Live from Las Vegas, Nevada, it's the Cube at IBM Edge 2014. Brought to you by IBM. Now here are your hosts, John Furrier and Dave Vellante. Hey, welcome back, everybody. We're live in Las Vegas for IBM Edge. This is the Cube, our flagship program. We go out to the events, extract the signal from the noise. I'm John Furrier, the founder of SiliconANG. I'm joined by Coach Dave Vellante, co-founder of Wikibon.org. Our next guest is Phil Schomburger, director of technical delivery, pro-active solutions. Welcome to the Cube. Thank you. I got to get you to take you guys one on a war.  What does the ecosystem look like here at IBM Edge? Mostly customers, partners, IBMers. I mean, give us a flavor of IBM Edge. Well, I've been focusing mainly on getting my technical aptitude up. I'm looking at all the different sessions that are out there, but we have a lot of customers and a lot of business partners. This is kind of a venue to educate yourself and get all the latest information on IBM products and offerings. So as a partner at IBM, how have they been to you guys to work with? Obviously the x86 transition to Lenovo is not, it's a new thing, but it's not new to IBM's ecosystem. They did that with the laptops and the PCs in the past. How's that affecting your footprint, your customers, and your partnership with IBM? We spend a lot of time working with Lenovo in the laptop desktop area. We're also a good x86 partner. I think that it's going to be a good transition. I feel like the x86 platform is almost like the Lenovo mainframe. That's the biggest product set they'll have, the highest in enterprise product, and I feel like we can, since we have a good partnership with Lenovo already, we're going to do fine in that space. So what about the award you guys won? You guys were featured. Just give it a little taste of the accolades, the award and the category and the reasons. Yeah, as a business partner, we have different categories that we sell, but our focus is on the IBM, pretty much the entire portfolio. We sell all the products across the board, but one area that we've invested a lot in our human capital and with certifications and new hire, strategic hires really, has really helped grow that space, and we received a winning edge storage award for growth and vitality in that space, and we had 700% year-to-year growth, so that's pretty significant for us, and we sold a lot of... 700% for the company? Yep, year-to-year growth, so that's pretty significant. Like I said, we sell a lot of IBM XIV, a strong growth area for us that, truthfully two or three years ago, we weren't really thinking about is flash, dedicated flash storage, and we had really good success. We've invested in trial equipment, where we can take that to customer sites coupled with IBM's sand volume controller, and we've had good success with our proof of concept equipment, and we've made a ton of investment in that space, and I guess IBM recognized us with the award for all the effort that we've put in there on the storage platform. So 700% growth, that's growing slightly faster than the storage market, so you're obviously gaining share, to what do you attribute that growth? Well, part of it is, like I said, we had real strategic hires in that space where we knew they were gonna be storage-focused individuals. SE types? Uh-huh, SE types, same sales staff. Yeah, that's right, Rockstar SEs. Some of them were ex-IBMers, you know, that had good relationships, and we've leveraged that the best we can. Part of the thing that they get, I think our customers get from a partner, versus just working with IBM directly, is we're very nimble. We put together packaged offerings with education and consulting. We're able to do incentives and rebates and bring education to the customer site. So we do have a different dynamic, and I think that's been very successful for us. We're very client-oriented and customer-sensitive. So given that you're growing so rapidly, a lot of partners are under major pressure to transform. The cloud's coming in, margins are getting squeezed. You got to go up the stack, you got to get an application affinity. You're presumably not feeling those types of pressures, but, you know, Andy Grove, you got to be paranoid. Absolutely, absolutely. So if you're always transforming, like a lot of organizations, how are you transforming? What's going on in the channel, in lightness here? We are retooling, as you can imagine. The hardware business isn't quite what it was even 12 months ago. So we're retooling, trying to get up-to-speed, IBM software offerings are exciting. There is a newly announced partner program. We're getting our education and certifications in that space as we speak. We're working on the storage as a service platform. There's going to be new offerings coming out in the software space, and we're trying to adapt to those. You know, there's this elastic storage. I guess you just heard that from one of the IBM executives that were here just a few minutes ago, but we're trying to retool in that space and we're getting more cloud-friendly, more software-oriented, but like I said, our success in the storage business isn't a fluke. There's a lot of customers out there that still plan on owning and will own their assets for years to come. So we're going to try to continue to grow and leverage those relationships, but we're not going to sit still and let the cloud world pass us by. So we're definitely focusing on that. I was going to ask, you guys sell across North America or just United States? We, just across the U.S. Okay, so presumably you're seeing more cloud, more public cloud, more Amazon, right? Coming in from the line of business maybe? Yep. Okay, so now you've got software now in the bag. So talk about what you're seeing in public cloud adoption. What are clients telling you and how are you helping them respond? Well, the logistics behind it, I think the biggest challenge is the bandwidth, customers bandwidth and security. That's typically been the conversations that I've had. And sometimes it's a business model. It's kind of like leasing equipment, either buy it or lease it. And a lot of folks are still on that edge where they're going to be in the cloud or they're not, but most of them are dabbling. We've seen a lot of our enterprise clients are hiring cloud specialists. So that just leads me to believe that sooner or later they're going to have cloud workloads. We do have one enterprise customer that's a large, large bottler, if you will. They have an initiative that they will price every new workload, new requirement on cloud infrastructure as well as internal. So public and private, it's a bake-off. Yeah, so they are not going to be biased at all. They're going to go to the cloud if they can. So what are the results of those types of bake-off? I mean, a lot of people say, I think we heard Tom Rosamilia say essentially the driver is not necessarily cost. It's the flexibility and the agility. At the same time, you're seeing new pricing models. You're seeing utilization models because it's elastic. So versus, you know, wasting capacity. So on a, and then this kind of apples to oranges, but when you net it all out, what are you seeing? And I know it depends on the workload, but maybe you can add some color to what you're seeing with the results of those bake-offs. What I've seen so far is that owning the assets are still a little bit cheaper than the cloud. But like you said, the flexibility, a lot of companies are, we don't want to be in the IT business. We want a couple really smart guys that can architect in the cloud and get our applications in the