Okay, so not too long ago, I did a video talking about my rules of programming. One of them is definitely when you have a long list to filter the list, whether it be names or whatever you're searching for. And one of the top comments on there was someone saying, oh, I work for a company with 60,000 employees. All the employee databases, because it's been mergers of different companies, are in different databases, and there's no good option for HTML for filtering that large of a list. Let me address both those issues. First of all, when you have an employee database, the employee database, the basic employee database, should be relatively small. It's your core information. You're going to have things in there like their first name, their last name, date of hire, date of birth, maybe the department they work in, and maybe like a phone number, but that might even be in a whole different database. Everything else for those employees are going to be cross-referenced to other databases. No matter what company you have, even if you merge with a small, small company and they don't have an employee database, they probably have a spreadsheet with that basic information on there of all their employees, because they're going to have their username, their username, their first name, their last name, maybe a user name, their date of hire, at least those core things. And it should be no problem to either export from their database and import it to your database or from a spreadsheet. So that's kind of a non-issue. Yeah, you might have different databases, a different company used for certain things, but your core employee database that you're going to use for forms, if these companies are merged at all and you're actually going to be searching for all these employees in one place, should not be that hard. Again, if you're working with hundreds of, even if you're working with hundreds of millions of people in a list, it should not be that hard to export them unless those lists are being updated real-time and you can't pull that information because it's being updated real-time. But for the most part, you should be able to dump that and then re-upload it into your database fairly quickly. So I don't really see that being an issue. I understand that having a lot of different databases for different things can be hard for companies when they merge to get all together, but your core employee list should be a very simple database and you should be able to pull that list of names and basic information and put it into your main database. So I don't really see that as an issue for what we're talking about, which is pulling people's names for a form when you have all your employees and you're trying to fill out an employee form. Now, as far as that list being large, that can be an issue. So I'm going to show you some examples I made. First, we're just going to use a shell script. We're going to pull a list of not 60,000 names, but 100,000 names that I generated from voter registration. So I took voter reservations that had millions of names in it. I shuffled the first names and last name, linked them up, sort unique them and put them into just a plain text file, which you can access right now on my website. You'll see. And what I did was I'm going to show you real-time. I'm going to write out the code, a one-liner that pulls that list, puts it in the Fuzzy Finder, prompts you to search through it, takes what you use, and then echoes out what you've selected. Very, very simple. I'm going to go through it quick. It's not a full tutorial, just a demonstration, but just show how quick something like Fuzzy Finder, which is a very advanced filtration application that runs on everything. Then we'll look at HTML and we'll look at the option of data list. Data list I talked about in the previous video, which is built-in function element of HTML that all modern web browsers, I believe, now support. And it's a little bit more advanced than just a drop-down select option because it will look for matches in the middle of the string instead of just at the beginning, which is nice, but it's not a full Fuzzy Finder. But yes, in certain situations, that may be slow. I'm going to show you how it runs on a desktop. Then I'm going to show you how it runs on a cheap cell phone and you'll see the difference. On a desktop, it's not an issue. On the cell phone, it works but kind of slow, okay? So in a situation like that, I'm not going to go over today, but it's not that hard if all this stuff is in a database to have as you type, after you get a couple of characters in your text input, to have it start submitting what you're typing to the server and the server filters it out and returns a list of matches. I've done this a number of times and I've done it very efficiently.  I created that a real long time ago or really, really long time ago and it's just a plain text file that is on my website that new videos get dumped into and I'm actually just using grep to sort through them. So as you type, it sends what you're typing to the server and it literally just grabs a text file and returns the results as you're typing. It is not the most efficient actually having a database and filtering through that using whatever server side language you use, PHP is what I normally use to search through databases, could be a lot quicker. 60,000, 100,000 things in a list is not very long at all. So let's dive right in. Again, I'm gonna go through this quickly. They're just demonstrations, examples, but to show you how quickly it is, and again, the HTML here, we're not gonna even write any code, it's just built in elements of HTML that you can make a lot more efficient if you just knew a little bit of JavaScript and a little bit of server side, whatever you use on server side, PHP to search through a database. So let's jump right in, jump right in as we're almost six minutes into the video. One more thing. I'm gonna be using a different mic than I normally use in this video. I feel like my good microphone picks up a lot of background noise so I'm trying a cheap microphone that's in my headset and I haven't adjusted the volume, tested it out yet, so forgive me if the audio is not perfect in this video. So again, I'm gonna go through this really quickly here because this is in a full tutorial, but more of a demonstration. But if you go to filmsbychrist.com, forward slash scripts, forward slash 2022, forward slash names, you'll find this directory. There are two files. One is one and a half megabytes. The other one says three, but really I think it's only two point something. I don't know if it's rounding up here, but I clicked on here. There are 100,000 names in here generated from voter registration.  So we have 100,000 names here. Again, it's a 1.4 megabyte file. So if I take this URL and we'll go into our shell first. So I come in here and I'm just gonna use Wget. I'm gonna say dash Q for quiet so we don't see the download information and then capital O dash for output to the shell. I'm gonna paste in that URL and we can hit enter and it lists out the names there for me. And again, if I was to word count this, so I pipe it into WC dash L, you'll see that there are 100,000 names in this list. Now, instead of putting into that, we'll put it into FCF, right? So how quick, it's loaded in no prime. That's downloading it from a web server freshly. It's not cached anywhere right now. And I can say something like Smith John and I got Smith John as an output. Great, we can use that. Let's do it again. We'll do Simpson and Todd, okay? Or Simpson and Earl. Great, fuzzy finder. It's working super fast. 100,000 names, no problem. Let's go ahead, of course, we can put this into a variable called name, like so. And then we can echo out, you selected, whoop, selected dollar sign name. Put a period there. Make it a little bit cleaner. I'll put these curly brackets. Okay, so now I should be able to type in again, Simpson, or at least close, if I typed it wrong. Simpson, Earl, and it says you selected Simpson Earl.  So in a real script, you probably do something like this. You'll say bracket, bracket, bracket, bracket, couple of spaces in here and in quotations, dollar sign name. And then we'll say, okay. And so if true, print that and we'll say pipe, pipe. So if it's false, we'll say you didn't select, select a name, a name, a name. So if I hit enter, if I typed everything right, we should be able to type in, Smith, John, hit enter and it says you selected Smith John. Let's go ahead and add a clear screen so we can get a nice view of this. And now I'll do Simpson, Todd, and it says you selected Simpson, Todd. If I do Simpson, Earl, I selected Simpson, Earl. Of course, what I'm doing here, it's not telling me what am I doing. I'm seeing a list of names. So really what, oh, well also let me demonstrate.  And of course, as I was saying, you want the user to know what they're selecting. So with FCF, you can do dash, dash, prompt, please, because you gotta be polite, select a name. And now it says down here at the bottom, please select name. And when I start typing, of course, Simpson starts narrowing down and down to 30 names already and I can pick whichever one I want. Okay, so that's in the shell. The shell is always super fast. Let's go ahead and look at HTML. Now, I would not necessarily use a plain data list. As I talked about in a previous view, data list is a built-in element into modern web browsers that allows not as fuzzy finding as a fuzzy finder, but it's a little bit smarter than just a dropdown select. But it's not gonna be as quick. Let's see how it loads. Again, it's about a three megabyte file for these 100,000 names with the HTML. On my desktop computer, actually laptop computer, if I click here, it loads it up. It didn't take long, maybe two, three seconds for the whole page to load. And again, I can go Simpson, or let's not combine the names. Smith, John, and it's filtering it pretty good. Let's select another name. I'm just picking the same names because I know they're in the list. Simpson, Todd, there we go. And also let me hit Control-Shift-R. That reloads the page and should clear out any cache. So you can see it still loads pretty quickly. I didn't autofocus that, which I should, which is a rule of mind, but this is just a quick example. And we'll do Simpson, Earl. Okay, that's great. That's on my laptop computer. You know, it's about a $400 used laptop think pad that I bought. What about this? What about on my $50 Motorola phone? So let me turn on my screen here. Let me make this full screen here. Oops, wrong. Full screen. And again, I, oops, I did not customize this to load on a mobile device, but let's see how well this loads on a cheap mobile device. I'll click on that same URL. Again, you can go to this right now. Filmsbychrist.com. Ford says scripts, Ford slash 20, 22, Ford slash names. And you can pick the full name list or the HTML here, see how it loads on your device. And you can see here, it's hanging, it's hanging, it's hanging, it's hanging, it's hanging, it's hanging. It's hanging, it's loading all that HTML. It's probably downloaded everything, but it's gotta process all that into HTML. That's not great.  So yes, on a mobile device, obviously the built-in HTML is not the best option. What you probably wanna do is have it, so as you type, it submits what you're typing after probably like three characters to your server and then have your server filter out and pass back the information. It's something I've done before. It's a little more complicated because right now with this HTML, we haven't written any code. We've just created HTML, basic plain HTML. And I would want to write the code myself, a little bit server-side stuff to filter through the database because we're not using a database now, we're just using a flat HTML file. So definitely searching through a database will filter that out and then you can use some JavaScript to submit that and filter out. We're not gonna go into details on that, but just showing you how simple it is to create an interface, not that great on mobile device. Once you start getting into those larger numbers and you're trying to filter stuff, you're probably gonna wanna do on the server-side if you have a slower device. As a developer, you gotta figure out the nice balance. You don't necessarily want your server being hit so much if you're having a lot of hits, but with 100,000 employees, odds are they're not all gonna be searching for employee information at the same time. If this is built in, if you're running Facebook or MySpace or something, that's beyond MySQL. You're talking millions or billions of users, whatever, hundreds of millions of users. That's a different scenario, but even if you're in a large company with 60,000 or 100,000 employees, this is doable without too much skill. Yes, what we've done here could be done better. So that's it. I hope you learned something here. Please visit filmsbychrist.com. That's Chris of the K. There's a link in the description. And as always, I hope that you have a great day.


