Good morning. Good afternoon depending on where you're listening in from my name is Austin Vock. Thank you for joining us today for dragnet live Listening to every episode of dragnet every Monday Wednesday and Friday until we listen to All 310 episodes currently available today. We're gonna be listening to episode 12 title is police Academy Mario Koski But before we get started I just want to remind people of the giveaway. We're doing if this is your first stream Actually, while I'm turning on these radios You'll notice we have comments coming down on the side if you're watching this on the OTR on the old-time radio archive channel You'll need to head to OTR gold and stream it there to participate in the chat I've linked to it in the description of the video So you should be able to click and you'll be taken right to this stream on my primary channel or what is now my primary channel? and Then when you're there if you subscribe you'll be entered It's you'll be Able you'll be eligible to win one of these two radios. These are two vintage style Bluetooth radios I'm gonna be giving one away when we hit 500 subscribers on the OTR gold channel If you're the if you're that lucky winner You'll be able to choose which color you want and then when we hit a thousand subscribers I'll be giving away the other one. These are kind of fun little things They look nice on your desk and it's fun to listen to some old-time radio through it Just connect it to your phone and play people are already sharing where they're from. Please continue to do that I love hearing where where our listeners are tuning in from and I'll be highlighting throughout the episode any relevant comments here on screen anything relevant to dragnet, you know some behind the mic factoids or trivia and But if you have side conversations, they're still fun, they'll just they'll just stay over here in the corner Let me think Last week or sorry on Monday we listened to We listened to episode 11 and there was some conversation at the end of the episode about the organ That's used at the end of these dragnet episodes when they do the the memorial for a fallen police officer I was trying to figure out what the name of that particular type of organ is After the stream I did a little bit of research. It's called the Hammond organ so I will share the Wikipedia page To the Hammond organ there. That's the that's the organ that they use in a lot of It was the first electronic organ. There's I think one that didn't use pipes if I'm Understanding it correctly and since it was electronic. It was it made it really easy to connect into PA systems at At stadiums another location. So that's kind of why it caught on But there's there's some fun reading to do on the the origin of the Hammond organ and then also the origin of stadium organists that we hear Great so Just wanted to share that and then also We talked about the four NBC chimes and I found a really cool YouTube video It's very short, but it talks about that fourth chime as life with Roscoe pointed out the fourth chime Added on to the end of the NBC the three NBC There was a fourth one that if you heard on the radio It was to alert you that news about World War two was coming. So quiet down. They're gonna share some news But in this video, I'll link you you will hear You'll be able to hear the four chimes and it's cool because they would ship out to stations just like a four-note xylophone And the first one would or I think it's a xylophone out or it could be something else But they would hit those chimes live on air. It's kind of cool Pre-digital music when you could just record it once and play it back as many times as you want Cool so today as I said at the beginning we're gonna be listening to episode 12 It's called police Academy. It was originally broadcast on August 25th Thursday August 25th 1949 Historical events since the since the previous broadcasts of dragnet, which was the week earlier on August 21st Canada's largest earthquake since the 1700s strikes Queen Charlotte Fault It said it was a magnitude 8.1 and it knocked cows off their feet I Assume they probably knocked more than cows off their feet, but this thing just specifically calls out cows Maybe because you know cow tipping is a thing and cows are notoriously hard to push over On that same day the Philadelphia fans caused the a's to forfeit a game this in baseball when they ride over a trapped line drive The Giants were leading four to two in the night But they're good winners August 22nd The long-distance swimmer Diana Nied was born in New York City. She was the first to swim from the Bahamas to Florida She did that in 1979 The North America Treaty Organization or NATO goes in went into effect on August 24th and Then August 25th the same day this episode aired for the first time Jean Simmonds Jean Simmons the The bassist from kiss the rock and roll band kiss was born in Israel so Hope you found that interesting and we'll get the show started Stuff works. Okay, here we go Hello and welcome to drag net from otrgold.com this episode will begin after a brief message from our sponsors Here's another in NBC's great parade of new shows Ladies and gentlemen The story you're about to hear is true Only the names have been changed to protect the innocent NBC brings you drag net You're a detective sergeant you're assigned to robbery detail an armed gang of blitz bandits has started to work in your city Their pace is fast four and five robberies each night. The criminals are not amateurs They're well armed dangerous your job Get them Drag net the documented drama of an actual crime Investigated and solved by the men who unrelentingly stand watch on the security of your home your family and your life For the next 30 minutes in cooperation with the Los Angeles police department You will travel step-by-step on the side of the law through an actual case from official police files From beginning to end from crime to punishment Drag net is the story of your police force in action It was Thursday October 23rd was windy in Los Angeles We were working the day watch out of robbery my partner's been Romero the boss is Ed back strand chief of detectives My name is Friday. I was on my way back from the statisticians office. That was 1142 a.m.. When I got to room 27a robbery detail How'd it work out Joe any good prospect? I don't know how good they are, but I got a handful. How many did you get? Let me see 15 1822 Ethel down in the stats office ran him on the IVM for me. There they are. Hmm. Let's see It's a gang of three men working on foot. Let's robberies. They only take cash I'm always tie-ups work from 8 to 10 at night one of the gangs tall the other two short And these are the men the machine sort it out under that heading you know if our information is wrong Then so is the machine got a good bunch of candidates here descriptions match up with what we got They seem to check the names on that last band some of the smartest thieves in the country. Yeah, Tommy Willis Rick Grapper Kim Satelli Manny Roberts George Cross Mario Koski Reads like June graduation of San Quentin. Yeah George Cross and Tommy Willis are in town We know that and Koski is around a couple weeks ago. And what about the rest? It's a big field have to check them out I guess might as well start at the beginning. Did you go through the overnight report yet? Yeah, no restaurants. No liquor stores That makes five days of gangs laid off. They can afford you can't think 18 robberies in 24 days That's pretty good. All this stop and go strategy of theirs Joe. It's got me They work hard for a week in one area and then they lay low. They just keep going.  