So, are there any questions? I have not been starting my classes with are there any questions? Some of the students I think. Okay, there are no questions. What we will do today is we are going to look at, I am going to do a couple of demos. We will see how much we are able to get through in this class and depending on what we are able to do this time around, we will spill over to the next class. Fine? The two sets of demos that I promised was one using a symbolic manipulation package, right? It is called Maxima. This is a useful package.  I typically learn, relearn whatever I need, I do it and then since I do not use it for a long time I tend to forget but there is a reasonable logic to it. So, I will just show you how this package works. I will spend a few minutes showing you how this package works and then we will look at the modified equation, right? For first order linear one-dimensional wave equation, maybe even for heat equation and we will see what happens if you add terms to it, how to go about, how would you use this package and how would you get all those terms, right? The second demo if you have a time will be the actual solution of the wave equation using FTCS, FTFS and so on. There is behavior that we have predicted saying that how the code is going to behave, we will see whether it actually behaves that, right? What do we expect, what do we get? So, let me just start with Maxima. I am running a version of it called WX Maxima. This is a public domain software that came out of a Maxima that was a commercial package earlier. It uses the WX front end which is the reason why it is called WX Maxima. What I will do is I will start that off and for the sake of these demos, of course I will give it an orange background. Normally it would be a beige background. The menus and all that are not important, right? So, I think all of you are able to see this reasonably well. So, what can you do with this? What is the point here? You can essentially do some kind of manipulation, right? So, you can x star x, 2 star x plus 1, you can manipulate in many ways. So, you can for example, say I am just doing this so that you understand what goes. So, percent basically means the last result, right? And all the results as you can make out, they are numbered. I do not know how well it will come out on the video, but they are numbered.  These are trivial things. I mean this is all school algebra. It is not a big deal. So, you can also define, you can define functions where you normally define functions. And what we want here is you can differentiate. f with respect to x once, right? You can differentiate, you can integrate. There are ways you can, of course, there are other things that I do not, I am not going to talk about right now which you may talk about in the future demo. You can basically do algebraic manipulation and calculus, okay? That is as far as, I will restrict it to that as far as we are concerned. There are lots of other nifty things that you can do that you can find out for yourself, okay? You can do Taylor series expansion for instance. So, you can say Taylor x star x and you can expand with respect to x about a, how many terms do you want? Three terms. And it will give you Taylor series expansion for, right? Whatever it is function that you will give, which is the kind of thing now you see where I am going. I am talking about modified equation. Taylor series is very important for me. So, yeah, you can define functions. So, you can just basically say even if you define say, g of x. So, if I say, if I take a derivative of and I do not, I, so this is an indeterminate function, the sense that I have not defined the function, right? g of x. And I define g with respect, I differentiate g with respect to x once. It gives me dg dx, fine? Okay. So, you can, you may say what is the big deal. It is just notation, but it is the ability to manipulate notation, which is what algebra and calculus is all about, right? It is the ability to manipulate symbols. So, because this d by dx is a bit cumbersome, right? I mean for instance, for example, if I, the reason why I say, so if I say, if I differentiate, what shall I differentiate? I will differentiate h of x, y with respect to x once, right? So, it should be a partial derivative. Of course, I could differentiate that result one more time with respect to y. So, I can say, diff that result with respect to y once, right? And the notation clearly gets messy. So, there is a package that will make it simple. I need it because I am going to use a time, I use this, right? In my little code that I have written for, there is a package called pdiff, partial differentiation, which uses a much more compact notation. So, effectively something like h of x, y, if I go back to this derivative, it will write the derivative as h and this one indicates this differentiation with respect to x. You understand what I am saying? And the 0 indicates it is not differentiated with respect to y.  It makes life a lot easier. So, in a same fashion, if I were to use this, then it become, the second derivative becomes h11. It is more compact. Notation is more compact and that is the only reason why I am using that package, right? So, but as I said, the whole game is about notation. The whole game, the whole mathematics game is about notation and manipulating these symbols. So, yeah, so now we are set. So, what is it, what kind of, what do you want to do? You want to look at a modified equation. We can look at it for FTCS. I will show you a fragment of the code that I have written. It is not the cleanest maxima code, but I will show you a fragment of the code that I have written for FTCS modified equation, right? The code can actually be, you will see, you will understand what I am talking about. We will go through it. You try to get an, just try to get a feel for, right? I am not saying that oh, you have to go back and write maxima programs or something like that. That is not what I am saying. Just try to get a feel for it so that you understand the demos. That is all I want, okay? So, I go back here and in my directory maxima, I have, you can see various files that I have created called .mac files. And what I will do is I look at the FTCS.mac, okay? So, you can note, you notice I start off, I load the, I load the pdiff, right? I load pdiff. Then in line 2, I am setting up. So, I will do these maybe one by one and see what it does, right? So, you have, I have defined something called tu, which is the Taylor expansion for a function u of x, t or wave equation is in space and time u of x, t. I am asking for 4 terms in x and 4 terms in t, right? Okay? Up to the 4th derivative in x and 4th derivative in t. Basically, I want up to the 4th degree. I want to retain terms up to 4th degree. We have already seen that the 3rd degree, 2nd degree, 3rd degree, 4th degree, they have an effect, right? We have already seen that. So, let me, let me just get back here, stick that in here and see what it does. So, Taylor's, we will get the Taylor expansion, right? For this and it gives a mess. But it is not that bad. I mean, since you know Taylor's expansion and Taylor series expansion in two dimensions. So, I am expanding about the point AB. So, I have u of AB, time derivative times, right? t-b, the 2nd time derivative times t-b squared, 3rd time derivative times t-b cubed and so on, 4th time derivative times t-b to the 4th, okay? 1st spatial derivative times x, x-, where is that? 1st spatial derivative, or the x-a is outside. 1st spatial derivative, 2nd spatial derivative, 1st spatial derivative, 1st spatial derivative, 2nd time derivative, 3rd time derivative, 4th time derivative, 4 multiplied by x-a. And it is doing it in a systematic fashion. This is not how we would write it. This is not how it was introduced to you when you did Taylor series in multiple dimensions. But this is a program, right? So, it is doing it in a, you can see it is doing x-0 first and then x-1 derivative 1, derivative 2, derivative 3 in a systematic fashion, okay? So, as I said, so this is, yeah, this is the kind of thing that you could manipulate manually. You can do it manually, right? And I have actually done it manually. But it is also convenient to be able to do it in an automated fashion. And once you have confidence in that automation, you can at least sort of check out exploratory stuff you can do. So, I have defined something called TuA, which is a convenient term, which basically is the Taylor series expansion in 2D with x equals a substitute, you understand? Right? So, you are expanding only in time. Taylor series expansion only in time, x is substituted as a. So, as a consequence, you get something that is very small. Basically, get a Taylor series expansion in one variable, okay? I do not want to, as I say, I do not want to sort of vary out with this, but there is a TuB similarly and maybe I will just do TuB also. Just for fun, TuB and yes, x-1 is a, right? The same thing. You get expansion, you get an expansion of Taylor series expansion about the point, right? About the point AB, purely an x in this case, okay, in the x direction. Fine.  I have defined a whole bunch of higher order mixed derivatives here. I tell you why I have defined them. I propose to retain only terms up to the fourth derivative. I do not want to track higher derivative terms, okay? The second thing is you remember from the modified equation. What you basically did was you substituted, you took time derivatives of the modified equation and substituted for those temporal derivatives in the sense that you are going to end up, if you keep taking time derivatives of the modified equation, you are going to end up with mixed derivatives, right? Modified equation has terms that are in terms of x and t and if you differentiate it purely with respect to t, then you will get mixed derivatives, right? And I want to just set, I want my objective is to use the modified equation itself and derivatives of the modified equation to eliminate all higher derivative terms in time whether they are mixed or pure derivatives in time, so that I have only t spatial derivatives on the right hand side. The only temporal derivative I have is dou u dou t, that is what I want, that is the objective of the modified equation, okay, for this setup. So all the other derivatives I want to set them equal to 0, these are various powers that you get for mixed derivatives. So I am defining them so that at a later date I can say if this term occurs set it to 0, okay. That being done, now say all of this is just what I would call setup time, then I define 4 quantities, upq, so just read it the way it is written upq, I substitute upq, does that make sense? You want me to show you what upq is? Upq I will run that, so the point pq is at the point ab, right? Okay, so upq is basically uab, is that fine, fine, we are approximating the differential equation at the point ab, right? So upq is uab, okay.  Upq plus 1 is b plus delta t, fine? So this looks familiar, this looks like what we have been doing so far, sigma that is s is the speed of propagation in this case is l, l delta t by delta x, that is sigma, I will go to the next page. I do have a lot of messy stuff, let me see if I can get you something that you can see, yeah, that is the one you do to be, there you go.  That is ftcs and after this it is all a matter of substituting Taylor series, so that is what I am doing now, when I define this ftcs, I substitute Taylor series into ftcs.  I will just run the batch file and we will get the modified equation right at the end and then I will tell you what it is that we have done. So ftcs, I open it, it runs through my script and comes to the end. This needs a little explanation because I made some substitutions and all of that stuff. In fact, you can see that up here I have substituted for the fourth derivative, third derivative and second derivative. I have called them f4, f3, f2, that is an operational reason, it makes it more compact, so I have just called them f4, f3, f2. So the fourth derivative with respect to x is f4, the third derivative with respect to x is f3 and the second derivative is f2. Is that fine everyone? Okay. So here we have it. What is this? l dou u dou x, right? I hope you understand now that this is l dou u dou x. This term is l dou u dou x. This is dou u dou t. So what I have on the left hand side is my linear wave equation, dou u dou t plus l dou u dou x. What I have on the right hand side is the terms that I have carried so far. There is a fourth derivative term, there is a third derivative term, right? This is the fourth derivative term. This is the third derivative term and there is a second derivative term. There is a divided by 12, so you have to appropriately take care of that. Is that fine? Okay. So the cheat sheet that I used that day and wrote it out was basically from here, right? Okay. I just basically took it from here and wrote that out. Let us look at but see how did this come? How did we get here? So if I type, if I go to FTCS which I have defined right in the beginning, right? So this FTCS is basically a substitution from the various terms, right? In our discretization and from there I have created the whole series. I have solved for dou u dou t. I have solved for dou u dou t because I need dou u dou t, right? I have to get dou u dou t differentiated once. I get dou square u dou t square, substitute back. Differentiated one more time, get dou cube u dou t cube, substitute it back, right? And I systematically go through trying to eliminate and each time I get, what do I get? Each time I get a dou u dou t which does not have certain terms in it, okay?  