Welcome back, in today's lecture we will be looking at some experimental design strategies. The references for this lecture are the book written by Mayors Montgomery Anderson Cook Response Surface Methodology, Process and Product Optimization Using Designed Experiments 3rd edition, John Wiley and Sons, New York 2009. You may also want to refer to Montgomery Design and Analysis of Experiments 7th edition, John Wiley and Sons, New York. The importance of central composite design will be stressed upon in this lecture. It is a very popular second order design used widely in both research and in industry. Three levels are employed and there are some features like rotatability and good prediction variance properties. The central composite design enables the development of second order model and incorporates curvature. What is meant by a second order model? So far we have been looking at the main factors and the interaction between the factors. When you want to expand in the model space, the response may show curvature and in a multi-dimensional coordinate system, you will have the response surface in the form of a 3-dimensional surface and to describe such kind of response surfaces, we need higher order terms in the model equation. Second order terms like x1 squared, x2 squared, usually we do not go for models higher than second order unless it is absolutely essential. So let us see how we may develop the second order model using the central composite design approach. This is also used in response surface methodology designs when searching for the optimum. So why do we emphasize so much on second order models? The experimental design space, the response surface is no longer planar but may be marked by peaks and or valleys. Second order models are required to estimate this response and enable the identification of optimum solution if any. Second order models are of the form y is equal to beta not plus i equals 1 to k beta i xi sigma i sigma j beta i j xi xj plus sigma i equals 1 to k beta i i xi squared and so on. So this is the main factors and this is the interaction, binary interaction between two factors taken at a time and then you have the second order terms x1 squared x2 squared and so on. This is of course the error term. So when you want to fit a model, you fit one intercept and k main factors kc2 binary interactions and k second order terms. So that would be 1 plus 2 k plus k into k minus 1 by 2 parameters. If k is equal to 2, you will have 1 plus 4 5 and then 2 by 2 is 1 that would be 6 parameters totally you have to estimate. So those would be beta not, beta 1, beta 2 that makes it 3 and then one interaction term x1 x2 that makes it 4 and then x1 squared and x2 squared coefficients that makes it 6. So when we go for central composite designs, we are no longer able to retain the orthogonal property and we shift our attention from the orthogonal property advantages to the suitable low values of the scaled prediction variance. So when we develop a second order model, we are very worried about its prediction capability and we want to make the variance in the predicted response as low as possible. So what would be the suitable design strategy which will bring down the scaled prediction variance is our goal. What is the structure of the central composite design? So we add a central and 2 k axial or star points to a 2 factorial design. So let us take a simple case of a 2 factorial design. First we add center points. We have already seen the center points at the geometric center of the design space. They were used to not only get an idea about the experimental error but also regarding the significance of the curvature in the response. Then on top of these center points, we also add points along the axis. For a 2 factorial design, we have 2 axis, the x and y axis or x1 and x2 axis and you put certain points at select locations on the axis. On each axis, you put one pair of points symmetrically. So when each axis contains one pair of points for a 2-factor design involving 2-axis x1 and x2, we will have 4 axial points totally or 2 pairs of axial points. So the design compresses of 2 power k factorial points, the ones which are located at –1 plus 1 and so on, NC center points and 2k axial points. So the center points enable the identification of curvature in the system. If curvature evidence is irrefutable from a t-test or a suitable test, the axial points enable the efficient identification of the pure quadratic terms. So each point in the central composite design has its own significance. So what is the central composite design when looking at it pictorially? You have a central composite design shown here for 2 factors. These are the points in the experimental space. As usual, the 2 power 2 factorial design has 4 corner points each located at –1 and plus 1. So this would be –1, 1, 1, 1, 1-1 and –1, –1. The usual factorial design and this is the center points. You can have more than one center point. And then what is unique about the central composite design from the regular factorial design is the presence of the axis or star points. You can see that each axis, this is the x1 axis is having 2 points located at 1.414 and –1.414. Similarly, you have 2 points located on the y-axis or x2 axis and they are also located at 0, 1.414 and 0, –1.414. So the factorial points belong to the orthogonal and variance optimal class of designs. And these enable the identification of the main effects. The factorial design we saw comprised of points which were located on the extremes of the design space for that particular design –1 and plus 1. And since the points were located at very far off positions, you can visualize that the x prime x inverse matrix would be, x prime x inverse matrix would be pretty small and that would reduce the variance of the predictions and hence it was termed as an variance optimal design. The factorial points are used to find the main effects and the interactions. You find the main effects and the interactions in exactly the same way as you did for the regular factorial design. The center points also enable the estimation of the pure error as they represent repeats. So you need at least 2 or more repeat points and rather than repeating the experiments at all the factorial points, you may want to do the repeats at the geometric center. By this way you can get an idea about the experimental error and also you can save time on doing the experiments at the corners of the factorial design. Of course that would lead to more number of runs but in some cases that may be inevitable for the simple reason that certain research requirements require the reporting of the experimental measurements averaged over triplicates. So the center points in other cases are helpful to find the experimental error but in addition to this they also have another utility. The central points also help in the detection of the second order or curvature effects but do not help in their explicit individual estimation. Center points also give us a hint on whether curvature effects are important or not and they tell that whether the curvature is significant but it does not help us to explicitly quantify the curvature. It only indicates whether curvature should be considered in the model or not. So in order to identify the curvature effects explicitly we require the axial points. Why should the axial points be located at minus root 2 or minus 1.414 and plus root 2 or plus 1.414? The answer to this would be given shortly. So the axial points contribute to the estimation of the individual pure quadratic effects significance and if the axial points were not present only the sum of the quadratic term significance could be gauged using the center points. And the axial points do not contribute to the estimation of the interaction effects. The central points and the axial points contribute to the flexibility of the central composite design. So by adding the new central points and axial points which are variance or enhancements to the regular factorial design we make the experimental design more flexible. And so where do we exactly locate the axial points is the next question. It depends upon the region of interest in the experimental space and the number of central points determine the distribution of the scaled prediction variance in the region of interest. So the location of the axial points depend on the region of interest in the experimental space and the number of central points determine the distribution of a scaled prediction variance in the region of interest. This is a very important statement because we want to have our model predict uniformly as much as possible in the entire design space. If the variability in the prediction is unmanageably high in our design space then the models utility is reduced. It is not enough if the model predicts well in the center of the region the center of the geometric design space, the geometric center of the design space but also as we move away from it as we approach the edges of the design space we want the variability in the predictions to be kept as low as minimum. Because we normally want to predict the response of the experiment at points further and further away from the geometric center. We may want to even extrapolate sometimes the experimental response beyond the factorial points. In such cases if the variance in the predictions keep increasing then the utility of the model is lost. So planning for this we should see what should be the appropriate design strategy and we should also consider parameters like number of center points that would reduce or minimize the scaled prediction variance. And an important thing to note here is when you are planning the design strategy you do not need the experimental data explicitly. You can find the scaled prediction variance even before you