You're looking good Hank Decker. How are you? So what are you waiting for applause?  All right, Hank and I are in service together Yeah, I just dropped in for a visit Joe. Are you busy? No more unusual Thanks Remembered you telling me you were on the PD. So I figured I'd drop around and get an inside track How do you mean I just filed with civil service to take the exam next month figure? I'd like to work at being a cop. He shall shop Joe Great pep talk you boys hand out.  Look, I'm 30 years old Joe. I'm married high school education, but a year of junior college What's your wife think? She's not sold That's why I dropped in. How about coming out to the house for dinner tonight? You want me to sell her just talk to her 7-ok Yeah, 7's okay Glad to met you Ben. Same here Decker. See you again. Bye. Bye Joe. See you tonight, Hank Well, what do you think Ben ought to make a good cop? We had a list of 22 possible suspects by 5 o'clock Ben and I had checked out Two of them who might possibly have had a hand in the blitz robberies of the 18 liquor stores and restaurants in the past 24 days Number one man was Thomas Willis Caucasian age 29 5 feet 11 inches 175 pounds dark hair blue eyes Number two man was Mario Koski Caucasian 5 feet 6 inches 170 pounds dark hair dark eyes Large scar under his chin running across his throat up to and behind his left ear According to our informants and after questioning some of their associates either Willis or Koski or both could have taken part in the blitz hold-ups We showed their mugs to the victims But none of them could give us definite assurance that either Willis or Koski were in the hold-up gang At 7 that night. I went out to Hank Decker's house for supper met his wife Linda his four-year-old twin boys We talked about the army played with the kids for a while Before we sat out to eat we put the boys in bed Hank was in the kitchen carving the roast His wife closed the door to the kids room and we started downstairs for the kitchen What do you think of our two Adam bombs? They're fine kids miss Decker Hank told me that you were worried about him wanting to join the force I Was 12 years old and my father was shot down He was a policeman in Des Moines. He was only 37 when he died. I Wouldn't know what to do if anything like that happened Hank What do you want me to say? But this Hank really want it Can't you talk him out of it? You're his wife. Can you? No, I think it's his choice miss Decker. He's gonna have to make up his own mind. I'm sorry It's what Hank wants. I Guess I worry too much a lot of women marry cops. They have and they will they all worry Hank will be all right. Will you guarantee it Joe? During the next month I heard from Hank Decker only once he was studying hard During the same month Ben and I were working hard trying to find some kind of a concrete lead to break the Blitz gang There had been no subsequent hold-ups which seemed to tie in directly with the gang or its operations From the list of possible suspects, which Ben and I made up 18 names had been eliminated for one reason or another either they were in jail at the time of the robberies Out of the Los Angeles area or out of the state But four names remained George Cross Tommy Willis Mario Koski Julian Brock During a latter part of the month George Cross was booked on a minor charge and we questioned him at that time He showed no knowledge of the hold-ups Nearly two months after the robberies were committed Ben and I were still without a solution as to the whereabouts of the gang Never know no Blitz gang like last night this way before Joe Once they get wound up they usually go until they caught yeah, did you get out those telegram checks of the east yet? Last night for went home sent out all three Willis Koski and Brock. I like to find just one of them Chicago might have something that's Koski's old hangouts Willis to what about Brock from Kansas City any yeah I got a Y2 might have a nicer from one of them tomorrow It's a slow job. We'll have to wait it out. Yes, so no follow-ups and the victims we talked to I'll get it Robbery Friday hi Joe Hank Decker congratulate me what for just passed my written exam got the letter this morning How about that? That's fine. When do you take your physical? Well, not till the end of the month next week I take the oral and agility tests and the physical if I get by them I'm in you're gonna have a full month at the police academy after the test is a lot of work Hank I can't be any worse than these tests It's a tough 30 days out there on the hill law court procedure evidence combat firing target practice You'll have to wade through all of them you ever gonna have anything encouraging to say yeah when you graduate I won't count on it. How's your job going slow? How's your wife feel now about that? She said to say hello Okay, keep us posted now. I'll do that job right by Hank passes written test. Hmm sure anxious Brandy Romero got a minute. Yes, careful. Come on. You got something Ed.  We were gangs disappeared not a trace of them so far. They leave town Oh, we're not sure Ed. We don't even have a good description. We're guessing most of the way What are your guesses? You've had a couple of months to make them 12 of the hold-up victims We talked to told us definitely that there were three men in the gang two of them short one of them tall We've just been working from there all three of them have dark complexion started with 22 possibilities and got it We did down to four no wait a minute three. Yeah, Tommy Willis Mario Koski Julian Brock Willis and Koski Eastern hoods Brock's from the Middle West and where are they now haven't showed their faces around town checking some of the cities in the East It's about all we God's giver and much for two months work thieves can't be that smart right now They are solid out every lead we had Ed. We're doing our best either of you ever hear of a man by the name of Al Mishukov No, I don't think so Chicago gunman the old days. What do you answer that? I thought he was doing time in Joliet parole last year Got a tip he was spotted on East Broadway night before last you figured might tie in with our job I don't know find out if I remember right Mishukov's brother used to be pretty friendly with Mario Koski I helped send both of them up 13 years ago same rap robbery was that all you heard Ed somebody spotted Mishukov That's all if you can track him down you might get some kind of a lead That's