Group asks INEC to conduct CVR exercise before E-mode by ELSA and Colgui Governorship elections and the People's Democratic Party National Working Committee reserves or reverses McCarthy's suspension. This is Post-Politics and I am Mary-Anna Cohn. A civil society organization catch them young community initiative has urged the independent National Electoral Commission INEC to conduct continuous voter registration before the forthcoming General and Governorship elections in E-mode by ELSA and Colgui State. The group said it is concerned about participation of youths in the November 11th Governorship elections in E-mode State. The group noted that while youths constitutes the majority of registered voters in Nigeria they also constitutes the highest number of citizens that are yet to register therefore called on INEC to ensure E-mode youths are able to register and have their voices heard during the November elections. We're joining us to discuss this. I have Reverend Raymond Annolieffo. He is the Director Justice Development and Peace Centre and also joining us will be Mosheud ESA who is a development expert. Thank you very much Reverend Annolieffo for joining us. I hope I got it right. Yeah you did do it. I tried. Okay now it's very important because in my opening I noted that Nigeria's population is mostly useful and every single day whether we like it or not somebody turns 18 that means that there is more and more need for us to have a continuous voter registration but INEC calls what it does in a short space of time a continuous voter registration but then they stop and then conduct elections and after that the process is stalled. Why is it so difficult for us to have a portal that's open to young people to continue voting every time they turn 18? Thank you very much Annolieffo for having me. Section 9 of the constitution, sorry of the 2022 electoral act, does provide that registration of voters of dating and prohibition of the register of voters shall not stop later than 90 days before any election covered by this act but like you pulled it out what we call CVR in this country is probably not in the best it's not CVR it's not continuous voter registration as much as we will go behind it to live up to its billing and do what the electoral law requires of it but we are in a country where INEC itself will go back on its guidelines will go back on its laws and probably nothing happens INEC already has ruled out a lot of activities leading up to the November 11 election for the three states in the upcycle elections but nothing has been said concerning continuous voter registration I think it's important like you pointed out a lot of young persons have just turned 18 and we saw you happen in the last in the election we just concluded that a lot of persons still couldn't collect their PVCs some couldn't even register I think it is only appropriate that INEC will do what it's needful by opening up its portal that young people and all many well many Nigerians in those three states who desire to be part of the electoral process should be allowed to vote and how to register. We also noticed that there are so many gaps and problems in terms of voters cards after the registration process we saw again that there was a high number and in fact unprecedented increase in the number of young people who registered just before the general elections in February but most of the complaints that were recorded were either that these people were unable to get their PVCs or their PVCs were missing and I'm sure that if you followed the news you had seen PVCs that were recovered in different places in sacks in bags for instance in Lagos on Election Day a bag of PVCs were recovered and people started going to knock on doors to ask people if you know they could receive their PVCs I mean so registration yes is one very important key issue that we're discussing today but again why does it seem like even if INEC throws its doors open to those who would register getting the cards might also be an issue the elections are almost around the corner whether we like it or not in a few months we will be gearing up for those off-cycle elections what's the guarantee that even if people are registered today those PVCs will be gotten in time for them to participate well there are no guarantees there are no guarantees but I could be a stickler for laws the law is clear that not later than 90 days so all that INEC needs to do is to open up exporters for people to register let we just get to that point in this country where we do what is expected the right thing I just think with all that INEC has said leading up to this to the off-cycle elections the focus was mainly on the political parties and of course on the politicians who are the third-year hearts in the ring in the race but not much consideration was actually given for the electorate no consideration okay as simple as register now let's register that's one thing when the registrations are done hopefully if we talk to calculate 90 days from November we'll be talking about the registrations and ending about sometime in August now after that INEC can do what it needs to do print the cards since the the states are fewer it shouldn't take them so long and then make a border and then of course with the push of civil society organizations and all the other interested groups for people to go and pick up your PVCs now the truth is because it's a smaller election the area must cover it's not so large I don't think we're gonna have the same problems especially logistics or preparations from INEC and all those bottlenecks that we experienced in the general elections which was of course a much wider coverage but I don't think we are going to experience that I think if INEC is interested in inclusivity if INEC is interested in working the talk then they have nothing else to do than to at least even if it's for a month or two allow for continuous voter registration a lot of persons are angry for it a lot of young persons are angry to get registered to be part of it you know the last election the general elections have already shown us that we can we can we can change the the status quo we can do something if given the enabling environment and that's simply what we're asking INEC to do in this regard allow for continuous voter registration at least up until 90 days to the general to the elections okay well Masud Issa is just joining us via telephone Masud just as we've been having this conversation before you joined us groups are calling on INEC young people are calling on INEC to open its portal and allow for continuous voter registration which I have a problem with I'm wondering why we call it continuous if it's being stopped from time to time what do you think the major challenge is for INEC and why is that portal not being open being that INEC doesn't need any serious logistics to keep that portal open Masud can you hear me well I don't think you can hear me so I'm gonna throw that question back to you Raymond well I don't think continuous like you pointed out it's ongoing probably not necessarily it has to continue add infinity probably at a certain point in time it can always stop so that we the data collected can be properly aggregated and then of course processed and then some and cleaned up generally that's what INEC is expected to do and that's why there's a provision of the law if the law says 90 days not later than 90 days before the election can INEC please try at least not to go back on its own guideline INEC has a guideline for this the electoral law has been passed in 2022 and these things are clear there we it's not so the truth is we're not supposed to be arguing about this we're not supposed to quarrel or fight about it or begin to make me make bones out of this but because of the country where we are where there are no penalties for reaching offenses no serious penalties to such malfeasance coming from a body like INEC who is supposed to be the electoral empire I think at this stage INEC has a lot of redeeming of its image to be to do and this this can be a process this can be at this step in the right direction by INEC. Lovely Moshouk can you hear me now? Yes I can hear you. Perfect let's talk about INEC redeeming its its image in the eyes of the average Nigerian because many people would say that INEC talked to a good game just before the elections but then they delivered something that looked like nothing close to what the you know apparently billions of trillions were sunk in the sunk into into the electoral process and the whole elections in fact if INEC had asked for more money I'm guessing INEC could have gotten it but here we are still looking at what happened during the general elections and the governorship's governorship elections that held across the country how what do you tell an 18 year old who sat and watched what played out in February and in March the fact that several people did register they could not get access to their PVC's and also the fact that hey we're asking them to register so that they can be ready for another election what exactly can we tell those people to get them involved in the process okay not not to hold a sweep of INEC or not to say INEC has done well but what it tells you an average 18 year old is that democracy is a process and then the process doesn't used to be as good as this like 10 years ago or 15 years ago of course we expected something much much better considering the fact that a lot of civil society organization had pushed and ensured that a new electoral law was passed to encourage electoral reform to encourage transparency of course we are not where we wanted to be but I promise you we are not where we need to be as we got our electoral process just that we had get a lot of hope and expectations to Nigeria in the 2023 general election and unfortunately we did not meet up to that expectation especially during the presidential election but we could see that the presidential election during the governorship election there was a bit of improvement from the process it means the process can actually be better than it used to be and it can actually be better than what we delivered in the 2020 presidential election from what we saw in the governorship election it means there is hope it means there is a good framework on ground to ensure that we have a very credible election we just need the right people we just need the right political will to ensure that we deliver credible election and when we talk about the right people and the you know the willpower people who have the you know the the interest of the avid Nigerian at heart who are these people because it sounds like these people are not anywhere within the space that we're conversing in we just finished an election are we supposed to hope that those people who have emerged will be the people that you're making reference to that will help us to push this process further because I wanted to ask you in the middle of the conversation if you because you said we're not where we're supposed to be but should we still be where we are right now in 2023 when the whole world is trying to go to the moon so our democracy is 24 years old consecutively right from 20 right from 1999 to now and when I say we need the right people to be in the right place I will need the political will I know there are a lot of accusing fingers on the on the island chairman but alone he's not the only person I recall that there was a time that the president's nominated some set of people to be resident electoral commissioners to be national commissioners and there they were agitation that this set of people are carrying members of political parties they are partisan they were called around that so those are the political will I'm talking about it is wanting to have a good framework it's a matter to have the right people in the right place we have national commissioners we have residents electoral commissioners we have electoral officers at the local government level that were known to be car carry members they are known to be partisan so this to a reasonable extent could have affected the delivery of credible elections in Nigeria of course in 2023 we should have gone better than this obviously but again democracy is a process