That is ut. So I solve for ut from the previous equation and this is what I get, fine? Okay? I am going to skip a few steps here because it will get you, otherwise I will vary you out. You will become very tired, right? This is too much detail. This is a lot of detail, right? So this is u sub t. I just want to show you. So if I go to ut one which I generate in between, so from u sub t, my very first one, what does it have? It has a third spatial derivative with respect to x, first derivative with respect to x, fourth derivative with respect to t, third derivative with respect to t, second derivative with respect to t. When I come back, by the time I have come to ut one, something funny has happened. The second derivative with respect to t is gone. That is what I did. I eliminated it. The 0, 2 term is gone. If you stare at it long enough, you will see it, right? The 0, 2 term is gone. But I have been gifted in exchange for that 1, 1 term across derivative term. So now I have a headache. That is the reason why this is a, this is a pain. You have to be systematic. You have to be organized, right? I managed to get rid of the time derivative, the second time derivative but I have got a mixed derivative. So now I have to take the dou u dou t differentiated with respect to x and eliminate the mixed derivative.  So you have to go through this in a careful fashion. It is like solving a system of equations. You have to do the elimination process in a systematic fashion. I will show you one more. Sometimes it is not quite an improvement, right? So you could sit down. So you can see that I have the second derivative. I have a third derivative which is mixed. I have a, I am sorry, a fourth derivative which is mixed, a fourth derivative which is mixed the other way around, right? Xt cubed and so on. Then I have all these other terms that I had. So I just eliminated, what did I eliminate? I eliminated the 1, 1 derivative, right?  You set it equal to 0, right? Every time you differentiate once you will get a bunch of fifth derivative terms but you know the nature of those terms. There are only so many terms. You set them all systematically to 0, right? That is what I have done. And finally you got the modified equation, is that clear? Right? If you were to do it manually that is what you would do. You have to be very organized, right? In fact, I apologize for my last quiz but it was a very quiz because you have to, there are a lot of key strokes involved, right? So if you look at, if you look at the time that you have 3000 seconds and the number of key strokes that you had to do, you will see the key strokes per second was quite large. I mean that fraction, it was a fraction but it was quite large. That is the key. So it gives you an appreciation for, it is an anticipation of demos like this. It gives you an appreciation for why we use these kinds of things, okay? It is a headache. You cannot, we cannot sit down systematically do, right? A whole set of these calculations manually, right? It takes a lot of effort. It takes a lot of care, fine? Okay? So yeah, that is basically what we have. In fact, I was just thinking whether I should narrate experience of my own as a student. I was given an assignment to teach me the same lesson. Of course, you had it sort of in the quiz to do the determinant of a 7 by 7 matrix by hand. I was supposed to do it the long way. It was an assignment, 1 out of 15 assignments. I was supposed to do it the long way and show all calculations. 5040 calculations. I learnt a lesson. I cannot do 5040 calculations in a row without making mistakes. I did it once. I got a number. I was not sure. I did it a second time. I got a different number. So then we do the standard engineering test. Do it a third time. It has to match one of these. It did not. Not only it did not match one of these, the numbers were diverging, right? So at that point, I stopped saying that. So my assignment basically said, which apparently what the teacher was looking for. The conclusion I had was I cannot do 5040 calculations in a row without making a mistake, right? So there is, but you have to, but when we do symbolic manipulation, you can be a little more careful because there are patterns. These kinds of things we can do actually. There are patterns. But a package like this will get rid of the drudgery, right? But I would always cross check, right? I would always cross check. Is that fine? So we have FTCS. If you want to see that, I can show you a few more of these. So the penultimate. So you go to UT8. You see my God. Before it simplifies, it gets really bad, right? Here now I have made substitutions, differentiated, made substitutions. You try UT9, right? So there are a lot of these, but this is just near that. And finally, let me see if I have an MW. So that is a modified wave equation. I have already simplified it a little, right? And then I decided that I wanted to gather terms, collect them and put them in a little more easier fashion, which is why I created the way F2, F3, F4 so that it came out in a compact fashion, right? So that is the sequence basically.  And as I said, I am sure there are better ways to write this program than the way I have written it. Are there any questions? So this is a pretty straightforward demo. I mean, it is not, there is nothing spectacular about it. I can try, if you want me to try another, if you want me to try something else, we can look at FTFS okay. And FTFS gives you, because I have shown you these terms. So this is the second derivative term here, right? Second derivative term. Second derivative term is multiplied by sigma-1, right? A sigma-1 in our notation. I used L here because when I was doing this derivation, I was talking, I was using lambda, dou U dou t plus lambda dou U dou x. So you can see that the terms, but these in this case, I am using the modified equation to eliminate the higher derivative, higher order temporal derivatives, okay. So you could also do it using the wave equation. So that is something that you can try out, right? So that is the third derivative term. So you know that any scheme that does this is going to be dispersive. It is going to be unstable because there is a negative sign in front of the second derivative term. FTFS is unstable. It is going to be dispersive because it has a third derivative term, right? The existence of the third derivative tells you it is dispersive. And the existence of the fourth derivative with a negative sign could stabilize it, but we do not know. Our analysis showed that it is unstable. We have to actually run it to see what happens. Is that fine? You know? Shall we look at something else? What would you like to look at FTBS? I think it is something that we have done. So there is FTBS. And again, just to bother you one last but one time, I am going to do this one more time.  FTBS as we suspected has a fourth derivative term. It has a third derivative term. It is dispersive. And yes, it has a second derivative term. There should be a negative sign outside somewhere here. That is a sigma minus 1 minus 12. Where is there a negative sign? Unless I made a mistake. Yeah. Anyway, that is something that you can, that is something that you can check up. Off-hand, I cannot seem to make it out. Right? You can look at that. You can look at that file. So FTBS dot mac upq minus up minus 1q, right? And I am substituting, I am solving for this term there. I am actually solving for dou U dou t, right? From the FTBS term. Is that fine? Okay. So yeah, indeed I am doing FTBS. It is a long painful equation in painful program. But you finally get to get here. Let me look at Mw1 just to make sure that I do not have a problem. Yeah, this is one of the reasons why I do the factoring because you get these terms that are, so this is positive, that is negative, a, oh yeah, fine. This is, yeah, this is sigma minus 1. It is not 1 minus sigma. Sigma minus 1. Sigma is less than 1. As we are negative sign, negative sign in there somewhere. Okay, fine. For a minute there I was a bit concerned. So if you look at the earlier one, see, you should not just let me get away with this, right? That is, so if you look at the earlier one, if you look at the one we had, oops, that is going to take some. Let me do FTFS just to convince you that I am not cheating you. The sigma minus 1 is what does it? So I go through do FTFS and here it is a sigma plus 1. That is the thing, that makes a difference. That sign makes a difference, right? Sigma is less than 1, so for stability. That is where that condition comes from. Okay, so yeah, so you can get the modified equation. What else can you do with this? Well, I have one file that I have created just for this reason and if you want we can play around with that file or we can, so I have got something where I have added artificial dissipation. I have something where I have added artificial dissipation. I am doing the same and you can see that what I have done is I have added a sigma squared UP plus 1Q.  I am just doing FTCS. I just add that extra term and then you can ask the question what happens to that. You can actually ask the question what happens to my, what happens to FTCS if I add that extra artificial dissipation term. That is the neat thing here. Now we can do this what if kind of, right? You can play around and what happened? F2 disappeared, the second derivative disappeared. So I figured out that term that I added was exactly the term that I needed to add, sigma squared by 2, second derivative, discretization of second derivative. But that is not the term that you get with the modified equation. There you get some sigma minus 1, right? We just saw that, minus 12, minus half sigma minus 1 by 2. What is the deal? Am I making sense? See if you add a second, so you have to realize this. If you say that I am going to add a second derivative term, you look at the modified equation, you look at the modified equation and you say, aha, there is a second derivative term. So let us look at the modified equation again. I will go back and I am going to just rerun the modified equation because this just generates a lot of, okay. Maybe I have, is it FTBS modified equation? Is that what it is called? Yeah, there we have it, okay. So there is a 12, remember there is divided by 24, so it is a half. So you can say, wait a minute, why do not you add a times sigma minus 1 divided by 2, dou squared, you dou x squared. That is what you should add to eliminate the term. Why do not I add that? Why am I adding something else? Does the question make sense to you? Do you understand what I am saying? I want to eliminate this term. I want to eliminate this term. In order to eliminate that term, I should just add that term to the modified equation. In order to eliminate this term, how come I am adding some other term? The key is, the key is in my discretization, I never add dou squared, you dou x squared. I do not add the F2 term. I add a discretization of dou squared, you dou x squared. Now I have a new discretization. I find the modified equation for that. Am I making sense? So the, am I making sense? I find the modified equation for the discretization of dou squared, I do not add dou squared, you dou x squared. I add a discrete representation of dou squared, you dou x squared. I do not add dou squared, you dou x squared. It is important. I add the discrete representation of dou squared, you dou x squared. I get a new improved modified equation which will still have the second derivative term. And if I go through systematically, I say, okay, I will add that, add that, add that and I keep on adding extra terms. All of those terms will combine into sigma squared by 2 dou squared divided by dou x squared. That terms out to be the modified equation term that you get if you were to use your original equation. That is what I was trying to say. I want you to, you need to think about that. You need to think about this. It is not that difficult but it is because there are so many different equations that are there, you have to be able to knock it out. I mean you have to be able to figure out how you can knock out that term, okay.  