more than you got now That night and for the next two nights following Ben and I had dinner downtown instead of going home And then we spent the rest of the night covering the lower end of the city in search of Al Mishukov We got more than a dozen leads on where to find him from some of our informants But none of the leads paid off. We kept missing him. No one knew where he was staying. No one knew or no one would tell us Worst thing about this job Joe leg work. You must be averaging 10 miles a night my feet say 20 Almost midnight. Here's McCarthy's place. Let's try it right Let's go down to the end of the bar, Ben. Yeah Come in. What's no no not much bird meet my partner Joe Friday. Hi Friday. Well, you fellas have Looking for a guy bird his name is Al Mishukov Chicago. You heard anything he was in here earlier tonight a couple of guys with him Are you sure? What do you look like six feet out 45? I guess big bill sounds like him. All right, Joe Is he staying in the neighborhood bird down here? I don't think so most of those big time to stay uptown some place You're looking for miss. I'd like to talk to him. How long ago was he in about eight o'clock a couple of guys with him They were talking about driving out to the airport something about Las Vegas. There's an 840 plane for Vegas, isn't there Ben? I'm thanks. I'll 848 50. I can't recall where Bert. Do you remember the exact time they left exactly? No, I say there's one of the fellas that was with Mishukov down there the middle of the bar Which one were there one with a sandy head big chin sim Yeah Pardon me, I'd like to talk to you a minute. Yeah, who are you police sergeant Friday? Oh Have a drink sergeant. No, thanks. I said I wanted to talk to you Square John, huh? Wait a minute George Square John wants to talk to me. Come on outside. We can talk better up there I ain't done nothing. What's the pitch? I got a right to know let's go outside Maybe I don't want to go outside.  What are you trying to do? All right down this way course parked up the next alley Joe Hey, look, what's this all about? I got a right to know you were seen with Al Mishukov tonight. Where is he? Oh, Al Mishukov you honest to spell it. I don't think you can spell your own nobody's asking you to play smart Where's Mishukov out of town? What do you care? Here's the car. All right inside you Look, you got me wrong. I ain't done nothing. Where's Mishukov you and some other guy drove to the airport with him tonight Let's have it. I'm clear. I tell you I just drove out with him. That's all where'd Mishukov go Vegas took the plane for Vegas when about date 30 quarter to nine. What's up? Anyway, who's the guy traveling with Mishukov? Nobody who's the guy traveling with Mishukov? Koski, I just met him tonight. Mario Koski. Is that the guy? Yeah, I'm leveling I ain't done I've been get to a phone call the office contact Las Vegas police asked them to pick up Koski and Mishukov When we got back to the office we questioned the man we had picked up for almost two hours His name was John Delmar an ex-convict He'd been paroled from Folsom prison two months before after serving three and a half years for burglary He said Mishukov was looking for a man to work with him and Koski. He didn't specify the work Delmar said he refused the offer, but they parted on friendly terms He said Koski and Mishukov told him that they were going to Las Vegas for a few days and returned to Los Angeles But when Ben and I checked back with the Las Vegas police the next morning They reported that nobody answering the description of either Koski or Mishukov was seen arriving or leaving the airport We checked with the airlines and sent inquiries to law enforcement agencies throughout the entire area No sign Three weeks went by still no sign Nothing in the overnight show Nothing Same here Reno Sacramento, San Francisco. Nobody's seen them. I've got to come out sometime. We can wait. Yeah, we can wait Gets on your nerves. Let's check with back strand. Maybe he's got a job force in the meantime You're getting as eager as your friend Hank Decker Joe Incidentally, how things turn out for me past all his exams putting in his months training at the Academy now You should do all right Oh, yeah, I'm Mike skip a busy not in his office won't be until afternoon. What's matter? He's got a lecture at the police Academy this morning. Thanks Mike. Come on Ben Ben and I drove out to the police Academy near Elysian Park We went out to check with that back strand on the Blitz robberies not to listen to his lecture When we walked into the classroom He was just finishing up so we sat in the back of the room and listened. It was a pretty good speech Arresting officer his talent for memorizing detail and his knowledge of how a criminal accent or a given set of circumstances The arrest was made Well, that's about it gentlemen. Thank you for your attention No, when I ran this speech over at home, my wife said it wasn't a very good talk, but at least it came out on time Now it seems I'm two minutes short. So I guess I failed on both counts If I may add I'd like to use the few minutes that are left to tell you what I think of being a cop after 24 years For one reason or other you men have chosen the career of a police officer Let me tell you right now without any qualifications. It's a thankless job Maybe you can't see it now. Maybe you think I'm exaggerating But when you graduate next week and get that uniform on your whole lives are going to change You're gonna lose friends a lot of them They'll want parking tickets fixed some other favors You'll have to turn them down.  That's the job And you buy a box of candy and bring it home for your anniversary Neighbors will say you chiseled it When you save up a few dollars and buy a new car or some furniture for the house, it's graph People are gonna want favors. They'll offer you things a free beer or a new dress for your wife If you take it, you're a chiseler if you don't you're a tough cop Well, here's a piece of advice Take nothing from anyone no matter how good a friend he is Pay for everything you get and don't ask favors treat everybody alike No matter what they look like or what they believe in you don't play favorites There are going to be times when a few men in the department get out of line The newspapers will play it up because it makes good reading and the average John public will love it Because that's the only way he can pay you back for that traffic ticket you gave him Being a good cop is a hard job But it's a good one Let me warn you just once more It's one of the most thankless jobs on earth That's all gentlemen The following week Hank Decker graduated from the police academy and hit the transfer list for a regular assignment He drew a job of teaching combat firing and boxing at the academy They didn't like it so he put in a request for a transfer and waited For the next six weeks Ben and I waited to for some sign of the Blitz bandits. There wasn't any The only possible suspects Mario Koski and Al Mishukov had disappeared completely We kept a close check on every possible avenue of information still no sign Ben and I were transferred to the night watch on robbery for a few weeks and That gave Hank Decker a chance to drop in and visit with us a couple of hours when he went off duty at the academy He was still as eager as ever Hi, Ben. Is y'all anything new? Hi Hank nothing here. What about the Academy? Oh big news What's up getting a transfer starting next Monday gonna start on a beat Thought you were all tied up with that boys club you started out there Oh, I was with Hanson's gonna take over when I leave the kids sure love it free swimming in the pool boxing lessons We teach them everything.  