and then of course we are hoping to have the right to put in the right place we're hoping the those those that have the power will appoint the right people in the right place remember in twenty two thousand seven when the yard you are the president it came out to say the process that brought him to power was a float process and that was one left to the development of the committee and one of the recommendation of the committee says that the appointment of the iron next shaman and national commissioners should not be in the hands of the president should be in the house of the state the judicial and maybe a judicial committee or something but then we have not been able to actually implement a substantial part of that recommendation again is a process for every electoral law that has been passed there is an opportunity that with every election that comes that opportunity to take those laws and see where the gaps are in those laws and see where we can bridge those gaps so beyond the appointment of the chairman we notice that some residents electoral commissioners are partisan some national commissioners are partisan some electoral officers in the local level and I'm not like yes boys to the governors of those things but those are some those gaps that we need to bridge but at the moment we need to harness the law we have we need to implement those laws to the latter to ensure that them this are these laws deliver a credible election to a very very large extent all right let me come back to you Raymond almost a similar question I asked and must shoot a few minutes ago we're here to canvas for people who are going to keep turning 18 so that we can increase the number of people who vaults who decide who leads us at state federal and local government levels but how easy is it going to be a task to get these same people like I said to him to register and be part of a process that they somewhat have lost trust in I'll tell you what there are people who the media was in the forefront with civil society trying to get people to register to pick up their PVC is telling them how important and how powerful that piece of card is but of course after the elections people still don't feel the same way they felt before the election how easy a task is this going to be Raymond well it's definitely not going to be an easy task you know at this time generally as the people we we have not fully trusted the independent national electoral commission and so there's a trust deficit that we are working from and somehow the hopes that the 2023 general elections we're going to assist greatly to assuage the hopes and the belief in the system once again to a large extent was dashed a lot of persons didn't feel that the 23 general elections went on as expected and hopes were lost we practice incremental democracy and then I quite agree with the machine when he finds that we were not where we used to be as much as we are not where we are supposed to there's some progress there's some progress but that said I think it's like it's like we a child who goes to school and out of 20 students and he comes in class and there's a query as to why are you performing badly in studies and the person points that at least there are those who came 19th and 20th you know we should I wouldn't want to always always cut the slack for the institutions of government I think the government knows what they are doing I think we have the enabling environment when these laws are put in place but the the people to drive these process just like Mr. Mashu the same the people the persons to drive this process we just have to keep fine tuning fine tuning hoping that we get the right people to do the right thing so that we can get square pegs into square holes and then hopefully things can get better I know a lot of young persons I work with them a great deal a bit devastated and sad and some are not particularly optimistic about future elections but this is where like we said at the introduction part of this conversation where I think INEC needs to do better to ensure and give the hope give hope to some sort of a hopeless situation it's not all doom and gloom but we must continue to push the agenda that things can be done better that we can actually get this process right and then of course we'll continue to encourage the young persons this is the only country that we have no matter what we say about it it is because we love this country it is because we want this country to be better and as much as it's possible we have to constantly constantly speak truth to power not because we despise or we are going to attack anyone but because we want this country to work for the greater majority of us for the benefit of everyone because I can tell you we have all it takes both human natural and all the resources that we have we have all it takes to make this country the toast of the world let's talk accountability quickly before I go back to Mahshoud how do we get at the independent National Electoral Commission to be accountable to Nigerians bearing in mind also that it stacks payers monies that was you know given to INEC to deliver on this election of course we know that many were many applauded when mr. president was finally accented to the Electoral Act that was amended recently it was you know an applaud people were excited that it was one of the things that mr. president would be remembered for when he does leave office but then in terms of getting the Electoral body to be accountable who holds INEC to accountability how do we go about getting INEC to be accountable including the man at the helm of affairs accountability is key accountability is key and even after the elections we had a press conference in the office where we give a preliminary reports and part of what we said was also the fact that there is a need to audit if not in else the voter register the voter register so that to a large extent when we begin to ban the figures INEC said we have 94 million about 94 million registered voters and then it is something about 86 to 88 million voters collected their their PVC's but the turnout of the elections left a lot more to be desired now the question is what exactly happened with that in that regard what exactly happened what happened to the cards we probably had a lot of ghosts or maybe fake registrations or people came out but somehow the entire voters were just under 35 million and we are wondering where exactly did we get it wrong and then when we talk about holding INEC accountable I think of course this where the National Assembly must come out hopefully the 10th Assembly as we said as they go about having what we call a gender setting for this 10th Assembly that is going to come probably they might have to we might also have to review again our electoral law beginning from the appointment of the INEC chair must it have to be the must it be the president so that some of those processes we can get them right and we can actually hold them to account for what has happened look at the how bevers to a large extent performed its function of accreditation but then when he got to transmission of results real time it was a completely different kettle of fish up until now I rev doesn't have the entire results from the country uploaded so there's a whole gamut of issues and a lot of money was voted for this election and I'm sure more money will be voted for the upcycle elections as well and who is going to account for all of that I think the National Assembly has some work to do the institution we must begin to build strong institutions that can you know possibly after the elections the professor Mahmood the Anna chair should be able to answer questions should be should be held accountable for certain things questions should be asked and answers should be provided because tax plans money like you said so I think transparency and accountability is key and this we must continue to emphasize okay back to you Mahmood let's talk about other issues aside from the accountability because you know when we say that though the National Assembly if the National Assembly seemed to be benefit or benefited from the lapses in INEC or the electoral process why would they want to in any way hold INEC accountable that's one thing again what are the other avenues that we can use to reach these young people because they are our target this conversation getting more and more of them to register and see the importance and the need to be part of the electoral process our young people today have been given to all kinds of vices whether we like it or not and they're very the the attention span is pretty short how do we go about to get the attention of these young people aside from those who go to school that have some access to civic education what about those who do not have basic education how do we get about go about getting their attention okay thank you very much again there are various tools for communicating and reaching out to to these young people no matter your educational status and then there's always opportunity to collaborate with other agencies and whenever this discussion comes up I always make reference to the National Orientation Agency the National Orientation Agency have office in Abuja they have 36 states offices and they have 770 local government offices it means they are down to the grassroots there's an immense opportunity to actually collaborate with these agencies to actually reach out to young people irrespective of their educational status religion or tribe there are also a lot of civil society organizations doing a lot of grassroots grassroots work so we have immense opportunity to actually collaborate with different groups and reach out to these people it is one thing to have an electoral law it is one thing to have an electoral process but it's another thing for people to understand the importance of participating in this process and they're nothing for people to even know how to participate in this in this process if you educate people enough to tell them why and how their votes will count and the importance of their votes and the importance of the fact that their cost of living their standard of living is connected to all the political decisions they make then it should go along with enabling them to participate but before then if you educate them that and promise them you are going to be starting things to make sure their votes count then you actually also also do your own past and ensure that their vote actually counts and there's also power in storytelling in 2003-2007 to the honest you might be on the tree wanting to vote and the results of that polly unit or the results of that state will even be announced if you tell them that story and how we were before and how we are now and tell them the progress we've made and tell them the potential of progress we'll make if we participate and ask the right question and demand accountability then it should go along with ensuring that their participation will not be futile. So my thought is that we have to collaborate with the right agencies to reach out to people irrespective of their educational strategies or their standard background and also do our own part in ensuring that the promises we've made about their votes being counted also goes a long way but again beyond the election we also know that citizens the role of citizens is just beyond voting you have to also demand accountability you have to also make the politicians know that immediately they emerge into position of power you have to ask them the right question you have to ask them to fulfill their promises I have to remind them that if they don't fulfill their promises you have the power to vote them out. Okay well I want to say thank you on that note to Moshudi sir he's a communications and development expert and of course Reverend Raymond Annolieffo he is the director justice development and peace center thank you so much gentlemen for having this conversation with me and we have to continuously have these kinds of conversations. Thank you. Thank you for having me. All right thank you so much well we'll take a quick break and when we return we'll be discussing the reversal of the PDP's suspension of former governor of Kaduna State Ahmed Makarfi stay with us.