See if you can figure out how to knock out the third derivative term. I have knocked out the second derivative term. See if you can figure out how to knock out the third derivative term. Is that fine? Are there any questions? So yeah, this is basically what we have as far as this is concerned. If there are no questions, maybe then I will go on to the solution of the equation and see what is the effect that these modified equations have on the solution of the equation, okay. So to that end, unless you mean, unless you want to try adding other artificial dissipation terms to see what happens. If you want to modify this thing and see if it makes a change, if you want to add any other term, you can add any other term. Maybe we will do that. Why do not we do that? Before I go on, let me just edit, I will change this, okay. So I will copy that ftcs underscore artificial dissipation to ftcs, I will just say NPTEL. It looks like I do not have a enter in the last term. What do you want to do? You want to make this sigma minus 1 and see what happens, right. That is what we had. We will make it sigma minus 1 and see what happens. Maybe I should have done that first, but anyway it is okay. Next time I do this. Insert f bracket s minus 1, 1 minus s because I have a plus sign in the front, okay. Fine. Everyone, that is what it is. Speed into 1 minus s divided by 2. I would not save it, I will just write it. In case you want to make a change, let me reload that batch file and see what happens. So I called it ftcs. Yeah, it got a lot messier. Modified equation got a lot messier, right. There is the 12f2 term that is still there, but this is what happened. And that does not look like it is going to cancel. It does not look like anything is going to cancel that. It is making sense. So as you can imagine, as you go through each time you made, so you can now potentially turn around and say no, no, I will add this term. Go back and say I will add this term to it, fine. That is what I meant. So in order to get rid of it, you have to find out the actual term that you need to add in a discrete form. You want to find the actual term that you need to add in a discrete form that is involving p plus 1, p, p minus 1. What are the terms that I need to add? Linear combination of p plus 1, p, p minus 1, so that the modified equation does not have a secondary. That is really the question we are asking. And it turns out that it comes from sigma squared by 2 to the square du du x square for the wave equation. For the wave equation you will have to figure out what it is. Is that fine? Yeah, there was one other thing that I promised to do for you. I mean unless you guys want to try something else out, I will go ahead. I do not know. What was the difference between FTBS, I mean central space, central difference and forward difference, do you remember that? That was just a sigma by 2. Sigma by 2 into a delta x actually. So let us see. So we have a sigma star dx by 2. That is what it was. If you go back and look at it, that is what it was. I will write that file. See if it makes what it does. So I run the batch file. I will run it again. And this is what you get. Hang on. Let me make sure that am I doing this to FTCS? Yeah, I am doing it to FTCS. Fine. Okay. So this is what I get. Does this look familiar? Right? You look at this. Let me see if this works. Percent minus FTBS modified wave. I am not sure if I have done that right. Sometimes let me just look at FTBS modified wave. FTBS modified wave should basically give me that and that are essentially the same. Okay. Here I seem to have some extra terms that I will have to possibly simplify. Question? Okay. So yeah, maybe I will get back. I will do FTBS minus modified wave. See what it is doing. Okay. So if there are no questions, what I will do is I will just start over. Yeah, I am sorry. There is one last thing that I wanted to do which was something that I have not done in class. This is a modified equation for the heat equation. Modified equation for the heat equation. And there is a reason why I want to do this. I am doing this simply because when we did the modified equation for the wave equation, right, I connected up the stability analysis, the linear stability analysis that we did for the wave equation for FTBS, FTFS, FTCS. I connected it up with the modified equation and the various terms appearing in the modified equation. Okay. And I basically showed that if the second derivative term was negative, the coefficient of the second derivative term was negative. That is the second derivative term was, right, what you are adding was negative, that you are, you had instability, that it corresponded, right, those corresponded. So I may, I do not want to leave you with the feeling that, oh, I just have to do the modified equation, which is a mess, but I just have to do the modified equation and I will get the same stability condition that I get with the linear analysis, linear stability analysis. Okay. So to do that, I know an equation where it does not actually work out exactly, that is the heat equation. So we will do the modified equation for the heat equation, so that you will actually see that, you will actually see that that does not work. So I run the modified equation, so this is just sort of thing streaming past. Heat equation is very simple, right. It does not have the odd derivative terms, nice dissipative system. Heat equation is very simple, dou u dou t, that is the first term, dou u dou t – l dou squared u dou x squared, that is heat equation. Equals, there is no third derivative, no dispersion, they are not going to get dispersion, it is not there. And you get a fourth derivative, right, you get a fourth derivative, am I making sense? So you can ask the question, the fourth derivative and now for stability the fourth derivative has to be negative, there is a negative sign in front, so you can ask the question, when is this positive, when is this, when is this thing in the brackets positive. And it does not give you the same stability condition that linear analysis gave us. The von Neumann stability analysis that we did by substituting exponentials, cosines and sines, gave us a one half, this seems to give us a one sixth, am I making sense? Okay, so you have to have an awareness. So if it is less than one sixth it will work, but you can actually go up to one half. The guarantee still works, if it is less than one sixth, yes it does work. It is just that you can actually go to a larger value. Okay, so that in itself should give you a clue about these stability conditions, what they mean, what is the analysis, what is the result that we get, what do we expect from it? Okay, what do we expect from the behavior? Fine, okay, so I think I leave it at that, of course this is the fourth derivative, so you expect that as it gets small it is going to get really bad, okay. And we will remember this one sixth maybe when we run, when we run our codes. Okay, let me now go to, let me now go to the, I will just start off the other demo, we will most probably not be able to finish it in this class, we will go on to the next class, right. Let us start off the second demo. This is for the wave equation, right, I have over the years these demos have evolved and now finally I have added a small sort of user interface to it, not a big deal. So what I will do is I will run the demo and we will see how far we can take it in this class. So let me quickly get that bright thing out of there, okay. Yeah, so this is what I can do, so some of this may not come out because the font is quite small, I was not able to figure out how to make the font larger right now before this demo, so it does not matter, maybe I will be able to fix it but anyway we will see. Right now it is ready to run FTCS, okay. The number of grid points is 10, that is what is set here. The number of time steps that I take at every time I click this go button is one time step. The CFL that I am running for, remember what I told you, so people you typically ask what is the CFL condition for which, not condition, what is the CFL for which you are running. That sigma is 1 and this other stuff I will tell you what it is later. So there are no scales because actually I do not care, I just want to see behavior, right. There are no scales, I have not bothered with scales. So that is the initial condition is a step, right. So with that initial condition of course if you have 10 grid points or what are that, you can only represent a ramp, you cannot actually get a step, right. By increasing the number of grid points you can make it better. But this is FTCS, so what was the expectation that we had FTCS? It is going to diverge, it is going to diverge, second derivative was negative, there was a third derivative. It is also going to be dispersive, okay. It is also going to be dispersive. So the question is, is it going to diverge? Yes, it is already gone above 1. So it is going to diverge and it is wavy, it is all I can say, I mean something that started off as a ramp now has waves in it. So it looks like it is dispersive, so maybe that is true, maybe that is a fact. Let us take more grid points and see what happens. So instead of 10 grid points, I will take 101 grid points. Let me reset that. I take one time step. Because I have more grid points, my ramp is closer to the step, I have a step function, it is much closer to the step. So if I take one step at a time, you know, of the first two steps it looks like it works but afterwards it is just not going to work and you can see indeed it is, I mean it is like you have a rope and you are shaking that rope. I mean it is really oscillating. I have not bothered rescaling nothing of that sort. I do not care if it is off the scale. When I start with 01, I already have problems, right. I already have problems. So indeed it oscillates. So there is not much that we can do. Can we take a smaller, you think maybe if we take a smaller time step it may work? In mathematics it is unstable but do you trust it? If I take a smaller time step would it work? So let us try 0.1. I will reset. If I do not reset it will sort of continue with that which is not what my intention is right now. That is 0.1. Well 0.1 basically means I am taking one-tenth of a time step. So maybe I will take 10 time steps at a time. So yeah for a minute there, for a minute there it looked very open but it does not look like there is one thing that is happened though. It is not diverging as fast. So the dispersion is becoming much more clear right because the coefficient in front of the second derivative term is small. It is going to diverge. It will eventually diverge, fine. It will eventually diverge but because the coefficient is small it is not diverging that quickly fine. So but it looks like the dispersion is very clear and you can actually make out that what started off what should have been a step function or what could have just diverged right. The values could have diverged is in fact oscillating. Is that fine? I will choose as I said in the next time that we do it I will choose a more what should I put it in the next class when I do continue with this demo. I will choose a more I mean I have a tuned set of I can tune this. I will choose and just for fun there seems to be some sinusoidal something riding on top of right. So you have to order what is that? So it does have to do with it does have to do with the fact that the scheme is dispersive that that is happening okay. It is not an illusion it is there. That is not an illusion you may think oh it is an illusion it is not an illusion it is actually there. Is that fine? Okay just so that we do not end this day with your disappointment okay. I will run FTBS right. We will run FTBS and from what I told you FTBS with sigma equals 1 was supposed to have worked. They do FTFS or I did FTFS. I will do FTFS in the next class FTBS with sigma equals 1 I want to leave FTFS see whether you guys can predict what is going to happen right. So before we work last word for the day we will run FTBS with sigma equals 1 first let me take 1 time step at a time reset it oh it is a ramp but that is the way it should behave 10 time steps right that step no distortion in that ramp but it is a ramp right. So you say wait a minute how do you know that it is let me run 50 steps. So if I run 50 steps it should come half way right I will reset it run 50 steps yeah it comes half way goes right up to the end just to the end okay. So I am picking up the propagation speed I am actually picking it up exactly is that fine okay. So when we come back in the next class I will run the rest of the we will see we will try to explore what happens with numerical solution to wave equation and the lots of lots of nooks and crannies that we have to look at lot of okay fine right thank you.