And Mali's presidency says a Colombian nun who was kidnapped in 2017 by Islamist militants has been freed. Gloria Cecilia Naviz was kidnapped by the Messina Liberation Front and Al Qaeda-linked group in February 2017 near the border with Burkina Faso. Naviz was seen smiling and dressed in a yellow robe and headscarf, meeting with Mali's interim president, Assimi Goyta. Naviz's freedom followed petitions for help from France, said Colombia's vice president and foreign minister, Marta Lucia Ramirez.


last time, we have seen that when we consider numerical differentiation. So, when we try to approximate f dash a by derivative of an interpolating polynomial, then there is some problem which we face. So, when we go on reducing value of h, then there comes a stage when instead of the error being decreasing, it starts increasing. And this phenomena is because the computations which we do, these are done in finite precision. So, a number is represented on a computer and there is some round off error. Now, this problem does not come into picture when we consider numerical integration. So, I want to quickly explain the difference between numerical differentiation and numerical integration using a composite rule. I am going to explain it for the derivative, first derivative f dash at a. So, this is let us look at central difference formula.  So, we have f dash a to be equal to f of a plus h minus f of a minus h by 2 h minus h square by 6 f triple dash at some point psi. So, this formula tells us that if you do exact computations, then as h tends to 0, the error will tend to 0 and the quotient f of a plus h minus f of a minus h by 2 h will tend to f dash a. In practice, what happens is f of a plus h is not represented exactly. So, instead of that we have f of a plus h plus some error even minus there will be similar error in the quantity f of a minus h.    So, thus our error consists of two parts. One part is the discretization error which is minus h square by 6 f triple dash psi and the other error is e 2 minus e 1 by 2 h which is because of the round off error. Now, there is no reason to expect that the round off error e 1 and e 2 they will cancel. So, e 2 minus e 1 this need not be equal to 0. Then e 2 minus e 1 divided by 2 h when you increase h or whether we are actually letting h to tend to 0. So, when you decrease h there will come a stage when this factor e 2 minus e 1 by 2 h this will start dominating the other factor which is minus h square by 6 f triple dash. So, this will be equal to e 2 minus e 1 by 2 h triple dash of psi and that is why when you are doing numerical differentiation there is going to be a limit to the accuracy which we attain. The erotically yes the as h tends to 0 error should tend to 0, but in practice it does not happen. After a certain stage when you go on reducing value of h after a certain stage the round off errors they start dominating the total error and they go on increasing because you are dividing by a small number. Now, in case of numerical integration there also we are letting h to tend to 0 because there h was length of our sub interval when you look at a composite numerical quadrature rule. We have our interval a b we subdivide it into smaller intervals and on each sub interval we apply some basic rule. So, this is how we construct the composite rules and then as the number of sub intervals increase and tends to infinity or equivalently when the length of the sub interval h which is b minus a by n that tends to 0 our numerical quadrature formula is going to give us better and better approximation of integral a to b f x dx. So, look at composite trapezoidal rule.   So, t n computed is going to be t n the trapezoidal rule plus this round off error. So, e 0 plus e n and then you have got e i and you are multiplying by a number h. So, this makes a difference and you are going to get a approximate value of integral a to b f x dx which is acceptable. There will be a difference between the two some part because of the round off errors, but that will not dominate the total error. So, we started with interpolating polynomials we wrote down the divided difference form that allowed us to get a error formula and we integrated interpolating polynomial in order to get numerical quadrature rules. Differentiating this polynomial gives us a way to calculate approximate value of derivatives. Now, we are going to start a new topic and that topic is solution of a system of linear equations. So, we will have n equations in n unknowns we are going to consider a square system. So, n equations in n unknowns we will assume that the coefficient matrix is invertible that means our system is going to have a unique solution. So, that is our starting point. Now, we want to solve this system we are going to consider real numbers. So, all the quantities involved they are all going to be real numbers. There is a classical way of finding a solution. So, that is known as Cramer's rule. So, Cramer's rule is theoretically important it is an elegant formula for calculating the solution, but it is going to be very expensive. So, in practice one does not use Cramer's rule for finding solution of system of linear equations. Our starting point is going to be Gauss elimination method a simple method to describe. So, this Gauss elimination method we will first describe then we will show equivalence of Gauss elimination method with LU decomposition of matrix A. What we will be interested in is the number of computations needed. So, we will calculate the number of operations needed in the Gauss elimination method for solving system of linear equations. From LU decomposition for positive definite systems we will show what is known as Cholesky decomposition. Then we are also going to consider the conditioning of the matrix. So, for that we need to define what is the norm of a matrix and so on. So, let us start with description of Gauss elimination method. So, we have our system. So, the system is a 11 x 1 plus a 12 x 2 plus a 1 n x n is equal to b 1. Then the second equation is a 2 1 x 1 plus a 2 2 x 2 plus a 2 n x n is equal to b 2 and a n 1 x 1 plus a n 2 x 2 plus a n n x n is equal to b n. The right hand side b 1 b 2 b n that is given to us a i j's they are also given. So, what is unknown is vector x. So, x 1 x 2 x n we want to find x 1 x 2 x n which satisfy this system. If you look at the powers of x i's they are all equal to 1 and that is why it is known as a linear equation. This system in a compact form we write as a x is equal to b n x n is equal to b where a is coefficient matrix a i j. I denotes the row index j denotes the column index. So, a is going to be n by n coefficient matrix. Our vector we denote by as column vectors. So, that is why b is equal to b 1 b 2 b n t that means transpose. So, this is the row vector and it is transpose that is the right hand side x is equal to x 1 x 2 x n transpose that is the unknown vector. So, the system is written as a x is equal to b a is the coefficient matrix and if to the matrix a we add one more column which consists of b 1 b 2 b n then you get a matrix of size n rows and n plus 1 columns. So, that is known as the augmented matrix. Now, we will assume that a is invertible matrix. If a is invertible a x is equal to b whatever is the right hand side it is going to have unique solution that unique solution will be given by x is equal to a inverse b. Now, let me first describe Cramer's rule. So, in Cramer's rule we are assuming that a is invertible matrix that means determinant of a is not equal to 0. If you want to calculate x j then what you have to do is look at the determinant look at the matrix a in that matrix a replace the j th column. So, the j th column of the matrix will be given by a 1 j a 2 j a n j. So, replace this by right hand side b 1 b 2 b n take the quotient that is going to be equal to x j. So, it is a very nice formula for calculating the unknown vector x 1 x 2 up to x n. So, x j is determinant of this matrix with j th column replaced by b 1 b 2 b n divided by determinant a j is equal to 1 2 up to n the problem with this formula is it is too expensive. If you want to calculate determinant of a where a is n by n matrix you will need at least n factorial multiplications of n by n matrix. So, you will need n factorial multiplications for plus n factorial addition slash subtraction and n factorial grows very fast with n. So, no matter how big your computer is if you try to calculate determinant of a by traditional way soon your computer memory will not be enough. So, this Kramer's rule is going to be too expensive to use in practice. So, now suppose your system is a per triangular that means in the first equation all unknowns appear x 1 x 2 x n in the second equation there is no x 1 in n minus first equation what is coming into picture. So, the next picture is only x n minus 1 and x n and in the last equation you have got only x n. The coefficient matrix invertible will mean determinant of u which is product of diagonal entries u 1 1 u 2 2 u n n this is not equal to 0. So, all u i i s they are not equal to 0 what one can do is start with x n x n is going to be equal to y n upon u n n. Then having determined x n go to this equation now x n is known. So, take it on the other side and calculate x n minus 1 as y n minus 1 minus u n minus 1 n x n divided by u n minus 1 n minus 1 and so on. So, this is known as back substitution. So, if your coefficient matrix is a per triangular then you can determine vector x in the order x n x n minus 1 x n minus 2 and so on. So, our aim will be to replace our system A x is equal to b by an equivalent system u x is equal to y. What I mean by equivalent is both the systems they should have the same solution. We are interested in solution of A x is equal to b. So, if you replace by another system then the new system should be replaced by the same solution because we are interested in the system of original we are interested in the solution of the original system not some other system. So, coefficient matrix A we want to reduce it to upper triangular form. Now, whatever you will do for A you will have to do on the right hand side because we do not want to change our system. So, we are going to use elementary row transformation. That means, what we can do is multiply a equation by a number alpha non-zero number and subtract it from other equations. If you do this you are going to get a system which is equivalent. Now, this equivalence we will show later on. So, first we are going to describe the Gauss elimination method, calculate the number of operations in it and then we will come back to equivalence. So, aim is to replace A x is equal to b by an equivalent upper triangular system u x is equal to y. Using elementary row transformations of the type r i becomes r i minus alpha r j.  