Yeah central right in the downtown district might learn something you learn a lot and want to forget most of it What gets a quarter after seven don't you ever go home for dinner Hank getting a wife used to it This new ship's gonna be night working on their way to your on it for a year And then you tell us how you like it a year I want to be in the detective bureau after a year Well, you're not even gonna last a year if you don't get home to dinner your wife's called twice this week already She calls me. Okay. When did she call tonight? She hasn't yet. I guess I better head her off Let me know if anything breaks. I'm Joe. I'd like to tag along. Okay, Hank Well on your way. Okay. Good night. It's all on good night Yeah, how eager can you get where we like that when we started not me? I never had that much energy at one time the whole life Hot shot Joe. I'll get it At 7 6 7 East Broadway a liquor store to 11 and slugging at 7 6 7 East Broadway a liquor store to 11 7 6 7 East Broadway to 11 liquor store. Let's go 7 6 7 East Broadway Kings liquor store We pushed our way through the small crowd outside the door and into the shop to patrolmen in uniform We're already interviewing the proprietor He had two large gashes on his head just above the right temple He was trembling and badly shaken, but he managed to give us a good description of the hold-up men Yeah, I can tell you what they look like three of them One short one tall husky another short fat. You remember what they were wearing coats all three dark coats One of the short men here a big scar here on the throat a lot like this After the three men robbed the store they slugged me and tied me up Turner. This man's hurt you call an ambulance That's fine We have just one more question. Mr. King. Here's a handful of pictures We'd like you to tell us if any one of these men were in the gang that held you up tonight Let me look there you are take your time No, no not him No No Oh this one here. Hey, he took the money from the register. Would you look through the rest, please anymore? Let me see again No No, oh here another one has a fat one with a scar. This is him. I think he's the one that slugged me Thanks, mr. King. Here's our card. We'll be contacting you later Turner Well, you and your partner take the crime report. We've got some checking to do right sergeant. Thanks. Come on Ben. Yeah Cossky and Mishukov and picked out both of them. Yeah, certainly did Come on Ben, let's roll When we got to the liquor store and restaurant at Broadway in each third Men and I knew for certain that Cossky and Mishukov were back in the city and working hard Their ammo mats down to almost the smallest detail We put a call through to communications and the entire central division was alerted Then we called chief back strand and told him the news He assigned a special detail from the metropolitan unit to patrol the area until further notice But at 9 23 p.m. Before they pulled out of the police garage the blitz bandits added two more liquor stores and one more restaurant to their list of victims Early the next morning Ben and I met with chief back strand in his office You gotta make on that third man yet We ran his description through R and I early this morning Ed closest candidates to gather the name of julian brock done time here in new york Any tie up with Cossky or Mishukov? Mama she says he knows Cossky pretty well and that's good enough Now how do you think you're going to get these thieves? You've got the alert out chief special detail from metropolitan divisions been brief communications all set. All right Here's a tip for you Tell them in if there's a holdup call that only the car in the area of the holdup will handle it These thieves are no amateurs. Let me try some decoy trick Tell the men to stay in the area. They're assigned to them until they receive a call jack We'll take care of it ed.  And when do you figure on starting? We'll have the full detail out for 6 30 play it safe and start at 4. Why chance missing them? At 3 30 that afternoon we left the police garage with a special detail from metropolitan division and we started to cruise the central area We weren't looking for any action the first few hours and we didn't get any The five o'clock traffic in the downtown area was heavy as usual Hope that gang holds off till after six. We couldn't get out of this traffic of our lives dependent on Now we'd probably do better on foot if it wasn't for radio content Control 4 to 8k control 4 to 8k your location get it will you yeah, we'll get the mic 80k to control 4 8 ok to control 4 our location on spring street between second and third 80k to control 4 roger kma 367 yeah now what do I do for a parking space? You know you're lucky that guy up ahead there. He's pulling out Good that hasn't happened to me in six months Okay, hold on Ben. I'll be back in a minute 2511 This is friday bill. You want us?  Yeah, yeah, I'm seeing the description of mario koski. Yeah get over here right away and question the guy If it is koski waiting, I'll go home early Ben and I went back to the office and questioned the man who gave his name as conrad larkin It was koski's approximate height and weight same color hair same color eyes The resemblance to koski's picture was evident We questioned him thoroughly about the blitz robberies and then we checked out his fingerprints The coincidence was hard to overlook but we were satisfied the man was not mario koski There was a phone message on my desk to call hank's wife I called her and then we checked with the chief backstrand again and started for the police garage It was 10 minutes past six Hey, friend joe, wait a minute. Will you oh hi hank? What's all the excitement? I heard about those jobs last night the blitz gang. How about tagging along tonight? What's the stare you suit yourself hank when he I do home for dinner. I told the wife I'd eat out tonight You sure you're not do home for dinner. No, not tonight joe. Uh Is he having luck yet? Not so far hank. Maybe later on tonight. Come on. Here's the garage How close did you come to the gang last night? Not close enough two steps ahead of us all the way She'll must work fast five jobs All right hank. Let's don't rub it in. Huh? Hey band watch it. Will you yeah, i'm a driver How about it joe? You think I can make the outfit you talk to your backstrand. He might get you transferred after a while Yeah, I might try it Joe look across the street. There's a guy coming out of the bar where in front of the bar He's standing there guy in the dark coach. You see yeah two other guys behind him. Who is it? I can't be sure ben you better pull up koski looks just like his picture. All right Come on All right, hold it mister. We want to talk to you run for it alcovers watch it joe Hank get down get down two of them down ben Other than went up valley. Let's go Did they get hank?  