cloud, get us cloud-ready as a business, but they don't really want to be in the IT business. And so, but the bake-offs have been just like you said, a little bit more expensive on the cloud, but I think that difference is closing. I mean, it's getting closer and closer to buying the assets versus going to the cloud or about even up. Renting more expensive than owning, but gives you a lot more options. Okay, so then, second part of that question is, is there enough motivation within the enterprise to duplicate those kind of economics? Certainly there are in some, certainly sensitive, if you have financial services. Sure. And certain other types of environments, but you're seeing a real rush to build sort of your own internal cloud on-premise hybrid. What do you want to call it? Yeah, I think internal cloud is almost a given now. Everybody's doing it. Using cloud loosely, I guess, depends on how you look at that. A lot of companies are providing services for other business units. So I look at that as truly being internal cloud and even service providers within your own four walls of your organization. IT is a service. Yeah, that's right. Service catalog. And that model has been adopted internally, even if it doesn't have charge back or build back or it's internal marketing kind of a concept. It's still happening in all organizations. So going to the cloud is almost, what I'm trying to work for in our organization and with our resources is to figure out a, almost like a checklist or line items where we can say, is your application cloud ready? And these are the five things we need to make sure that it can do to be ported to the cloud. And once it's there, it should be fine. But those are the types of things that we're trying to do to adapt to those requirements that customers are coming with us. Phil, I got to ask you though, and getting out to the mainstream marketplace, actually I'm in Silicon Valley where the Kool-Aid injection is at an all-time high right now. So it's certainly booming. DevOps is driving everything. That's clearly the cloud culture as DevOps. Are you seeing that translate in the field? Are you seeing DevOps being a key driver in the culture and also into the delivery? Yeah, I mean, that's something that we're seeing. And I don't think that, like I said earlier, the, all of our customers are looking at cloud and IBM statistics, I feel like I came out here for another IBM conference a couple of years ago and the cloud was the word, right? That was the buzzword. And they said, all of our customers are going to be looking at or have workloads in the cloud by 2015. Well, I was a skeptic and with DevOps as well as even large workloads like SAP, I see a lot of large database companies are still providing services in the cloud now. And that's, I'm pretty shocked to tell you the truth, but it's truly happening. So I guess if you listen to the experts, it'll come true. And that's where everybody is moving. All right, well, thanks so much for coming on theCUBE, really appreciate the stories, what's going on in the trenches. This is theCUBE in the trenches, getting the data, sharing that with you. We're live in Las Vegas for IBM Edge. I'm John Furrier, Dave Vellante. We'll be right back after this short break.


Let us now look at a saturated 2 power 3 factorial design X matrix and so in addition to the intercept we also find A, B, C, A, B, C, A, C and A, B, C that would be 1 plus 7, 8. So all the 8 settings are being used up to determine 8 parameters and when you look at the A column you are having minus 1 plus 1, it is an orthogonal design and so the number of minus 1s would be equal to the number of plus 1s and so the total will be equal to 0. Similarly for B you will again have a total of 0 and so on for C as well. If you look at A, B again you are going to have a combination of plus 1s and minus 1s in equal numbers and so it will become equal to 0 and when you look at A, B, C also we are going to have as 0. So we can say that the first order moments are 0 because we are summing the elements in the X matrix column wise for a given X. In this case X i will be equal to A or i is equal to 8 if you want to put it that way. So the first moments are all 0 and this is the second mixed moment because A is different from B, again that is equal to 0. So it is B, C and AC and when you are looking at the third moment which is also mixed because you are having A and B which is different and also B and C are different, A and C are different and so when you look at the sum it is again equal to 0. So we can say that the third mixed moment is equal to 0 and even A, B squared even though you are having a B squared term you are having A to the power of 1 and hence you are having a mixed moment here and that would be a third mixed moment which is equal to 0.  So this is the way in which the pure and mixed moments are computed for various designs. Now when you look at a central composite design which are now having centre points and also the axial points the moments are carried over up to order 4. So we will take the design matrix for the central composite design and use it to investigate the values of the different moments. So all odd moments through order 4 that is the moments that contain at least one odd power. So i, i to the power of 1, i cube, i to the power of 3, i squared j, i to the power of 2 and j to the power of 1. So it is a odd moment or a mixed moment, i, j, k all of them are different and all of them have odd powers, i cube j. So 3 is also odd and 1 is also odd. The 3 is the exponent for i and 1 is the exponent for j. Both of them are odd numbers and so we can call them as odd moments or mixed moments. And then you also have i squared j, k are 0 for i not equal to j not equal to k. So the tables which are shown next will illustrate this concept. Also when are we going to have the non-zero moments? It appears that many of the moments are 0. Are there any moments which are non-zero? And for the central composite design involving 3 factors the non-zero moments are for k is equal to 3 corresponding to i squared, i squared, j squared, i to the power of 4 for all i not equal to j. So these are the cases where the moments will not be equal to 0 but will the moments be equal to 1. Again this is a very interesting question because n is the size of the run. So n would be the number of experimental settings and for a central composite design it can be shown for 3 factors you have 8 factorial points 2 into 3, 6 axial points so 8 plus 6 that makes it 14 and then you have 14 plus nc center points. But what would be the values taken by the non-zero moments such as i squared, i squared, j squared, i to the power of 4 we will have to compute them. Let us look at the table. So let us look at the moments table for a 2 power 3 design with 6 center points, 8 factorial points that would be again 6 axial points a total of 20 points. So this is 20, 1, 2, 3, 4, 5, 6 so this entire column comprises of 20 elements this is for a and you can see that in addition to the minus 1 and minus 1 plus 1, plus 1, minus 1, minus 1 these correspond to the factorial points. So the number of plus 1 and the number of minus 1 points are matching so that is fine and this minus 1.682 and plus 1.682 refer to the axial points. Similarly b also has its share of equal number of minus 1 and plus 1 points and then it also has 1.682 and minus 1.682 which correspond to the axial points same way we can do for c. Now if I add up the elements in the a column that will correspond to the first moment and that would be equal to 0. So would be the first moment corresponding to b and c but if