What's up everyone it's your girl Kenzie here from Leighton Sports Guards, and I'm ripping some personals here for Antoine G We've got a 2021 Panini Immaculate football hobby box a 2223 prism basketball hobby a 2020 Bowman baseball jumbo in a 2021 prism football hobby. All right. Good luck Antoine. Thank you so much as always Let's start with some basketball Start with basketball here. Good luck little basketball baseball and end with some football Yanis prismatic silver Gary Trent Jr. Wilkins Yovitch rookie and Tim Duncan got Ruby rookie of tie-tie Washington, Jr. Rockets Lottery Dyson Daniels. We have a hyper of Russell Westbrook Graham Ewing and Pippin Jr. Rookie blue ice is gonna be a kawaii Leonard for the Clippers Sharp looking card there that is three out of 125 kawaii Fireworks Randall silver Gordon Hayward Steve Nash Jalen Williams Rookie and Dylan Brooks Blue rookie is a Kennedy Chandler for the Grizzlies out of 199 fearless Yanis hyper magic Johnson Caleb Houston Rookie Stockton and Shade on sharp with the base Silver fireworks KD charismatic Paul George silver Danny green Shet on the rookie base And dang rookie base fireworks hyper Ruby Hachimura And I'm not rookie and Chris mullin. All right, Otto's where you're hiding. Come on Got Ruby wave Chris Middleton bucks Lottery dang silver Evan Mowley second year Lofton Rookie Johnson and a Walker Kessler Rookie We've got red Andrew Nembar to 299 Pacers First auto up here for Antoine.  For the Hornets charismatic Trey young silver Rui Coloco Rookie Christian Braun and Tracy McGrady Ruby wave potty mills widescreen Lamello Dyson Daniels on the hyper pelicans Jabari Walker D-Wade and Isaiah Mowley rookie Two packs left so I prefer one more auto here silver lottery. It was money dang fireworks Levine silver rookie is Dave and Roddy for the Grizzlies Thanks, and Daniels rookie and AJ Griffin last pack here. We've got blue magic Johnson the 199 Lakers Yeah, this and auto is gonna be a cake cutting-hand of 25 That's that is sick mojo's are so sick. They really are wow I'm about to say Lane brings a good luck pulls the Charizard sits down last night if y'all didn't see the gaming box Sat down ripped one pack and pulled up what a hollow Charizard first edition for myself That was the most insane thing all right Pope on the pole star Wow, what a last pack there That's crazy. They look like they were in great condition to they're probably nice nice. What's what it is go for? They're not that expensive. No If it was like a shadow listen over a nine, then you're looking at like 15 to 20,000. Holy cow What maybe like a couple grand If it somehow Wow, that's crazy. All right, we're gonna do baseball next All right Again not all cards ship out of this Antoine you'll get your bigger name paper Of course your chrome any autos and any numbered paper Lewis There's Domingo's right there Lane speaking the stuff into existence man Alamance Hope a Again, India Lewis really green Collins brown Two nice first papers usually runs with those. Yeah So we got something in the back here some color. Okay Gavin Lux for heat Cardi Kaboom a la Cruz Swaggerty Lede Seth beer Brandon Davis and a Alec Manoa on the Aqua shimmer that is two out of 125 He's solid. I like I miss the twine like the 2020 design there Yes We have a bonus auto I believe baseball factory all-american is a Quinn Priester the national team Nice on-card auto there Can I do believe that is a bonus hit if I remember correctly?  Oh my gosh, that's kind of ridiculous and it's counseling That's good old prism release week Alvarez Ricky You know a lot of a I Was talking to chat. I was like I wonder when the last time a magic Ricky has one Ricky the year 2001 Mike I forgot what what his name was. I don't even remember. Do I didn't win it? No, I think so before that was Shaquille O'Neal in 93 Yeah, there's some good magic Yeah, we've got our first auto it's gonna be a Mike a bellow for the brew crew Mike Miller that's who it was. Yeah. Thanks, Jason. That's fair Mike Miller was had a pretty good career power to Brian Hayes I was like wow the whole history of the NBA Orlando's only one of the rookie of the year. Hopefully this will be the third year I don't see how Palo doesn't get it. Yeah, you got it unanimous minus one vote from the solid week Yeah They haven't like actually formally announced it, but the winners of the awards got Dominguez on spinning the globe Alright second half here so looking for two more autos And we've got a Piara for 71 out of 499 on the refractor first auto Ever soon period Pereira It's got a nice looking autograph too And you just have a bunch of the hits in here. Yeah, just to make it like four chases. Yeah And all of them are actually like Legit The rookie class and this product is insane. Yeah, just this whole 2020 Make a horner for us Rodriguez Duran first paper Pull your Rodriguez on the chrome De La Cruz Perez neighbor talent pipeline for the Giants Duran hidden finds Luciano Walker Barlin we've got a Duran on the chrome Aaron Shortridge on their factor to 499 first pirates 10 for Hondo. Nice Pereira alright you packs left and got something back there some color Nice messa Kelnick Gus Barlin Bobby Whit jr. On the first paper and we've got a Andrew Vaughn yellow paper to 75 Focus shut on the rookie paper. How Lewis rookie boy Lord on rookie paper Gavin Luxe rookie talent pipeline Rockies Dylan C's rookie six toe wander paper Bellow and Bradley. All right last pack Baseball then we will get into it some football. Um a box of this Yeah, nine nine fifty nine ninety nine nine ninety nine Kyle Lewis rookie of the year favorites Pull your rubber you guys paper Let's Mauricio Gorman little cossus And Pete Alonso. All right nothing too crazy out of that box. Take a career though Chrome does ship this paper will not Alright up next. We'll do prism 2021 prism here Good luck, then we're gonna end with some 21. I'm back. All right. Good luck on the prism long-wind rookie PS2 rookie Orange is gonna be a Damian Harris for the Patriots 148 of 249 and new recruits rookie of Najee Harris Scope coming up here Mine Arts Schwartz green scope is gonna be a Tyus Bowser Ravens 72 of 75 and Silver rookie of Jared Dokes Bins Reverend Jordan rookie ETN rookie base. We got purple Miles Jack for the Jags. That is 75 a 125 And Calvin really fireworks Devin Bush bright. Well Justin Fields on the rookie base Got hyper of Gary Brightwell Giants and sensational signatures is gonna be a Shaquille Griffin for the Jags Silver out of there 97 of 99 Big rookie on here Los Acor Moa at well red wave of Rocky sin for the Colts to 149 emergent rookie Mac Jones Frank Darby rookie Otto and Sean Wright. We've got blue wave Trey Kwan Smith Saints And rookie Silver Otto Mac Jones. All right, we'll take that. Here you go Antoine Silver Mac Jones auto if we can have a bounce back here this upcoming upcoming season there. Very nice Silver pretty nicely center there a little little to the right Get that one in a mag for you. Nice. I'm nice. Otto's coming out of your boxes We round tree we got the Vonte Smith rookie blue ice is gonna be a Jesse Bates the third for the Bangles to 99 And Derek Henry brilliance make Bolton rookie Elijah Moore. We've got purple ice of Pete Warner for the Saints To 225 and touchdown silver Aaron Donald Bunk rookie. We've got Mac Jones on the rookie base Hyper Khalil max 175 bears and silver will fuller the fifth Packs left and prism and we'll get into the iMac Pete Warner got Davis Mills rookie blue wave rich again for the Raiders to 199 and silver Chris Jones chiefs Smith rookie Michael Carter rookie hype Jerry Judy and Last pack of prism here And we got iMac first got a Kellan Mon rookie base a Marquette Stevenson you got a full purple power city lamb And it for the Ravens little color match here rookie is gonna be a Tylen Wallace on the purple power Let's have a pretty big print line through there right by his ankle Yeah They never had it Yeah, I look sick like some of like the color matches to with that is just All right ending with a bang here. Good luck Antoine 2021 immaculate football Come on. Let's see a huge RPA Yeah, all right up first we've got to 75 Derek car Raiders and we've got six of ten for the Jags a DJ shark on the patches That's a nice looking patch there three color patch We've got to 49 Brian Dawkins for the Eagles. I got a 49 Cool one here out of 49 moments trick play does the trick for Steelers. How about an Antoine Randall L? That's so cool Got any redemption up next immaculate rookie shout box signatures card 19 a tray sermon Tray sermon there on the RPA card 19 and Nice patch on this one. How about true RPA Broncos 75 and 99 Javante Williams nice three color patch there Hopefully you can come back to Had a solid start to his rookie season then what towards ACL, right? Yeah Yeah, for sure we'll get this one in Mac 42 Antoine solid boxes there again sick Mojo signatures Cade Cunningham on the second year again 21 out of 25 on that one Then we had silver rookie auto Mac Jones And then that nice true RPA Javante Williams all right Antoine that'll do for your boxes Thanks as always congrats, and we'll get these right out to you