carry out the experiments and see whether for the experimental strategy you have adopted the scaled prediction variance is manageable and is acceptable. So what we do is we add central and 2k axial or star points to a 2 power k factorial design. Suppose you have a central composite design with 3 factors then you locate the axial points at plus or minus alpha 0, 0, 0 plus or minus alpha, 0 and 0, 0, plus or minus alpha. How to determine the alpha is an important question we will answer it shortly. So the design comprises of 2 power k regular factorial points, NC center points and 2k axial points. So let us look at the MINITAB output for a central composite design involving 3 factors. You can see the 3 factors are represented by x1, x2, x3 here and then the first 8 experiments are the regular factorial design points. You can see minus 1, minus 1, minus 1, 1, minus 1, minus 1, so on. Then the 8th one is 1, 1, 1. Then you have these axial points minus alpha 0, 0, plus alpha 0, 0, minus alpha 0, 0, plus alpha 0, 0, 0, minus alpha 0, 0, 0, plus alpha, where alpha is 1.68179. What is a special magic number? We have to see shortly. And then you have as many as 6 repeated points at the geometric center of the design. So let us estimate the model coefficients which are in associated with data that are in coded units. We have to estimate the model coefficients for the experimental data that are in coded units. So we have to estimate the intercept main factors, binary interactions and quadratic effects only. So in addition to the intercept beta 0, we need to estimate the main factors coefficients. The coefficients associated with x1, x2 and x3. Then we have to identify the binary coefficients associated with x1, x2, x1, x3, x2, x3. And then we also have to find the coefficients associated with x1 squared, x2 squared and x3 squared. So the total number of design points is 20 for a 3 factor design with 6 repeats. So you can see that there are 20 independent experimental settings. That is not correct. It is not 20 independent experimental settings. You have 14 independent experimental settings and then even though you have 6 repeats that will constitute only one independent experimental setting. So that would mean 14 plus 1, 15 independent experimental settings are there. So you have total number of design points as 20. The degrees of freedom for model is 19 excluding the intercept and total number of regression coefficients estimated each with the degree of freedom is 3 plus 3 plus 3 that is equal to 9. The remaining degrees of freedom is 10. So the number of center points is 6. Lack of degrees of freedom for pure error is 6 minus 1 which is equal to 5. So lack of it degrees of freedom is equal to 5. So this is a very interesting calculation for the degrees of freedom for lack of fit. So even though we have fitted 1, 4, 4 plus 3, 7, 7 plus 3, 10 parameters the model possibilities are not exhausted. So there is still some scope for expanding the model and adding more coefficients. What can be the number of coefficients that can be further added to the model has to be first estimated. So if you look at the model you are having 20 experimental settings but out of that you are having 14 central composite design points, the factorial points and the axial points that would be 8 plus 6 because you have for 3 factors, 2 factorial design you are having 8 factorial points and for 3 axis you are having 6 axial points. So that makes it 8 plus 6, 14 and then you are having 6 center points. But the center points are repeats only that means that would constitute only one independent data setting. So in total we have something like 14 plus 1 which is 15 independent experimental settings and if we have already estimated 10 parameters and there are 15 independent experimental settings we can quickly say that we can additionally estimate 5 more parameters to the model that may not be really necessary but it gives us the option of adding another 5 parameters to the model because of process knowledge and prior experience there may be some unusual terms like x1, x2 squared or x2 squared, x3 these kind of terms may have to be added to the model because of the peculiarities of the process and then you may need to identify the coefficients associated with those variable combinations. Hence we have 5 more degrees of freedom for fitting additional model parameters and this is nothing but the lack of fit degrees of freedom. Sometimes even with 10 parameters there may be scope for model development and so the analysis of variance table would indicate that the lack of fit degrees of freedom is significant and hence we may have to consider adding of more terms to the model. So the lack of fit degrees of freedom is 5 as we discussed just now. So we can fit additionally 5 more regression coefficients after expanding the model appropriately without the risk of aliasing and now the distribution of experimental design points has a profound influence on the scaled prediction variance okay. So recall that the model developed is expected to fit the experimental data properly in the design space the SPV is a measure of how well the data is fitted by the model. So these concepts are very interesting for the simple reason that these are over and above what we usually are aware of in experimental design. There are numerous instances of siting of central composite designs in research papers and they get the justification that they are being mainly meant for considering the second order terms in the model. But many of these papers do not discuss further as to why the central composite design was chosen among different options available and how good is the prediction capability of the model developed using the central composite design. So these are probably beyond the scope of the particular research article but it is very important for us as data analysts and researchers to assess the quality of the developed model. How good the model is and it is also good to be informed about the limitations of the model in the design space. One important indicator of the limitation of the model in the experimental design space is the scaled prediction variance and that is the reason why we are harping on it for so many slides. In some cases the model may get frayed at the edges so that the scaled prediction variance may be very high at the boundaries. Even though the scaled prediction variance may look manageable in the interior portion of the experimental design space as we go further towards the extremes or the boundaries of the experimental design space the scaled prediction variance may shoot up very alarmingly and then the model is not very good at the edges of the design space. In certain cases there may be problems even at the center of the experimental design space the scaled prediction variance may be high at the center of the design space as well and hence to keep it down or control it we need to increase the number of center points in certain designs. So the scaled prediction variance if you recollect is given by spv of x is equal to n which is the size of the experimental run. The total number of runs in the experiment is n variance of y hat x divided by sigma squared and by doing so we are making the prediction variance independent of sigma squared which we do not know anyway. So we are also getting rid of sigma squared and we are also scaling the design for the size. Certain designs which are having large number of observations may artificially bring down the prediction variance because of the large size of the runs to account for that or to normalize for this effect we are multiplying by the term n. As an example if an experiment is performed with large number of repeats let us say 25 experiments have been performed with large number of repeats the prediction variance in such a case would be lower than another experiment where the number of runs was only restricted to 20. So to compensate or account for the size of the run we multiplied by n and so the prediction variance which is multiplied by n and then divided by sigma squared is termed as the scaled prediction variance and we have already seen how to determine the scaled prediction variance. We use x prime x inverse matrix and we also take the coordinate at which we want to estimate the scaled prediction variance and expand it to model space as was discussed in one of the previous lectures. We introduce at this point the moment matrix m which is defined as m is equal to x prime x by n. We saw that the variance covariance matrix is given by x prime x inverse sigma squared. So the x prime x inverse or the x prime x matrix is a very very important term because it captures the essence of your experimental design. Whatever design strategy you are implementing is present in the x prime x matrix and the inversion of that matrix help us not only to determine the coefficients of the model proposed but also the variability in the model coefficients and also the variability in the process response. So these are very significant in experimental design analysis, experimental data analysis and linear regression and in such a context the x prime x matrix assumes the center stage. So what is the moment matrix? It is x prime x divided by n. For a first order factorial design of order k with that means k parameters, the moment matrix is identified with an identity matrix of size k by k. Suppose you are having the order as k, the identity matrix would be having order of k by k. So let us now look at the second order models more closely. We define the moment matrix m as x prime x by n. For a first order factorial design of order p, the moment matrix is the identity matrix of size or dimensions p by p. We recollect that p is equal to k plus 1 where k is the number of regression coefficients beta hat 1, beta hat 2 and so