All right. Let's return the fire He had his chance. Yeah grab his gun. Let's get back to him Did you get the guns from the other two? Yeah, they're dead hank got them more All right one side, please officer. Did you call an ambulance? Yeah, they're on their way. Come on ben one side, please. Will you let us through? Hank, how you doing? That's a good job.  All right easy hank they'll be here in a minute Hank, how's it doing joe? What have you got joe? phone message from hank's wife For you? you know You returned the call Before we left the office Who was it? She wanted me to remind hank He was due home for dinner at seven o'clock The story you have just heard is true Only the names were changed to protect the innocent You have just heard the twelfth in a new series of authentic cases from official files Technical advice for dragnet is furnished by the los angeles police department Tonight's program is dedicated to patrolman james frank goggen of the cleveland police department Who on the morning of january 13th 1939 gave his life So that yours might be more secure Dragnet came to you from los angeles if you enjoyed tonight's production of dragnet You'll want to listen to richard diamond private detective as played by the screams romantic tough guy dick powell heard saturday on most of these nbc stations This is nbc the national broadcasting company Thanks for the comments on the side. Yeah as mark pointed out. That's uh That's a sad one. I I kind of expect i mean the first time i listened to it I kind of expected that outcome because they're focusing so much on this guy's excitement to be a police officer It always makes you nervous when they put a bunch of attention on like a side character at a certain point You know like something something major is going to happen to them because they want you to like, you know become attached but Yeah, being a police officer. That's a that's a tough job. I I really did like the Chief backstrand's comments in there about Regardless what you do You're gonna have people that that do not like you so I think Well, that might be true in in other Situations, maybe like lawyers feel that way about certain things um I think I think police officers get Just just get a lot of hate a lot um Anyway, thanks all thanks everyone for being here. I forgot to mention at the beginning. Let me hide this screen Stop sharing screen So I've I've started something new and um Just want to tell people about it. I've put a qr code up here in the corner I I rotate the qr codes if you scan them, they should take you different places One will take you to otrgold.com if you're interested in getting the the Podcast we had a conversation on the side Some people want to listen while they're on the go or they want to listen when they're offline You can do that if you subscribe to the podcast, you can then just download it on your phone and take it with you um Another one I would throw a qr code I throw up occasionally is to this channel the otrgold channel So if you're watching from the other one, you could just scan it um mark asked if this is a scheduled thing every week this is so we are streaming every monday wednesday friday at 9 am pacific And we're gonna do it till we've listened to every episode of dragnet Um that I have access to which is 310 of them. So we're gonna be doing this for a while If you like dragnet And you subscribe and hit the notification bell. You'll also get um an email or like a phone notification whenever I go live so We'd love to have you on future streams I also wanted to so I forgot to Finish what I was going to say here I've started a 24 seven stream. I'm not like on camera like this one Um or interacting in the chat all the time I jump in there when I when I can But that one's focused on gun smoke. I have A playlist that has I think 477 episodes of gun smoke in there and it's just going to play In continually until it plays through all 477 and then it'll start back over at the first one and keep playing again So that one is going to run in perpetuity and if people like that You know the goal then is if you have time and you want to listen to it, you can jump in But though there's comments on the side So you can interact with the people that are listening At the same time and just like we're doing on this You can share your favorite things about the story. You can share what you love about old-time radio You can share facts about that particular episode or actors in the series um I started it like 30 hours ago Started started streaming at 10 p.m. On the 15th So if you um go to the channel, you should be able to see it Otherwise you can scan this qr code and I'll take you right to it But if that's something that people like I'm considering maybe doing additional series I think dragnet. We're gonna keep this schedule But might do a suspense 24 hour stream And maybe a cbs radio mystery theater one. I'm just I'm just considering I'm thinking about those because um Oh, someone tells me that gun smoke stream needs my attention. I'll go check that right after this But anyway, I'm trying a bunch of things the goal is to build community around this You know this medium that we love old-time radio. So I appreciate all the comments and Appreciate your participation Please share with fellow fans of old-time radio and let's uh, you know, let's let's grow this audience I think you can grow into something Great, it's already fun for me and I think you just continue to Be just continue to be Something great as as we grow the audience Anyway, I hope Everyone's doing well and I hope to see you on Friday. Have a good one