I look at a squared I am going to get 1, 1, 1, 1 so I will get 1, 2, 3, 4, 5, 6, 7, 8, 1 and then I am also going to get square of minus 1.682 and again square of plus 1.682 which turns out to be 2.828 and 2.828. So when I total the elements of the a squared column vector I am not going to get n as it did for the pure factorial case because now the central composite design we have added the axial points. So the axial point coordinates also will contribute to the moment which is not vanishing. If I look at the a squared vector or the a squared column I am seeing elements which are all 0 or only positive. When I add up the elements I am not going to get a value of n where n is the design size here n is equal to 20. I will get a value different from n because we have 8 ones that could be 8 and then you also have 2.8282 times which is approximately 5.656. So 13.5656 so that value is not equal to n which is 20. I am just illustrating the difference between the central composite design and the regular factorial design. Similarly for b squared you have again a pure second order moment and when you total it up the value will be same as that of a squared. Similarly for c squared when you however look at the second order mixed moments or the odd moments comprising of ab or ac where a is different from b and a is different from c we see that the total adds up to 0. So the moment values for the second order mixed moments are 0. We can go on for bc, c, ab, c cube, a squared b and abc, b cube, ac squared, ab. So as long as you have odd moments and the moments are carried over up to order 4 we can see as long as there are at least one different term in the product. For example in c squared ab, ab and c squared are different and when you look at ab cube, a and b are different, a squared b, a and b are different. All the cases the moment value becomes 0 when you add up the elements in the column they all become 0 here. So now we are going to the second order models. The scaled prediction variance is normalizing the design size by multiplying by n and removing the variance effect by dividing by sigma squared. And so we simply get n into xm prime x prime x inverse xm. We saw that xm prime is the coordinate point in the exponential design space expanded into the model space. So that xm reflects the model we have chosen to represent the process. And we have also seen that the moment matrix is given by x prime x divided by n. So for a first order factorial design of order k, the moment matrix is the identity matrix of order k plus 1 by k plus 1 that can be easily shown and we have also shown it a few times earlier. So we get using the definition for m, m as x prime x by n. So x prime x inverse would be substituted in terms of m and n. The n cancels out and then we get m inverse here. So this derivation is pretty straightforward. If you want you can try it out. So what we are trying to prove here is the scale the prediction variance at a point x in the exponential design space depends upon the moment matrix. And the scale the prediction variance of x would be xm prime m inverse and xm and you just put the identity matrix here instead of m inverse. So identity matrix inverse is also an identity matrix. So you will have identity matrix here and then it will be each element multiplied with itself in the xm prime and xm. This can be easily verified in our earlier lecture on orthogonal design concepts. We did calculate the scale the prediction variance. The scale the prediction variance we showed in the orthogonal design as 1 plus square of the distance of the coordinate from the exponential design center. You may want to verify that. So what is the importance of the scale the prediction variance in the design space? It is important to have a stable scale the prediction variance. If the stable nature of these SPV is violated then you will have shooting up of the variance at some locations in the exponential design space and the model predictions can be considered to be reliable no longer. So another thing is the quality of the y hat of x should be as uniform as possible throughout the design space. You cannot have certain pockets in the exponential design space where the scale the prediction variance is hitting the roof. Now let us look at the concept of rotatability. This was defined by Box and Hunter in 1957. Rotatable design is 1 for which n into variance y hat of x by sigma square which is nothing but the scale the prediction variance has the same value at any 2 locations which are equidistant from the design center. And for k is equal to 3 n into variance y hat of x by sigma square is constant on spears because any point on the spear would be equidistant from the center. So let us take 2 points in the exponential design space x1 and x2. If you have x1 prime x1 to the power of half is equal to x2 prime into x2 to the power of half then x1 and x2 are said to be equidistant from the origin and the scale the prediction variance is equal at both these points. In other words the predicted values at y hat x1 and y hat x2 should be equally good that is have the same variance. And just because the design is rotatable it does not mean that the SPV is stable everywhere in the design space. But the concept of rotatability also helps us to find the number of center points and also the coordinates of the axial points in the central composite design. So now if you look at the first order models a design is said to be rotatable if and only if the odd moments through order 2 or 0 and the pure moments of order 2 are all equal. So you have i is equal to ij is equal to 0 this can be easily verified for i is equal to 1 2 so on to k and i is not equal to j. And then you also have i squared is equal to lambda 2 where lambda 2 is equal to 1 for 2 power k factorial design with 1- plus or minus 1 settings. So we are looking at the necessary and sufficient conditions for rotatability we are discussing first order design and in the first order design for rotatable conditions to exist the first order moment as well as the second order odd moments or mixed moments should be equal to 0 that means i is equal to ij is equal to 0 for i not equal to j. i squared is equal to lambda 2 where lambda 2 is a constant and it is not equal to 0 and for a 2 power k factorial design alone with plus or minus 1 settings lambda 2 is equal to 1 this also we have seen previously. Again looking at conditions more conditions for rotatability for second order models this is very important all the odd moments through order 4 or 0 and there is a difference between the mixed moment and the odd moments if you have i squared j squared they are considered to be a mixed moments because i is not equal to j. On the other hand you are looking at the power the power is 2 for i as well as j. So you cannot call this an odd moment but it is a mixed moment but if you have i cube j then the power of i is equal to 3 and the power of j is equal to 1 and so here you have odd moments. Now when you are looking at odd moments through order 4 or 0 you have i i cube i squared j j is having a power of 1 ij k all the ij and k are having powers of 1 i cube j i squared j k are 0 for i not equal to j not equal to k and very interestingly the ratio of the moments i power 4 by i squared j squared is equal to 3 and i squared is equal to lambda 2. So this is a very interesting condition i power 4 divided by i squared j squared is equal to 3 for a rotatable design and so when you look at i power 4 you will have the elements all 0 or positive you would not have any negative values you will have 0 1 and then you will also have the axial points