We have learnt the construction of interpolating polynomials for a given data set. We have learnt two ways of constructing interpolating polynomials. One is Newton's form of interpolating polynomials and another one is the Lagrange form of interpolating polynomials. In this class, we will learn to implement the Lagrange form of interpolating polynomial as a python code. Let us quickly recall the Lagrange form of the interpolating polynomial. We are given a data set where we have x coordinate and y coordinate. The x coordinate includes n plus 1 node points and the y coordinate includes the corresponding values of the given function at the node points x naught x 1 up to x n. Now, given this data set, we can construct the Lagrange form of the interpolating polynomial which is given by p n of t is equal to sigma k equal to 0 to n y k l k of t where all this l k's are the Lagrange polynomials given by this expression. Here, I would like to highlight the change in the notation when compared to the notation we have used in our lecture session. I have used the variable t here whereas, in the lecture session we have used x instead of t here. This is just for the sake of convenience in the coding part. In this lecture video, let us take the Lagrange polynomial and have a close look at it. First point to note is that we have to construct the Lagrange polynomial for every k is equal to 0 1 2 up to n. Remember what is this n? This n is coming from the data set where we have given n plus 1 number of node points and the corresponding values at the node points. So, for each node point, we have to construct the Lagrange polynomial as the first step. Here, you can notice that for each node k, l k of t is written as the product of the terms t minus x i divided by x k minus x i where the product excludes the term i is equal to k. That is l k of t is given by this expression. Here, t is the variable you can see t appears in the numerator where all this x i's are the node points given in our data set. Note that the Lagrange polynomial depends on the node points and therefore, depends on the number of node points given in the data set whereas, they are independent of the y values given in the data set. Also note that the denominator does not depend on t. It only depends on the node points and the numerator includes t. These are something which we have to remember when we are coding since, the denominator does not depend on t. We can compute the denominator once for each k and store in an array of dimension k whereas, the numerator has to be computed for every t. Let us keep this observation in mind and go ahead once the Lagrange polynomial is computed for each t that is once this quantity is computed for each t and for all k then we can go to obtain the interpolating polynomial t n of t using this formula. This is given by y naught into l naught of t plus y 1 into l 1 of t plus so on up to y n l n. Remember this summation has to be done for every t at which we want to obtain the value of the interpolating polynomial p n of t. Let us now go to the coding part. Let us see what are all the inputs that we are taking in our code. First is the function f that needs to be approximated and then we will take the number of nodes as the input. We will also take the node points as the n dimensional array and finally, we have to take the t values at which we want to finally, obtain the interpolating polynomial values which may be taken as an n dimensional array. Remember n has to be given as an input then we have to generate the nodes and separately we should also generate the variable t at which we want the polynomial values. Let us get into the code and see how to take these inputs. Of course, the first part of the code is as usual containing the import commands where we are importing two modules numpy and matplotlib. I hope I do not need to explain you these commands now. We are familiar with these modules as we have used them in our previous lectures of the python code. Let us go to see the inputs as we have seen in our previous codes. If you want to define a function through its expression you have to use lambda and then the variable name. Here I am using x for the variable of the function f therefore, we have to type lambda x and then a colon after this we have to give the expression of the function. Here I am interested to develop the interpolating polynomial to approximate the function sin 2 x therefore, my expression is sin of 2 x remember sin is not an inbuilt command in python, but it is included in the numpy module. Therefore, we have to give np dot sin. The next input is the number of nodes in the data set. It means I am interested in constructing the Lagrange interpolating polynomial of degree 3 here because I am giving the input as 4. Suppose I want to develop the Lagrange polynomial of degree 2 then remember I have to give n is equal to 3 that will generate a quadratic polynomial right because from our theory class we have seen that if your data set has n plus 1 nodes then the interpolating polynomial should be of degree less than or equal to n right. Therefore, if you have 3 node points then you should have the degree as something less than or equal to 2. Here note that in the theory part we have used the n plus 1, but the same here we are using only n this is just for the programming convenience. So, you have to keep this discrepancy in mind between the notation used theoretically and the notation used in the code. Let us go to the next input here we are taking the node points as our next input observe that we are using the command called arrange. Again this command is borrowed from the numpy module and since we have to prefix np to the command arrange. Well what does the command arrange do? Let us see the arrange command generates an array with value starting from minus 1.5 that is what we have given here and then ends with the number approximately equal to 1. I have given it 1.001 just to take care that one is surely included in our node point and it generates in between numbers with step size given like this that is 2.5 divided by n minus 1 where n is given here. Observe that 2.5 is nothing but the length of the interval minus 1.5 to 1. So, this arrange command precisely gives us the partition of the interval minus 1.5 to 1 with n number of partition points. This is precisely what we want as nodes right. So, we are generating a set of equally spaced nodes in the interval minus 1.5 to 1 using the arrange command. And stored in the variable x this is what we are doing at this line. Our final input is the variable t at which we want to finally, get the approximate values of our function f through the interpolating polynomials. Again we are generating points between the first value of the array x which is in our case minus 1.5 right that is stored in the variable x naught. And it goes till the last point of the x array which is denoted by x of length of x minus 1. Remember length of x is nothing but n here that is the way we have created the array x. Therefore, we are again creating a partition of the interval minus 1.5 to approximately 1 but now with the step size much less right. It is fixed here as 0.001 this is because I want to get the approximation of my function f through the interpolating polynomial at many points in the interval minus 1.5 to 1 that is why I am generating the t variable with step size much smaller. Well, I hope you have understood the input commands. Let us now go to the main program well before going into the main construction of the interpolating polynomial. Let us see how we want to get the output finally, from our code the output is obviously the interpolating polynomial values at the points specified in the variable t. Note that we are not going to construct a polynomial explicitly but only the point wise values of the polynomial are computed in our code. We would also like to display the graph of the polynomial along with the graph of the function f. With this note let us now go into the main construction of the interpolating polynomial. As I have mentioned earlier the denominator of the Lagrange polynomial that is this expression does not depend on t. Therefore, this part of the Lagrange polynomial can be constructed once for all and then stored in a variable. The denominator is therefore computed separately and let us store it in a variable called l d Lagrange denominator and use this expression in the denominator to compute the Lagrange polynomial for every t here. You do not need to compute this value for every t that will reduce the computational cost drastically. Let us see how to compute this denominator terms. Let us first see how many loops are needed to compute this. Well we need two loops to compute l d's. One is the loop with index k and it varies from 0 to n. Remember n is the number of nodes that we have taken in our data set. That is we have taken n plus 1 nodes in our data set. Then we should also have another for loop to compute this product and this for loop will run from 0 to n and let us use the index i for this loop. Remember in this loop we have to exclude one term which is precisely i is equal to k. Let us now see how to compute l d of k for each k. Remember l d includes the product. Therefore we will initialize l d with the value 1 in it and the length of the array l d is n. That is it has to start from 0 and it should go up to n minus 1. And l d is computed in this loop. Let us go to n minus 1. Go into this loop and see how we are computing the product involved in the expression of l d. Remember we have initialized l d with value 1. That means l d will hold the value 1 when it enters into the loop for the first time. Remember the first loop will run for k is equal to 0 to n minus 1. That will correspond to l d of k and in each l d of k we have a product. That product will run from again 0 to n minus 1 and we have to exclude one term that is i equal to k. Again I emphasize theoretically we are taking totally 0 to n minus 1. n plus 1 node points. In the input we have given 3 as n plus 1 but for the notational convenience we have stored it in the variable n only. Therefore wherever you see n in the code you have to theoretically remember that it is n plus 1. There is a slight confusion here. Historically theoretically we take the index from 0, 1, 2 up to n and take the data set as x naught, x 1 up to x n. Therefore we have n plus 1 node points that gives us the polynomial of degree less than or equal to n. Since we do not want to define our variable as n plus 1 we are just giving the name n for it. But keeping in mind that wherever we have n it is actually n plus 1. So this is slightly confusing but we have to remember this and then see the code accordingly. Therefore all our loop should go from 0 to n minus 1. Theoretically it will go from 0 to n. Let us now understand how this inner loop works. As we have initialized l d of k as 1 initially when you come for i is equal to 0 you have l d of k is equal to 1. Therefore l d of k will be 1 into x k minus x naught and that will be computed and stored in the variable l d of k. When you come for i is equal to 1 that is once this line is computed then again the control of the python code will go to the first line of the for loop. Again it will come check whether i is not equal to k if this is satisfied again it will go into computing this product. Suppose this happens at i is equal to 1 then again the control of the python code will go to the first line of the for loop. Again it will come check whether i is not equal to k if this is satisfied again it will go into computing this product. Suppose this happens at i is equal to 1 then what will be now stored in l d of