So, this was our original one original i th equation. And this is the new equation. Now, we are going to make an additional assumption. A is invertible, but we will look at principle leading sub matrix. So, that is formed by first k rows and first k columns. Our assumption is determinant a k not equal to 0 for k is equal to 1 2 up to n. When k is equal to n that is determinant of a not equal to 0 that we have already assumed. Now, we are saying something more. What should happen is a 1 1 should not be 0 determinant of a 1 1 a 1 2 a 2 1 a 2 2 should not be 0 and then so on. This is additional assumption. Like, let me look at example say 2 by 2 matrix 0 1 1 0. This matrix is such that determinant of a is equal to minus 1 which is not equal to 0, but when I look at determinant of a 1 then that is equal to 0. So, this assumption that determinant of a k not equal to 0 for k is equal to 1 2 up to n this is additional. Now, we are going to show that there is a class of matrices for which the this condition is satisfied and those are known as positive definite matrices by one flop. Because as I said we are going to calculate the number of computations. So, one flop where flop stands for float. So, we are going to calculate the number of computations. So, one flop where flop stands for floating point operation, it consists of one addition or subtraction plus one multiplication slash division. Addition and subtraction they are considered on par and multiplication slash division they are also considered on par. Generally, total number of multiplications slash divisions is same as total number of addition slash subtraction. So, one flop is going to consist of this one addition slash subtraction plus one multiplication slash division. In the first step of Gauss elimination method what we want to do is we want to look at the entries in the first column below the diagonal entry and we want to make all of them 0. This entry a 2 1 can be made 0 by multiplying the first equation by a 2 1 by a 1 1 and then subtract it and then so on. So, when you do that the first row will remain as it is all these entries they will become 0 and the entries in this sub matrix they are all going to get modified. So, that is going to be the first step. In the second step we will work with this sub matrix we will not touch the first row or the first column. So, first we have to notice that a 1 1 is not equal to 0 that is because we are assuming that determinant a 1 is going to be not 0. Next we define multipliers m i 1 to be a i 1 divided by a 1 1 i goes from 2 up to n. A 1 1 is not equal to 0. So, m i 1s they are well defined and i th row from the i th row we will subtract first row multiplied by m i 1 for i is equal to 2 up to n. We want to economize the computations. So, these 0s we will write down directly we want to make the subtraction because we have chosen the multipliers in such a manner that this operation will produce 0s in such a manner that this operation will produce 0s in the first column below diagonal a i j 1. These will be given by a i j original entry minus m i 1 times the corresponding entry in the first column. The first suffix denotes the row. So, that is why you have got a 1 and then j.  You have to do it for the last column also. So, it is b i 1 is equal to b i minus m i 1 b 1 i going from 2 to n j going from 2 to n. So, let us now calculate the number of operations. First you are going to have one multiplication here and then one subtraction here. This you are going to do it for this whole square. So, that is going to be n minus 1 square, but you are also doing it here. So, it is becomes n minus 1 into n multiplications plus those many subtractions. So, n minus 1 into n subtractions plus in order to calculate m i 1 you need to do this division. So, there are n minus 1 divisions. So, these many computations are needed for the first step. In the second step we are going to work with a matrix which has got n minus 1 rows and n columns and exactly the same computations. So, now the number of operations will be obtained by replacing in this relation n by n minus 1. Now, we have to confirm that our procedure is going to be n minus 1. So, we are going to work for the sub matrix also. To start with our matrix in our matrix a a 1 1 is not 0 because you are assuming determinant of a k not equal to 0 for k is equal to 1 2 up to n. You do some operations you get a new matrix. In the new matrix which consists of second third up to nth row and second third up to n plus first column. Now, the entry which we are going to divide by that is going to be a 2 2 1 the modified entry. So, we have to make sure that a 2 2 1 is not equal to 0. What we have done is we have used to implement elementary row transformation. That means, we have multiplied a row by a fixed real number and subtracted from other row. Now, this operation does not change the determinant of the matrix. The determinant of the matrix remains invariant. So, look at the 2 by 2 matrix which is formed by first 2 rows and first 2 columns. So, that is our capital A 2 by assumption determinant A 2 is not equal to 0. And this 2 by 2 matrix after the first stage of our Gauss elimination method it is transformed to the first row as it is A 1 1 A 1 2 second row 0 below the diagonal in the first column we have got 0 and then A 2 2 1.  A 1 1 is not 0 A 2 2 1 also should not be 0, because determinant A 2 is not equal to 0. So, that means, our second step of Gauss elimination method we can perform and then one uses the same argument that you can do this process till your coefficient matrix A 2 2 1. So, this A is reduced to an upper triangular form. So, our starting matrix was A B augmented matrix we transformed it to A 1 B 1. Then using similar operations we have transformed it to A 2 B 2 and so on. In order to do this transformation we need the fact that A 2 2 1 is not equal to 0. So, now, the number of computations we have seen that for the first step of Gauss elimination method we had n minus 1 into n multiplications plus n minus 1 into n subtractions plus n minus 1 divisions. In the second step you are performing a similar operation on the sub matrix with n minus 1 rows and n columns. So, everywhere you have to replace by n by n minus 1. So, it will be n minus 2 into n minus 1 multiplications plus n minus 2 into n minus 1 subtractions plus n minus 2 divisions. So, when you consider total number of operations which are needed to reduce the system A B to a system U y where U is upper triangular matrix it will be given by. So, here write this n as n minus 1 plus 1. So, you will have n minus 1 square.  So, that is why you will have plus n minus 1 from here then n minus 2 plus 1 and now I am writing as flops. Number of multiplications and subtractions they are the same and one multiplication plus one subtraction is one flop. So, that takes care of this and what is remaining is divisions. So, you have n minus 1 plus n minus 2 plus 1 division. Now, this is square of natural numbers. So, we have got a formula. So, it is n minus 1 n 2 n minus 1 by 6 plus some of this will be given by n minus 1 into n by 2. So, these many flops plus n minus 1 into n by 2 division. Now, this Gauss elimination method which I have described it is for solving big system of linear equations using computer. If you are trying to solve a 3 by 3 system by hand it will not matter which method you use you can use Kramer's rule, but in practice one comes across big systems of equation. So, then one has to worry about the number of operations. Now, we have calculated the number of operations. These number of operations they are some constant times n cube plus another constant times n square plus constant times n plus constant. Now, when n is big what matters is what will be coefficient of n cube like between n cube and n square for n big enough you can ignore what is n square like if your n is 10000 then n cube is going to be much bigger than n square. So, the dominating factor becomes n cube, but you should retain the coefficient of n cube because there is a difference between n cube and 2 n cube. The 2 n cube is double the number of operations. So, in this Gauss elimination method coefficient of n cube is 1 by 3. So, one says that you can reduce your system to a upper triangular system by doing the number of operations of order n cube by 3. So, now, we have reduced our system to upper triangular system, but still it remains to find the solution. We do this because we want to solve A x is equal to b. So, now, let us calculate the number of operations in the back substitution. A x is equal to b is our original system. This we have reduced it to upper triangular system u x is equal to y by performing number of operations of the order n cube by 3. Now, let us see what effort is needed for getting vector x 1, x 2, x n from u x is equal to y. So, that we are going to do it by back substitution. A x is equal to b. A is invertible matrix. So, determinant of A is not equal to 0. All the operations which we have used, those are elementary row operation r i minus alpha times r k. So, this leaves the determinant invariant. So, determinant of u will be same as determinant of A. u is a upper triangular matrix. For an upper triangular matrix, determinant is product of the diagonal entries. So, you are going to have u 1 1, u 2 2 into u n n as determinant of u. Determinant of u not equal to 0 will mean that all the diagonal entries u i i, they are not equal to 0. And we have already talked about the back substitution. Start with the last equation, determine x n, then go to n minus first equation, determine x n minus 1 and so on.   So, now, x i will be equal to y i minus summation j is equal to i plus 1 to n u i j x j divided by u i i, i is equal to n n minus 1 up to 1. With the convention of u i i, x i will be 0. So, the convention that if i is equal to n, then this summation is absent. Now, how many number of operations? So, here you have got j is equal to i plus 1 to n.  You have got n minus i terms, when you add them up, you will need n minus i minus 1 additions, because when you want to add two numbers, you do one addition. But, then there is one subtraction here. So, that means, in order to calculate the numerator, you will need n minus i flops. And there is going to be one division. This you will be doing it for i is equal to n n minus 1 up to 1. So, the total number of operations they will be given by summation i goes from 1 to n minus 1, n minus i flops plus n divisions. And this summation is nothing but n minus 1 into n by 2 flops plus n division. So, that means, it is going to be of the order of n square by 2. So, thus the major chunk of our computations, they are needed to replace our matrix A by an upper triangular matrix. So, this is what we are going to do. The once you have done that back substitution is of the order of n square or n square by 2 if we want to be really precise. So, suppose sometimes one wants to solve the same system of equations for different right hand side. So, in that case what you should do is, you should retain your say number of operations or whatever you are doing because see what you have now is A x is equal to b. So, the coefficient matrix A is the same, but on the right hand side you have got b 1, b 2, b n those will be different. So, you should keep the track of the operations, reduce A to upper triangular for once for all, reduce A to upper triangular. Whatever are those operations you have to perform them on the right hand side also and then solve system of linear equations. So, this is Gauss elimination method. It is also known as Gauss elimination method without partial pivoting. So, we will see what pivoting means, but at present this is the simplest method. This method is applicable provided that A k is not equal to 0 for k is equal to 1 to up to n because if at any stage the number by which we are dividing in our multipliers we need to divide by certain number. So, if this becomes 0 then our system or our method will be, it will fail then we cannot proceed. So, there is a big class of matrices for which this condition determinant A k not equal to 0 for k is equal to 1 to up to n is satisfied and that class of matrices that is known as class of positive definite matrices. So, our definition of positive definite matrix is going to be matrix is a real matrix it should be a symmetric matrix A transpose is equal to A and in addition if you look at a non-zero vector x then x transpose A x should be bigger than 0. A is n by n matrix x is n by 1 vector. So, A x is going to be a n by 1 vector our x transpose will be 1 by n row vector. So, when you consider x transpose A x what you get is a 1 by n matrix or a real number if that number is bigger than 0 for all non-zero vectors then our matrix is going to be positive definite. Now, for the positive definite matrix when we look at its Eigen values. So, we are going to look at the Eigen values of matrix little later, but at present lambda is an Eigen value of A provided there exists a non-zero vector such that A u is equal to lambda u that is definition of Eigen value lambda is going to be equal to u transpose A u divided by u transpose u.  