to the power of 4. So for the factorial points they will all be 1 so the minus 1 will be converted into plus 1's so they will all remain as 1's 0's will of course be 0's so when you total them up that will be equal to the total number of factorial points and then you are going to have 2 alpha to the power of 4 because the axial points for each column would be plus alpha and minus alpha when they are taken to the power of 4 it will become alpha to the power of 4 and alpha to the power of 4 so it will be 2 alpha to the power of 4 and so the fourth order pure moments would be giving a total of f plus 2 alpha to the power of 4 whereas i squared j squared it can be shown very easily will give you only f that is very interesting the fourth order mixed moments i squared j squared is independent of the alpha term whereas the pure fourth order moment is having the alpha term in it. So the ratio of these 2 i to the power of 4 by i squared j squared moments is equal to 3 for a rotatable design and here it can be easily shown that from this relation we are going to have 3f minus f which is 2f so f is equal to alpha to the power of 4 or alpha is equal to fourth root of f and so if you want your central composite design to be rotatable adopting this criteria helps you to find the value of alpha this is what I have been telling about early in the lecture we will as to how the alpha values are going to be set if you want a rotatable design so using this criteria we set the value of alpha as the fourth root of the f where f is the factorial number of points okay f is not the number of factors but the total number of factorial points for a 2 power 2 design f would be equal to 2 power 2 which is 4 for a 2 power 3 factorial design f would be equal to 8 so f refers to the number of factorial points and is independent of the number of center runs again you can see that the alpha value which is recommended to meet the condition of rotatability is independent upon independent of the number of center runs. Please note that the rotatability is achieved if alpha is used as above regardless of the number of center runs. Let us now look at the 2 power 3 central composite design we are having 20 runs how do the 20 runs come about we have 8 factorial points 2 power 3 factorial points which will be 8 and then you have also 6 axial points they are located at minus 1.682 plus 1.682 and that would be 6 so because you are having 3 axis and so each axis has 2 axial points so you have 6 axial points totally 8 plus 6 is 14 and then you also have 6 repeats the repeats are not located in one group you can see that this design has been randomized and so you are having the center points at different locations this is one center point that was one this is the second center point because all the coordinates are 0 0 0 0 that would be 2 so this is 3 and this is 4 5 and 6. So we have 6 center points and you can see that the a squared will not vanish either the terms are 0 or positive but for a b and c you have equal number of negative and positive values and so the total would be equal to 0 a squared and b squared are not going to be 0 a squared is minus 1.68 is squared is 2.83 so these calculations are pretty straight forward so I would not be discussing them any further but when you look at the other elements we are having the fourth order pure moment c power 4 when you total it it adds up to 24 interestingly the axial point has become 8 you can see that the axial point has become 8. So what is 1.68179 according to the conditions of rotatability alpha is equal to fourth root of f where f is the number of factorial points so the fourth root of 8 gives you 1.68179 if the fourth root of 8 is 1.68179 the fourth power of 1.68179 will be equal to 8 and that is the reason why for c power 4 column we are getting 8 here and when you total it up it adds up to a nice 24 and when you look at the fourth order mixed moments i squared j squared the sum is equal to 8 because you are going to have b squared and c squared and you are not having the contribution from the axial point because the axial point in the b column is located at a different place than the axial point in the c column it is very easy to verify here the axial points are here corresponding to the location of the axial point in the b column the corresponding values are both 0 the axial point in the c column for example I was pointing to the wrong column this is the axial point in the b column and corresponding to that the values are 0 okay and the axial points in the c column are located at points where the corresponding points in the b column are both 0 so you are having 0 0 and then you are having these 2 and you are having these 2 and then you are having 0 0 here so when you do b squared this term will of course be positive both will be positive but when you are doing b squared c squared you can see that it will become 1.68179 squared into 0 squared which is 0 so that is why the b squared c squared has 0s even at locations corresponding to the axial points for the b and c columns anyway if you take the ratio of c to the power of 4 and b squared c squared if you take the ratio of c power 4 to b squared c squared you get 24 by 8 which is equal to 3. Now let us see the values of alpha for rotatable central composite design for k is equal to 2 and 4 factorial points the total number of design points would be 4 plus 4 plus nc and alpha is equal to 4th root of 4 which is 1.414 4th power of 4 would be root 2 and that is why you are getting 1.414 and for k is equal to 3 it can be easily shown just now we saw that the alpha is 1.682 for a design involving 4 factors k is equal to 4 we have f is equal to 16 and alpha is coming to a whole 2 and when you look at 5 factors the number of factorial points would be 2 power 5 which is 32 the total number of points would be 32 plus 10 plus nc and alpha is coming out to be 2.378. Now let us see whether the design is spherical for a spherical design you want the points to be equidistant from the origin. So for meeting the condition for spherical design the design points should be located at square root of k where k is the number of factors. The value of alpha for k is equal to 3 is 1.682 for a rotatable design and it is 1.732 for a spherical design coming again in the above table it can be seen that the value of alpha for k is equal to 3 is 1.682. So this is actually meant for a rotatable design but this value of 1.682 is not equal to 1.732 which is corresponding to square root of 3 here k is equal to 3 for a factorial design with 3 factors and hence this alpha value is 4th root of 8 which is 1.682 and not square root of 3 which is 1.732. So all the design points in a rotatable design are not equidistant from the center and the design is not completely spherical. So if you look at central composite designs with k is equal to 2 and k is equal to 4 for k is equal to 2 it is 1.414 for a rotatable design and square root of 2 for a spherical design or a circular design if you want to put it that way. So square root of 2 is equal to 4th root of 2 is equal to 4th root of 2 power 2 the number of factorial points. So both of them are equal to root 2. So the design is both spherical or mean if you want to take it for a 2 dimensional case circular and also rotatable but when you take k is equal to 3 you are getting 4th root of 8 which is 1.682 which is not equal to square root of k which is 1.732. So even though the design rotatable design is not strictly spherical the values of 1.682 and 1.732 are pretty close to each other and so we are getting a nearly spherical design for k is equal to 3. Now coming