of the most Muslim countries in the world are more progressive.  They are opening up more doors for women even. They are allowing women to drive. They are allowing women to vote in, you know, more religious countries than Nigeria. But we're still here, which is a shame. While also moving to Kaduna State, where the governor, following all of the insecurity concerns, of course, he had to bring the president about all that's going on. And we have also had statements from the president saying we're going to be very proactive. The regular were condemning and what have you. But of course, the governor of Kaduna State, Nasi or LFI is saying that nothing like repentance, Boko, I mean, repentant bandits, because they only are repentant when they are dead and in the grave. That has also generated a lot of reactions and conversation. Because prior to this time, you remember where we had the pardon, we were granting pardon to repentant and accepting them, trying to integrate them back to the system. Now for, so it still brings me back to the issue of does our laws make provision for issues of mother and crime and all of these issues. Because if you look at it, if there's an offense, that's why you have a government and that's why you have laws, you know, to address some of these issues. When people begin to say, oh, it's because XYZ offended and so therefore we're going to attack and then there's reprisal attack and all of this attacks. People are dying. People are dying, just killing, whether for a just cause, because I don't know if there's killing for a just cause. But what does the law say about killing? Why are we not allowing the law to take its cause? And then we say they are repentant. How are we sure that they are repentant? Because I feel like this would constantly encourage people to continue in the act, continue committing crimes. And then they feel like the ghetto points, oh, we're no longer committing this crime, we're surrendering. How do we now measure that? How do we now believe that they're no longer committing these crimes? And then, you know, we integrate them into the society and it continues. So a lot of people just feel, okay, let's continue this. Nothing is happening. We can continue and the government will just give us pardon. How come the laws are not catching up with these persons? Well, so I think the idea of forgiving, you know, bandits and terrorists and repentants, you know, it probably came from two things. I think it came from one of them is some of the military programs that were run in the north. Some of them included the chance of rehabilitating these bandits. And so they had to find a way to explain why they had been rehabilitated. And that's where the idea of repentant bandits or repentant terrorists came from. Which is, in my opinion, another way that Nigeria has shown its level of seriousness with fighting insecurity and fighting terrorism. As for Governor El Rufi, I think we also, as Nigerians, place too much, you know, power. We place too much interest in personalities instead of the strength of our institutions and our laws.  These are just very interesting statements to make. What we should be focused on is what the law says and what the Constitution says. If you have committed terror, then there is, of course, laid down laws that should take place, you know, and should take precedence. Not, you know, whether the governor believes this or the governor believes that. The governor should not be the one to tell people whether to, you know, to forgive repentant terrorists or not. You know, we shouldn't even have that conversation because there's a law that already has been put in place that should guide, you know, our actions concerning these persons. But because we continue to play around with these things, that's why they continue to persist. I shouldn't be bothered, you know, what any person thinks or what any politician thinks. Yes, those are some of the things that should guide you into deciding whether to vote for them or not. But as long as there's two laws in place, as long as there's still a Constitution that really shouldn't care whether he thinks that they should be killed. And remember also that these are also, you know, ways that we eventually push ourselves into extrajudicial killings and then eventually start to regret. If a governor says that they should not, you know, be forgiven, it's not like repentance. What he says is there's nothing like repentance bandits that they should, you know, be killed. And of course they should repent when they meet God. It means you are simply opening the door for extrajudicial killings. Which shouldn't also be, there should also be a, you know, pathway through which the judicial system takes these persons once they are pre-ended, once they are caught. So I don't, you know, necessarily, I'm not necessarily moved by governor of fire statements because I know that the law says that if a pre-ended should go through whatever it is that they deserve, according to the terrorism, the anti-terrorism act, and of course according to the laws against murder, nobody wakes up in the morning and repents as a terrorist.  And even if you do, you have still committed crimes against the country. You have committed murder.  So in that light, yes, I agree with governor of fire. Never the person who has said that repentant terrorists do not exist, repentant bandits do not exist. But once again, our focus should not be on what he's saying, but what the law says should be done to terrorists. And you know, that's simply it. Nothing more, nothing less. It doesn't matter what any other person thinks. This is what the law says and that's what you happen, basically. But of course, you know, this is of course coming after about 40 people were reportedly killed in Kaduna state. And no matter what the governor says, those lives will not come back. What we and what Nigerians and the people of Kaduna state need is justice for those lives that were lost. And justice for the thousands of other lives that have been lost in the last couple of years in Kaduna state and the whole of northern Nigeria. Doesn't matter whose emotions or whatever, you know, sweet statements. Like I always say, it's not rocket science. Whenever we're ready to tackle the issue of insecurity in our country, we all know what to do as governors, as, you know, president, police officers, as individuals as well. We know what to do. And until we get to that point, then we will continue to talk about this every other time. It will continue to dominate the papers of our national dailies. We'll talk about it in different platforms, you know, the radio, television and what have you. So we'll constantly talk about it without any action. We're getting to 2022 and I really do not know what the plan is, but of course it's security.  But we don't need to know. All we need to do is see action. And that's the only thing we need to do. But it's just a reminder that government at all levels should understand that security is the number one priority. It's the reason why you were elected. That's the first thing. And when people begin to act helpless, because I've seen it feels like it's a helpless situation. So we hear governors, we hear people who just act like, oh, we don't know what to do. We can't do XYZ. We're rather asking that you have, you know, experts from China come through. We're rather thinking that to kind of, I think that when we're ready to sort out the insecurity issues in our country in Nigeria, we'll get to work. Absolutely. And of course, you know, moving away from Kaduna State just briefly, we of course heard yesterday that the National Examinations Council has, you know, made plans to make NECO examinations compulsory nationwide. And as I said in the Cross River State, I believe, and the Eboni State Governor also, you know, jumped on this same conversation and agreed that, you know, the students and pupils in the Eboni State will very likely also join in and be, you know, take NECO examinations as a compulsory examination. Governor Ben Ayade, I remember also in the news said, you know, always, you know, thanking NECO for improving the educational sector in the state. I don't understand how NECO did that. Well, I'm thinking that NECO has a lot of work to do because over time, there's been several complaints with administration in terms of, you know, computerization of names and all of these errors. We can constantly have all of that. So if they're going to, you know, say they're waking up to say it has to be a compulsory exams. I want to also believe that they are putting their act together. For instance, you have cases where names are misspelled. I don't know how you do that over time. I mean, wrong names, wrong names and certificates. And I hope that that's sorted out. I hope that all the issues also bordering, you know, administration of exams and what have you has been sorted out before, you know, they're now demanding that this exam should be a national thing.   But it's not just, you know, the, you know, secondary exams. NECO has different exams that they conduct. And of course, it's a continuing conversation. We'll see where this leads. This is where we end the top trending this morning. Stay with us. We'll take a short break when we come back. What major stories are making headlines across Nigeria this morning? We'll be sharing with you with our analyst. Good morning.