Okay, so this is pretty random, but I'm here in a dick sporting goods looking at discount clothing. I pulled a pair of pants out that I thought was cute, but I looked at the bottom and I just cussed on the bottom and I immediately felt like oh, I can't wear those because like they always hurt my ankle so much like any pressure on it was super uncomfortable. And then I realized like that's not a problem anymore. Um, it's cool to have another moment of like oh, this is why I did that. Like I could totally buy these now and they wouldn't hurt. That's really cool. Well good morning beautiful friends. We are on our way up to Denver for my first, I mean, I guess second, but first really amputee specific event April, little did I know a year ago is Limlas Awareness Month. And so up in Denver, the amputee coalition is hosting a Limlas Awareness event. It's going for a few hours and we're going to check out what they're doing and bring you guys along with us. Absolutely cutting edge, riveting content. Did you say that I can have a one-legged crawl of grace?  What would you say to that? Oh my god, Brian. For the record, I'd win. We made it safely up to Denver. We're going to learn about some amputee things. Learn about healthy living and good nutrition. Sounds good. I wonder if nutrition for amputees is any different than like nutrition or just humans. We're about to find out. We just hit the halfway mark and I'm tapping out.  See that this actually blankets from when I was coming home from surgery. That's how quickly I clean out my car. It's pretty bad. It was really cool to go in here. Some of the speakers get some more information, resources, see a lot of amputees and meet them. And then I just got super, super overwhelmed. Amputee coalition of America, I believe is their official name is incredible. They do really, really cool work. I think one of the coolest things I learned today about is about becoming, I think it's a peer counselor where essentially if someone has recently gone through an amputation, generally like a traumatic amputation where they wake up without a limb, you can be on call for that and you can go meet them and go talk with them. And I would really love to do that. I think that would be really cool because I had someone there for me to help me walk through the process and it made all the difference in the world. And you have to be an amputee for at least a year. So I've got another six months to go, but that's something I would definitely like to go through the training for. So that was really cool to learn about. Side note, these shirts came today. They are not for sale. I just made one for Brian and I just kind of for fun or like for going to events or things like that.  Plus, who isn't excited when more sweatshirts arrive. It's kind of strange to me how I'm going through this because in previous like big, big deal things that I've gone through, I've really wanted to talk to other people who were in the midst of it, like who were going through it. And not the more the merrier, but like usually it's hard to find someone who really understands what you're going through. Like when I went through two house fires, which I will talk about in the near future, it was important to talk to people who were also dealing with their house, having burnt down and losing literally everything they owned like that. And when I went through everything I went through with like domestic violence and sexual assault, talking to people who were survivors of that was insanely important to healing and like those conversations were like life to me. Like I needed to talk to people who got it. But that is just not the case with this. I'm at an event surrounded by a lot of people who are going through similar things or who have gone through similar things or might have wisdom to impart. And I have no desire to actually engage in a deep conversation. And you know what? That's just where I am right now. And I think that's part of learning too. You know, everyone goes through things differently, even ourselves at different stages in our life. And I think that that is probably something that's important to remember. If you're a peer counselor, like if I went into that, which I think would be cool to do. I think I'm definitely going to pursue that. It was really cool to be able to go to this event. And I'm really glad that we did. And yeah, it was a morning well spent, but I am super overwhelmed and ready to be done with this day. So we are heading home and I am probably going to take a nap because naps are the best. I don't know why we all hated them as kids. Like did you hate naps as a kid? Like it was like a punishment. I have to take a nap and now just like the best feeling in the world. All right. So a couple of videos ago, I modified my eye walk and I wasn't sure if I would actually make that much of a difference to have like the shorter platform. It does. Like it really makes a difference at home. So I'm going to give it a shot in LaTage Target and see how it goes. I've got to pick up a present for a party and some gum because I obsessively chew gum. We'll see how it goes. Just a thought. Maybe don't put carts in handicapped parking spots. Note to self, I should have gone to the Target I know the layout of from my pipe distro art from one side of the store to the other. It's a good workout, but that was so much better with the new eye, not the new eye walk, with it modified. It actually really helped. It's still really sore after surgery, but it's like just post-surgery pain. It doesn't hurt like it did before even. So success.


Well, he obviously you know, he's one guy on our team that is is irreplaceable. I mean You know what he brings on a daily basis You know, not just offensively with his bat and his ability to get on base at such a high level But his defense his energy is enthusiasm. He makes everybody around him better So, you know, he'll still be around and still find ways to do that But obviously we might be without him for a little bit So we'll just see what kind of news we get and you know hope for the best and You know, obviously our depth is gonna get tested a little bit more.  There's 12 guys on the I al potentially with judge if the news isn't great That will be 13. Is there a point in time where you think maybe we can't weather this storm? No, not me. I've been here too long and seen too much You know, so, um, you know, I think You know at this point you just have to roll with the punches and you know and play the cards that you're dealt and obviously You know, it's less than ideal, but you know, I think the good news is we'll be getting some guys back relatively relatively soon and You know, hopefully obviously thought it was a good win today a good overall team win I thought master threw the ball really well. So that was encouraging and You know, hopefully hopefully we'll get to May and our luck will be a little better With all that's gone down How good is it to see guys like Frazier and talk man or shall I step up? Oh, it's big time. I mean, um, you know guys coming You know coming up that maybe you know coming out of camp it didn't look like they were get the opportunities that they may be wanted And here we are a few weeks into the season and you know, we've obviously had a lot of a Lot of injuries arise and things go on and and guys obviously have done a great job of stepping up having good professional bats and just keeping the line moving not trying to do too much doing a good job of getting on base and Really good to see What's the confidence level like when you have a guy like Tanaka taking them out even when his stuff's not a hundred percent there He still manages to get through seven.  I think the Billy Hamilton hit Really just bearing down and just super super focused and not allowing him to score That's not easy to do right there with no outs. So, um, you know, he just He's just a professional out there. It's a lot of fun to watch him pitch and play behind them and Was a big big game from today Yeah, I mean at this point I don't really know what to think of it.