to k is equal to 4 we are having 16 factorial points and the 4th root of 16 is 2 and the square root of 4 is also equal to 2. So for this case we have both the conditions of rotatability and a spherical design being met. So for both k is equal to 2 and k is equal to 4 the design is both spherical as well as rotatable. The design points are equidistant from the centre and the design also is rotatable. But when you look at a factorial design with 5 factors the condition of both rotatability and sphericity is not met simultaneously. So to reiterate what we said just now for k is equal to 2 we have for a rotatable design 4th root of 2 power 2 which is root 2 and that is equal to root k the condition required for a spherical design. For k is equal to 4 the condition of rotatability stipulates 4th power of 2 power 4 which is 2 which is also equal to root of k is equal to 4 and hence we have both the spherical as well as rotatable characteristics for the central composite design with either 2 factors or 4 factors. When you look at central composite design with 3 factors it is said to be a nearly spherical design because 1.682 and 1.7321 are not very further apart. So central composite designs with k is equal to 2 and k is equal to 4 contain 8 and 24 design points apart from the centre runs that are equidistant from the design centre. For these cases the design is exactly spherical. However for k is equal to 3 the axial points are located at 1.682 and the design is said to be only nearly spherical. For k is equal to 2 and 4 the design points are exactly at root k from the design centre whereas they are only approximately so for a design involving 3 factors. So now we are looking at centre runs. The importance of centre runs we already emphasised as estimation for pure error to detect the curvature effects significance in the model. Now we are going to see another role played by centre runs in the central composite design. For rotatable central composite design it is actually a rotatable central composite design. So the centre runs are important to try and import stability to the scaled prediction variance in the design region. We saw that not necessarily the scaled prediction variance should be high only in the design boundaries or design extremes but it is also possible for the scaled prediction variance to shoot up in the centre of the experimental design space. So to have a check on that we increase the number of centre points. If there are no centre runs in a second order design the matrix X prime X becomes singular and the scaled prediction variance is infinite. So adequate number of centre runs are recommended. Spherical or near spherical designs require 3 to 5 centre runs to avoid severe imbalance of the scaled prediction variance in the experimental design region. So for factors ranging from 2 to 4 it is advisable to have 3 to 5 centre points so that the scaled prediction variance does not shoot up and when you are going in for a rotatable or a nearly rotatable central composite design a few centre runs only is not desirable. So adequate number of centre runs are required for rotatable and nearly rotatable central composite designs. Recommended that you use at least 3 to 5 centre runs to avoid severe imbalance of the scaled prediction variance in the experimental design region. It is not desirable to have very less number of centre runs for the rotatable or nearly rotatable CCD. So we will demonstrate the importance of centre runs with a few examples in the next lecture. So thanks for your attention.


Those are medieval robots. She ends up walking to the register with a box of spray string, presumably for a child's birthday. Near the corner of the camera she's seen in, that same Spongebob balloon can be seen peeking out from behind a small shelf of candy. Lonnie was interviewed days after leaving the store. She had this to say... It kept following me. Everywhere I went. I don't know why it freaked me out so much, but it did. I saw it slowly floating towards me when I left the store. I saw it bumping into a door to the bank when I tried to get a withdrawal, and it even followed me home. It's been floating outside of my window watching me for days. Not once did it deflate. I didn't see it go down, not even a little. Log 2, February 14, 2014. Ezra Culver, a 22-year-old male, discusses his experiences with this balloon and what it did at 3 a.m. After a house party went down, involving plenty of beer and games, he'd announced that the night was over and that everyone had to go home. Later that night, he'd lie awake in bed, and see the airwalker floating near his doorway, with his hall light switched on. Ezra would tell us about what went down afterward. I never bought a damn SpongeBob balloon. I don't know if someone brought it with them or not, but I'm positive I didn't see any of my guests bring one in. Hell, most of my friends don't even like that show.  Something along the lines of, I just want you to love me. I opened my eyes, and it was right next to me. I shrieked and fell out of my bed, but it didn't respond to me. It didn't even move. I thought I was hallucinating, but I still wanted to get rid of it if that caused it.  LOD 3, February 27, 2014 Emma May and Terry May explained the situation that went down in a birthday party, ran by them for their two-year-old son. They had bought several SpongeBob airwalkers for their child, and everything seemed normal at first. Twenty minutes after the party started, Terry would walk outside with the cake and see every single balloon slowly spinning into a circle above them, with one balloon still grounded, but centered. After giving the cake to their child and attempting to ignore it, the speed of the airwalkers would accelerate above in an almost impossible racecar-like speed. There were no heavy winds reported that day. Emma and Terry would rush inside and grab their phones. When we came back outside, every balloon was gone except for the one that was on the ground.  He looked genuinely terrified, and since then, he still doesn't want to tell us about what happened. We aren't sure whether it was a supernatural thing or not, but we're never buying those things again. Ever. LOD 4, March 12, 2014 Interviewee prefers to remain anonymous. He states that his niece came over with a SpongeBob balloon and ended up leaving it there when she left. He'd see that it was floating into his hallway. At first, I thought nothing of it, because it's an airwalker. Then, I heard footsteps. Yes, footsteps in the hall, as if there was something haunting my house. I turned the lights on, and the balloon's shadow didn't even look like something that would come from a balloon. It lost all punky, and it looked human-shaped. The shadow raised its hand up to me, which made me wonder if I was having some sort of weird vision.  Nothing. No shadow. It didn't even revert back to its original shape. LOD 5, April 1, 2014 This is the last occurrence of whatever this phenomenon was. There is no interview because the victims refused to talk about it. David Scumacher, Maya Alvaro, and Thomas Alvaro were having a cookout in the backyard of David's home. Upon investigating the area, we found several holes burned into the grass and certain objects within a 12-foot radius, a wooden board with bullet holes punctured in, and several balloons. Two of which were of the SpongeBob airwalkers, with one of the two being punked. Surrounding the area was a stinging, foaming, acidic material that seemed to have melted through the porch the victims were standing in front of. The victims suffered third-degree burns across their face and torso.