k well it will be l d of k which now has this value into it will take this value that is x of k minus x of i. Now i is equal to 1 therefore it takes 1 and then it puts this product value into l d of k. Again the control will go to the first line of the for loop then it will check whether i is not equal to k. If i is equal to 2 and i is not equal to k then again it will come to find l d of k and that will be now this entire product will come here into x k minus x of 2. So, like that this product will go on for each i ranging from 0 to n minus 1 and every time it will check this condition if it is not satisfied then it will find the product otherwise it will simply skip to the next value of i. At the end of this loop we will have precisely l d of k which is given mathematically as this expression. So, we have computed l d of k for each k is equal to 0 1 up to n minus 1 in the python code whereas mathematically it should be 0 to n. Now we will go to compute the Lagrange polynomial note that the Lagrange polynomial have to be computed for each t also the polynomial p has to be computed for each t therefore it may be computationally efficient to construct both l and t together. Let us first understand how the loops are to be made to compute l and p well you can clearly see that the outer loop is a for loop for t variable this is because both l and p have to be computed for each t. Let us use the index j for this for loop and the outermost loop is running for the t variable with index as j therefore it has to run from 0 up to 1 less than the length of the t array for each t we have to compute l k where k running from 0 to n minus 1 and for each k we have to compute the numerator product which needs another loop whose index is denoted by i. You can see from this expression that for each t we have to find all the l k's what are they they are the Lagrange polynomials and k ranges from 0 to n minus 1 in the code and for each l k for each t the l k computation includes a product remember this product is very much similar to how we computed l d. So therefore once you understand how we computed this product this can be similarly coded once you find this product then finally you have to divide it by l d of k and that is precisely the expression for l k that we have seen in our slides. Let us see how to do this product so we are doing this product in this line remember for each k we have to find l k and for each l k we have to do the product and in this product we have to take care that i should not be equal to k this is something similar to what we did in computing l d k also. The same idea will go on here and we can compute l k for each k equal to 0 to n minus 1 and the product will run from 0 to again n minus 1 excluding i is equal to k. Once you finish this product then you have to come out of this loop and then find l k divided by the denominator term that is computed here right. You will divide the numerator product by this denominator product and that is precisely defined as the Lagrange polynomial remember this has to be done for each t and observe that this denominator value will not change by changing t that is why we once for all computed it here and stored in the r a l d and we are using it directly here otherwise this entire product has to be once again calculated here for each t that will drastically increase the computational cost but here we are not doing it therefore we are saving all this computation so we have computed all the Lagrange polynomials l k's right remember this l k's are computed for every t right. So, that is very important this needs to be done for every t once we are done with all the l k's for a given t then we have to go for finding the value of the interpolating polynomial at t and store it in the variable p j ok. So, this is what we are theoretically doing here also you find all the Lagrange polynomials for a particular t and then come to find p of t with this expression where all this Lagrange polynomials are plugged in here and then you have to multiply them with the corresponding function values. Let us see how to do it in the code so as the last part of this main loop we are now running a loop with index i varying from 0 to n minus 1 and here we are summing the terms in the interpolating polynomials for this we are first initializing all the p arrays as 0 remember p should have the length as the length of the variable t because we want to find the interpolating polynomials value at each t right. Therefore, p should have the same length as t variable and when we are initializing this array we are initializing it with value 0 because we are going to run the loop for summation whereas when we were initializing l d here we were initializing it with value 1 similarly the Lagrange polynomial l was initialized with again value 1 and that is done for each value of t right because once you find the value of p at a time then when you go to find the value at the next t variable you have to re-initialize this l that is why we are putting this initialization within this loop all other variables are initialized previously. So, once you get the polynomial value at one particular t again you are going back to this for loop you are forgetting all the Lagrange polynomials constructed for the previous t now you are initializing again the Lagrange polynomials as 1 with the array length as n and then again going and computing the Lagrange polynomials for the now the new value of t and then once Lagrange polynomials are constructed then you are coming and using the interpolating polynomial formula with the function value f v which we have initialized at the beginning itself f v is taken as the function values at the nodes remember we have taken the function values at the nodes and saved that values in f v right and this variable is finally used when we are constructing the interpolating polynomials here because if you recall p of t is given by sigma i is equal to 0 to n right f of x i l i of t right that is the formula f of x i is computed and stored in the variable f v of i and l i's are computed here and then this summation is done in this loop remember the only thing is theoretically we are running from 0 to n that we are making 0 to n minus 1 in the python code by appropriately giving the value of n. So, this completes the construction of the Lagrange polynomial and now let us see how to take the output just for the information we are printing the number of nodes used and the degree of the corresponding polynomial which is one less obviously and then we are showing the output in the form of a graph I leave it to you to understand how this graph is plotted let us go to see the output of this program well the code is executed and the output is shown here you can see that our print command is executed and the output is shown here you can also see that our plotting commands are executed and the graph is generated and shown here the black dots denotes the position of the data given in our data set red solid line represents the graph of the function f and the blue dashed line represents the graph of the computed interpolating polynomial p n of x using the Lagrange form of the interpolating polynomial for the given data set right. We can change the value of n to see the corresponding data positions let us go to do that let us change the value of n as 4 with this we are supposed to get a cubic polynomial let us see the position of the data sets are now shown here we have given 4 node points and the corresponding function values are obtained in the code and then they are plotted here and the interpolating polynomial is shown again in the blue line now it is a polynomial of degree 3 that is cubic polynomial and you can see that the interpolating condition is satisfied how are you seeing this at the node points the function value and the polynomial values are coinciding right that is precisely the interpolation condition in the previous case we have plotted the quadratic polynomial let me go back to that and show you when you put n is equal to 3 it means you have generated the quadratic interpolating polynomial you have generated 3 node points and therefore the degree of the polynomial is 2 and the quadratic interpolating polynomial is shown in the blue line and the polynomial value and the exact value are coinciding nicely at the node points confirming the interpolating condition. You can also increase the number of nodes as you want and also you can change the function here and you can play around with this let me put the value of n as say 5 and you can see now you will have the interpolating polynomial as the 4th degree polynomial which is shown here and the corresponding graph of the 4th degree interpolating polynomial is shown in the blue line I hope you understood the python implementation of the Lagrange form of interpolating polynomials thank you for your attention.


President Obama signed legislation ending the federal government shutdown October 16th. This is a continuing resolution that funds the government through mid-January and raises the federal debt limit through mid-February. Chief of Naval Personnel, Vice Admiral Bill Moran said our Navy priority remains funding forward operating forces, training them, and in the future of the force. Visit the Navy blog for more information. Meanwhile in 6th Fleet, the amphibious transport dock ship USS San Antonio rescued 128 men from a raft near Malta. San Antonio was more than 60 miles from the scene when the Maltese government requested assistance. San Antonio provided food, water, medical attention, and temporary shelter. Read more about these stories at navy.mil. From all hands update, thanks for watching.


horse for the speed of light, the cloud of dust, and a hardy high old silver, the Lone Ranger. With his faithful Indian companion, Tonto, the masked rider of the planes led the fight for law and order in the early western United States. The stories of his strength and courage, his daring and resourcefulness, have come down to us through the generations, and nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the great horse Silver. The Lone Ranger rides again. Come on, Silver! Tonto's life is in danger! Oh, Silver! In camp, he wakened at a whinny from Scout. Instantly alert, wondering the cause of Scout's uneasiness, the faithful Indian companion of the Lone Ranger listened to the night noises in the woodland clearing. Suddenly those noises stopped. Men, come here, Scout. Come on all side. That white cricket stopped noise. He knew he was surrounded, but by whom? Then suddenly... Close in, boys! Don't make a break! We got you, Redskid! Shoot him if he moves! Drop your hands! What's the matter, you fella? Grab him! You wanna rear horse, Steve? Me not struggle! You fella make big mistake. Yeah, there's no mistake. How about it, Jim? Is that paint horse yours? Sure it is. That's the horse that was stolen from me. I'll bet all I got on it. Throw more brush in that far so we can see this place. I'll do it, Red. Drop that Redskid. We'll make him tell where the rest of the stolen horses are hidden. Right. Stand still, Redskid. You fella got branched around here. The dog going right. We've all lost horses. Hey, fellas, this Redskid's got a partner. Look, there's signs of two men use this camp. Where's your partner? Me not horse, Steve. Never mind the lies. I know the truth. Why, you're caught right here with the goods. That's my horse there. That's not true. Well, I didn't prove it. Red, come over here. What is it, Jim? Let me prove that this paint is my stolen horse. Sure. Go ahead. We want to make sure of things. I'll prove it some minor. My name is Jim Jones. You remember Red the other day when I was painting my house with yellow paint? Sure I do. Well, my horse came alongside and got a smear paint on his room. Now, look. You take a look and see if there's not some paint there. I'll move the cutter to the fire.  