on to beta hat k in addition to the intercept beta hat 0. So we are having p is equal to k plus 1 regression coefficients. So the x prime x matrix will also have dimensions of p by p and the moment matrix x prime x by n would be an identity matrix. The x prime x matrix for a first order factorial design would be a diagonal matrix and when you scale this diagonal matrix by the total number of runs, we get an identity matrix of dimension p by p. Let us demonstrate it here and we are having the x matrix which is given by 1, a, b, c, a, b, c, a, c the 3 binary interactions and then you have the ternary interaction a, b, c. So this is the x matrix and this is the column of ones and this is the column containing minus 1, 1, minus 1, 1, minus 1, minus 1, 1, 1 and so on. So we have the entire x matrix. To generate a, b, we just simply multiply the elements of the a and b column vectors similarly for b, c and a, c and so on and then you also have a, b, c which is 1 because it is minus 1 into minus 1 which is plus 1, 1 into 1 is 1 and so when we do m is equal to x prime x by n, we take the transpose of the x matrix and we then multiply with the x matrix again and then divide it by the number of settings n in this case is equal to 8, 1, 2, 3, 4, 5, 6, 7, 8. And when we do that the x prime x matrix would be diagonal matrix having 8, 8, 8 and all that but when you divide it by 8 then it becomes an identity matrix of dimension 8 by 8. So very interesting. So now let us define the different moments. You have the first moments represented by i and that is given by 1 by n sigma u is equal to 1 up to n xi u, u is the index for incrementing from 1 to n and i refers to the ith column or the ith model parameter. For example if you look at this particular column if we are talking about x1 u then we take this column corresponding to all ones in the first index and then u is running from 1 to n. So we go from x11, x12 so on to x1n. So the simple thing to note here is we are referring to the ith column and summing over the elements present in the ith column. So and that summation is carried over all the experimental settings in the data set and when you look at the second pure moments we have no adulteration of i with j and vice versa, i is present with the i and since it is present as a couple it is a second pure moment. And how do we find that? We take the square of the column elements we are choosing. Suppose we have chosen bracket i close bracket corresponding to the third column then it would be we will go to the third column in this x matrix and then we will do x31 squared, x32 squared so on to x3n squared in this matrix if i were to be 3. When you have second mixed moments the column vectors we are considering are different from each other. We are considering 2 column vectors and in these 2 column vectors i and j are different and so we multiply the individual corresponding elements in each column vector so that we get second mixed moment this i and j, i is not equal to j, i and j are different and hence it is called as mixed moment and that we do 1 by n sigma u is equal to 1 to n xi u into xj u. So we also have the third pure moment i, i and i which is since it is pure there is no additional or different term in the moment consideration it is i, i and i that means 1 by n sigma u is equal to 1 to n x cube i u. So for the 8th column vector we just take the cube of each element in that particular column vector and then sum it up over all the experimental settings. And similarly we can have all these other moments also third mixed moment the total order of the moment is 1 plus 1 plus 1 which is 3 and mixed moments means there can be elements which are different from one another you can have 2 same elements and then you can have a different element j. So this i's and j's obviously refer to the 8th column on the jth column in the moment matrix. So we have 1 by n sigma u is equal to 1 to n x squared i u and xj u okay a correction at this point these do not refer to elements in the moment matrix they are referring to the elements and column vectors in the x matrix okay we use the elements in the x matrix we use the column vectors in the x matrix to find the different moments. And if you look at the third mixed moment ij k it is 1 by n sigma u is equal to 1 to n x i u xj u xk u. Fourth pure moments are also possible where we take the fourth power of the elements in the 8th column vector and then submit over the n experimental settings. Fourth mixed moments would be the presence of different elements even i squared j squared is considered as a fourth mixed moment even though you are having 2 of a species or 2 of certain type together and that is let us say i is present together and jj is present together but since i and j are different we term it as a fourth order mixed moment and that would be given by 1 by n sigma u is equal to 1 to n x squared i u x squared j u. So you can also have ij k l where all the elements within the brackets are different so they obviously refer to different columns the ith column jth column kth column and lth column in the x matrix and all the i's j k and l are different from one another. Here we have the case of i squared j k the elements again are being different from each other and hence it is called as a mixed moment. So for a first order design a factorial design the first moment for any i is 0 so when you are looking at the x matrix if you look at any column we are not having columns with the contributions from x i squared like x 1 squared or x 2 squared. So all the elements in the x matrix for this case would be comprising of minus 1 plus 1 and so on except for the vector of 1's all other columns would be having minus 1 and plus 1 and when you total it up for each column it will become 0. For example if you look at the main effects x 1 or x 2 or x 3 each column would be having minus 1 and plus 1 in equal number and so when you take the sum it will go to 0 and that is what is meant by the first moment for any i is equal to 0 for the first order design and the second pure moment is unity. You may ask how it is possible the second pure moment is either i squared or j squared and so each of the minus 1 or plus 1 will uniformly become plus 1 only after squaring. So when you are having let us say 8 runs you are going to have the sum as 8 but please remember according to the definition of the second moment we are or for that matter any moment we are dividing by n. So that 8 will get cancelled with the 8 and hence you will get 1. So you can see the second pure moment is having 1 by n here sigma u is equal to 1 to n x i squared x squared i u and so all these things would be once and you are adding it up to n times means you will get n and n by n would be equal to 1. The second pure moment is unity that is what we saw just now because we are dividing all the squared elements with the size of the run and so they cancel out and the resulting answer is just 1. The first moment is analogous to the sample mean and the second moment is analogous to the sample variance and this mixed moment is analogous to the sample covariance. For a first order design the moments are up to order 2 and for a first order design the first and second mixed moments also called as odd moments at least one variable with odd power are 0. So the odd moments are 0 for a first order design. The second pure moment called as even moments are equal to 1 for the first order design. So now let us look at a saturated 2 power 3 factorial design x matrix. So you are having typical pure and mixed moments for a 2 power 3 design x matrix and so you see that the x matrix is having the usual column of once. It is having the column of A, B, C the main factors A, B, C, A, C the interactions A, B, C which is the ternary interaction and then you also have B into A, B, C squared. So all these things are created very easily. For example the column B, AB or B squared A is created by squaring B squared sorry by squaring B. So these values will all become 1 and then multiplying with A. So when you get B squared A 1 into – 1 will be – 1 and similarly B squared will be 1 and A would be 1 and so you are having – 1. Similarly you can find out C squared and B squared A would be a third order moment, third order mixed moment because A is also present here and when you look at the first order moments corresponding to the main factors when I am totaling all these values it becomes 0 and if I am even looking at B squared AB it is also equal to 0 because it is having equal number of –'s and plus here but when I do C squared it becomes 1 throughout the column and when I add it up 1, 2, 3, 4, 5, 6, 7, 8 it becomes 8 and the size of the run is also equal to 8. 8 by 8 will be equal to 1 and that is why you have 1 here. For a central composite design it can be shown that the moments are carried over up to order 4 and let us take the design matrix for the central composite design and use it to investigate the values of the different moments. So for the central composite design we can look at the values taken by different moments. All odd moments through order 4 that means orders 1, 2 and 3 are also included. It says that is why through order 4 that is the moments that contain at least one odd power like I or I cube or I squared j. So there is at least one odd power corresponding to the power of j and then I j k and this is all completely odd moments because I is different from j and j is different from k and I cube j and I squared j k are 0 for I is not equal to j not equal to k. So tables are shown in the next slide as examples. So in this design it may be easily visualized that only non-zero moments for k is equal to 3 or I squared, I squared, j squared or I cube to the power of 4 for all I not equal to j. So we will continue on this topic after taking a break.