Oh my god! Are any piers gonna hit him? Oh, they're just laying into a Godzilla terrified! Hello everybody and welcome back to an episode of Totally Accurate Battle Simulator, also known as Tabs. It has been such a long time since we've played this game. However, the reason we're back is because they've done the best thing they could have ever done, and that is added like a custom unit creator. And not only that, but you can submit your things through Steam. Uh, so I, myself, if you upload something I can find it and try it out in said videos. But what really got my attention was something that if you remember Ultimate Epic Battle Simulator back in the day. Um, well, yeah, look at this. Godzilla. Or at least a form of Godzilla that likes to dance. I mean, these are all custom created so apparently. This one's the most expensive, even though he's not the biggest. And then this one's super cheap. So shall we see who wins between cheap on the left and expensive on the right?  He looks like he's shocked at himself like, did I just do that? He's just like threw up in his face. Oh, that was amazing. Didn't stand a chance. Oh my god. How many expensive Godzilla's do we need? Look at him. He's got a bath. He can't even hold it in. Oh, did he kill him? Yep, he killed him.  He's running away, Pukin. Oh, what's he doing with this one? This one's completely on fire. They're really struggling.  Oh no. Will they be able to catch up to him? That was the question. Oh, he killed him. Will the last one be able to get there? Oh, he's close. He's close. Oh, he died as well. How about this guy? These are roundabout the same price. How will the battle go with these two? Oh, he's got lightning and god knows what that is. Is that like plasma breath? Oh, oh my god. Okay, this one's a little bit more close. Hitting him in the crotch, that's disqualification. Oh, what is this? Some weird powers. But they do seem to be evenly matched. They're now going in for a hug. Didn't like the hug apparently. No, no, no. Didn't want that. This guy does like a weird purple bird. He's like crying on the floor like a baby. Oh, they're both up. They're both like classed. This is the most, this is what the next Godzilla film's going to be like. Just you watch. Oh, has anybody made King Kong? We could do King Kong versus Godzilla. Oh, somebody make all the Kaiju. So, oh, he's far now. He's far. What is this guy? Oh, oh, he's dazed. Is he in rage mode? Oh, I think he's in rage. Oh, he won. He hit him right in the crotch. He got like a rage mode. Is that when he's close to death or something? The one with the fire breath seems to be the best. How does he face up against the US Army? Yes, we're recreating the battle from what's it called? King Kong, was it just King Kong? I guess it was just King Kong. The most recent one. And how about all these bullets? Oh, are they, oh my god. Oh my god. Any fire going to hit him? Oh, they're just laying into him. Bushing him back. Godzilla terrified. The US Army just marching forward. Look at them go. This looks amazing. Although they're just out of range with, I don't even, whatever rifle ladders they've got. I don't know about guns. I'm not American. Cowarding in the back. I wonder. He's never been killed by anything, but can the humble US military take him on? Well, I don't know if there's anything humble about them really. Oh, now he's always, his weakness. He's backs into a tree. Oh, I don't know. I don't know. He's being impaled, I think, unless, are they even hitting him? Oh, look at that guy. Oh, he's dying. Oh, the bullets backfiring. Oh, I think they are. Oh, he fires them backwards. Well, they've taken one casualty so far. They are shooting at him.  Oh, no, he's up. He's up. Never mind. Never mind. The fire is just, the fire can't reach him. However, he is completely impaled on a tree. Six now, six casualties. They're slowly falling. Will they not learn that they're bullets of no effect and they're only just giving Godzilla ammunition to fire back? Oh, no, it is actually taking some damage. I actually can't get up now. Oh, so left mouse button is my fire. And right mouse button, I'm guessing, is like fire the... Oh, no, they're both fire. They're both fire. I think it's two, just a passive. Two might just be a passive, like, spray back the bullets. Okay, what's C? Oh, that's what he looks like inside. There's literally nothing I can do. I can't even, like, control a move him or anything. But eventually, they would be able to kill him if they had the numbers. However, the longer this goes... I don't think they can do it now. I don't think they can do it.  So we'll end up there. How about this one? Okay, and to take him on, we've got this. What is this? This is the modern. Modern crossbowmen, a shotgun, a stealth. But I like actually this SCP, which is loads of weird monsters. Nightmare. Build a bear. That's it. Can all these build a bear? Like, what do these even look like? What do the build a bears even look like? Oh, so pretty. But what can bears do against Godzilla? Let's find out. Oh, are they falling? I think... Have they died? Oh, oh, they're getting close. Why do they sound like ducks? Oh, the stump! Oh, this Godzilla's... Oh, he's on the proper offensive. The build a bears... Oh, god, the fire. Some of them are dead. Some of them are dead. Some of them are like going rage mode or something like that. Or maybe it's an effect. Oh, god, he's... Oh, he's almost... He was in a worry there. He was about to be consumed by bears. If you come down to the woods today, you'll be eaten by bears! Oh, god. Oh, they've got a curse on them. They don't know which way they're going. Oh, that's what he does. He makes them a bit crazy. Oh, the bears, they're just falling. Godzilla, are you... Oh, are you okay? Have you lost any health? No, he hasn't lost any health. Oh, that's beautiful. Okay, so he definitely won that one. How about we get their SWAT team in? Oh, we've got a heavy breacher. There you... Oh, look at those guys. Followed by some MP5Ks. Let's... Oh, let's get some snipers in the back there. We've got to take out Godzilla. But we'll have a medic just to keep in there. Some shields at the front to bat Godzilla back. They're the most... Oh, they're...  