He is a stubborn cuss, Jim. Come on. Now, give me a hand with him. Get over there. That's my horse. Him then scoff. No use you trying to lie out of it, Redskins. Here, Jim. I'll fetch your brand from the fire so we can see. Good enough. Take a look, boys. There's a smear, a yellow paint, just like I said. Jim's right.  It's the same color paint that Jim Jones used for his house. There's no doubt of it. This must be his horse. He described the horse to us ahead of time. Remember? Sure. He had the description right down to a T. What about it, Redskins? You ready to confess to horse stealing? Me not steal horse. Denying it, eh? Look here, engine. There's been horses stolen from all of us ranchers. We suffered plenty from horse thieves. Now, we don't figure yours much to blame as the man that works with you. He's not a Redskins, is he? Me not talk. You tell us where the stolen horses are and where we can find this partner of yours and we won't hang you. Me not talk. You sure as thunder hang if you don't talk. Tell us, look here. Take a look at what I found. The only fool can't steal other things as well as horses. Look what I found in his saddle bags. My spurs, the fancy ones that I had hanging in my saddle shed. Silver one. And here's a good hunting knife that was in my saddle shed. Got my initials on it, see? Was that in the saddle bag too, Jim? Yeah. This dog going Redskins has been prowling all over my place. I reckon a few boys want still more proof I can supply it. Oh, we got proof enough, Jim. I had a hunch I could find this critter. You see, that horse always had a special long stride so it wasn't hard to follow the tracks to this woods. In the campfire, let us the rest of the way. Redskins, you're slated to hang. Me not horse thief. Boys, remember we want to be triple sure we've got the right man before we hang him. All right, Hank. There's more proof as I said. You can match the footprints of this Redskins against the footprints in my saddle shed. Look, Markison, see? Jim's got it right. I remember him showing me the footprints of a man in Markison's. All right, then. Who's got a rope? Here's one. And who's already in it? I'll put it around the engine's neck. Make sure it's fixed, right? Let me have the end. I'll toss it over that branch up there. This is as good a hanging tree as any wood find. No more wooden fire. I want to have plenty of light to see what we're doing. Jan, sir, hold on a minute. What is it, Hank? Well, taking the life of a man isn't something to do casual. That's the Eastener talking out of you. You'll get over that when you've been out here for a while longer, Hank. But the Indian says he's not a horse thief. You don't expect him to confess, do you? Well, I don't know. Hank, you don't want any part of this. You can clear out any time you want. But the next time you get into trouble with horse thieves, don't come to us looking for help. We agreed to stick together. Well, maybe it'd be better to go to the law. Law? What's the law? Old Parker. He hasn't caught a crook in the three years he's been served. He jugged the Redskins and the Redskins' pals and bust him out of jail. Let me handle this. Stand clear. There's the rope. Grab that freer now. Yeah, I got it.  Me? Not steal him. Lift him to the horse, fellas. He can't mount up with his hands tied. Lift him up. Uh, hoist him now. That's it. Grab his leg on that side. Yeah, that'll do it. Here's a branch to snap the horses. No, wait a minute, boys. Well, now what do you want, Hank? Well, let me speak to him once more. Look here, Redskins. We aren't a pack of killers. We're just ranchers that have been robbed. Now, if we could get back the horses that have been stolen from us, we'd be willing to turn you free, wouldn't we, boys? At least we wouldn't hang you. Now, where are the horses? Me, not steal them. Come on and tell us. Where's your partner? Me, not talk. It's no use, boys. Red, slap the horse out from under him. Let the critter hang. Scout, not move. We'll see. Get up there, Scout. Scout, not move. Slap that critter again. Get along there.  Maybe master a horse, make a mind. You say this is your horse, you tell him go. Get up there. Get along with you.  You not master. You not owner. Horse not obey you. This horse named Scout. Him my horse. I'll get the ropes. Who's that? Hey, where is he? Get him up, Scout. I can't see for them trees and dark. That must have been the engine's parking. Get our horses. Pay them. We've got to run them down. Hold on, Jim. Wait a minute, boys. Listen to me. Jim, are you dead sure you didn't make a mistake? You saw the proof. But the paint horse wouldn't pay attention. Are you a red? At the minute the engine spoke, girly, did you see the critter travel? The man had shot that rope in two. Where'd he come from? Who is he? I don't know or care. But I'm going to get after those two. You men can come or stay as you please. If I've got to run those horse thieves down alone, I'll do it. Where were they, Jim? Come on, boys. Get to the horses and get after them. The sheriff was a troubled man, haunted by the ranchers who had suffered heavily at the hands of horse thieves. He had tossed sleeplessly for hours. And finally as he dosed, he was suddenly wakened. Hey, what? Let me go. Where's my gun? Take it easy, Sheriff. I want to talk to you. But who? You don't need a light. You can hear in darkness and you don't need to see me. But who are you? What's the idea of busting into my house like this? What in tongue did you want? I want to know about those horse thieves. Horse thieves? Well, now I'm awake. Now I am awake. What do you know about them? You tell me. Nothing. I'm here to learn. And who are you? Jim Jones tried to hang an Indian. Oh, yes. I heard about it a little while ago. That red skin stole his paint horse. That's not true. I was with the Indian when he stopped at the Jones ranch. Jones saw both the paint and my white stallion. He had ample chance to learn what the paint looked like. Yeah? I left footprints near the saddle shed where he went to water his horse. And Jones led the ranchers to try and lynch my friend. Your friend? The red skin? Yes. But I understand there was evidence. A blob of yellow paint. Which Jones himself could have put on the horse when he found it. But there was a knife in the saddle bag. And spurs that belonged to Jim Jones. Both of which Jones could have put there when he claimed to find them. Oh, go on the way you tell it. But it sounded like proof that couldn't be shaken when the ranchers told me about it. How many horses have been stolen? Two scorn more. From whom? Red Tarbock, Jim Jones, Hank Fielding, Sam Blake. Why, from almost all the ranchers around here. How long ago was the first horse stolen? How long ago? Yes. A couple of weeks? Since then there's been thefts most every night. First from one ranch, then from another. Always horses? Yeah. No cattle? Never so much as a heifer. Well, isn't there any trail to follow? The ranchers are so cluttered with hoof marks that a trail wouldn't show very much. One horse's hoof looks same as another. All right, Sheriff, thanks. All right, now hold on. Don't you start a way till I've got my turn at asking questions. Go ahead, Sheriff, ask all you want. But don't light the lamp and don't leave the side of your bed. Who are you? Where'd you come from? Why are you so interested in that red skin? Well, answer me. Hello, sir. Go on it all. He's gone. The lone ranger hurried to the shadows of the rural buildings on the town's main street. Tonto was there waiting for him. Well, Tonto, I talked to the sheriff and learned that almost every one of the ranchers have lost horses. That's right. And those men put their search for us. They reported to the sheriff. They'd built a pretty strong case against you, Tonto. Me, no. But why? Jim Jones seemed muddy anxious to hang you. I wonder if he didn't want to hunt for the thieves to be called off. If the scout had obeyed those men, you'd be dead. You come just in time. At first I knew there were men in our camp that would make Scout move if he had. Well, you'd have had your neck broken. Scout, plenty smart. Jim Jones knows about these thieves, Tonto. He must. Otherwise, he wouldn't be so anxious to hang an innocent man. How we make him confess? I don't know. Are there ranches still over there in the cafe? Ah, then there now. All of them? Ah, Jim Jones, red there, the father named Hank, many other. All right, then. It's a matter of silver.  We've got you covered. The sheriff. Close in, boys. No, Tonto, no, no. Have us surrounded. Don't shoot. These men are lawmen. Here we are. This plenty big mistake. Oh, you should fight now. Don't shoot. You won't be shot. Take their guns, boys. All right. You were the one that was in my house. Yes, I am. I told you the case against Tonto was a flimsy one. It still is. You'll see. We'll see about that. Boys, take him inside the cafe. We'll let Jim and Red look him over and see what they've got to say. This Indian's the one we catch it all right. You gotta wait. Well, I got him again. And his mask partner along with him. Take the mask off that one, boys. One minute. We're not guilty and we'll prove it by showing you how Tonto was framed and naming the leader. He was not framed. Now wait a minute, Jim. What is it, Red? Boys, listen to me. The masked man's right. He's not the horse thief. Maybe he can name the real one, but he don't need to take the trouble. I'll confess. I stole all the horses. Red, you don't know what you're doing. Now hold on, Red.  You're saying I have to save these two. I don't know why you're confessing to it. Why you want to save these two, but you're not the thief? We won't let you confess. Why don't you do that, Red? What'd you confess for? You know it ain't so, Red. Boys, I've made my statement. It stands as is. Take it or leave it. The curtain falls on the first act of our Lone Ranger story. Before the next exciting scenes, please permit us to pause for just a few moments. When the sheriff captured the Lone Ranger and Tonto and took them before the ranchers in the cafe to charge them a horse dealing, a rancher called Red suddenly confessed.  Well, Sunday, you've got no reason to steal horses. You're the richest man in the valley. You heard my confession. If you want to jail anyone, you've got to jail me. I'll be hanged if I'll jail you. You've got to prove you stole those horses before I'll believe a word of it. Where are the horses? Well, I sold them. Who, too? I don't know. They're way off by this time. The cash is in my bank account. A pack of lies to save this mass man. If you jail the mass man, you've got to jail me, too. But I... I know enough of the law to know that, Sheriff. You can't jail a man who claims he didn't steal the horses and let go free the man who claims he did. Now, can you? Well, I was never up against anything of this sort. I'm doggone if I know what the law says. It's no use, Red, to see him.  The mass man knows the truth. I confess to the stealing. What's that? Jim Jones?  