criteria for deciding whether a point is maximum or minimum how do you qualify a point to be maximum or minimum the problem at hand was minimizing a function a scalar function from m dimensions to 1 dimension rm to r and we wanted to qualify which point in the state space qualifies to be an optimum point so we said the point at which the first derivative the gradient goes to 0 that point is a stationary point to be very precise it could be a maximum it could be a minimum it could be a saddle point we do not know okay. So to come up with you know qualification further qualification we have to look at the second derivative the Hessian matrix and if Hessian matrix is positive definite or positive semi-definite it gives us way to qualify the point to be a minimum or a maximum so it should be strictly positive definite if it is to be a minimum it should be strictly negative definite it is to be a maximum okay. So let me just summarize what we looked at so this was so we are looking at necessary and sufficient conditions for optimality we have this function phi x from rm to r and we said that this phi function is twice differentiable okay at any point right now this x belongs to rm, m dimensional space okay and then we said that if a point x equal to x bar if this point x equal to x bar we want to see whether this is a stationary point then gradient of phi with respect to x at x equal to x bar so this is nothing but dou phi by dou x1 dou phi by dou x2 this gradient vector should be equal to 0 and the way this necessary condition was proved by considering the fact that if you take it non-zero it contradicts the fact that x bar is a local minimum well we are talking only about local minimum this is a condition to be satisfied at a local minimum because all the arguments regarding a point to be local minimum or a local maximum that is a stationary point we are made using Taylor series expansion. Taylor series expansion holds only locally it does not hold everywhere globally so these conditions necessary condition is a local condition just remember that so first thing is given an objective function first thing is to compute its gradient and set it equal to 0 that will give you if you can find such a point then that qualifies to be a stationary point a stationary point where you have gradient equal to 0 we further qualify so this x bar is a stationary point it is a stationary point and whether the stationary point further qualifies to be optimum that is maximum or a minimum that will depend upon this matrix so by the way this derivative is computed at x equal to x bar this computed at x equal to x bar okay now phi of x of x bar plus delta x we wrote this as you know phi of x bar plus phi at x bar transpose delta x plus half if we approximate this locally using Taylor series it is delta x transpose del square phi and now we are set that this is a stationary point so this is 0 so this is 0 right and then then locally we want to look at this difference which is governed by locally in a small neighborhood of x bar this difference is governed by this delta x transpose this term governs the local behavior in the neighborhood of x bar okay now if x bar is a minimum what should happen if I move away from the minimum what should happen value should increase so this difference should always be positive any direction I try to move away from x bar if x bar is a minimum any direction I try to move away from x bar I should have this difference to be positive that will be possible only when this matrix is positive definite if this matrix is positive definite what is definition of positive definiteness x transpose ax is always greater than 0 for any non-zero x anyway any direction I try to move okay this will always be positive that is positive definite matrix if this is always positive irrespective of whichever direction I try to move away from x bar then x bar is a minimum okay just whatever you can visualize in two dimensions or three dimensions same thing holds in n dimensions if you try to move away from that point just think of being in a valley any which way if there is a lowest point in the valley any which way you try to move you will only increase height will not go further below okay if you are at a minimum then that is the logic simple logic okay how do you mathematically express this using positive definite matrices okay mathematical quantification of simple fact that you know that when you are in a valley at the lowest point in the valley any direction you try to move okay height will increase it cannot further decrease same thing same thing is being said here just remember that simple thing and correlate with this mathematical analysis then you will understand it better now other way round now if x bar is a maximum you are at a peak what should happen anyway which you move now height will decrease anyway which you move so what should happen is if I move make any movement delta x from x bar this difference should be negative okay when will that happen for any delta x that is very important for any delta x that will happen if this is negative definite if this Hessian matrix is negative definite I am sure that any which way I move okay this is going to be negative so that means x bar is a local peak of course this local condition should also be satisfied at the global condition however this analysis does not tell us how to reach the global conditions it just tells us given a point if the derivative is 0 how do we qualify minimum or a maximum locally okay now this condition can be checked for objective function which is twice differentiable of course you cannot check it if your objective function is not differentiable or twice differentiable so that is very very critical so this is how what if your matrix is neither positive definite nor negative definite then the point is neither a minimum nor a maximum you know in terms of a hill it could be you know something like this like a step where gradient with respect is becoming 0 or a saddle point in what you know as a saddle point so a multi-dimensional extension of a saddle point you know let us say you have a valley but a valley which is something like this well it is difficult to draw I am not good at let us say there is no one unique point there is no one unique point where you have you know you have multiple points where the gradient goes to 0 so you may have minimum with respect to one variable not a minimum with respect to other variables so you may have a saddle condition where there is not a unique point where so a saddle point is qualified by looking at property of this matrix local matrix the nice thing is that definiteness of this particular matrix will allow us to find out whether particular matrix is a particular point is you know maximum minimum or a saddle point okay now let us come back to our problem of fitting CP versus temperature okay I am going to generalize this set of equations and then going to solve it so now let me rewrite this problem which we had at hand we had this CP values CP1 CP2 CPn I had this n values I had n values I had collected this CP values at different temperatures that T1 T2 T3 Tn large number of right I am just rewriting those equations in a matrix form earlier I had just put them one below each other as single equations I am now just writing them as one matrix equation that will help me solve the problem very easily so now this is one T1 T1 square one T2 T2 square just have a look at those earlier equations I am just revisiting them writing them in a different form everyone with me on this same equations how many unknowns n plus 3 and number of equations right now we have are only 3 okay so first thing that we need to do is to define an objective function that objective function should be twice differentiable right that objective function should be twice differentiable and then we should you know minimize that and see whether the minimum is a positive definite matrix or negative definite matrix then we will be