In this discussion, we will discuss the discussion question of discuss cash controls as it relates to cash sales using a register. When we look at the internal controls related to cash using a register, we're going to apply some of the principles of internal controls, one of them being the separation of the handling of cash and the recording of cash. So how can we do that with a register? That's one of our major principles. Our objective, of course, of that principle will be to have accurate record keeping and reduce the likelihood of theft to safeguard our assets, our cash, which is a very liquid asset, of course, and something that we have to make sure that we have that objective over, given the liquidity of cash, the ease of theft of cash. So if we take a look at this system in terms of a cash register, if we have a system where we have cash register sales, then typically we want to make sure that each individual has their own register. We don't want two people to be sharing the register because then we're not really assigning accountability. We don't know if the cash is over a short in the drawer. We don't know who is accountable. So in order to assign accountability, we need to have one person in control of one register. And then we know that that person is responsible for that register. And that's a good thing for the person too. It's not necessarily a negative because then we can praise the people that do a good job and count the cash out perfectly every time. It's not just a negative thing. We're just, we can blame people when there's a problem. We do want to see whether there's a problem. But accountability is really can be an empowering thing for an organization because we actually get to see who's doing well where we can't see that if we don't have a good delineation of separation of duties and applying who's responsible for what delegating responsibility. We also want to make sure that when we have the system of recording the register that we have a clear display to the employees or to the customer, what the totals are and what the return is for the cash sale that was made. And therefore that the customer will be able to provide a kind of an audit check for us by by verifying the cash receipts as we do that as well. We do want to make sure that we have a cash receipt process, that we print out the cash receipt and give that to the employee. And the goal here is to not have the employee being a system where they can basically just take the money and not register into the system, not record the cash sale. We want to have the customers to be saying, hey, why don't you have to register? Why don't you record the cash sale into the system? Otherwise, they can make a sale and keep the cash without ever recording the sale. We also want to have some type of approval process. For example, if there's a return of merchandise, then rather than just having the register to be able to enter the return and then having the possibility of entering a fictitious return and keeping the money, then we want to have to have a separate person to approve the return process so that so that we have two people involved there, that giving us a second kind of review process, that giving us the idea that two people have to be involved in order to make a theft of that kind. If they wanted to steal money by recording a return that was fictitious and take the money out, it would take at least two individuals to do that. Now, we've got the clerk at the register that's collecting the money and handling the money. They can count the money at the end of the day, at the end of their shift for the money that's in there, but we want someone else to have access. They shouldn't have access to the sales drawer to what's in the system. The system then is the second component, the second piece that's recording everything which the employee doesn't have access to. They can't tamper with or change the information that's in the sales record. And that sales record then should go to a different employee, possibly a supervisor, who would then make a make a sales sheet based on the tape, based on the information in the computer system. And then we can compare the computer system to the cash receipts. We can separate those two things so that the person in the drawer never has system to access to the tape. And therefore, we have that separation of duties between the record keeping and the tape. We can compare the two. Once we compare the two, if there's any over or short in the drawer to the tape, then we can record that information as we enter the data. So once we enter the information into the journal entry, we're going to debit, of course, the cash in the system, we're going to credit the sales according to the tape. And whether the tape is over or short, the sales over or short to the cash receipts, we will record the debit or credit to the cash over or short account. Then of course we can assign accountability and we can say, okay, who is responsible for the drawer here that was over or short? Is it significant? And we can sign accountability there as well as praise the individuals whose drawer are doing well or write on as we do this comparison.


We just announced today that the BC tech fund, which is $100 million, which has the ability to put about a half a billion dollars out into the tech space for small and medium sized tech companies to grow into large companies to grow big and stay home. We just announced that the fund-to-fund will be managed by Kensington Capital and a very enthusiastic crowd. This takes young companies and makes them into more mature companies and it's going to grow thousands of jobs, well-paying jobs all across British Columbia. The excitement today is about launching the new BC tech fund to be able to grow the market here and build up the tech sector here in BC. This is a great time to be investing in technology globally and so this is the right time to be taking this kind of initiative for the province. Having access to capital is important in part because it allows us to have access to the best talent in BC. But we're going to spend this money primarily on people, people that are going to help us deliver on the products that we've already built and sold to our carrier partners. If you've got capital behind you, then you can be attractive to them. Without that capital, you have no ability to grow. We've come a long way in helping our BC tech community and you can see it thriving. You can see companies that originally started here and now they've spun off to new companies and new initiatives. But I think this BC tech 100 million funding will do so much more to carry that a lot further than it is today and certainly further than it was when we started 17 years ago.