I'm your horse thief. This don't beat all I ever do. Give me those guns. I'll stand back, all of you. Back there. Against that wall. You can't get away with this. Leave your brush, Sheriff. Get your guns, Tutto. Let me get them. Boys, close your eyes. Move quiet. Move back. Back some more. Jim Jones, Red, you two step forward. What if we don't? I'll help you. All right, all right. I'm forward. Never mind grabbing me by the shirt. I'll do what you say. Take the guns, Tutto. Let me get them. The Sam Hill's a matter with you. You heard me confess to the horse. Stealing what more do you want? I want the truth and you're not telling it. Of course he isn't. Jim Jones is no thief. I'm the thief. Neither one of you can tell where the stolen horses are. I said I sold them. You didn't, Red. I sold them. I sold them and put the cash away. That's enough. Me got the guns. Take them outside, Tutto. They'll go to a new camp and we can make them talk. Huh. You hear what Lone Ranger say. Oh, Red. Great guns, that's who it is. The Masked Man's a Lone Ranger. And you go outside. Sure. If you make a mistake, if you let any of your posse try to follow us. No, this ain't right. Ain't fair or square. You're doing me wrong. First, I got four men to charge with horse stealing. Two of them self-confessed. And next minute, I got none at all. And not one of the four is a real thief. What I have? Perhaps the real thief will be found after we hold the meeting. Ready, Tutto? Uh-huh. Tell us on horse. Ready to ride. Get started, then. I'm with you. Get after him. Get him back. I want on for him. Give him yourself. That's a Lone Ranger. Let's see what he can do. I'll steal the land. Camp some distance from town. The Lone Ranger permitted Jim Jones and Red to dismount. Can you find us here? No one follows from town. Why'd you do this? What are you after? The truth, Jones. You're going to give it to me. No matter what he says, Jim Jones isn't a thief. Neither are you, Red. Why did you confess? That's my business. I've got nothing to say except that Jones isn't a horse thief. I know why you think he is. He tried to frame Tauno. Sure I did. I wanted someone to hang so the whole thing would be cleaned up and the rest of the ranchers wouldn't want the sheriff to keep hunting clues. Now listen to me. You did enough lying in the cafe. Now we'll get some truth. Sit down there. It's nothing to discuss. I said I was... I said sit down. All right, then. You too, Red. We'll sit next to each other so I can watch you both. The following day, the sheriff was in his office when Tate wrapped one of his deputies and sauntered in from the hitch-rike. Well, how'd the office go while I was away, Sheriff? Good enough, Tate. Can't complain. Had a little excitement last night. Yeah? How's that? The ranchers thought they was in the track of horse thieves. Yeah, the horse thieves that had been operating around here? Yeah. Did they get them? They trailed to Redskin to camp in the south woods. Claimed there was a lot of evidence against him. His Marcusons fitted footmarks that was found around Jim Jones' saddle shed. Uh-huh. And the horse of Redskin had, a paint, was like one of the Jim Jones string. It even had a smudge of paint on it. Paint like Jones used on his house. For a time, I reckoned the boys was dead. Sure, they'd captured the horse thief. It didn't turn out that way. But who was the Redskin? He wasn't the thief. He got away all right without too much trouble. Say, it's one of the boys who didn't string him up. You know, Sheriff, it seems to me Jim Jones himself might be involved in horse stealing. Oh, why should he be? He's got plenty of cash. No, I don't know about that. I've heard he hasn't as much as folks think he's got. Hmm. As a matter of fact, Tate, the evidence did point to Jim Jones. Have you investigated him any? Not yet. I wanted to sort of think it over for a time. Wasn't any more horse of stone last night? No. I haven't been a robbery since you went over to Pine Flats. But you never know when it'll break out again. That's right. Since you left three days ago, the Lone Ranger's turned up around here. The Lone Ranger? Hmm. You've heard of him, haven't you? Sure. Who hasn't heard of the Lone Ranger? What's he doing around these parts? Looking for thieves. Horse? Ah. I see. Has he got a lead? Says he don't need one. He's just waiting around in town to see the horse thief trap himself. Trap himself? How can he do that? Here's a good one, Tate. Sit down, let me tell you. Yeah. You know, the last horses that were stole was took from Jim Jones. Yeah, so I heard. There hasn't been a robbery since then, huh? No. I suspected at the time that Jones robbed his own livestock to throw off suspicion. Everyone else but Jones has been robbed. Here's what happened now. It's going to be funny. Wait till I tell you. Well, go on, tell me. Jones came here with horses he'd bought real cheap. Now, you know a man can buy real cheap horses if he doesn't insist on a legal bill of sale. Did Jones buy stolen horses? I'm not saying. But the fact is, those horses had an old brand on them. A brand that could hardly be seen. It was sort of a secret brand, see? Huh? Well, when the Lone Ranger came here and told how certain parties were buying stolen horses, he and Jones got to compare in notes. And here's where the funny part of it is.  What? Won't that be a humdinger? And they'll come right in here with blood in their eyes. Hutton and the critters have sold them back their own horses that have been stolen. Oh, did you see? We don't have to do a dog-gorn thing but just sit back and watch what happens. That's why the Lone Rangers hang around here. Well, then we'll take a walk. You watch the orbits like it back. I'll watch things. Bye. There goes the sheriff, Tunner. Uh-huh. Let me see him. Now we see what deputy and officers do, huh? Are there ranches where we can reach them in the hurry? All ranches in town. All waiting cafe. Good. Look, Tate's leaving the office. He's hurrying to that house across the street. Come on, Tunner. Hey, what's the hurry? You needn't knock the door down, Tate. Jake, take this note and travel fast. You know where to take it. Get there as fast as the best horse will take you. What's the matter? Anything wrong? Got to change the plans. Now don't waste time. I've got to get back to the office. The sheriff will be back in a minute. Hurry. You've been in this office long. The sheriff? Oh, hello there, Jones. Hi, Red. Tate, we want to talk to you. Hi. A mask man. You bet it's a mask man. It's the Lone Rangers. Come on, Tate. You're riding with us. Uh, riding? Following the man you just sent out with a message. Man? We saw you. I baited you and you took the bait.  We'll see where your partner leads us. No, wait. Listen. Come on. Ouch, wait. I don't mean my neck. As your horse, get on him. I will. I will. But tell me what this is. You know what about. No, no, man. There's Tonneau at the top of the hill. He's watching the messenger. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. Come on. You're too strong, and you've got two men. Well, those are your horses. It's mine. And mine. Yeah, you see my horse is too. They're shooting, boys. They've asked for it. Let him have it.  You'll need them as witnesses against their leader. Take them alive. Come on, Silver. With the lone ranger and the lead, the ranchers raced into the valley firing into the air. They quickly surrounded the rustlers, forcing them to surrender. Don't shoot. We give up. Do we surrender? Hey, you double cross and pull cat.  No, Jack, I couldn't help you. Save your talk for court.  All right, you've got me, Sheriff.  Sure you did, you crook. You thought the Lone Ranger knew who you were selling horses to. You thought you'd sell them to the ones they'd been stolen from before Jones got them.  But, but who talked? Someone must have known about me. I'd give everything to know who it was. No one. I'm sorry, Tate. Jim Jones had been made to believe that his friend Red was a thief. To save Red, he tried to frame an Indian. I'm sorry about that. I don't know what I'd have done if the Indian had died. I never knew I'd go that far for Red. When I realized that Jim had framed the Red Skin, I figured Jim was guilty. I sooner confess and hang myself to see Jim Jones hang. Friendship, Tate, is something you wouldn't understand. You see, Jim and Red were partners Each is alive today. Well, because the other saved him. Each was ready to confess and hang to save his friend. Yes, they did confess. Then the lone Ranger took things in hand, got them together and found out that you was the one that gave each of them the idea the other was a thief. And no one told on me? No, Tate.   If you hadn't been such an adult head you wouldn't have sent me here. Then they wouldn't have followed me here. Enough talk. Get them back to town, boys. We'll see what the jury says about them. Where's that mask man now? Hey, hold on there, mister. We'll meet again, Sheriff. Good luck to you. Hey, hold on. Wait a minute. I want to tell that Red Skin that I'm sorry. I'm sorry. Wait! It's no use, Jim. Those fellas don't wait for thanks. But you can bet your life they were glad to help you. It is a copyrighted feature of the lone Ranger Incorporated.


Hello and welcome to the International Daily Roundup with People's Dispatch where we bring you some of the top stories from across the globe. Let's take a look at today's headlines. Kiko Kujumuri alleges systematic fraud in Peru's election as Pedro Castillo leans. Over 100 activists arrested during protests at Python construction site in the US. Residents of Luxembourg Islands protest Indian government's autocratic reforms and in a video section we take a look at the blocked vote campaign to prevent Israeli ships from docking in North America. As the vote counting in Peru enters the final stages, left-wing candidate Pedro Castillo has pulled ahead of far-right presidential candidate Kiko Kujumuri. Kujumuri in response has launched allegations of fraud and irregularities in the election process but has yet to provide substantial evidence. During a press conference on June 7, she accused Pedro Castillo's left-wing free Peru party of stealing votes and committing fraud. As of 8.30 am local time on Tuesday, with 96.9% of the votes counted, Castillo has won 50.2% of the votes. Kujumuri from the popular force party has won 49.7% of the votes. Castillo's party has denounced the allegations and urged election officials to protect the vote. In the National Office of Election Processes, the run-off election on June 6 saw a voter turnout of around 77%. Castillo in the first round of elections held on April 11, with 18.9% of the votes. He is a schoolteacher and a trade union leader. He led a nationwide teacher strike in 2017 against then-president Pedro Pablo Kuczynski. His platform includes a set of anti-neoliberalism policies, including the naturalization of natural resources and industries such as mining, oil and communications. He has also expressed support for rewriting the country's constitution. He has supported Latin American regional integration and he has supported calls for the creation of a plurinational state. Meanwhile, right-wing candidate Keiko Fujumuri is the daughter of former dictator Alberto Fujumuri. She is in favor of the existing neoliberal and exclusionary constitution. She is currently placing charges of money laundering and if convicted could face 30 years in prison. In our next tour, we go to the state of Minnesota in the US where over 100 activists were arrested on June 7. Protesters led by indigenous women and two-spirit people gathered at a construction site operated by the Enbridge Company. The protest was part of an ongoing struggle against Enbridge's Line 3 pipeline route. The cross-border pipeline is around 1,000 miles long and stretches from Alberta and Canada to the US state of Wisconsin. As part of this project, Enbridge wants to construct a 340-mile pipeline through northern Minnesota. The company has claimed that it is only replacing the old pipeline, however, the new plan will double the flow of tar sands oil. The pipeline will curve through the indigenous