So, for positive definite matrices Eigen values of A they are bigger than 0 and determinant of A is product of Eigen values. So, determinant of A is bigger than 0. So, that means for a positive definite matrix determinant of A is going to be bigger than 0. So, A is going to be not only equal to 0 it will not be equal to 0, but it will be strictly bigger than 0. Now, what we want is additional condition we want determinant A k should not be equal to 0. In order to show that positive definite matrices satisfy this property what we are going to show is that A k which is a sub matrix formed by first k rows and first k columns of the matrix they are also going to be positive definite. So, in order to show this we will have to go by definition. So, for positive definite first it should be symmetric. So, checking symmetry of A k is no problem, but showing that y transpose A k y is bigger than 0 for y not equal to 0 that will need some proof. So, we will show next time that if A is positive definite then all its principle sub matrices they are also going to be positive definite which will mean that determinant of A is bigger than 0 for k is equal to 1 2 up to n which means equation method which we described just now we can apply it to this class of matrices. And then we will also see some decomposition of positive definite matrix which is known as the Cholesky decomposition. So, we will continue next time. Thank you.


and they need to adapt to this speedy change that the world is seeing every single day. That's my answer. And you finish with education. Clearly it's at the main point of your statement. Let's move to the private sector. Michele Baker. She's a co-founder and executive chairwoman of Mozilla. Yes. And first I'd say private sector. We're more of a hybrid organization. We're a non-profit or NGO at its core, but have a private subsidiary business. Fair enough. It's not often that I'm the representative of the private, certainly not of the private tech industry of Silicon Valley. So let's just start there. And I would, in a way, it's building on the president's comments for technology. How do we embrace disruption, which is difficult, and also engage in sustainable development. I'd like to add the critical component of encouraging and increasing civil society participation in problem-solving and the results. Because the technology, certainly the internet, and messaging, communication have the impact of changing structures. Not just government structures, but communication, interaction structures, and the sense of being involved. Both the ability to find something that you're either interested in or that outrages you and to get involved in some manner seems to come with this technology. And it has a life of its own. And that has power both for dramatically good results and the potential, if ignored, to be highly disruptive in socially undesirable ways. And so, for example, our experience is that the technology products coupled with local engagement, Mozilla has massive communities actually in Mexico and Bangladesh, and where especially young people, those who are able, I have some degree of education, are really interested in participating. What is the technology? How does it work? How do we develop solutions with it? How do we engage with others? How do we collaborate? Can we develop some positive interactions on a cross-border style? And so, left alone, of course, you can get all sorts of social movements that are aimed towards violence and disruption, but there's also a huge possibility, and we have seen over our 20 years of working in tech, an amazing hunger for citizens to find a way to be engaged and participate and help craft solutions of their own. And so, I think the combination of structural reforms, government reforms, perhaps regulatory reforms of the global private sector, and a reform in the participation opportunities for civil society would be extremely powerful. Thank you. Talking about private sector now, I'm sure that you are private sector 100%. Alex Gorski, Chairman and Chief Executive Officer from Johnson & Johnson. Well, thank you very much, and it's a real honor to be here and participate in a panel of such distinguished guests. And as you might understand, given the privilege I have of working at Johnson & Johnson, the world's largest healthcare company, I guess the main vector that I would take in the discussion today is one about the intersection of innovation and healthcare and the important impact that they can have on these sustainable development goals around the world. And I think it really starts with a strong belief that we have that health is just a fundamental issue for families, for children, for mothers, for fathers, for cities, for communities, for countries, and frankly for all of us around the world, because it enables us first to enjoy life. But of course, beyond that, it has to do with productivity. It has to do with stability of society and so many other issues and how we engage. And so understanding the importance that healthcare has in really touching so many of these issues is critical. I think second, I think the good news is, is that we made a tremendous amount of progress over the last several decades. And if we think in our life spans, the average lifespan, even within that time, has increased by several decades. Improvements that we've had in things like cardiovascular disease, prenatal care, even with something like HIV, I can remember in the early 80s when it was first really discovered what the issue was, you could expect to live perhaps two years. Today, it could take several years off an average lifespan when treated with the right therapeutic regimen. The challenges, we still have a lot of work to do. And as we think about it, there's several areas where innovation is going to be absolutely critical to our path forward. It will start with great science. There's still a lot of things we need to figure out. We need to do a better job with Alzheimer's. We need to do a better job with infectious disease. We're making great strides in areas like HIV, like TB, like polio. But there's still a lot of important science that needs to be done to actually move from treatment to cures in these conditions. Second, we've got to be more innovative about taking a lot of the existing therapies we have and making sure that more people can get access. And sometimes that can be as simplified, as simple as color coding pills so that people take the right regimens to ensure compliance. It can be taking an old medication and finding a way to extend its duration of activity, therefore increasing the potential for it to have a therapeutic effect. It can be taking simple surgery and making it more accessible to greater numbers of patients. And last but not least, I would say what's really important is how do we take some of this new technology and employ it in new and unique ways to health care? We're doing programs right now where we're trying to educate, provide mothers just prior to the birth of their child with a phone, and by giving simple messages on a recurring basis to these mothers, both pre-term as well as following the birth of their child, it can have a dramatic effect on the long-term health of that child. So I'm confident through public-private partnerships by working together, focusing on some of these things that can have a real impact on these goals. That's the point, private partnerships, public-private partnerships. And we have public representations here in the panel. We're going to finish this first round with Mark Groot, the Prime Minister from the Netherlands, is a developed country. I mean, here we have two developing countries. What's your point of view? Well, first of all, let me make one preliminary remark, which is towards my colleague from Bangladesh. She mentioned the Rohingya crisis, and I really want to applaud the way Bangladesh is helping to deal with that crisis, which is not easy. So I just want to make that preliminary remark and really my respect for how Bangladesh is working on this. Now to the question, and yes, it is education, it is disruption. I think I would like to make one point from the government. What we can do with these transformative technologies like artificial intelligence, the digital revolution, the fourth industrial revolution of Klau Hek, Klau Schwab has from the WEF has written a book about this, very authoritative. From government we can do two things. One is to look at the negatives, the issues on privacy, the issues on people getting scared, the fact that it might distinguish between countries and people who have access to these new technologies and who don't. And yes, we have to deal with that. We have to deal with privacy. We have to deal with all the other issues coming out of these new technologies. But I do believe being a developing country, being a developed country, I think all of us we should also embrace this. Because in the Netherlands, but also in Kenya, I now know of young people who on their own can start a multinational because they can have access to the whole world market, be it from the capital of Kenya or the capital from the Netherlands. It doesn't matter anymore. When I go on a trade mission now, I originally would only have the big companies like Unileve or Shell or the others or Johnson and Johnson on the mission. Increasingly so we have small companies. There's only a couple of people working there who are working worldwide making use of the latest technology, making use of the latest distribution options we have in the world. And I think what we should do as governments is, yes, address those negatives and the impact it might have. But particularly look how we can channel these new technologies in such a way that they are really funneling and fueling our economies. So don't look at it as a problem, but as a huge opportunity. And this is, and there is no difference, be it Kenya or the Netherlands, how this will impact on young people starting a business on society as a whole. And there are huge advantages. That would be my main point. Thank you very much. I think there is one agreement between all of us, which is the technology is going to help in deal with the challenges that every country, every company, every human being has in the future. But as President Peña Nieto said, education is critical. And in my opinion, we have challenges from the education point of view in developing countries for sure, but also in developed countries. President Peña Nieto and Prime Minister from Bangladesh, Sheikh Hasina, how do you deal with this challenge to educate people, especially in your countries where other basic education needs are not fulfilled? And you have to prepare your societies for this fourth industrial revolution? Thank you very much. It's a very important question. Well, as because we declare that we will develop our country as a poverty free country, I feel that education is the key. And that's why education is up to like for women up to 12 class, it is free. We distribute free books up to the secondary level. From primary to second, I mean her education is all free. But you have the teachers, we have to educate