What's the word y'all? It might be time for Rob Palinke to wake up. Have you been around the channel for some time? You see my new strategy where I start off the video with a super strong statement to get new people to click on it and new people to subscribe. I just did it again to you. Subscribe if you're new around here. The Lakers are curling the five game win streak after winning Sacramento. And no matter what you think, no matter what I think, no matter what nobody think about the officiating, was it a foul? Was it a foul? It doesn't matter. Because the last buzzer ring and Lakers have more points and they're on a five game streak. Even if the last two men in the report come out and say he was not fouled, there's nothing we can do about it. You know what I'm saying? So we just got to accept the fact that this is won by the LA Lakers. And I'm being honest with you, I thought there was no chance they were gonna keep their head above water without Anthony Davis. Once he went down after that legendary streak he was going through, I thought the season was over. I mean, you might have assumed that the season was over beforehand, considering the expectations for LeBron, James, the team, whatever. It felt like they were gonna be a team on the outside of Lickenian. And I'm recording this video. They're the five game win streak. They're 19 and 21. And they're still currently on the outside of Lickenian because the Tim Wolves are also winning games. Shout out to them. So they're in the midst of playing some of their best team basketball, five game streak. The longest active streak of basketball tied with the Memphis Grizzlies and they're still not even in the play-in. But hey, I'm just saying there's a blueprint. There are things happening that you could be excited about as we continue throughout this season. And with them having these crumbs, these little pieces, them staying afloat without Anthony Davis and eventually them getting Anthony Davis back some day. They said he was progressing well so I don't know exactly what that means but he will come back eventually. The promise that Rob Polinka made this season, going into this season, he might have to actually try to fulfill those. So he might have lied to Bron. Polinka made his feelings clear that he wants James to retire as a Laker and promised to provide. Listen to this. He promised to provide him with every resource possible to compete for a championship each year. He's with the organization. And again, as I mentioned earlier, there's been a lot of reports about their hesitancy to throw the 2027 pick in the 2029 pick in any trades because they feel like this season might be somewhat lost. They felt like this was one of those seasons where we come back next year because we're gonna have another spot to sign another person to be alongside Anthony Davis and Bron and then we run it back. But the way the Lakers are playing now and the way LeBron James is talking in these post-game interviews, I don't wanna just play basketball for no reason. I wanna continue to compete. There might be pressure now to potentially throw in a 27 or 29 to get a player, the players, to keep this streak alive so they can feel more excited about making the playoffs, first of all, and making some noise once they're in there. And I think the most exciting thing if I'm a Lakers fan is seeing the other step up. I mean, we can make a 70-hour documentary about how great LeBron has been in this season with him being 38 years old at this point. Even tonight, another 37-point game clutch basket down the stretch.  But we kinda expect that from Bron, even though he's still old. We don't expect the others to be performing well and in the midst of the streak, a lot of the players have been reliable. Dennis Schroeder is playing like the Dennis Schroeder that almost got well as the 80 a.m.s, 90 a.m.s, even though him and his agent say that was never on the table. He's playing like the player that we know he could be but he hasn't been in the last couple of seasons. Patrick Beverly is playing like the player. This is crazy. We give him Patrick Beverly, so look, it's a Pat Bev. He's playing like the player we've seen him play over the last couple of seasons. This season came to this, he couldn't hit a shot. But in his last 10 games, he's shooting almost 44% from the three-point line. That's a dub. And I gots to talk about that man in the middle because you lose the production that is Anthony Davis and you look at that roster and say, how the hell do we replace that? His name is Thomas Bryan. And Thomas Bryan has always been an up-and-down player but pre, was it Achilles, ACL, whatever, he had a major injury obviously. He was looking pretty good. And now, I mean tonight, he was a lot of the cases, the best player on the court outside of Bryan. And I guess outside of fourth-core Fox. And I guess outside of what DeMonte's about. Regardless, they're getting high-quality production from Thomas Bryan as well. And listen, Russ Ceasen has been as up-and-down as anybody. When he started off the year as a starter, he was terrible. And then they put him onto the bench. He was in sixth man in the year. I think he still might be the front runner for sixth-man of the year. They put him on the bench for a month. He was to guarantee that.  But in the last couple games, at least during his streak, he's been playing some of his best basketball as a Laker. So you're getting all of that happening at the same time. And you're like, Rob, okay, we doing our part. Now, what can you do to help us elevate even further? Because outside of that, you still have like, want to scorn on Anderson, get him in it. And I know once Anthony Davis comes back, you're probably not gonna get a lot of those. But still, he's getting minutes. And I got a lot of love for Juan T, man. I'm super happy that he was able to get his championship and to get another contract post that. But like, as of right now, when I'm watching him play, I'm like, get those minutes to win you, Gabriel. That's the point we at right now. And I felt to mention Kendrick Nunn was an amazing tonight, but the previous night, he was really good to get Selena Hawks. So a lot of the role players are now stepping up to the point you want them to step up. The only thing is I would hope that for LeBron's sake, because I do want to watch Bron and playoff atmosphere again. There's not a lot of things about it as an NBA fan throughout the, I came in in 2003, 2004. So basically for the entirety of my lifetime, I've seen LeBron James competing playoff series at least until the last couple of seasons. I want to see it again. But the question is, and this is a conversation me and the guys had on the podcast here, our podcast here, the Studiwire podcast, if you're interested, what is out there? Cause right now it's not necessarily a buyer's market. How many teams have pieces that are selling right now that you can be interested in, that you can use 27 and or 29 to increase your odds? Cause I've been reading a lot of articles about potential deals and none of them make me be like, yes, that's the one. I am actually more interested in the traits that it's like two separate deals. One of them throw 27 and one of them throw 29 for two different players or a combination of three players or whatever it may be. Cause again, outside of, who's selling right now? If I look around the league, you can make an argument that the watch's wizard should be selling. Again, they probably never will. You can make an argument that the Toronto Raptors might end up selling, but Masai Ujiri doesn't take me as a seller. He always takes me as a move, a piece here and there and then we retool. He doesn't seem like a guy that's gonna like really, really sell. Hornets may have got some stuff that you received, but like this is not a buyer's market. The Pistons are always going to be the team that everybody's talking about because they have Bojan Bogdanovich and we know for sure that the production that we get from Bojan Bogdanovich is can be applicable, is that the word? Can be applied to every single other 29 teams. It don't matter if you're the Houston Rockets or you don't got nobody to create for him or if you got the best passer of all time on your team, he is going to be a productive and really good NBA player. And of course his name is tied to a team like the Lakers but like when this deadline hit, will the Lakers be able to put together the best packets for a guy like Bojan? But the thing that makes me the most excited about what the Lakers are doing right now is that the offense is good. If you remember they were the worst three point shooting team ever through the first couple of weeks of the NBA season. And during the last two weeks, they're a top 10 offense. The defense struggling, but they lost Anthony Davis who was a DPOY candidate before his injury. And I know everything is not sustainable. I don't expect Dennis Shroder to go out there and start averaging 20 points per game regularly like putting that up every night. But again, you're starting to see the corner be turned from them on the roster. And again, I said, I could talk about LeBron James and his greatness all day.  So ridiculous that Skip Bayless who had been a hater of Bron for 20 seasons. It's like, I like him now.  