They're beautiful. This is Rainbow Six Siege. Uh... Oh, a scar. Is that like... Well, there you go. That's what that is. Okay, so let's see how these guys look.  That's nice. Okay, so already the bullets coming in. Oh, that's a grenade launcher. Oh, and the snipers have just fallen on the floor. Probably been knocked back by their own missiles. Okay, let's speed it up. Can they do anything? Oh my god. Oh, they've... They've... Oh, there's fire. Oh, there's fire. Okay, I mean... Oh, it's ice. Oh, it freezes them. Okay. Okay, they've got them down. They've got them on the floor. Is that what they want them? It's... Oh, no. Oh, no. You probably don't want... Where are the snipers? Oh, the snipers are hanging back. The caliber of their guns. They're pretty much going to kill themselves. There you go. Stay back. Stay back. Where's the medic? Where's the medic? Oh, god. Oh, it's not looking good for the snipers, guys. Guys, you might want to... You might want to think about a different tactic, because a lot of your men are dying. Oh, there he goes. I can't tell if he's being... It was a big attack. Oh, Godzilla's face planted.  He's been nailed in the ground. And here they come tactically surrounding them with the shields. Oh, there's a heal. The medic's still here. There's the medic. Where's the healing gun?  Well, is he alive? Oh, he is alive thanks to the medic. The medic is... I think this is the medic. He's got his little healing gun. There you go. There you go. Oh, god. He's just got sat on by Godzilla. Oh, medic down! There they've lost the medic. That's it. They're going to lose. I think they're going to lose. Now, the snipers are still... Still trying their best there. Definitely trying their best. But how much of a dent have they made into Godzilla? Oh, they've made a big dent. They've made a massive... The SWAT team has taken out Godzilla. Oh, god. Are they going to be frozen? It's the shield guys. It's the shield boys. They're the ones that have done it. I kind of want to try. I want to try and... Damn! Oh, they can fire quite fast. Oh, apparently I can't shoot anymore. So I'll let you take over. I shot once and that was enough. Oh, god. Godzilla is looking worse for where he's... He's red. If that means anything. He's been taking some pretty hefty shots there. You see the side swipe there? Round the shield. There's still a... Oh, look at that. That shield stands strong. Although I think that's it. I think they're done. It's the snipers now. And whatever this guy's doing. Oh, they did it! They actually took out Godzilla. Oh, amazing. I think it was just the snipers left. And whatever this guy was doing. We're gonna... I'm going to put Venom in here because Venom looks awesome. I'm also going to put Batman because why not? And this guy. Oh, he looks so sweet. Let's see if these guys are right. So Venom is the most expensive. Look at that. That looks so cool. I've also got Batman. Okay. And we've got the dragon slayer. Who ever made that? Oh, Venom is firing out his... What are these? Are these harpoons? I think they are harpoons. Oh, they all land in Godzilla. How many? How many other? Oh, okay. A few missed. Batman has yet to do anything. I like his... Oh, hold on. He might be... Is he gonna... Is he rearing up to do something? I think he is. Is he gonna throw it? He might do. Okay. Um... I think the dragon slayer is getting caught up in the... In Venom's whatever you want to call him. Ooh, look. You can see what he looks like normally. Ooh. He's got a little red nose. Oh, dragon slayer. Dragon slayer goes in. Oh my God. Has people made dragons in this? Oh, Batman. Look at him go. Look at Batman go. Oh, he's going crazy. Go on, Batman. You got this. I love this dragon slayer, dude. He could fly almost. Okay. Venom just keeps on throwing out the hooks. Oh, and his dragon back the dragon slayer. Nice one, dude. Well done. Oh, look at... Look at Batman. Oh, look at him go. Oh, Godzilla's flying. Godzilla's flying. Exploding. A whirlwind. The dragon slayer can apparently fling his axe so quickly he can make hurricanes. I think. Oh, there you go. Some ice. Ice breath from Godzilla. I suppose that's supposed to be the radioactive breath. Oh, there you go. Get him while he's down. Although he sniffed his butt and didn't do Batman any favors. Oh, there you go. Wait. Oh, he's launched him. Batman. Get out of there. Oh, that was... Oh, I don't know if this is looking good for Batman. Wait, where did Batman go? Oh, there he is. There. Look at him go. Look at him go. Where is he? Where is Godzilla? Oh, look at the spitty. I don't know what the dragon slayer is doing. Dragon Slayer doesn't seem to do... Oh, no, he's alive. He's alive. I thought he died. I thought he died. Venom, however, has not been hit at all. There's just kind of like... Batman. Batman's gone. It's up to the dragon slayer and up to Venom now. With those hooks, though, he might be able to right himself. What you're going to do? Oh, income hooks. Oh, he's hooked. Oh, no. He's hooked the dragon slayer. Oh, oh, that's good. I think Godzilla's on a very low health if he's doing this rage kind of ability. Don't know what the dragon slayer is doing. He's going for him, though. I do want to do one more and see just how many of the regular infantry... The U.S. infantry can take out. Oh, god. He just gets dragged so fast. Have you helped us here? Oh, he's on like full health. What is Godzilla on? Is this Godzilla? Okay. Okay. And I'm just assuming Venom is on full health, too. Yeah, Venom is on full health. Oh, let's get him in close. Right. Oh, that's one hit. That's one hit from Godzilla. And it didn't really do much. Yeah. Yeah. Oh, yeah. They've definitely defeated Godzilla at this point. Just get up close for some hits here. Oh, god.   