these people, we give training to the teacher. And also our up to her education, we give stipend for the poor people and also for intelligent people. And we started build up. It's a up to is a village level. Now we have schools in the primary primary section, 98% student, they go to school because we help the mother, we send money to the mother directly through mobile phone, some lump sum, some money, so that mother send their children to the school. We have made a meal. We get little help from other, but now our education level, it is already increased up to 72% literacy rate. We increased it. And also for educational side by side health care, we have community clinic for every 6,000 people. There is a community clinic from that we distribute 30 types of medicine free of cost. We distribute books free of cost. We ensure that each and every children should go to school and get education side by side vocational training. We give vocational training so that everybody will not get higher education or they will not interested, but they should get the opportunity for job opportunity. That way we get more importance to them. Side by side, we feel that for, I mean, development industrialization is very, very important. But you mentioned, you mentioned already education. Sorry, health care. I want to offer the floor just before the president of Mexico to the private sector to talk about health. How important is health in societies in order to achieve these challenges in the fourth industrial education? Well, I would, I think it's absolutely critical. I mean, it starts with the very birth of a child. What can we be doing to help ensure that morbidity, mortality rates at birth are improved? We have much of that technology available. It's a matter of how do we improve the access to that? How do we think about it in terms of increasing productivity for all of our societies? And that, of course, means what do we do with the burden of disease? How do we keep people well? Prevent them from getting sick in the first place? And then, of course, it's a matter of also longer term treating disease so that people can maintain their lifestyle, can continue to be productive members of society. And by the way, that's for men, that's for women, that's for children, that's for all of society. And which role plays the PPPs here? Exactly. It's critical. Absolutely critical. I will talk about education first and then I'll talk about PPPs. In some countries, this has been a tool to find uncertain projects. And in my opinion, we start seeing some crisis and problems. But let's begin with education. I would like to say that all of the countries present here and the representatives from the private sector, we see that there are solutions. And specifically, we can learn from success stories in terms of what needs to be done to address each country's needs. However, we must say that not necessarily every solution can be replicated elsewhere because we need to address each country's reality. Imagine, let's try to use the same medicine to heal a different disease. We need to understand the different factors involved in a disease because one single medicine will not heal everything. Education in Mexico was a challenge. It's one of the 14 structural reforms that my country underwent. Of course, it was tense at points and it required a confrontation to a specific degree because there were vested interests. You mean the teachers? I'm describing the vested interests, not necessarily the privileges that teachers had. Some teachers had taken ownership of the largest union in Latin America, two million teachers, which are part of the teachers' trade union in Mexico. And some teachers, well, they have taken hostage the state due to their vested interests. So we decided to take ownership over education. Now the state governs over education in Mexico. We have education for free. We have 30, we have 36 million students. It's twice as double the population of the Netherlands, 36 million. So with this number of teachers, we had to create a method that would place evaluation as the best way to screen the best teachers. We needed to give teachers a possibility to improve their level of income by means of a system of merit by training. And we needed a better infrastructure and better learning content. So this was the basic purpose and this is what we decided to do for Mexico. At the end of the day, I believe that each country has to tailor its decisions to its own reality and by creating the reform and adjusting it to Mexico has been a challenge. It's not an easy task, but I want to share this with you in this discussion because it is easy to give away solutions, but the thing is how to put them in practice and you have to understand each country's reality and it can take a toll politically. It took a political toll. Yes, yes, it was exhausting because it is linked to other reforms as well. Mr. Groot. It is exactly getting to the right point because two things are now being discussed. One is healthcare. Let me also mention distance healthcare. When you talk about developing countries, how can we bring the best healthcare to the far out parts of that country? And with the latest technology from companies like Philips or Siemens or General Electric, we are able to do that. And again, this is to my point that as a government, we should grasp the opportunities of these newest technologies and make them of use to our population so that not only in the developed countries you would have a doctor in every small city, every small town, also in developing countries where you might have fewer numbers in terms of doctors and hospitals that you are able to get the best possible healthcare to the most distant parts of those countries. And this is what the newest technology is providing us. It is really fantastic on education. I completely agree with the Mexican president. It is not just about skills. It is also about how to bring the education to the young people and how to create a right mindset of being able to deal with transformative change, which is taking place at the moment. And for us, for example, it means that coding increasingly is now part of the educational system. It is not just being able to count and being able to read, but also being able to understand what coding means and being able to deal with that is also part of the educational system. Increasingly so. Again, we have to deal with all the negatives of the newest technology, but these are all examples of how it can help us to really, in a transformative way, improve our societies. President Peña Nieto, okay, go ahead. If I could maybe just add one comment that I think is a bit of an intersection between education and science, certainly that we see from the many different STEM or technology fields that we're involved with, is just the fundamental premise around education of not only learning what, but understanding how to learn. And it can seem very, very basic, but many of us in here, and I'm making a big assumption, much of our education was based upon what we knew at a particular point in time. And when you think about how quickly science is advancing, the half-life of an education today versus what it was only 10 or 20 years ago, what's much more important is the ability of young students to be able to learn and perhaps reeducate themselves several times over throughout the course of a career. And we see that, particularly to be true in the basic sciences. And so thinking about how we build our education systems, thinking about how we build our employee development and education systems with this idea of continuously learning, continuously developing yourself and your particular area of expertise throughout your career is going to be more critical than ever to ensure that people don't lose their relevance, don't lose their ability to contribute and really make a difference for a company or a country or society.  Sorry, I said brief because I want to hear from Michel Baker that everyone is talking and you are quiet right in the middle and I am sure that you have plenty of things to add to this conversation. Thanks, what I was going to say is there's the education and the learning and then the question of what are the jobs and where do now, students go, how is job creation handled and what is the changes structurally to the nature of jobs and what kinds of investments. So one of the things that we look at through innovation work and the classic makerspaces, but where is innovation happening? And so one other way I hope that governments grab on to the opportunity, because I'm a big believer there's huge opportunity still, is where are their investments for local solutions and is their investment in social enterprise or are their investments the new emulating VC funds sometimes, their innovation funds or challenges and we find that there are many people trying to emulate Silicon Valley global platforms, but there's also a surprising number of people who are really interested in solving local problems and looking for government investment programs that are at least a corollary to the more glamorous piece of how do I actually get seed funding, how do I try to solve a problem for my neighborhood and so I would hope that we can show the promise of this and then encourage these kinds of government programs as well so that more people are actually have some steps to take in addition to looking for jobs of the already prevalent companies. Well just reacting again very briefly, I get very enthusiastic about this. We have introduced the system of the right to challenge. That means if the local government is providing solutions for the local community the people can then tell their local counselors hey we have a better option, we have a better solution and this is the right to challenge, we are implementing that at the moment, it's very difficult again, like lifelong learning is not easy but government is not easy but that's why it is so fascinating but it is a it is a great program because exactly as you are saying is making use of the enthusiasm of the energy of the people who know best what they want for the local community and making use of the latest in science and technology. Yeah but you talk about education and if the young generations are prepared and are receiving the right education to face the challenges of the future and I was wondering if the because President Peña Nieto mentioned that he had to deal with a very strong teachers union. Are the teachers in Netherlands, in Mexico or in Bangladesh with the skills the right skills to face and to educate these future generations? Well obviously still a lot has to be done there but at the end for us as politicians we should be on the side of the teachers and not of the unions and we are there to make sure. Which is for many people it's the same. No it's not the same unions, no no I mean I'm not against unions but they are a grouping which we should talk with and discuss with but at the end we don't work with teachers through the unions and there is a direct relationship between the government and the teachers and the unions are there as an NGO to be part of the social fabric of society. I want to mention one thing for developed country there is no much problem problem with the developing country you must well as well from developing country now we have graduated to developing country least from least developed country to developing country how we could do it within 10 years we give more importance to education well if we think about the industrialization we need educated people it is important and education must be diversified education it is not that just they will pass and take the certificate no they have to