I'm so happy that he's doing at least decent. And I mentioned that they're on the outside looking in still even with this five game winning streak. But you still do have teams like Utah Jazz who of course come down to earth and lost another one in Chicago today. You got the Portland Trailblazers who sit at 500 after a really good start. They're struggling, especially on the defensive side of the ball, the Phoenix Suns on a five game lose. So there are a lot of teams that are teetting around the edge and with another win from the Lakers and maybe a loss from one of these other teams I'm talking about, they're right back in the mix of things. They're right back in the mix of things. Things are so crunched up in both conferences basically that one win for the Lakers from have them going from the 12 seat all the way up to being out of the play in but one of the guaranteed six, that's how close it is. So if I'm Rob Polinka, I got to look at that and say if there's a chance we get in, there's a chance that we can win considering we have two players that are still playing at a superstar level when they're healthy and LeBron, James and Anthony Davis that has to be the things they're talking about. And I know they keep thinking about the future, the future, the future. We don't want to throw 27, we don't want to throw 29 because at that point we don't know where we're going to be as an organization. About 20, 27, LeBron, James is 42, something year three, he's 48 plus years old, Anthony Davis is mid 30 sweet. That pick might be number two. Think it might be something you're willing to trade if I'm Rob Polinka because we want to, like you promised to LeBron at the beginning of the season we want to maximize the opportunity for Bron to win. And right now what you've done to maximize they're still at 12th even though they're playing good basketball. And not even just good basketball doing this five game stress, they started off two and 10 and since then they're 17 and 11. 17 and 11 at 60% win rate, a 60% win rate would have them as the foresee behind the pelicans or tied with the pelicans. Now again, you can't just say, hey, we throwing away the first 12 games of the season but that's how good they have been recently that we can say that we're trending upward. And because of that we need to do, we got to do to get them in a position to win. Probably the worst thing that happened to them though or it's happening actively with them is the fact that the Bulls are seven and three in their last 10. I'm not there yet. I'm not there yet ladies and gentlemen. I think I made an apology tweet, like a pseudo apology tweet. I'm not there to check because I still believe that even though we're playing good basketball as of late other than us giving up 71 points to Donovan Mitchell we've been playing good basketball of late but I still think there is a hard ceiling on the steam but in the last couple of weeks, again other than that 71 we gave up, I've been enjoying the Bulls and a lot of people believe that if the Bulls are still struggling that DeMar DeRose is going to LA he been trying to get to LA for seven years now it feels like with something that they could have made happen. And now if the Bulls are winning they might say hey, instead of us being sellers or retoolers we might use that Portland Trailblazer picking by right now. So the Bulls winning right now is probably not the best for them but it is a long season and it is still a long time a little over a month until the trade that line and a lot of things can happen in a month's time. Again, if they keep this up. I mean the next couple of games against Denver that's the tough when Denver's playing great basketball and they don't lose at home and they're playing at the ball arena. They go against Dallas, Philly, dang. They go against Houston, Sacramento again. They have the fourth toughest schedule left in basketball. So it's not about to get easier. It's definitely not about to get easier but they got some good wins under their belt. Okay, so let me know what you think about Rapalinka, the LA Lakers and all the things above and I'll be in the comment section as I always am. Leave a like.


We know from Faraday's law of induction the strength of the voltage induced in a loop We know that it's proportional to the rate of change of magnetic flux through that loop And it's also proportional to the number of turns that you apply to that loop But we haven't yet discussed the direction does it go clockwise or anti-clockwise? And there are so many right-hand rules and letter magnetism It would be very confusing if we'd add yet another and there are so many different things You'd have to add into your mind to get this correct, but it turns out There's a really simple way of figuring out using the conservation of energy Using the conservation of energy when you're talking about induction is usually described as following lenses law It was developed by Heinrich Lenz in 1834 before the ideas of energy and conservation energy had really reached their final form Though these days we can see that they are one and the same. So Lenz's law states That you can't get something for nothing if I have a coil making a magnetic field And then I have another coil that's going to have a magnetic field induced in it Now if I'm putting current in that first coil It's going to make a magnetic field that reaches right down into the second coil And remember that this is often helped by having a bar of some ferromagnetic material running through the two of them However, the key point is when we change the current We're going to change the magnetic field when we change the magnetic field in the first coil We change the magnetic field in the second coil and that changes the flux flowing through it And that's going to induce some kind of current in the second coil And the question is which way should it go? So if we take an example that this current increases that current increases That's going to increase the strength of the magnetic field Which means it's going to increase the amount of magnetic flux going through the second coil Now if an increasing magnetic flux going through that coil caused a voltage that would increase the magnetic field even more Then you would have a runaway effect. We'd have more flux So we get more of that voltage and so we get more current so we get more Magnetic field and so we get more of that voltage and it will go on to infinity And so that obviously can't be the way it works And so the voltage that's induced has to make a current that resists that magnetic field change So to resist the flux going up we need some Magnetic field made that way and if I look at that and that wire I see that I need the current to be going out of the page here And that will make a magnetic field that goes up And so I'm going to need the current to be flowing in that direction around this loop And so we're going to have to have a potential going in that direction And so if the magnetic flux is increasing We know that the potential has to be going that way and if the magnetic flux is decreasing then it would go the other way


This video is going to provide an overview of object-based threshold classification techniques using eCognition. For this example, I have a 4-band 1-meter aerial image dataset. If I go into File and Modify Open Project in eCognition, you can see that I've assigned alias names to each one of my 4 image layers. We'll start over in the process tree while I'll right-click and choose a pen new to insert a new process. This process will just serve as a parent process for all my algorithms to fall underneath. This is handy because I can execute this single process and all other algorithms will subsequently execute as well. Object-based classification requires that we have image objects, so I'll insert a child process and use the multi-resolution segmentation algorithm to segment my pixels into objects. I'm to call my new level, that is the level that the image objects are stored on, as level 1. I'm then going to adjust my image layer weight settings to emphasize the near and for red band, given that I've got only a single near and for red band and three visible bands. Finally, I'll update my scale parameter to make my image objects a bit larger, and then adjust the shape and compactness settings to emphasize the shape a little bit more, and also to try to get more compact objects. To execute the multi-resolution segmentation algorithm, I simply right-click on it and choose execute. This runs the algorithm, grouping the pixels into objects. I can then toggle on and off the image objects, using the show hide outlines button. The attributes about image objects known as features within an e-cognition are displayed within the image object information window. Not all features are displayed by default, so by right-clicking and choosing select features to display, you can choose from the available list of features. Some of the most popular ones are under object features, layer values, and the mean values. So I'm going to add the mean values for my four image layer bands. Now I'll go down to geometry, extent, and double-click on area to add the area feature. This is the area of each image object in pixels. Now when I select an object, you'll notice that the corresponding feature information is displayed in the image object information window. The goal in this example is to classify vegetation. Clicking around on our image objects, we see that the mean band values are somewhat useful, but not perfect for separating out vegetation from non-vegetation features. So we're going to create a customized feature. A customized feature allows us to create indices, such as NDVI or the Normalize Difference Vegetation Index. We can simply give the feature a name, and then plug in the