able to qualify whether we have reached a minimum or not okay so now I am going to call this as x I am going to call this as x I am going to call this vector as capital E x is a vector which is three dimensional in this case in general x will be a vector which is m dimensional suppose you have cubic equation which you are fitting there will be 4 okay and so on so if you fit a higher order equation you will get higher order polynomial and I am going to call this matrix as matrix A let me be let me see whether I am consistent with the notation slight change in the notation I am going to call this as theta I am calling it theta because theta is typically if you see literature on parameter estimation a parameter vector is called theta okay that is why I am calling it theta no nothing particular about this also in the notes I have developed everything with notation as theta so when you read the notes it will be easier for you to follow okay so this particular vector this particular vector I am going to call as capital U this particular vector I am going to call as capital U this is A this is theta this is E my large number of linear equations which are these linear equations why but there is t1 square t2 square they are known I have taken measurements of temperature t1 t2 t3 tn are known I can compute this so these will be just columns of a matrix with some numbers so this is the linear matrix equation okay so my equation reduces to U is equal to U is equal to A theta plus E E is the vector of errors is a vector of errors okay now I need to define an objective function it will define an objective function and then this objective function should be differentiable I should take its first derivative I said it is equal to 0 take its derivative with respect to ABC okay now I am just moving from this specific problem to a general problem where theta in general could be m dimensional okay this A will be n cross m matrix see here m is 3 so this is n cross 3 matrix it is a tall matrix no so this n could be 100 and you have only 3 parameters to be estimated okay so I am going to define a phi of theta which is E transpose E which is nothing but E1 square plus E2 square En square some of the square of errors what are these what is E1 to En errors in modeling we are developing a correlation model of Cp versus temperature okay it is not exact fit it is an approximate correlation this E1 to En are errors okay I want to develop a model that minimizes some of the square of errors simple idea which probably you have heard or done in your undergraduate studies for single parameter probably we fit a line we very very usually fit a line I do not know whether we do in undergraduate we are taught to find out the best or v square fit but we fit a line by many times in experiments if you fit a line by you know just observing what is a trend visually okay we do not try to do all this business but then if you ask excel or matlab they will do this for you and give you okay so now so what is this this is equal to U minus A theta transpose U minus A theta right what is E U minus A theta U minus A theta okay now when do I get when do I how do I find the optimum this is a scalar function is this a scalar function why this is a simply this is simply norm E2 E2 square right some of the square of elements from norm E2 square norm is a scalar function if I it is a positive scalar function always be positive well an objective function need not always be positive but in this case it turns out to be strictly positive the smallest value E transpose E can take is 0 that means all the errors are 0 okay well that is possible for this particular problem on a different story but the smallest value it can take is 0 in this case okay so what I want to find out is I want to find out doh phi by doh theta that should be equal to so this should be doh phi by doh theta 1 to doh phi by doh theta m this should be equal to 0 vector okay now I need to know something about how do I differentiate so this is a this is a function of a vector which maps into a scalar how do I differentiate this how do I differentiate with respect to a vector we know how to differentiate with respect to a scalar value right so how do I differentiate with respect to vector I am just going to state the rules you can derive them they are not so difficult to derive you need to be a little bit patient and then do your algebra correctly so in terms of notation I am just digressing a little bit because I want to differentiate this E transpose E with respect to theta set that is not equal to 0 okay I will get m additional equations see these are already n equations I need m more equations m here happens to be 3 I need m more equations those equations will be obtained when I do this but before that I should know how to differentiate a function which is a scalar function which is function of a vector so let us say I have this function f which is x transpose by I have a function x which is x transpose by b is a matrix x and y are vectors I just want to differentiate f now f is a scalar function you can see that f is a scalar function okay how do I differentiate so doh by doh x of doh f by doh x differentiating this scalar function with respect to the first argument x okay that is b y doh f by doh y is equal to b transpose x okay and a straightforward corollary of this is that doh by doh x of x transpose b x is equal to 2 b x if b is symmetric if b is symmetric matrix then it looks b symmetric matrix okay then it is well if it is not a symmetric matrix then what will it be b plus b transpose b plus b transpose if it is not a symmetric matrix it will be b x plus b transpose x okay so we can use this rules to differentiate this function with respect to theta and come up with a solution so how do I do that so can you differentiate can you tell me what is the solution just differentiate just use these rules can you expand this say this will be phi is equal to u transpose u minus u transpose a theta minus theta transpose a transpose theta transpose a transpose u plus theta transpose a transpose a theta I have just expanded this I have just expanded four terms u is a vector u is a vector a theta is a vector right and then I am just expanding this simple matrix multiplication okay now what is u u is a vector of known values is a constant vector so what is doh phi by doh theta this part will be 0 what about this guy apply the rules correctly will be a transpose u a transpose u so if I differentiate this doh phi by doh theta I will get minus 2 a transpose u plus 2 times a transpose a theta I do not know whether you all agree with me why I am writing 2 times here this a transpose a is a special matrix what kind of matrix it is but me no why 1 by 1 it will be m cross m no in this case it will be a 3 cross 3 matrix can I say that a transpose a is always a symmetric matrix you take you take transpose of a transpose a you will get back a transpose a okay positive definite matrix matrix naturally appears here we do not have to make any effort okay it just plops out