Hello, Massachusetts Rhode Island and Connecticut UC Sears. It's a joy to greet you today. I'm Sarah Drummond, Dean of Andover Newton Seminary at Yale Divinity School. My name is Ian Douglas, and I am the Bishop Diocesan of the Episcopal Church in Connecticut. My name is Stephen Ray, and I'm the President of Chicago Theological Seminary. Greetings, friends, and blessings. I'm Sue Phillips, and I'm a co-founder of Sacred Design Lab. This is Bishop Jim Hazelwood from the Lutheran Church here in New England. I am the Reverend Dr. John C. Dorhauer, General Minister and President of the United Church of Christ. I'm Mary Elizabeth Moore, Dean of Boston University School of Theology. Hello, my friends, in the UCC Church. I'm Doug Fisher. I'm the Bishop of the Episcopal Dioces of Western Massachusetts, and I am so blessed to share a ministry with you. In John chapter 11, we hear of that wonderful story, that miraculous story of the raising of Lazarus from the dead. In the Gospel of John, we learn about the story of Lazarus, who had died and was bound up with bandages and placed in a tomb lovingly. But then Jesus came to him and woke him up from the sleep of death. And as Lazarus came out of the tomb, he had to be unbound before he could walk again. Jesus says to the crowd, unbind Lazarus. Jesus said, take off the grave clothes and let him go. Narratives that we rehearse to one another of decline and diminishment have simply got to stop. You are messengers of life to the Church. If we have resurrection around us, are we willing to take off the bandages? Or do we want to stay in the tomb? Lazarus is unbound and what appeared to be many of us as the decaying rot of a dead body is simply the pause of a body in need of new breath and new life. And the question is how are we going to respond and live into it? What we have to learn how to do is to liberate all of what we're great at for repurposing in the modern world. UCC's mission and message are more alive now than they ever have been. And so in the untie of those bonds from Lazarus, we untie the bonds that others feel in their lives. Jesus invites all of us as Christians to be unbound, to be unbound from those things that hold us back from living the life-giving gospel of Jesus. We're a future-focused tradition, constantly reexamining our call in light of the current generation and looking to the next horizon for how we can love more, care more, and heal more, especially with those who most need love, care, and healing. So I invite you to be set free to a world of creativity and collaboration. Unbind your Lazarus. You members formerly of the Rhode Island, Massachusetts, and Connecticut conferences now together as one. We can do what Jesus did, feel our feelings, lick our wounds when we have them, and then get busy bringing about new life. I invite you to be unbound, be free in the gospel of Jesus to serve God's mission of restoration and reconciliation in the world. We have a profound responsibility to ensure that our part of the Commonwealth, our part of the world is maintained so that all indeed may benefit from whatever it produces and whatever it brings. Now is the moment when you are shouting the Holy Shout. Come out Lazarus. Unbind the body. It is not dead. New life, new breath, new vision is breathed into it. Then may the Holy Spirit send you forth from your time together to breathe that new life into a world desperately in need of it. May it be so. The world needs you my friends and know that I'll be cheerleading right alongside you as you learn how to do that. God bless you.


A resident of Miami's Little Haiti reacted to the overnight assassination of Haitian President Jovenel Moise on Wednesday with some saying that there is uncertainty and fear in the community. Florida has a large Haitian-American population and Republican Senator Marco Rubio of Florida called on the Biden administration to help bring the killers to justice. The only word that could go through everybody's mind is being scary. We are scared. We don't know what's next. What's the outcome? Are we going to be able to go to our country? Are we not? Are we going to be able to at least to have like a news from our people? Because most of us has at least the family members there. We have to take care of, we send money to, we make sure we're there okay. Now we don't even know the outcome of it. Are we going to see them? Are we going to listen to them? Are we going to talk to them? The same guy, he put in a people hand, the same guy killed him today. Nothing people can do about that. That's his fault. You know, you might hear things, but nobody really knows for sure what's going on. And until, you know, people know, then I can say the community can have, let's say, a reaction towards what's taking place. So right now, everybody's trying to kind of put their heads together and see, you know, what happened. This morning, when they hear that news, they keep that president, everybody upset. That will go too far.


How's it going everyone Caleb here with late in sports cards next tonight Michael D going with five national silver packs Good luck Michael. One two three four and five See what we got for you Michael D. I start on the wander Orange Cade Cunningham to 199 good start there very solid Got Bryce Harper Cade Cunningham rated rookie to 50 Wow There you go Michael Sick, man. Hope you like Cade. Hope you like Cade Fav orange press got to 199 soda Spencer Torkelson rookie orange to 199 Last one here Thanks again Michael D. Walter Payton and a purple Traylin Burks to 25 You go Titans and nice hit there for you Michael Thanks again so much man. We'll have them all well protected Michael and sent right out to you


Good afternoon, and welcome to House Judiciary Committee. We are continuing our discussion on the Bureau or Division of Racial Statistics. And we are joined by Kristen McClure. And welcome. Very glad to have you here. I think you play a very important role to this process and look forward to your testimony, really guiding us through this and helping us understand how everything connects and works together and to really, really be with us. And sorry, I need to step out to make a phone call, but I'll be back as soon as I can. Great. Well, thank you so much for having me today. For the record, Kristen McClure, Chief Data Officer with ADS. And for today, I'd like to hit on three key points. One, regarding some minor modifications or recommendations to the bill. The second, to talk about de-identified and identified data and how that relates to siege of data. And then the third, which will be a good segue, third to cover technology costs. Does that sound good to everyone? Excellent. Yeah, thank you. Thank you so much. OK, great. So for the minor adjustments, modifications, there are two of them. The first one we recommend is on page four, number six. This is under duties of the division, where it lists making technology recommendations. And we feel like it's more appropriate for this to be a duty of ADS versus the division as ADS is responsible for technology for the state. Could you point me to where that was again? I'm sorry. Yeah, it's page four, number six, starting with line item eight. And again, so your recommendation is? For that duty to be owned by ADS, where reference is making technology recommendations. This is by 46. Yeah, sorry. We're just a moment. OK, so right now the duty is within this new division. And then you're saying, pull that out. Correct. Pull that out, put that under ADS, or you could delete that correct, because that is an ADS responsibility. OK, great. The next one is on page five under data governance, number three. And this, my feedback is consistent with what you heard from the state archivist. The record retention is most appropriate or more appropriate to be of a SAR responsibility versus an ADS responsibility. And for the data collection and data governance, we would recognize this as a division responsibility versus an ADS. So we would, much like we interact with the other businesses, we consult on that item, but we recognize ownership that the business would have for data collection and data governance. The other items associated with that, which are security and storage and management, I believe is ADS, that's totally appropriate. Security, storage. This is on line 14 and 15, I believe. Can I ask just real quickly, is that on, I'm looking for data collection, digital services. Oh, I see, on the collection and retention. So collection is a division. Correct. Retention is an archivist. Data governance is presumably the division. And data security is also the division. Or did you say that's ADS? That would be ADS and storage would be ADS. And how about management? Yeah, I think that's appropriate to leave as ADS too. Thank you. So that covers the modification recommendations. We have on that. The next item I wanted to talk through is about de-identified and identified data. So as I read through the bill, it wasn't clear to me the intent of do we want the division to receive de-identified data or identified data. And identified data includes a person's first name, last name, and date of birth. De-identified data does not include any of those three items. And when I heard some of the other witnesses provide testimony, some had assumed it would be identified data from the sound of it. And some had assumed it would be identified data. So it would probably be good to clarify which data set, which type of data you want to receive, want the division to receive. So yeah, that's a question about that. So you're not necessarily taking a preference one way or another. It's just make it clear. Is that a factor of clarifying in the bill itself or just under, I mean, yeah, I could forget that question. Yeah, I can understand. Yeah. You know, I'll take over. I'll be right back, but I'm going to take over. I lost that. Tom, I think the difference, at least, hi, Kristen, how are you? Hi, Coach. Good, thank you. I think the difference is in the particular study that's being done. A lot of the data doesn't have to be, let's say, age-identified, name-identified. Whereas if we were talking about school settings, we would almost need to be able to identify age. So was it from pre-K to 12, for example? If we were looking at the effects of policing or police supports within a school setting, like the big discussion now is with SROs. So how would you disaggregate that data unless you had age-identifiable? I would recommend, including age. Anyway, in any data sets, the option the committee has is do you want to include specific data birth for a person? See, that, I don't think, is necessary. And I think one of the other things that I think Martin was alluding to is that the advisory panel that would be working with the division would be making recommendations. And presently, those recommendations are going to be rule set. So they'd go through the rule-making process. But I think in order for us to get started, a lot of the initial data, I would agree with you. Having age would cover 98% of the information that we need, if not more. You see me, Tom? I just want to raise my hand. I know it's hard for you to see from inside your square. You're one of those phone hands. I do have my participant list up. So anybody who is zooming, I guess, I would be able to see their hand. But anyway, go ahead, Martin.  I think I've just decided that that's what we're going for. Anyway, I apologize. So this probably isn't, I'm going to try to work this out into a question for Kristen as opposed to a statement, but we'll see how that goes. I think it's probably critical that it's actually identified data because the idea is we're getting data from multiple agencies that we in fact may want to be matching up a particular individual's journey through the criminal justice system. So that may in fact require having the birth date and all that additional information. We just, I agree we need to make that clear. And I agree when we talk to the archivist, we also need to make clear as far as how the public records act applies to that because it should apply. If some of that data comes through that is exempted from being released, that should continue to be the case. I guess I didn't have a question in there. I apologize, Kristen, but unless you wanted to comment on that thought. No, if the intent is to link across the data sets, like you mentioned, then you would want to receive identified data to enable that. Right. We'll need to make that clear. I appreciate that. Thank you. Oh, go on coach. No, no, I was saying thank you. I do want to mention there are some additional responsibilities that the employees will have if they receive identified data because it will mean that they're responsible for C Just data, which is now a specific compliance cat, a federal compliance category. What that is, I'm sorry. What kind of data C just data CJ is, it stands for criminal justice information. And there are a few key elements that's probably worth sharing here about see just data. So much like federal government also has a compliance category for FTI tax data and has certain regulations and security measures specified for that. They have the same procedures data. So there's certain security measures that would need to be put in place for the technology wherever the data touches. So how it's received, where it's stored, how it's used, that whole environment needs to be just compliant. And so additional security measures and a firewall and configuration, specific audit and logging, but ADS would take care of that and enable the environment to be so you just compliant. So I wanted to mention that because it'll be reflected in the technology cost too. Okay, thank you. Oh, there are three other items I think may be useful for the committee to know about COGIS data. And it's really on the division responsibility but probably good to be aware of. One is around access control and this is a shared responsibility that ADS and the division would have. Essentially who is granted access to the data. And COGIS says basically it's a need to know. Only people are granted access to the identified data that need to know to work on it. And it's called lease privilege. So people are assigned the very least privilege necessary to execute their job function. The other item that I think is probably worth mentioning is NCGIS references it as information exchange agreements. In the state, we have Bolton 3.5, which says we need data sharing agreements between any external entity in the government as well as across branches. So he just takes it one step further and says any entity sharing data needs to have a data sharing agreement in place. And then the last item