formula for NDVI. Now when we select an object, NDVI appears in the image object information window. It's clear that NDVI provides a very robust means by which to separate out vegetated from impervious surfaces. We can use the values within the image object information window to help us assist with classification, but we can also display the actual values by going over to feature view. Double-clicking on NDVI, for example, assigns a grayscale color ramp based on the NDVI values to each one of my objects. By going into the lower left-hand corner of the feature view window and selecting the checkbox, I can play around with the actual value ranges. Prior to doing this, you'll probably want to right-click on the feature and choose Update Range to get the full range of values. You can then use the arrows to select the lower and upper range of values. This isn't actually doing a classification, it's just previewing what would happen if you use these threshold values for classification. Splitting your view will allow you to display your data side-by-side with feature view. You can then also go in and choose side-by-side view. This will sync the two views, allowing simultaneous panning in both views. Now let's add another customized feature. This time we'll create one for visible brightness. This is simply going to be the mean of the visible bands, so the red, green, and blue bands added together divided by three. Just as with NDVI, once we've created the visible brightness customized feature, it appears in the image object information window whenever we select an image object. Now that we have a good idea about the features we can use for classification, let's right-click on our multi-resolution segmentation algorithm, choose a pen new, and insert a new algorithm. For classification, we'll use the assign class algorithm, which is a very simple classification algorithm for threshold-based classification. For the class filter, we'll check the box for unclassified, so they're only focusing on objects that are unclassified. Then we'll go to condition, and we'll click the ellipse button. The first condition we'll use is going to be based on NDVI. So under value one, we'll choose front feature, we'll go to our customized features, and select NDVI. And we're going to choose anything that has a value greater than zero. So our threshold condition says any objects that are unclassified, which is all of our image objects that have an NDVI value greater than zero. We're going to assign this to a new class we're calling veg. Because veg is a new class that we just created, the class description dialog pops up, and we can choose a color to represent that class. Once we right-click and execute this algorithm, any objects that meet the criteria, that is they have an NDVI greater than zero, will be assigned to the veg class. The view classification button will display the classification, and then we can choose to display the classification as either outlines or a solid fill. Overall, NDVI was very effective for helping us classify vegetated objects. But in this example, let's say we're unhappy with some of these small bright patches of bare soil. How could we separate them out? Well, we could use visible brightness. So let's go back into our sign class algorithm and add an additional condition. We'll use the visible brightness feature this time, and it looked like those patches of bare soil had values greater than 150. So we'll change our condition so that if the visible brightness is less than 150, they won't be assigned to the veg class. If I go ahead and execute the assigned class algorithm, I'm going to receive an error domain as empty. The reason for this error is that I've already classified objects whose NDVI was greater than zero. As a result, there are no image objects whose NDVI is both greater than zero and with a visible brightness less than 150 in the unclassified class. How do we resolve this? Well, one way is to go up to the top, that is my threshold classification demo parent process, and re-execute the entire rule set. Running the rule set from the top created brand new image objects, which were then classified based on my new rule, NDVI greater than zero and visible brightness less than 150, which does not classify those bare soil patches. Now let's look at an alternative approach in which I separate out the classification into separate steps, rather than using both conditional statements within a single assigned class algorithm. I'm going back into my assigned class algorithm and removing that visible brightness condition. I'm going to insert this later in a separate assigned class algorithm. Re-running the segmentation algorithm every time I change my threshold parameters for classification isn't very efficient. So I'm going to insert a new algorithm here, remove classification. This will go right after the segmentation algorithm and it simply clears the classification from the image objects. This is a very quick algorithm and it's an efficient algorithm to run if I want to play around with my classification parameters. Now we're back to our original rule with all objects with an NDVI greater than zero assigned to the veg class. Now I'm going to put in another algorithm assigned class here, and then I'm going to change the domain from unclassified to veg. I'm going to say if you're assigned to the veg class and you have a visible brightness greater than 150, you're going to be assigned to a new class called false veg. Now when we run this classification, any veg objects with visible brightness greater than 150 will be assigned to the false veg class. By adding another assigned class algorithm, we can reclassify these false veg objects back to the unclassified category, effectively removing them from the classification. The second approach requires more algorithms but allows us to clearly see what's happening with our classification as opposed to stacking multiple conditions into a single assigned class algorithm. This video introduced you to threshold-based classifications and e-cognition. We looked at two approaches. In the first, we stacked our threshold classifications into a single algorithm. In the second, we broke those classifications out into a series of steps which gave us visual confirmation as to what our classification was doing.


So in this lecture, we've talked a lot about complex numbers. Now let's kind of focus on square roots in general, because when I see these complex numbers with the number i, we talk about the square root of negative 1, but what about the square roots of other negative numbers? Because, for example, if we have some positive number capital N right here, how does one take the square root of negative N? Well, there's always two square roots. So let's first talk about the principal square root for which this, by this, we'll denote the square root of negative N right here. When you take the square root of a negative number, its principal square root we'll just call this i times the square root of N. Or if you want to, you can put the i in the back.  So generally speaking, I would put it in the front, but when you take the square root of negative N, this just means i times the square root of N. And since I recall is the square root of negative 1, the idea here is the square root of negative N, you can factor it as the square root of negative 1 and the square root of N giving us i square root of N. So in order for the square root to be multiplicative, even for negative numbers, we define it the way we do. And notice, of course, that when you square this number, you're gonna end up with an i squared times the square root of N squared, where i squared is negative 1, and then the square root of N, or as in the positive number, the square root of N is already a real number, you get N, and thus you end up with a negative N. So this number is a square root of negative N. It's the principal square root. There's always two square roots, so you're gonna get this one right here, but then if you take the negative square root, that's the other one right there. The principal one is what we refer to as the positive one. So as we're trying to calculate these square roots, we get things like the following. What is the square root of negative 1? Well, that would just be i, as we were referring to it earlier, nothing fancy there. But then if we come down to here like the square root of negative 4, well, this would mean i times the square root of 4, which the square root of 4 is 2, 2 times 2 is 4, and so the square root of negative 4 is what we refer to as 2i. Then if you look at, for example, the square root of negative 8, well, the first thing to do when you take the negative square root is always pull out an i, and then we have to calculate the square root of 8, which the square root of 8 itself is not a perfect square, but it is 4 times 2, 4 is a perfect square, and so we can take the square root of 4, which is 2, that does leave a square root of 2 behind, and I would probably write this as 2i times the square root of 2, and so that's how I like to write these things. I always, if there's any whole number coefficients or even decimal coefficients, put those in front. If there's an i, then put it between the coefficient and the radical, then anything else that can't be simplified with the radical without a numerical approximation, you'll leave that inside of the square root. So 2i square root of 2.


The future is growing so fast and we are everywhere. We are all over the world right now and we need to get bigger, grow more.