learn how to run the industry or how to run school then teacher teacher also need education and training which we are doing we are trying but I don't really diversification of education are they willing to to educate to re-educate themselves educate yes the themselves also we give facilities we give facilities to do training for the teacher we are giving like we have established digitalized Bangladesh now we have internet service all over Bangladesh for computer 1996 when I found government I found nobody use computer some people they have computer just it is it is like a showpiece keeping in the table that was the situation now we change it now everybody using it now we are giving we have multimedia classroom we have different I mean we we started for from student to teacher we are giving training to them now industrialization we want we have a already started establishing industry all over countries inviting foreign investment like PPP basis G2G basis or personal private sector we open up private sector but for that also we need technical look science technology education this is very very important and we we are taking all the steps for that so education is the key for everything education you need it's also the key we've heard what it's going on in Bangladesh in each country and on addressing your question this is a process that takes time you can't reach that outcome to provide you are you asking for a second mandate oh no no no time for teachers we need time to train teachers prop properly so they can teach properly and that's what students deserve and what is the right content as as it has been said we need to learn how to learn and as Alec and the change is so fast that more than giving them formal learning contents we need to teach them how to learn they need to keep on learning throughout their lives otherwise they're going to be left behind and the first question was how do we use technology to solve today's problems I believe that there's a huge window of opportunity in the area of technology used but there's a challenge that we have identified first of all we're living in a world that is growing in population we're eight billion people in this world 50 years ago 60 years ago it was half the population we're seeing I've always said this it's like going on an elevator when you were one or two writing the elevator when you click on one or two floors but when you have 20 people in one elevator and you have 20 floors so it becomes excruciating so that's the challenge of governments how can you keep up 20 people in one elevator clicking on different floors with calm with patience how can you keep them calm to get to the floor that they have pressed on the elevator and that's how we describe the state of society and I believe that technology has demanded governments to present outcomes fast because that is what society demands and as a consequence we started sitting in the world well practically the non-conventional approach people sometimes are against the system because it might have taken years to build we're starting to see opposition to democracies political parties and in this has happened so fast that people are questioning if it is working or not what has what is the best alternative because what do you think this is happening we're seeing it we are seeing it in Latin America in different parts of the world there is an anti-system approach the recent election in our country for example where we have government already elect with great support from from voters and the traditional parties got the worst voting results ever and my parties included and this shows clearly and this is the case of Mexico it is clear that the society supported one political option and I'm very glad that that was the way to go because that's the next president of Mexico's level of support and we see the same thing in Europe in Latin America we see a break in this status school we see that the momentum is being broken that was creating positive results but now the society is asking for fast results and we have an anti-system approach you can convert population to your asset like in our country we believe that we have younger generation if we can give them proper education and if we can give them opportunity they can be our asset because for agriculture for education for industrialization for healthcare everywhere you need trained people educated people so I believe that it is not a burden rather through pop-up plan program you can achieve your goal you can give them training you they can be your asset now within 10 years we achieve our GDP 7.86 percent under these circumstances we have so many problems but even then we are making progress how? as because we are encouraging our people giving them opportunity giving them more facilities that's why we achieve our GDP 7.86 percent and also our poverty we reduce to 21 percent from 40 percent to 21 percent so that way our country is making progress now we are as I told you as before that now we are going for industrialization but industry it must be diversified different type of industry so that it can it is not only that we will export but our purchasing power is increasing our own market is increasing so that way we are working so education is the key that I can tell you can I tell you something? now I understand why you are a politician I have a question for you I know that you are a strong advocate for open internet and open source which role in the education challenge has the open internet for developing societies? and I want to place mark I'd like to come back to the anti-society bias at the end if I might so open internet and open open source let me separate them out for a little bit and talk about open source which I think is pretty fundamental positive building block for many levels first as an educational tool if you actually want to learn coding but how it works in the world especially in a large project those are hard to do in schools and individual projects so open source as a way of learning by doing and seeing what's actually real as well as bringing trustworthiness into the system because clearly one of the issues with technology today is trustworthiness and how do we build a system that's trustworthy enough that your point of view will be successful that we still grab hold of it and try and fix the problems rather than be afraid and so open source is the ability to actually verify that what someone tells you is happening is actually happening and we can see across a range of technology products but also other institutions that once you learn that what people told you is happening is false then all sorts of anti-society problems come out so I see open source as a huge educational tool for something that is a public good open source is the only way for it to exist that's why Mozilla is trying to build part of the internet as a public good and everything we do is open source it's a public asset and finally it is a huge tool for building something that's trustworthy but in your opening remarks you call for participation and local engagement how do you help to achieve or to reach people who live in rural areas in developing countries who don't have access to internet which is in my opinion one of the main tools in nowadays education so Matt might be your first question about open internet and how important is it but access to the internet with a broad range of content is obviously the fundamental activity and so one of the questions is very much like education what we've been finding in our research and activity is that the solution to internet access in rural areas is very local solution and needs a community whether it's community networks or community engagement often there's a regulatory problem related to spectrum and how it's managed but very often getting out into the highlands of I'd say Bolivia versus getting into the rural villages in India they are very different solutions and so that fundamental piece needs like the flexibility of government to enable many local solutions flexibility that's my next point for the politicians that regulation do you want to add something to this and when flexibility is involved you should ask me a question I would just like of course this debate is focusing on the positives and the negatives of this technological revolution it's only logical but let me try to combine the two and because on the one hand we know through technological change particularly women might lose jobs because many traditional jobs in many countries where many women are involved will be the first to be involved in this new technological revolution take for example the healthcare sector at the same time we know that when we are all getting older that we need more people to be taken care of so the technology here will help us for example in Netherlands we have 130,000 vacancies over the next 10 years in the healthcare sector we can if we would not have technological innovation one in four people will would work in the healthcare sector in 2025 that's simply impossible we're already spending one in four euros on healthcare we cannot have one in four people working in the healthcare sector that's simply impossible so you can combine the two which is to make use of the latest technology the fact that you're all getting older and then also to mitigate this negative of that many people might lose their jobs and this is the role for us politicians this is difficult if you don't play this well you will have a populist backlash if you play this well it would also be a new lease for the more traditional centrist parties to be able to continue to govern their countries but this is a key test which will come up and technology providers and a final point will be on a totally different issue which is the fake news debate we now have that these newest technologies will also help us to fight because this is one of the biggest risks our society are confronted with the fake news it will also help us to fight that if you play it well so there are many again many positives but at the same time we have to play this extremely well as politicians and this is not easy I would like to invite now Alex Gorski President Peña Nieto mentioned that everything goes super fast today and talking about regulation policies red tape it seems that the governments are big monsters and to change anything within the government it's a huge effort and the private sector usually goes faster than the public sector no okay we have a debate here a different panel what would you ask the governments to change in order to go faster with the current speed of the changes of the revolution that we are living in look I think that the government has an important responsibility to always be balancing the right level of regulation with obviously the impact that it's ultimately going to be having on society in our world it's then one for example about the approval of new products and carefully balancing safety quality access with speed to patients and what we have found is that there too it takes partnership it takes education it takes transparency of information and that's what as we were talking mentioning earlier I think being a more of an optimist I think having greater ubiquity greater transparency of information more sharing between what's available in government what's available on the private side can facilitate this kind of balancing that we're talking about to have it be more effective and more efficient interesting we have four minutes left I don't know if a question was asked to politicians but what's specifically the question you were going to ask a question about stability what that's really odd oh my god politician asking a journalist to ask a question