and shun arbitrary activists have stated that the project will violate indigenous lands and endanger the sacred wild rice plant. Moreover, once completed, the pipeline will carry 760,000 barrels of oil per day, increasing chances of possible environmental disaster. Hundreds of protesters scaled a metal fence to reach the construction site near Park Rapids on Monday. They climbed on top of equipment while some chained themselves to bulldozers. Other activists blockaded the road leading to the construction site using a fishing boat, bamboo and steel cables. The indigenous-led Guinevere Collective has been one of the groups at the forefront of the struggle. Police forces arrived at the site shortly after. By afternoon, a Department of Homeland Security helicopter could be seen flying over the protest, keying up clouds of dust. Police and ride gear arrived at the site towards the evening and began arresting people. Pipeline activists have previously accused Enbridge of paying for policing along Line 3. They reported that police officers have poloed activists put over their vehicles, detained people in cages and used surveillance drones. In our next story, we go to India, where residents of the Lakshadeep Islands held a 12-hour hunger strike on June 7. Communities on the islands have been protesting against a set of proposed laws which will impact their culture, livelihoods and their local ecology. The Lakshadeep Islands are a union territory, which means that they do not have their own legislative assembly, rather they are under the direct control of the central government through an administrator. The proposed laws that are at the center of the ongoing unrest include major changes to land ownership and regulation. The administrator, Praful Patel, who is a member of the Bhartajanda Party, will have absolute power to grant permission to develop land. The government will also have the power to evict and displace people. These regulations have been widely opposed by local residents, 94.8% of whom are part of scheduled tribes. Local dairy farms have also been shut down and the multi-billion dollar amul company has been allowed to sell and franchise its products instead. The proposed laws also include the ban on the sale, transport, storage and purchase of beef and beef products. 96.5% of Lakshadeep's population is Muslim and around 65% of residents eat beef. The proposed ban will affect local cultural food practices as well as livelihoods. It is important to note that the beef ban has been a part of the right-wing BJP government's anti-Muslim sectarian rhetoric since a long time. Other proposed regulations include the disqualification of candidates with more than two children from council elections, the government is also planning to impose an anti-social activities regulation, otherwise known as the Gunda Act. It will give the administrator broad and discretionary powers to detain people. Police officers will also have the power to search and seize a house, vehicle, etc. if they have reason to believe that it has been or is about to be used for illegal activities. And for our final survey, we take a look at the Block the Board campaign by activists and workers in North America. Launched by the Arab Resource and Organizing Center, this campaign aims to block Israeli ships from docking in North American ports following the attacks on Gaza and the occupied Palestinian territories activists have been picketing at ports in several cities. They were able to successfully turn away two ships owned by the Israeli ZIM company in Oakland last week. Protests are also taking place in New York, Houston, Los Angeles and Vancouver, Canada. Here is a video feature on the campaign. In response to a call by the Palestine General Federation of Trade Unions, PGFTU, for an international week of action between June 2nd and 9th, thousands organized protests in major ports of North America. In a move to hold Israel accountable for its crimes on Palestinians, activists and workers movements have put up pickup lines on major ports in the United States and Canada to block entry for Israeli ships. The protesters stopped operations and blocked ships operated by Israeli cargo companies from docking. Protests have been held at the ports of Oakland, Los Angeles, Houston and New Jersey, among other places. A wide array of anti-imperialist and progressive groups and coalitions across the United States have joined together to organize these actions. We're here today to sort of send a message to the ZIM company that we are going to do what we can to make sure that you do not do business on our shores and continue to profit off of the Israeli apartheid. We're participating in global movement for white-hot domestic sanctions in embargo with Israel and if our government is going to continue to support Israel economically, support them together through the military aid, we're going to do what we can. The campaign targets incoming ships operated by the Israel-based ZIM Integrated Shipping Services Limited, or ZIM. Historically, ZIM has been tied to the Settler Colonial Project of Israel, having been one of the shipping companies to transport early Zionist settlers. ZIM is also currently one of the biggest transporters of weapons to and from Israel. Oakland witnessed the first of these pickets and prevented two ZIM ships from docking. ZIM had not attempted to use the Oakland port since 2014, when pro-Palestinian activists blocked its ships from docking for months. On June 2, the Oakland Dock Workers' Chapters of the International Long Shore and Warehouse Union, ILWU, Local 10, joined organizers from more than 30 organizations from the Block the Boat Coalition to pick it. On Friday, June 4, an estimated 1,000 people showed up to the port to prevent the docking of the ships. A picket in New Jersey was met with heavy police presence an armored vehicle sent by the police departments of New York City and New Jersey. According to reports, there was an initial standoff between peaceful and unarmed protesters and the police, as the latter were refusing the picketers from entering the docks. But eventually the protesters prevailed. Similar demonstrations are happening elsewhere, with more pickets planned for ports like Detroit, Michigan and Vancouver in the coming days. Dock Workers in Italy's Livorno and across South Africa also heeded the call for action and boycotted Israeli cargo ships during the bombing of Gaza. Follow us on Facebook, Twitter and Instagram. Thank you for watching.


Hello, and welcome back to the craft box. My name is Brenton today We're in Minnesota 156 of the wizard one-on-one death walk-through last episode if you haven't checked it out already we You're wrong thing. We made it into the cloudburst forest and Yeah, we're gonna be basically doing the whole of the club as far as today They are searching for Lady Zenzen seven star those foul wings Princess Zenzen is the king's granddaughter Lady Zenzen must be hiding down here to keep out of the Shadow Queen's clutches if they caught her King Nessa would break we must find Lady Zenzen before the shadow servants can search for any evidence of Lady Zenzen's trail you can find Okay Thank you So basically in between episodes I had to defeat three of these guys Um Yeah, they were kind of annoying, but it's fine. They didn't spam to our shirt as much as I thought they would so I suppose that's good And yeah, I gave that is a good nice Gave or whatever you want to call it Yeah, this is the best place to get this ground nest looks recently abandoned and there are signs of a struggle You find some feathers and a few sparkling rings could be evidence of the princess a trail leads off into a nearby clearing Okay Yeah, this is the best place to find that sort of stuff. I believe That or in the main growth marsh But yeah, there's also black glitters here. So that's always nice All that us here on in here. It is a boss and I believe it is a hard boss from memory Oh, this is a fine. Yeah, okay. We should be fine. Should be fine though. Let's do this How could you have lost that songbird lady Zenzen? It wasn't me that first founder. It was you I not turn out of the sky You barely scratched her so she got away from me. Never mind We have a scepter and cloak and a handful of feathers we can use that to convince King Nezah She is a prisoner. He will have no choice but to believe us. Wait. What was that noise? Two bosses, okay, um, I wonder if this I don't think that someone anybody no should be just this these two What else do we need I am worried now Hmm-hmm, you know what we are just gonna go for it. I think We boost on both so we should be fine. If not, we can just skip again. Okay. They can't have too much health Exponent they have like a billion health Yep, a billion health. Okay. That's great Hmm Well, then we will definitely use double feints today. That's for sure What was that noise? Okay, um, let's do this this is gonna take a while, but it's fine. We should be fine Okay, okay, that puts a fuel on us didn't know that one little fire beater Wow, do you know it had a master in there for something I put you about it's work That's weird. That's really weird This could go really badly I'm just saying Let's do that see how much Didn't expect to see this one. Okay. Mmm. Okay, then what's this? Okay, this could be going badly Hmm. Okay, maybe I should put some fortifies them. It'll be fine. We'll be fine. Um, Mm-hmm Let's just start mess-blading Okay, okay Did a bit? Okay, this could be bad.  No, it's not good. Okay. We don't need you So we can draw Um We use you Okay, must be lifeblade for him just in case he decides to use a life spell. I understand that Completely understand that I mean he has a master in death. So why not life, you know? um He could also use camera and that would use it. So who knows Um, what does he have? He has TC Um, let's do this Wow, okay I think I called that one.  Oh my god. We're dead. We're so dead.  I am back just Um, his thing. Hopefully this kills. Um, I teamed up and got some help from a fire wizard. So shout out to um KFC Firetail. Amazing. Um, and yeah, hopefully This or the overtime will keep him. Which would be good Um, yeah Um Yes, definitely accept. So yeah, let us Um Do that because I need health need health need a health need a heal And rip. Yay. There we go. Fantastic. Okay Look at that Amazing. So that's done Okay, um, what are we collecting? George scepter. Hello You collect all of the lady zin zin's trappings that the bad guys were holding. No other sign of the princess though Okay, let us head on back to Chiantico I need some health as well So, um, yeah, that wasn't It wasn't too bad. That's a lie. Um, it was terrible Uh, yeah, those guys are kind of hard. Is that life wasn't still there? That is unfortunate and a half That is really unfortunate that life was it's been there forever. Um So, yeah, let us collect some of these. I'm on like a really populated realm. So That's probably what why you're seeing a whole bunch of random people that aren't usually there It's good that you heard and foiled their plot. Lady zin zin must still be safe in hiding Go to alto alto village and tell king nesa that his granddaughter is still free How to get there you can't fly. Can you ask onyx rein son the jaguars travel freely throughout the realm She'll meet you by the eternal. I will keep my men fighting the shadow queens forces down here Okay, um, let us hit over to Onyx rein who is again following us. She seems to be everywhere. Um But as as he says that she has free path passage to everywhere, which is quite Okay, I'll be back in just a bit you need to go up to alto alto. There is no easy path for those of us who don't have wings There is an ancient path to alto alto which takes you up by way of the eternal falls I will help you with the ritual First drive back some of the tehuano spirits so you can climb to the cave of poison water flower A cruel priestess you need the pulp of the prickly pear cactus that grows in her cave Okay, um, I'll be back in just a bit Okay, I am back finished off defeating those guys um my game crashed And now I'm hitting it.  