is really for, yeah. I'll go ahead, Mark. In the bill itself, is there language we need to add or do you consider that to be part of ADS's purview that we're going to try to make clear with the security issues? Or is there something that we need to add in your view? I would defer to the attorneys on it, maybe a line item of need to abide by federal and state laws. Right. And it could be inclusive there. I think in order, Martin, if as we're talking to Ledge Council, we refer to sieges compliance because then people have to search for that and understand it. If we just say federal compliance, it's like, oh yeah, just another federal thing. No, but when you talk about sieges, sieges is pretty intentional. And so I think that would clarify for internal and external viewers or requesters of any way, if that makes sense. So I guess the question though for Mr. Clore is, is there, are we leaving something out if we just say sieges or is that really the main focus here? I know we have Public Records Act, we're going to be dealing with that separately, but is there anything- I don't think we're leaving anything out if we just call out the sieges requirements. Yeah. Okay, thank you. I think Coach is going to say something. Well, I was going into a strange place, Martin. That's a strange place. All right, I guess not. Anything else on that before we talk about the technology cost? I don't think so. I think that was helpful. Okay. So I'll focus on the identified data technology cost and then just kind of note the difference in it where it would be for de-identified data. So again, these are kind of rough assumptions with a lot of, I assumed information about the data and the size of the data, the number of different data sets that would be sent just so we could have a ballpark estimate to talk through. So the bottom line, ADS cost which includes both the technology cost and resource cost ranges from about 450, 450K to 550K. And the 450K is the de-identified ballpark cost. The 550K is the identified data ballpark cost. Do you want me to break it down by technology and resource and like the division of ADS kind of standard charges? Actually, I need something probably a higher level. Okay. Sure. Tom, I didn't know if you saw me again, Tom. Yeah, yeah, go ahead. Martin, just jump right in. Not a big deal. Okay. So when you're talking about identified and de-identified, is this cost specific? What's this cost, well, I guess I'm all of a sudden said specific when I said I wanted to hear general. I mean, is it for the various agencies within the administration and cost associated with the data coming from there? I assume it doesn't include the court or is this something different? Well, if you could describe that kind of a higher level and then into the specifics. Sure. There, these would be cost incurred to support the data that the division would be receiving and the analytics that the division would need. The difference in the cost for the de-identified and identified data. One is around that C just compliant environment for the technology. And that's about 40,000. That's a one-time setup cost. So you would incur that really in the first year to set up your compliant environment. And then going forward, you wouldn't have that $40,000 cost. The other component is around resources. And with identified data, as you mentioned before, it has that matching component. So that drives additional workload on the DBA resource. So we're estimating about three quarters of the DBA resource for identified data to do that matching. The difference that DBA cost, it would drop to about a half a resource, a half FTE for the de-identified data. So is that DBA? DBA, I'm sorry. Oh, sorry, database administrator. Oh, okay. And they would be receiving the data that the different entities send the division. They would get that data, load it into a database, and then perform that matching for the division. So if I could ask, this is a higher level question. And this is great that you're getting into this. This is exactly, I'm delighted that we are getting into these details. So the way that, I mean, this document does not spell out nicely the staffing. But I will tell you what it was based on, just so you know, and it was just really as a placeholder. And that was, we calculated, this was based on a bill last year, H317, which is kind of the precursor to this bill. And it was based on having a deputy director, two IT analysts, essentially, and one administrator for this division. And I guess what I'm wondering is whether that's appropriate, or whether it's not as many people in the division because we're relying on a lot of work on ADS. If that's the vision, and I'm happy to work with however the administration wants to work on this, and I'm just trying to understand that for our ask. So if I'm falling correctly, forehead count for the division? Right, right. Yes. I have no idea if that's the right number. I mean, I just want to, we put that in there as a placeholder because we're not the experts on this. Yeah, she's got it. But she was just getting ready to tell us. How that equated. Yeah, reading through the bill that seems like that was my gut feel. I estimated in this about five headcount for the division. This would be additional headcount from ADS to support that, to support the data the division receives. Okay, great. Thank you very much. So as I mentioned, we have that database administrator resource. We also in this estimate included a project manager because we assumed this is, well, this isn't a very tech heavy item. It is a very resource intensive on the division and the business area is sending the data. So we assumed one project manager for at least a year, potentially two may be needed as part of this cost estimate. So I guess Martin, in order to help not only our committee, but other of our colleagues who might not see the back end of ADS, this has offered a lot of clarity, actually. You know, and I think that it could be because we wanna ensure that everybody understands what this is all about. We might need to go into a little more detail in our noting information in our bill. You know, I'd rather have a little more volume, especially if people are gonna understand that ADS's supports are this, in the background over and above what the division is actually doing with their manpower or people power, so to speak. Does that make sense? Yeah, I think that what we can ponder this a little more, what I envisioned and was gonna ask Mr. McClure if we can get this information in writing as well, just so, because I'm trying to keep it up and to understand what is a one-time cost versus what the estimate might be for down the road. Maybe that's hard to do, but I mean, the estimate for down the road is not obviously as critical because we're not gonna ask the appropriations for that. But I would think that would go all into a joint fiscal office report and that's as much for appropriations to parse through as us. So I don't know if I wanna be overly prescriptive in the bill as opposed to here's the bottom line number and the backup support is the JFO report. Isn't that how that would run? We could do it either way. I think that it would be if Kristen felt being that you've been doing this for us across other agencies. If there's a standard protocol for dissemination of the information so that the folks on the policy side can implement, however you feel is best, I think Martin's point is well taken that because they just did a fiscal note on the per diem bill actually and we just got that back today and it was very informative. So I think when JFO does their piece, that analysis is critical for a lot of our members in the body. So, Mr. Claw, did you have more as far as, I think I may have jumped in there before you had finished and I apologize. That covered the cost discussion. Okay, all right, thank you. And I can send you that in a document as well. Great, great. That would be very helpful. I wonder if I could ask kind of your opinion from that when you saw this, you estimated five FTEs necessary. Can you just explain that a little bit more? Because again, that four, it wasn't made up, it was based on some other things, but I would certainly like to understand where you came up with the five, that's very helpful. Yeah, I was estimating like you were a lead for the division and two data stewards. Again, the majority of the work and it is a substantial piece of work will be on the division and potentially the area sending the data. So it's gonna be intensive from a process perspective for the division. So I was ballparking two data stewards and two data analysts to do the analysis work. So did you have a chance to read the RDAF report on this from November? I'm just curious if you- Not the one from November from the previous year. Because it was just, they didn't really specify the number of people but they specified in their recommendations, they came up, look, here's what FTEs should cover. Here's kind of like the responsibilities they set out. I guess if I could ask you, if you would have a chance to perhaps review that and get back to us if anything jumps out at you because you probably will be having you back in again, almost certainly not here. It's gonna travel for the government operations committee and then to appropriations and almost certainly we'd be reaching out to you among a number of other witnesses. And kind of having had a chance to look at what they suggested may be helpful. Sure, I'll share. Yeah, and it might be just in terms of having done a little bit of this before. I think that sometimes it'll be a question of terminology where we might say, we might say Dana analyst and someone else will say, data steward, you know. And so... Exactly, right. Yeah. So once we get clear on our language, that'll hopefully help people as well. So just a point. And as a question. So good afternoon. So just to be clear, we're talking about four additional people to handle this now. Not from the ADS perspective. How many are we talking from ADS? For the identified data, one PM we would recommend and three quarters of an FDE for a database administrator. Okay. And what about, is there enough? I don't have the proper word. I wanna say computers, equipment, stuff like that is ADS equipped to handle this extra load. Yeah, I think you're asking the load of the work of the data coming in and the hosting of it. Right. And in that case, that's where we factor in the one or the three quarters of a DBI and the hosting costs are also factored into this. The PM that we have factored into this that I mentioned, we have it factored in at a rate for a contractor because to your point, can ADS handle this load? We have a number of projects that are ongoing this year into next year and we're hitting the limit of the number of PMs we have at the state level. So it factors in the contract rate for the PM. And that was my next question of clarification is you're already understaffed over there already, correct? So you're having a difficult time with workforce just like everybody else. I assume that's a fair statement. Thank you. Bob. Just for clarification, I'm hosting financial culture for Martin or Kristen. So two questions, exactly how many employees are we discussing here with ADS, without ADS? And is this proposal to bring on more state employees or these all-contracted positions? Well, I can start answering. The division would certainly be state contractors and presumably the three-quarter FTE, I would assume, and Mr. Cork can answer that part of it. But I did have another question actually related to this when you addressed this. Well, actually go ahead and I'll ask the question afterwards. I was basically, I just want to total to the specific. Yeah, well, here's the question related to a division and what ADS is going to be doing. Yeah, yeah. And that's part of what it was great testimony that to help us clarify who does what. The question, I guess, if Mr. Cork could answer this, is the estimated five FTEs that we have for the division, this kind of project, would you understand that that's not for the life of the project? It's a lot, I would assume there's a lot of upfront work to get these systems talking to each other. So this may be a two or three year, or what would be your estimate before we can lower the number of people that we have in that division? That's exactly right. It would be a bubble of upfront work, realistically probably for two years for the division. Again, it's a pretty work-intensive project for them. So I would see a bubble of upfront work, which is where, again, I was ballparking five headcount. And I would see that kind of trail off when it reaches steady state to maybe two or three. And if I may, Bob, to Bob's question, when we do our JFO analysis, they will disaggregate the behind the scenes piece from ADS and the front-end piece of the Bureau. So we will be able to see clearly what Ms. McClure has shared with us from ADS as far as their labor need and the recommended need for the new division. So we will have a very clear appraisal of that at that point in time. So will the committee see that or just guess? Oh, yeah, yeah. No, that's the whole idea behind the fiscal note. When somebody makes that request, the whole idea is so that it's visible, so that we can all make good decisions. I testified in government operations yesterday about per diems and one of our colleagues asked for if we had a fiscal note. Well, they had a fiscal note this afternoon. So it's something that we all need in order to make qualitative decisions. Thank you. Just to be clear here, this starting point with this money and stuff like this, I don't think anybody should be under an illusion that the price is gonna drop down as this gets easier because it's not.  So just to add on to what Bob was, I think, looking for, I don't want to speak for Bob. Well, those are costs of living, you know? We had a 3.6% increase in our 438 employees in another organization I'm working with, so I fully understand what you're referring to. So there isn't any drop-off, even though the efficiency and effectiveness changes as we go. So it isn't what it is. Yeah? Not the first rodeo, so to speak. I realize I stepped out of the room, but it sounds like this is a very helpful test of money. And thank you. I'm not seeing any other hands right now, right? So you have Michelle who's available for to make up what we can do this morning. So anything else before we? No, I think we're fine. And I appreciate whatever you can send me so I can get that joint fiscal office starting to work on that list before. I really appreciate your testimony. Thank you. Thank you. Thanks, everyone. Thank you. Thanks.