and all right this is okay that's getting interesting all right no I want you to to be focused now in the time that we have left in the transformation of jobs the industrial revolution is transforming jobs and for many people that means that their traditional job are disappearing and that has political consequences just to mention I live in Washington I I see what happened in Wisconsin in Ohio in Michigan how this globalization has changed those states and that had an important impact in the political arena in Washington how do you deal with the people who are not skilled to change their jobs in their 50s 60s or 70s in many countries but they lost they lose their jobs because of this transformation very brief we're going to start with the three politicians that we have here well what I feel that we have some traditional I mean production we are giving them special training and all the facilities so that well it can be modernized so that they can continue their traditional activities side by side job opportunity now in our country we have internet service all over the country even up to a village level we establish digital center people are getting job opportunity and people are using internet and side by side the light broadband we have broadband all over we are started giving them and we have satellite now it's give people like for agriculture agriculture now we are encouraging people that I know the traditional job they will not do as because they are educating now mechanized agriculture we have started teaching them and also engage them in the traditional job it is not that we will just bring them out from their traditional one but they will I want to keep them there but with the giving them mechanized ones so that they can continue that way we trying to do it so and also the mobile phone now we have mobile phone in each and every people they have so the new technology and new thing they should learn so how much you can teach them and training them then you can Prime Minister yeah I know time is short la tecnología yes technology has brought consequences and technology will bring about solutions I believe at the end of the day it should not be seen as and as a problem it should be seen as a breakthrough that has happened very fast but we're going to see many solutions deriving from technology and from my opinion I would say that being open is part of the solution what might be a problem and we've seen different views already if is it positive for different countries to join globalization well that might give rise to the development of global value chains several regions for example the European Union North America and the generation of value chains and job creation in regions is linked to technology if we isolate ourselves if we impose protectionist measures well it seemed to be that that we have managed to do several decades ago it's been seen today by some countries has been seen the formula to solve the problems that globalization has brought along but I believe that globalization will allow us to face the challenges of this time we should not close our doors technology is bringing us issues to solve but technology is going to be part of the solution now you ask for questions would you say that it is a failure that Canada decides not to add up to the to NAFTA I believe that the ground is set so we can take advantage of this platform to revamp the agreement that we already have Mexico has reached an agreement with the United States already Mexico expects that Canada reaches an agreement with the U.S. as well and we hope to have a partnership of three partners for North America I believe that for Mexico the United States is the biggest partner it represents 90 percent of the trade we do in North America and for Canada of course trading with the United States it's extremely important it's even bigger than the trade that Canada has with Mexico so some portion is already sold we're very positive and we're optimistic that the the portion that is left we will give us three three partners your response has been very sensitive it's it's too in a nutshell no failure answer your question is two-fold first of all you need to put in place deep-rooted reforms because from that you will get growth the Netherlands is now growing twice the pace of France and the United Kingdom and one percent above Germany because I think we put in place the necessary structural reforms and now they're delivering and from this growth you will get new jobs it is the engine to job creation at the same time you need modern labor laws a modern labor market in which particularly the 40s and over 50s and 60s are able to be as flexible as possible within that labor market whilst maintaining a maximum of security at the same time which is necessary for them to be willing to adapt to these new circumstances I think if you have those two in place you can deal with these disruptions and you have to as a society because otherwise all these vacancies will not be filled and if they are not filled and they are not taken care of by the newest technology then you might have a big issue within the health care sector and within your educational system we ran out of time but I think it's fair and nobody in the Walgreens Forum is going to tell me not to give the floor 30 seconds for the two last panelists to close the panel so let's no no no no from the private sector so Mr. Goski the floor is yours well as you could probably tell from the comments earlier I think that there's more reason to be optimistic about the opportunity that innovation and technology presents in helping us deal with many of these issues however with the strong caveat that it's going to need to be done in a balanced way with the right sense of security for workers with the right balance of regulation by governments but I'm convinced many of the examples that you heard up here today when we create the right kind of partnerships that have got the right kind of trust and accountability that we can make tremendous strides forward Ms. Mitch but we haven't heard anything from the journalist of what excuse me say it again maybe I'll finish up and we could go on okay later okay we're not done with disruption but we're seeing the early phases of disruption of democracy I too believe technology can be a part of the solution so we have more disruption coming I'm not sure that any one of us will embrace all of it or how much of it we you know will each wish we could avoid so moving into I think more and faster disruption one of the key aspects for grabbing hold of technology has got to be trust and trust in institutions I don't know if we can go back to being slower again but what is a quick enough response of institutions to maintain credibility and be able to be respected enough to move forward and solve problems and so this question of transparency and accountability and engagement and how do we use technology I think to build trust in the underlying institutions will be key to almost everything with that we have to leave it here Mr. Root Mr. Gorski Ms. Baker Mr. Peña Nieto and Ms. Hasina thank you for sharing your thoughts thank you please please I you have to cash out if you can stay be seated we are going to watch a video and after that there are going to be some closing remarks but stay in your chairs please


Sharp Sword by Bernard Cornwell Read by Paul McGahn The tall man on horseback was a killer. He was strong and ruthless and young to be a colonel in Napoleon's imperial guard, but no one took advantage of his youth. His curiously pale eyes gave his handsome face a chill of death, enough to make men offer respect. Le Roux was the Emperor's man. He went when Napoleon sent him, and he performed his tasks with skill and pitiless efficiency. Now he was in Spain, and he just made a mistake. He cursed himself for it, but he was also planning how to escape. He was trapped. He had ridden with a cavalry escort to a miserable village at the edge of the Great Plains of Lyon, and there had found his man a priest. He had stripped the skin inch by inch from the living body until the priest talked. They all talked to Colonel Le Roux in the end. Yet this time he had taken too long. At the moment of victory when the priests screamed out the name Le Roux had come so far to learn, the German cavalry erupted into the village. Men of the king's German legion, who fought for Britain in the war, savaged the French dragoons, their sabers rising and falling, their hoofbeats drumming a rhythm behind the screams of pain, and Colonel Le Roux had run. He had grabbed a captain of the cavalry escort, and they'd written desperately north. Now an hour later they had stopped at a wood that grew about a stream that tumbled towards the river Tormes. The dragoon captain looked behind. We've lost them. We haven't. Le Roux's horse was streaked with white sweat. Its flanks heaved, and the Colonel felt the terrible heat of the sun smashing through his gorgeous red uniform jacket, looped with gold. The light breeze could not stir his sweat-plasted blonde hair. He suddenly smiled at his companion. What's your name? The captain was relieved by the smile. He was frightened of Le Roux, and this unexpected friendliness was a welcome change. Delma, sir. Paul Delma.  Well, Paul Delma. We've done great things so far. Let's see if we can lose them for good, eh? Delma, flattered by the familiarity, smiled back. Yes, sir! He looked behind again, and again he could see nothing except for the bleached grassland silent under the heat. Colonel Le Roux was not deceived by the emptiness. He had spotted the dead ground as they rode, and he knew the Germans, good professionals, were out in the plain, spreading the cordon that would drive the fugitives towards the river. He knew, too, that the British were marching eastwards, that some would be following the river, and he guessed that he was being driven into an ambush. So be it. He was trapped, outnumbered, but not beaten. He could not be beaten. He had never been beaten, and now, above all, he had to regain the safety of the French army. Then he would hurt the British. He felt the surge of pleasure at the thought, by God, he would hurt them. He had been sent to Spain to discover the identity of El Mirador, and he had succeeded. And now all that remained was to take El Mirador and squeeze from the British spy the names of all the correspondents throughout Napoleon's empire who sent their messages to El Mirador in Salamanca, but first he must escape this trap. He let his horse walk into the cool greenness of the wood. Come on, Delmar. He found what he wanted, a fallen beech tree, its trunk rotten in a tangle of brambles and leaves. Leroux dismounted. Time to work, Delmar. Delmar didn't understand what they were doing, but he followed Leroux's example, stripped off his jacket, and helped the Colonel clear a hiding place behind the log. He smiled diffidently at Leroux. Where do we hide the horses? In a minute. Leroux dismissed the question. The Colonel seemed to be measuring the hiding place. He drew his sword and poked at the brambles. It was a weapon of exquisite craftsmanship, a straight-bladed, heavy cavalry sword made by Clegantar, as were most of the French cavalry blades, but this sword had been made specially by the finest craftsmen. It was longer than most, heavier too, for Leroux was a tall, strong man. The blade was beautiful. The hilt and guard were of the same steel and the handle bound by silver wire, the sword's sole concession to decoration. The weapon proclaimed itself a beautiful, killing blade. Leroux straightened, seemingly content. Anything behind us, Delmar? The dragoon captain turned. Leroux... Sample complete. Ready to continue?