Who is this? Balance and storm. Okay then um We should be fine Who dares intrude on me? I see doom for my people and yours. Let me hasten your end Your end. Okay. Um, so yeah these guys we had to defeat there Not too bad. Um This boss could be a bit annoying, but you know what? We don't really care. Do we nope? Definitely not um We're gonna do that I also changed my deck um from the last fight because it was such a mess. Um So yeah from the last boss, I should say So yeah, it's much better now and hopefully we can Do this and not die too badly. I mean use kind of like in this area. You're kind of just The difficulty kind of gets quite a lot higher. Um And it doesn't really like chill out So yeah, you just got to kind of work hard for this um It's even worse because most of the time Well for like the last like forever double fame of um You you don't get like bitter gear. So like it's kind of like you just got to like power through with like level 60 here Luckily, I managed to snag some level 80 boots from the professor sword pack, which are actually really good um, so yeah, I had like level 60 ones and I swapped it out for level, um I'm gonna do this actually actually we're gonna draw And then we'll do that Stop giving me double things.  So Yeah, I did that. Oh, bye um So, yeah So Yeah, they give decent and other things as anybody online Let's just go for you and just compare for a sec. Um Yep. Hello, uh, I don't need you Would appreciate another blade though. Thank you um You You helped me the other day. She's great. Um So what do they give they give? Um Resist accuracy current damage It's for the bit of health.  You just can't go wrong with that. Um, yeah We are going to blade Um, I'm dying here, which is a surprise because you've done a lot.  Oh good good That is just unfair Like what the hell? No, that's not even fair.   What what am I need to do? Fizzle Okay, bye. We're dead. We're dead. We're dead. Okay Okay, then that's not fair Wow, okay, I'll be back in a bit. Okay.  Um, but anyway, we're hitting. Um, it's just as well. I put a spirit blade on last Uh, I'm didn't actually expect him to do that at all. So Kind of shocked. Um, but yeah This should hopefully do a lot of damage We'll be so close Yeah, um, we will quickly finish him off and then we should all be good Hopefully Um, so yeah, we have that which is great 1000 Okay, let's just pass about once we've got that That should Yeah, we'll just wait for that. It should be fine and wait for dr. Vaughn and do dr. Vaughn Oh yuck get out Stop while bolting. It's not fair. Not cool. Don't appreciate it. Um Why not? Why not? We can do this. Why not? See if this kills hopefully it does Do we have enough damage? I don't know. Do we? That'd be great No, okay, that's fine Oh, we did it. Yeah, there we go. Fantastic He did Bye Yes, take what you must but know that you only quicken your own demise Okay, prickly pear cactus Okay, I'll be back when I'm at onyx Okay, I am back and we're at onyx Well done. I'm glad poison waterflowers dark omens did not put you off your game You'll need to defeat more of the evil winds the taiwan or spirits to reach the second cave The cave is home to a hungry caiman You'll have to conquer him to reach the altar at the back of his cave Drop the pulp of the prickly pear cactus on to the altar. It will release an emblem glyph that we need Wow More of these mobs. Okay. I'll be back in just a bit once I've defeated these mobs. I gave yas Okay, I am back Just finished defeating those mobs and now we are heading in here Life and storm. Okay That's fun Welcome to my jaws Um, okay one thing that I got to say is like there should be a sound effect when you click that like Like these ones have sound effects But like this here doesn't and it's like confusing Like that has a sound effect and all that but like this it doesn't have a sound effect And it should just saying um, anyway, clearly off to a quick. I don't know why but like it's kind of important Like that's something that I think they should add but um Um, yes Um Remove you how much health 20? Oh my gosh He got a short much health just ain't even there 20 that's quite a bit quite a bit That's fun Oh That's cool Crossword also takes place I was questing on my life, um And obviously The only spell that life can do if you don't have the cookaburra here is crossword um And questing on my life solo takes forever Like seriously Like can life either get another aoe at a low level um Will become or shouldn't that down like that would be great like honestly Crossword just takes way too long in my opinion. It needs fixing Life in general just needs more aoe or another one at a lower level because at the moment it's just ridiculous Because you don't even get Crossword into like level 58, which is even after death. So It's like, whoa, what okay It's like through celestia you have to use random Like centaur and stuff because it's literally the only spell that's good that you have Um, yeah, it's ridiculous. Honestly.  I suppose Your life go on a group honestly Stick to what you're good at I suppose It's probably what they were thinking when they made it anyway Let's not give them like a good spells because they shouldn't be hitting anyway. They should be healing Because you know school should have certain roles But then you look at myth and you're like, well, what's at certain role, huh? Oh, seriously, what is it certain role tell me? I don't know Summoning minions. Whoa, that's cool because you can do them.  Hey There That is three blades That what okay Um, just got to you Draw Okay, I don't need you. I'll do you Okay, amplify. That's cool But this is gonna do a bit Let's go and do a bit 800 That did quite a bit. Hey I'll say just chill out a bit more. All right um I think we need another blade Yes, we need another blade Um, we'll enshrine you with this card of you. We'll draw for a blade. Thank you And then we will hit next Um, hopefully we don't die Which we could because here's lots of tips and a hundred health and We could be dead My hundred nine hundred Um, so yeah, we'll see how this works See how this goes Don't hit me that could be bad. Thank you Thank you for not hitting me. I appreciate it much Oh even the fortify right now. This is like perfect Like this is perfect timing. How do I how do I get this perfect timing? Please tell me This is not possible. This is all a lie. This game is a lie one minute. It doesn't want me killing in the next it does Bye Yay, I really do This um There we go Um, yeah, I will turn you into boots because that's what you deserve.  Um, what are we doing? Ulta hello You drop the prickly pear cactus pulp upon the altar. It has a sweet and syrupy smell There is a song of a howling wind rushing through the cave When it silences you see a stone inscribed with an emblem waiting for you The emblem glyph has a picture of a huge waterfall with a tall stone pillar beside it Okay Here we go. We're gonna be hitting up to alto alto It's fantastic. Actually. I really love alto alto Um, it's really cool Just like all of the areas in s teca. Just like the look and feel really cool. And then you do the quests And you kind of like wow this this is annoying. I hate this and behind that waterfall is terra de brea Um, which is another area, which is pretty cool. I don't actually really like the cenote and um terra de brea just I don't know. I don't really like them just because they're like kind of similar Whereas you look at things like this and you're like Wow, okay. We haven't seen this ever before whereas like terra de brea and like cenote, they're like basically the same thing. So it kind of like, you know, well, they're just the same You got the emblem glyph. Yeah, I did Take the emblem glyph to the cloud bearer pedestal. You will see a groove where you place it It will raise the sky pillar climb up quickly and don't look down.  That's a bit rude. Um How do we get up there? Oh, yeah, we have to go this way. I remember. I remember. I remember. Hello I'm gonna use this The emblem glyph fits perfectly into the groove on the cloud bearer pedestal Is a deep low grinding the sound is something you can barely hear But the sky pillar suddenly lurches up into the clouds something that huge should not move so quickly No, it definitely shouldn't, you know, correct about that narrator. Um, yeah, let us head up to auto Fantastic I should really impressed Um, yeah made it to auto auto and only took me Three hours to record this episode amazing You made it quite the view. Hmm The shadow queen's forces are strong here as her attention is focused on the avian king Fight some of the beak breakers who have gone over to the shadow to get the lay of the land branches Okay, so i'm gonna end off the episode here because I go Defeat some of these beak breakers to get the lay of the land Because I have to um record another one. Uh, here's the teleporter. It goes back to three points Yes, um, so yeah, that's cool. Anyway, thank you for watching leave a like and subscribe And if you're very subscribed press the little bell so you know exactly when I post another video and remember craft outside the box


Erin said that might have been as short as you've been this season. Did you feel that way out there? Yeah, I felt pretty good a couple of two-seamers Cut back, but yeah, I mean for the most part, you know, everything was pretty good. The change-up was good The cutter was a lot better tonight And my slider was good So yeah, the cutter just a matter of you were able to get it inside more than your previous start Yeah, it just just felt a little better coming out of my hand and you know I had a better direction of where it was going so I was able to use a lot more effective tonight What has it been like being around this group in this room as you guys have kind of been on this room on this run working your way back to first place? It's been amazing.  It's been it's been fun to watch What are you thinking as that ninth inning is unfolding? We got this especially when Gio came up. I said turn off the lights From your spot, what's the most impressive part of that rally?  Alvarado? Yeah, I mean I've never seen that, you know I don't only watch him pitch against us But I mean the way Luca that ball and you know Glaver hitting that ball First time I've ever seen that you know us against him It's early in the season, but you take first place for this one Does that mean something is this rivalry kind of heating up a little bit? No, I mean, yeah, it's always good to be in first place I mean especially against the teams in your division you want to play well and we've been doing that so far So we just keep it up You struck out low to end the sixth inning did you yell something towards the Yeah, probably but I don't remember what I said Is it anything relating to last weekend or just excited about the way the inning went? Oh, yeah, just excited about the game.   I mean, especially when you got DJ out there, you got Glaver, you know, these guys are making a great place for me You know all season, so it's been a lot of fun You've had a lot of third baseman that you played with what is geo defensively rank? I mean, he might be right at the top. I don't know anybody that I can name that's better than him that I play with