For the people that have been both on campus and for the people that are going to be off campus, what recommendations would you have in order to stay successful and happy and safe in the spring? I think that being on campus, I've learned that wearing your mask and just being socially distanced, six feet away from people is very helpful. Just doing that will keep COVID from spreading, even if it does come into the college. I also think that there were stalls in the bathroom and sinks and the showers which were assigned. I think sticking to that is very important. I know that it will be hard initially because we're not used to it but I feel like it's very important to just stick to the ones that you're assigned to because that will help a lot. Is that for contact tracing? I think yeah definitely adding on to that since in the spring semester people had the option of choosing who will be in their pod. Just trying to gather safely and adhering to the room limit for space because that's really important for the safety of everybody else who's living with you in the building on the same floor or everybody else you interact with. I'm not too sure if the same regulations will be in place as last fall but being on campus wasn't so bad. Kind of like the freedom of going off campus but within the 10 mile radius so just sticking to those rules. There's so much you can do within 10 miles. You can go to Holyoke Mall, you can go to Hampshire Mall, some parts of Amherst. There's really no need to break the rules and go beyond that because it's really for our safety. Just taking care of yourself and thinking, being safe for everybody else around you. I would also want to strongly recommend to people to not neglect your mental health. I think we are all very much focused on our physical health, have wearing your mask, washing your hands. Oh no like why did I just call off that kind of thing but it's also important to recognize that there are so many stressful things going on right now and like our mental health is still really important and it can be easy to put off to the side like it can be something that we deal with later and so I would really want to emphasize for students in the spring to take some time to take care of yourself. That is an important thing that should be put into your Google Calendar for every day or every week like it is something you should make time for but also Mount Holyoke still has counseling services. I think it's telehealth now which is amazing so it should be more accessible in that way. I think I like saw a lot of my friends and myself be really stressed out, really anxious, really sad and all of those negative emotions which are fun to feel but just making sure that you're also like prioritizing your own self and happiness is something that I would want to share with everyone just because it's easy to forget but yeah any other tips for successful remote learning or remote living or living on campus or living off campus anything? Haya, do you want to speak to like a time difference? Like how do you manage that? I mean on one hand I'd say just outside of the time difference I'd say try new things in this time because I think keeping like a fresh thing going in this very like monotone time period it's really nice like you feel sort of more a natural college student and a little less I'm just at home sitting at my desk all the time or in my bed all the time so I definitely think trying something new or like keep taking on new small projects is really it's a really good helpful thing that I took on and I think with the time difference again just like finding a schedule is remarkably annoying at times but I think just finding a schedule and also being really open like communicating with your professors like for example like my 5 a.m. class I told my professor who's also my thesis advisor but I told them that I was like it's 5 a.m. if I don't come like I really tried but like it's 5 a.m. and I think our professors are remarkably understanding at just like communicating with our students and also what Maya was saying focusing on mental health our professors are also like super open to like listening to concerns and making sure you take the breaks that you need so I think open communication with professors and students around you and then also just trying new things that's what I'd say that's amazing that's really good advice


Welcome back to theCUBE's continuous coverage of AWS re-invent 2021. I'm your host, Lisa Martin. We are running one of the industry's most important and largest hybrid tech events of the year with AWS and its ecosystem partners. We have two live sets, two remote sets and over a hundred guests on the program talking about the next decade in cloud innovation. I'm pleased to welcome John Baki, Chief Revenue Officer for MariaDB as my next guest. John, welcome to the program. Thanks for having me, Lisa. Talk to me a little bit about MariaDB. What makes it unique? What differentiates it? What gaps in the market does it address? Yeah, so we have a lot of passion here at MariaDB because we are at the end of the day with a backbone of services used by people every day all over the world. In fact, you might not realize that but you've probably hit a MariaDB database in the past 60 minutes, it's true. For example, if you're using a Samsung mobile phone we provide data services for the Samsung cloud. In fact, we've provided services for 5G networks all over the globe. And so at the end of the day we actually process trillions of transactions per day and I think that's really cool. Awesome, talk to me a little bit about the key problems. You mentioned Samsung, big fan, lots of Samsung devices in the house. Talk to me about some of the key problems that MariaDB SkySQL specifically solves for customers. What are they coming to you looking for them, looking for help for? Yeah, so we launched SkySQL and AWS earlier this year it's become wildly popular. And so SkySQL overcome some of the limitations of the cloud, 1.0, 2.0 era. In fact, we went from having zero customers to a slew of customers in just a short period of time. There are a ton of pent up demand from MariaDB and distributed SQL in particular and that's our expand product. And where Samsung uses expand use it to store data for the phones just like you might if you're an iPhone user on the iCloud they have the Samsung Cloud. So what we do is we provide expanding database services for them for a large user base across the globe. And they do that because they just can't get the scale out of some of the community databases that are offered by the major CSPs. And obviously that scale is critical. We've seen so much change in the last year and a half, two years with growth with acceleration to cloud acceleration of digital. Talk to me about what you've seen as the CRO of the company from a customer lens perspective. How has the last 20 months really affected acceleration adoption of Maria's technologies?  I grew up in the database business. In fact, I've been in the database business for 30 years and during the last 20 months during the pandemic and even before that really, you know companies like MariaDB strive to create a beautiful database and what it really is a beautiful database. It's a database that is flush with features that make applications work lightweight, portable and fast for the cloud, but still reliable and familiar so that application developers can use it for multiple workloads. So when it comes to, you know, the database industry we're still going after those characteristics and we provide world-class support. My team just rocks it for our customers and it's really important to them to get that. And at the end of the day, our costs while at the end of the day, we're the least expensive. So it really is a beautiful database and we're very proud of it. Beautiful databases. That's the least expensive. That sounds like music to probably a lot of companies ears. Talk to me about where it runs. Obviously AWS, you mentioned SkySQL was launched earlier this year on AWS. That's correct, yeah. Talk to me a little bit more about the capabilities there, the partnership that Maria and AWS have, what you bring to your customers. Yeah, so we have a great partnership with AWS. They provide the tremendous levels of support to help startups like MariaDB get going, the SaaS factory and everything about their go-to-market strategy to enable partners like us. But you know, we have a customer that is, well, it's their major trading application on the internet and they were an AWS customer, right? So they were an existing AWS customer but they were struggling with some of the community databases in AWS to find that scale and that elasticity that they were looking for on their platform. So enter MariaDB expand where we can scale a relational database out far and wide to make it possible for a customer like that who's really pushing the limits of what a database needs to do to remain an AWS customer. So in this particular case, we worked with AWS to land them on SkySQL and use expand the distributed database technology. So we went together and that's a really great story for everybody. Talk to me about some of the technical requirements as we've seen so much change in the last 20 months, as I said, but so much growth and scale and needs are changing so dynamically. What are some of the key technical requirements of a database to keep up with that? And how does MariaDB exhibit those? Yeah, that's a great question. So in distributed SQL in particular which I see is sort of the next wave of database particularly in the cloud, right? The database needs to leverage familiar application paradigms like relational and document databases do and connection protocols so that existing applications connect to those. But at the end, they have to be highly scalable for the cloud by design and highly available in the cloud by design. Expand just screens. It's really fast. It's really reliable and transactional integrity is inherent to the architecture. So our customers love it. And so really what's not to love about a database that does all of those things. What's not to love about a beautiful database, that speed, I mean, the speed is critical. I think one of the many things that we've learned in the last interesting couple of years of our lives is that real time is no longer a nice to have, right? Nobody wants less