Fire the hooks. And I'll let go of you. There you go. I got you in close. Got you attached to him. I don't have Godzilla out now. I got some... Yeah, Godzilla's lost that one. There we go. 200 regular U.S. soldiers. Vietnam soldiers. That's the one. Vietnam. Okay. So we've got a few at the front and then we've got all these guys at the back. So it's going to be... It's not like 200 firing right away. So let's see how these guys do. Oh, oh, there's the ice breath. Targeting ice. Oh, god. Okay. I'm going to have to slow this down, guys. There's just so much firepower coming in. Look at that. So that means you don't have to reload. You can just lay into Godzilla. Oh my god. It's even doing anything. Oh, there's the curse. And the front flip. Okay. Okay. There's a few deaths. Oh, that's the first squadron taken out. Now it's up to Godzilla to try and engage. Oh, the biggest platoon isn't here yet. They're about to engage. Oh, god. Just big nails. Military doing their best. Just pinning Godzilla to the floor. There's nothing he can do. I think it's the weight. I think the weight of the bullets are actually weighing them down. You can't do anything. If Godzilla was to attack the US military, we would absolutely... Well, as you can quite clearly see, we're going to be doing a little crying, baby. Oh, yeah. Oh, there you go. Oh, the one felt like an hour. They finally took him out. Is it this one? It is that one. Okay. Let's try this other Godzilla, because he might be heavier. So he might be able to like lift himself. Let's have a look. Made it. The first company is going for the second company now. But can he get through the... Oh, he looks like he's being weighed down. He's being weighed down, but he can still... Oh, he took out the other one. This Godzilla is posing much more of a threat, apparently. And he's going to get this one. Oh, he's got ice breath, too. Is he going to do his huge hit? Oh, God. Oh, God. Back away. Get away from him. They are absolutely plowing into him. However, they've taken more losses in the first few seconds than the other one did. Oh, there they all go. I think they're all dead. Oh, wow. Oh, they have just... Oh, wow. There is so... Okay. I'm going to slow down. There is so many of them firing at Godzilla. Look at this. Can they take him out? I don't even know. They're only hope. They're only hope is to get him before he gets closer. There it is. Oh, I don't know. There's not many bullets left to slow him down. And boy. Oh, God. All that was two hits. Oh, three hits. No, I don't think they're going to do it. Whatever reason this Godzilla has the power, he's got a tabby toes and fury. He's revving up. Oh, there you go. Take some more. Look at this. Fire. Oh, no. Look at them. Back away. Run away. Brave soldiers. They're attacking his tippy toes. Oh, God. There's not many left. Oh, there it is. The final hit and Godzilla wins. 200 is not... That Godzilla is way better. Okay. We're bringing in a small breacher team. I should have checked to see just how... How much damage they did to this Godzilla. How much damage was left? There they go.  Off they go. Help the US military to swat team. And then these breaches, I think that's grenade launchers, is it? It looks like they've got grenade launchers. Something like that. God, you guys, if you... Is this all like fan creations? This is absolutely crazy the amount of effort that you guys went to. This is so cool. Okay. Here we go. Here we go. Okay. Well, already the first company's taken out. Now this was the second one that got killed pretty quick. Oh, yes. They're always doing a high stand. Oh, and it's just from a wallop like guy. Okay. Oh, we got some frozen peeps. Income the glocks. They get it in close for whatever reason. And the breaches, have they even fired yet? Have the breaches even... I want to see if they do fire. He's like, hello. Hello.  Go on, you guys need a fire. You need a fire. But don't... Oh, look, look there. There you go. The glocks getting stuck into the thick of it there.  Yeah, there they go. Just like as if they were made of nothing. Oh, he's shooting them up the bum bum. Have you guys shooting yet? Please tell me... Look. Oh, look at the surprise. Oh, there it is. There. Oh, right for the... Oh, he's missed him. I think he might have missed him. Oh, he did. Yes, he completely missed him after all that. Oh, please tell me... Oh, there's another one. There's another one. Is that gonna... That's gonna hit. That's gonna hit. Oh, there you go. It's the huge explosions. There's a few of them landing now. Oh, there's another little one. They're gonna hit the floor. Boom. Okay, let's speed this up. Can they help? Oh, God. Oh, God, where's the mass of the army? Okay, there isn't much of an army left. There's a lot of SWAT team, though. But because they... For whatever reason, all the ice breath... Oh, it didn't affect them, though. Because the SWAT team like to get close, unfortunately, they have just got flattened. Is that... Is he still alive? Are the Renys still alive? Okay, I don't even know about the breeches. I don't know if the breeches are gonna last much longer. Yep, the breeches are gone as well. Oh, no, there's a few. There's a few. Let... Oh, he shoots him in the toe. And this guy's doing the amazing tactic of shooting out his arse. Oh, did he shot that way? Did she find him? No! He's got his gun glitched. No, he's shooting every which way, but the way he needs to be. He might still be alive, though. He's in the dead bodies. Nope, never mind. He's dead. Yep, he's dead. It's just up to the US military. However, when he's doing his little handstands like that, there's no stopping Godzilla as he goes on a rampage. And... Oh, they didn't actually do anything to him. There's a guy on the... Can you see him? He's like staring straight up at me. There he is. This guy's gun stuck underneath some bodies. This guy has his gun behind his back. Don't know what he... This guy, bless him. He can't do anything. He's just stuck there. And he's also got his arm a bit broken. How will this... Oh, he's shooting. He is shooting. Ah, and he got stepped on. Very close. Well, there you have it guys. What a battle, Godzilla. Well, some Godzilla's are very good and some are absolutely rubbish. Well, that was loads of fun. If you guys have any suggestions of battles that you guys would like to see, leave them in the comments below or even like a kind of unit that we could make or something like that. But until next time, I'll see you later. Bye-bye.