In this video, I'm going to talk about the circumference and area of a circle as it pertains to geometry. So again, a couple of things that you need to know, you need to know what the circumference of a circle is, which circumference is a fancy word for the perimeter of a circle, just the distance around it. And then the area of a circle is all of the space that's inside. Alright, so these first couple of examples, what we want to do is we want to find the circumference and the area of a circle with a diameter of 3 meters. Leave your answers in terms of pi. Okay, one thing to note, leave your answers in terms of pi and then if I scoot over here to this other problem, find the circumference and area of the following figure using pi as you go to 3.14. Notice that the directions are a little bit different. This one we want to leave in answers in terms of pi. This one, we actually want to multiply times 3.14. I will show you, I did this specifically because I want to show you the difference between leaving answers in terms of pi and getting actual decimal answers for your problem, okay? So hopefully this will answer some of those questions for us. Alright, so find the circumference and the area of a circle. So what I'm going to start with is I'm going to write down the area and circumference. Actually, no. First thing I'm going to do, this problem here, it doesn't have a picture to it. This one over here has a picture, this one doesn't have a picture.  Here's my circle, here's my center, and I have a diameter, I have a diameter of 3 meters, 3 meters. And that goes from edge to edge, okay? Now, you might not need a picture for this, but it is very helpful if you want to get an accurate description of what this is. Okay, so in this case, one thing that you need to know, you need to know what the diameter is, which is 3 meters. And then you need to know what the radius is, which in this case is half the diameter, so that's going to be 1.5 meters. So I've got a diameter of 3 and a radius of 1.5. A little vocabulary there. Alright, final circumference in the area, circumference, there's a couple different ways to find it. You can either do pi times diameter, or the circumference is 2 pi times the radius. Either one of these works, it doesn't matter. Since they give us what the diameter is, I'm going to use the diameter. I'm not going to use this one, but I could use that one if I wanted to, since I actually know what the radius is. But just for simplicity's sake, I'm going to use this one. Alright, so circumference is equal to pi times the diameter. My diameter is 3, so there we are. So circumference is equal to 3 pi labels. Labels is meters. 3 pi meters. Now, notice I didn't grab a calculator and multiply it times 3.14. That's because they want me to leave my answers in terms of pi. So notice I did not multiply times 3.14. Leave the pi where it's at. Leave your answers in terms of pi. That's what that means. So my circumference is equal to 3 pi. Now, the reason that we do this is because sometimes when we're calculating circumference area, whatever it is of a circle or a sphere, whatever we're working with, sometimes the math is easier to work with if we simply just do not multiply times pi. We don't multiply times 3.14. So that's kind of the reason behind it. It just kind of depends on the problem. But in this case, we're just leaving our answers in terms of pi. Alright, now for area, area is equal to pi times the radius squared. Now for circles, we only have one formula for area. Circumference, we have two of them. You can use either one, but area, we're only going to use one of them. Alright, so pi times the radius squared. Now, we do need to know what the radius is. That's why I put the 1.5 here. So the area is equal to pi times the radius 1.5 squared. So we have to take the radius, we have to take 1.5, and we have to square it. Now, if you know what, if you kind of treat this like a 15, if you know what 15 squared is, you know that 15 squared is 225. Okay, but if I have decimals now, if I take 1.5 times 1.5, that's two decimals. So I can have two decimals in my answer. So that's actually 2.25. Okay, so 1.5 squared is 2.25. Alright, and so we're in a room here. My area is equal to, leave this in terms of pi, 2.25 pi. And my label is meters squared. Make sure you get your labels correct on this. You know the difference between a single dimension of circumference, which is just meters and two dimensions of area, meters squared. Okay, now notice that I have the 2.25. Yes, you could have decimals here. Just make sure you put them in front of pi. Don't put them behind. That's not usually how we write it. So make sure you just leave it there. If you have a repeating decimal, it's a little bit different. Sometimes you round that repeating decimal. Sometimes you don't. It just kind of depends on the problem. But this one, we didn't have to worry about it because our decimal came out nice and neat, 2.25. Okay, so on to the next one. On to the next one. Alright, let me change my color here. Alright, so find the circumference and the area of the following figure. Use pi is approximately 3.14. Alright, so now we're actually going to take our numbers and multiply times 3.14. Alright, so let's actually, let me give myself just a little bit more room here. Can I give myself more room here? Yes, I can. Smart boards are awesome. Find the circumference and the area of the following figure. Use pi is approximately 3.14. Okay, so I'm going to do the same thing except for I'm actually going to multiply times 3.14. Now, I'm also in this problem going to show you the difference between multiplying times 3.14 and multiplying times pi. There is a difference even though it's just a small difference. But here we go. Let's go on with it. Alright, so my circumference, so in this case 8 meters, it says it's right by the center. This tells me what the diameter is. The diameter is 8 meters and so my radius is 4 meters. Okay, this half of it is going to be 4 meters. Alright, so my circumference is equal to, I want to do the same thing I did last time. Circumference is pi times diameter. So I'm going to take pi times diameter. Circumference is equal to pi times, what is the diameter? Diameter is 8, I just said it. Alright, so in this case circumference is equal to, now this is where you grab the handy dandy and you take 8 times 3.14 and you get 25.12. Again, I mentioned earlier, you're going to get different answers depending on how you do this. If you multiply times 3.14, this is the answer that you get. If you multiply times 3.14, this is the answer that you get. But if you take 8 times pi, if you take 8 times pi, you're going to get a different answer of 25.13274 and more decimals after that, which this rounds to just 25.13 if you want to round to 2 decimal places. So notice 25.13 and 25.12, those are two very different answers. This one we multiply just times 3.14, this one we multiply times pi. Why the difference in the answers? Well, we have a difference in the answers because pi is a repeating decimal. It goes on and on and on and on. So what we're doing here is we're not multiplying by all those decimals as we go on.  You have to keep this in mind if you're working with a teacher, if you're working with your classmate, whatever it is, keep this in mind. Sometimes you're going to multiply times 3.14, sometimes you multiply by pi. The answers are going to be off a little bit depending on which way you multiply. Just keep that in mind when you're doing problems like this. So if they ask you to multiply times 3.14, go ahead and use 3.14. Don't use the pi button on your calculator. That way this answer that you get is similar to what other students are going to get, but the teacher is going to get little things like that. So now that that's over, make sure that you label this. Circumference is 25.12 meters. That's a pretty big circle. Circumference is 25 and a little bit more meters. That's pretty big. All right. Now area, I'm going to go kind of quickly through this. So area is equal to pi times the radius squared. Our radius in this case is 4. Area is equal to pi times 4 squared. Area in this case is pi times 16. Now remember we're taking, we're not using pi. We're using 3.14. So if I take 16 times 3.14, that's going to be 50.24. 50.24 meters squared, meters squared for area. And there we go. That one, I went kind of a little faster. Also on the same notice last time, if I don't use, if I use pi instead of 3.14, I would get an answer of 50. It's a bad 50. Bad 5. 50.26548 with more decibels after that. And this would, if you want to do two decimal places, this would be 50.27, which is very, that's 300s off. Okay, that's actually a pretty big difference there. So this is, if we just use 3.14, this one over here is if I use pi. So again, just keep that in mind, especially with these larger numbers. You're going to get differences depending on if you use pi or if you use 3.14. Okay, so there's a couple of examples of doing circumference in area. Now, one thing to summarize to go back to, leave your answers in terms of pi. This is what the answers look like if you leave them in terms of pi. You don't actually multiply by pi or 3.14. You just leave it. Okay, you just leave it. Or some of the problems are going to ask you to multiply times 3.14, and then you're going to get decimals for your answers. Just to make sure you know the difference between multiplying by 3.14 and multiplying by the pi button in your calculator, you're going to get a little bit different answer depending on who you're doing your work with, something like that. Just keep that in mind where you're doing these problems. All right, I hope that helped you with the circumference in area of a circle. And again, just make sure you know the difference between leaving answers in terms of pi and using 3.14 or the pi button to get your answers.