data slower. That ability to deliver real time data, real time analytics is critical for businesses in any company as we're seeing and you're probably seeing this as a Sierra every company becoming a software company. Or you too. Absolutely, in fact, yeah. So some of our biggest customers are major SaaS providers. So if you work for a business that is using ServiceNow, one of the largest SaaS companies in the world, you're using MariaDB every day. Billions and billions of transactions by ServiceNow on an hourly basis. And it's all in the cloud. So when we look at how we've evolved to this point, we're offering services to companies big and small. We're being tested by companies like ServiceNow in their infrastructure on a regular basis. What are some of the trends that you're seeing as we end 22 months or so in this pandemic? What are some of the market trends that you're seeing from a scalability perspective? And what is it that a distributed SQL database can deliver to help customers meet those trends? Well, certainly, I think when you look at what is a good database for the cloud and the future, it really does need to have the features that make applications work. So you had mentioned, analytical databases and transactional databases. One thing that is inherent to our strategy is the ability to use hybrid approach to transactional and analytical. Because a lot of applications are both at the end of the day and why use two different databases in order to get there, right? Our databases lightweight and fast, it's portable, it's reliable and familiar to the customer and versatile in the workload. So those are the things that are trending at the conclusion of sort of this year going into next year as we roll out more technology in subsequent versions, we'll just enhance those capabilities, make it possible for even more and more workloads to find their way into SkySQL. And talk about the adoption of cloud, the acceleration. We've been talking about that a lot in the last year and a half about the acceleration of digital transformation, the acceleration to cloud. I mean, it was so critical for so many businesses, especially if you think of the SaaS adoption, the collaboration tools. But what are some of the things that you're saying? How are you helping customers on that migration journey? Yeah, so migration is a key element there. I mean, there are customers leading older proprietary database technology. There are customers trying to enhance their cloud experience and go from the early cloud databases up to more modern architectures. And so migration is a constant activity that we work with our customers on. And so over the years, just as a matter of course, we've become better and better at getting database workloads from proprietary older databases, and even other open source databases on-term radioDB so that we can consume those workloads and get those in the cloud and make them work for customers better than they ever have before. And I'm curious as the Chief Revenue Officer, how your customer conversations have evolved in the last year or so. Where is cloud database security? Where are those things with respect to the level of conversations that you're having with customers? And is that conversation going up the stack? Yeah, so, I mean, security has always been a key cornerstone of the database industry. Really, when you think about it, databases, information assurance and confidentiality is a key tenant to information security and information assurance in general. So it's always an ever-present in the discussion. MariaDB is enhancing its list of compliance that we've gone through like SOC2. We're on the precipice of that. We've got ISO certifications and we have US Department of Defense install guides that are secure for MariaDB, all sorts of activity around that to make it possible for customers to standardize on MariaDB. We have customers that have taken out every ounce of their legacy relational database, the older incumbents and replace that with lighter weight MariaDB because we have the security qualifications. But we also meet their functional needs and their information assurance needs. And so that's what's made us really successful. In addition to compliance, you talked about this database being beautiful. You described what you meant by that, but also you said it's least expensive. So I'm wondering from a business outcome perspective, are customers all across the board reducing TCO, leveraging MariaDB? Absolutely. And in cases where we displace a proprietary database, the TCO can reduce by as much as 90%. And so it's very attractive to customers that are looking for the next wave. Not only do we take them to a lower cost, but we bring them to a more modern multi-cloud architecture. So AWS is our primary focus for certain in this conversation, but also just generally because they're such in a huge install base. But they do like the option of being able to say, hey, I can use this database on any cloud. It works everywhere. And the vendor that makes it is supporting it in all environments. So for us, that's a huge strong point in terms of what makes our business strong. And we're seeing so much, we're talking so much about hybrid, hybrid IT, hybrid cloud, hybrid work from anywhere environments. So I imagine MariaDB runs on, we obviously AWS Azure Google Cloud Platform so that customers that are in that multi-cloud world and those that will be can take advantage of the services. That's correct. That enters in our near-term pipeline, our roadmap for the cloud, but we're already present in GCP and we're available on other clouds as well. Excellent. So talk to me a little bit about what customers can do. Can they test out MariaDB? Can they test out SkySQL, expand? If so, where do they go? How do they get their hands on it? Right, so existing AWS customers, they can get to SkySQL on the AWS Marketplace. That's incredibly easy. AWS customers go to the Marketplace. They can find us by doing a search, but not to be outdone. There are customers that aren't on AWS and they can come to MariaDB.com. You can start SkySQL there and select AWS as the deployment cloud and try it for free. It's super cool. It's really easy. What's the, I'm just curious, what's the typical deployment time from doing that from the free trial POC to deployment? What do you normally see from a time span perspective? Yeah, customers are up and running with a live database in just a few minutes. Minutes, minutes up to 90% TCO, big business outcomes there that affects every business in every industry. John, we appreciate you coming on, talking to us about MariaDB, the solutions that you offer and how you're partnering with AWS and where folks can go to get started. Thank you. For John Bakke, I'm Lisa Martin. You're watching theCUBE's continuous coverage of AWS re-invent 2021. Stick around, more coverage coming up next.


Hello, and welcome to this presentation of the STM32 General Purpose I.O. interface. It covers the general purpose input and output interface and how it allows connectivity to the environment around the STM32-F7 microcontroller. The general purpose I.O. pins of STM32 products provide an interface with the external environment. This configurable interface is used by the MCU as well as other embedded peripherals to interface with both digital and analog signals. Application benefits include a wide range of supported I.O. supply voltages as well as the ability to externally wake up the MCU from low power modes. The general purpose I.O. ports provide bi-directional operation according to the input memory map. I.O. ports are directly connected to the AHB bus. This allows fast I.O. pin operations such as toggling and output with an independent configuration for each I.O. pin. They are shared across 11 ports named GPIOA to GPIOK, each of them hosting up to 16 I.O. pins. I.O. ports support atomic bit set and reset operations through the BSSRR and BRR registers. It allows I.O. toggling every two clock cycles. Most of the I.O. pins are 5 volt tolerant when supplied from VDD above 1.8 volts. Up to 10 I.O. pins are supplied by independent voltage supplies, VDD USB and VDD SDMMC. These supplies are independent of the VDD provided to the MCU. This functionality allows users to adapt logic levels of the MCU's I.O. pins to the levels required by external logic which may be supplied by different voltage domains without the need for external level shifters. General purpose I.O. pins can be configured for use in several operating modes. An I.O. pin can be configured in an input mode with floating input, input mode with an internal pull-up or pull-down resistor, or as an analog input. An I.O. pin could also be configured in an output mode with a push-pull output or an open-drain output with an internal pull-up or pull-down resistor. For each I.O. pin, the slew rate speed can be selected from four ranges to compromise between maximum speed and emissions from the I.O. switching and adjust the application's EMI performance. I.O. pins are also used by other embedded peripherals to interface with the external environment. Alternate function registers are used to select the configuration for the peripherals in this case. The configuration of the I.O. ports can be locked to increase robustness of the application. Once the configuration is locked by applying the correct write sequence to the lock register, the I.O. pin's configuration cannot be modified until the next reset. Several integrated peripherals, such as the use art, timers, SPI, and others, share the same I.O. pins in order to interface with the external environment. Peripherals are configured through an alternate function multiplexer, which ensures that only one peripheral is connected to an I.O. pin at a single time. Of course, this selection can be changed during run time of the application through the GPIOX AFRL and AFRH registers. During and after reset, the alternate functions are not active. Only debug pins remain in AF mode. JTAG SWD debug pins remaining in AF configuration mode are listed on this slide. When the external oscillator is switched off, pins related to this oscillator can be used as standard I.O. pins. This is the default state after device reset. When the external clock source is used instead of a crystal oscillator, only the related OSC in pin is used for the clock and the OSC out pin can be used as a standard I.O. pin.