h activities that threaten the sovereignty of India. Now that the enforcement body of this act is the national investigation agency that is NIA which is India's central counter-terrorism agency. Now let us see some of the key provisions of unlawful activities prevention act. Now first let's take section 15. See section 15 of UAPA defines unlawful activities. It says that the unlawful activities are an action which intends to bring secession or disrupts the sovereignty and territorial integrity of India. Then the other important provision is that nonlawful activities prevention act empowers the central government to declare any association as an unlawful association by notification in the official gasset. Then under the act the central government may designate an organization as a terrorist organization based on foregrounds. Firstly the organization commits or participates in any acts of terrorism then secondly if the organization prepares for terrorism and thirdly if the organization promotes terrorism and finally if the organization is involved in terrorism. See if any of the organizations is involved in any of these four activities then they may be designated as a terrorist organization by the central government as per unlawful activities prevention act. And note on another fact here nonlawful activities prevention act was amended in 2019 and that act came to be known as UAPA amendment act 2019. See this amendment act additionally supports the central government to designate individuals as terrorists on the same grounds to that of organizations. Now talking about the punishment see as per the unlawful activities prevention act the unlawful or terrorist activities are punishable with imprisonment for a term at least five years to life imprisonment. Even the death penalty can be given for a terrorist act which resulted in death. Apart from this the unlawful activities prevention act allows for the confiscation of properties used for any unlawful activities. Now coming to the jurisdictions of unlawful activities prevention act see the jurisdiction of UAPA is applicable to Indians outside India then persons in the service of government and wherever they are posted and finally the persons on ships and aircrafts registered in India. Now with this information let's solve our practice question. Now look at this four statement national investigation agency is the enforcement body of unlawful activities prevention act as we saw this statement is correct NIS the enforcement body of UAPA. Now coming to the second statement central government is empowered to designate an individual as terrorists as per the UAPA amendment act 2019 as we saw this statement is also correct UAPA was amended in 2019 and this empowered the central government to designate an individual as terrorists okay. Now look carefully the question is asking for incorrect statements here both one and two are correct so the correct answer is option D neither one nor two. Now let's move on to the next question. Now look at this question here this question is about biological oxygen demand and chemical oxygen demand now before solving the question let us see some points about BOD and COD. See to have a better understanding about biological oxygen demand and chemical oxygen demand that is BOD and COD we have to first learn about dissolved oxygen that is DO. See dissolved oxygen is a measure of how much oxygen is dissolved in the water and note that this is the amount of oxygen available to living aquatic organisms okay. Now with this basics let's learn about BOD. See BOD or biological oxygen demand is all about the tiny organisms that live in the water bodies such as lakes, ponds etc. See while the tiny organisms consume the organic material in water it use up oxygen in the process. So the oxygen needed to break biodegradable organic matter in water bodies is called biological oxygen demand or BOD. Therefore BOD is a great way to analyze organic pollution in the water. If there is high BOD it means there is a lot of organic stuff in the water and that can be bad news for fish and other aquatic life okay. Now coming to COD COD is different from BOD. COD measures the total amount of organic material in the water. It includes the stuff that can be broken down by those little organisms we were just talking about. So if the COD is high it means there is lot of organic material in the water and note an interesting fact here COD is usually higher than BOD in the same water sample. This is because COD measures both biodegradable and non biodegradable organic matter while BOD only measures biodegradable organic matter. So if you only measure BOD you might not be getting the full picture okay. Know that the COD test is quicker and easier to perform than the BOD test. But the BOD test is considered more accurate and reliable. This is because BOD test measures the actual amount of oxygen used by microorganisms to break down organic matter okay. Now with this information let's approach the question. Look at this first statement BOD is usually higher than COD in the same water sample. As we saw COD is usually higher than BOD. This is because COD measures both biodegradable and non biodegradable organic matter. While BOD only measures biodegradable organic matter so statement 1 is incorrect. Now coming to the second statement a high BOD indicates a large amount of organic material in the water. This statement is correct. As we saw biological oxygen demand indicates a large amount of organic material present in the water. So statement 2 is correct. Now coming to the third statement the COD test is quicker and easier to perform than the BOD test. This statement is also correct. As we saw COD is done quickly and easily as compared with BOD. So statement 3 is correct. Here the question is asking for correct statements. Here statement 2 and 3 alone are correct. So the correct answer is option C213 only. Now let's move on to the final question. Now look at this question here. This question is about great 100 rhinoceros. Now before answering this question let us learn some points about 100 rhinos. See the greater 100 rhinos is one among the five different species of rhino present in the world. The other four rhino species include Sumatran rhino, Javan rhino, Black rhino and White rhino. And know that there are three species of rhinos present in Asia. They are greater 100 rhino, Javan and Sumatran rhinos. And know that only the great 100 rhino is found in India. And it is also known as Indian rhino and it is the largest of the rhino species. The greater 100 rhino lives in Northern India and Southern Nepal. And they inhabit reverent grasslands and adjacent woodlands. In India rhinos are mainly found in Assam, West Bengal and Uttar Pradesh. Know that the greater 100 rhinos are herbivorous. That is they feed on plants and the pasture land. See when they are not grazing on land they like to immerse themselves in water. When they immerse in the water they also graze on aquatic plants. In this period of 100 rhinos last approximately 15 to 16 months. And the mothers give birth to one calf every 2 to 3 years. Now talking about the conservation status of rhinos, see the 100 rhinos are categorized as vulnerable in the IUCN Red List of Threatened Species. And in the sites that is the convention on international trade in endangered species of wild fawn and flora, the 100 rhinoceros is protected under Appendix 1 of sites. Also know that Assam has an estimated 2,640 rhinos in 4 protected areas. The areas include Pavitura Wildlife Sanctuary, Rajyugandhi Orang National Park, Kazeeranga National Park and Manas National Park. About 102 rhinos are protected in the Pavitura Wildlife Sanctuary. Now with this information let's approach the question. Here 4 statements are given. We have to find how many statements are correct. Look at the first statement. The only place where it currently exists in India is Kazeeranga National Park. See this statement is incorrect because as we saw 100 rhinos are found in 4 protected areas in Assam. So statement 1 is incorrect. Commit to second statement it is classified as vulnerable by the IUCN. See this statement is correct. Great 100 rhinos are categorized as vulnerable in the IUCN Red List of Threatened Species. So statement 2 is correct. Now commit to third statement they typically prefer to be a part of a herd. See this statement is incorrect because the great 100 rhinos usually enjoy being alone except for female with Yngwan. So 100 rhinos do not live as a herd. So statement 3 is incorrect. Now commit to the fourth statement they are smaller than Sumateran Rhino which is the largest rhinos species in the world. As we saw 100 rhinos are the largest rhinos species in the world and not Sumateran Rhino. So statement 4 is also incorrect. Here only second statement alone is correct. So the correct answer is option A only one statement. And we have came to the end of this session. I hope this session is very useful for you. We found this video to be useful. Do comment and share it with your friends. 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