from the equations so this is a positive definite matrix in fact this will be turn out to be positive definite matrix this is a symmetric matrix this is a symmetric matrix will go on to show that this is positive definite also so this particular matrix is a symmetric matrix so I can write 2 a transpose a okay that is because that is because a transpose a just check this a transpose a transpose is equal to a transpose a so whatever is this matrix just remember that this particular matrix whatever is this matrix you know also at all it is thousand equations and 3 variables and it might be filled with all kinds of strange numbers this matrix that is a transpose a will always be symmetric matrix always be symmetric matrix in fact we will show that if these columns are linearly independent then that particular matrix will be positive definite matrix okay it will be a positive definite matrix so now the task is done if this is 0 if I set this equal to 0 what do I get I set this equal to 0 then what is the theta how do you compute theta what is this matrix what is size of this matrix it is m by m okay so if m is 3 this will be 3 cross 3 okay so this particular matrix so setting gradient equal to 0 gives us this equation a transpose a times theta is equal to a transpose u okay so this is m cross m what is dimension of this matrix a transpose is so this is m cross n into n cross 1 so this is m cross 1 so finally you are getting an equation which is 3 cross 3 matrix and how many equations you wanted and m equations or you wanted 3 equations in this particular case we wanted 3 equations we have those 3 equations now this is m equations okay in how many unknowns m unknowns this is m cross 1 this is m cross 1 m unknowns I solve this problem now if columns of a are linearly independent just think about what I am saying I am not going to prove it if columns of a are linearly independent then this matrix is invertible not only that not only that this matrix will always be positive definite okay before we proceed further and I show that why it is positive definite what is the second derivative of this a transpose a right so the second derivative dou 2 phi by dou theta square is equal to 2 times a transpose a right so now depending upon whether this matrix is positive definite okay if this turns out to be positive definite matrix then we are done then we have reached the minimum okay in fact this is the linear equation you can show that this minimum is not just local this is the global minimum for linear set of equations we reach the global minimum okay now my task is to show so that a transpose a is a positive definite symmetric matrix is very straight forward positive definite matrix okay now let us assume that a has columns are linearly independent columns of a are linearly independent okay what does it mean when will you get a x equal to 0 when will you get this if columns are linearly independent which vector x will give you 0 vector only 0 vector if columns are linearly independent this will be this will be 0 is same as saying x is equal to 0 you cannot get if a columns are linearly independent only where you can get a x equal to 0 is x is equal to 0 okay now how do you check what is the definition of positive definiteness positive definiteness is that x transpose a transpose a x should be greater than 0 if x is not equal to 0 right okay I am just going to write this I am going to write this as I am going to write this as a x transpose a x am I correct I am just clubbing x and a x and a a x transpose x okay so what is a x transpose x norm a x to square when will this be 0 if so there are two situations if a is a singular if a has columns which are linearly dependent there might be an x which will give you 0 but we have said that columns of a are linearly independent so if you have an x which is non-zero this vector is going to be non-zero and this is square of the norm square of the norm is always a positive number so whatever x value whatever x vector you give me a transpose a is going to be a symmetric positive definite very nice matrix okay matrix which we keep studying in linear algebra here it just pops out naturally as part of the development so a transpose a is a symmetric positive definite matrix I am showing here that for any x you know you will always get a positive number if x is not equal to 0 so this will be greater than 0 if x is not equal to 0 so this satisfies the definition of positive definiteness okay I do not there are algebraic conditions like eigenvalue should be positive and all that let us not worry about it right now we will visit that little later but here using the basic definition of positive definiteness I am showing that this a transpose a is always positive okay which means not only that I have reached a stationary point I have reached the minimum is the linear model there is only one minimum I have reached the minimum okay if I have to do all this using one norm of e or infinite norm of e is not possible because one norm of e is not differentiable I cannot use this nice theory okay infinite norm is not differentiable I cannot use all this nice theory so there are problems if I use some other norms two norms very very nice you know you can differentiate and get this result now I am going to relate all this to projections I will show that this is nothing but projecting a vector onto a subspace geometric interpretation what is happening here that is what I am going to do next so why we are able to relate it to projections because as I said in a product space in a Hilbert space you know with an inner product norm gets free you get a free norm two norm and you get angle you can talk about orthogonality you can talk about projections you can just you know generalize the ideas which you know from three dimension school geometry okay so this is a symmetric positive definite matrix we have reached the global minimum this is the solution any such problem I can solve using now do I have to stick to polynomials I really do not have to okay I can talk about any function approximation so I am going to take a scenario here I looked at cp as a function of temperature that was one specific example okay I do not have to stick to only polynomials I could any function which is linear in parameters I could actually estimate the parameters by this approach let us say I am approximating a function say u which is I have this function uz and I know its values at z1 z2 zn and these values are say u1 u2 un this is my data set I do not want to fit a polynomial I just let us say I want to fit sin and cos you are perfectly allowed to do that okay so I want to fit a function which is I want to fit a function say fz which is which is or let us call this function by some other notation okay so I want to fit a function say u cap z okay which is theta1 well this did not be function of only one variable right it could be function of multiple variables in this case okay let us take first situation when you have function of only one variable say z1 plus theta2 f2 z2 so I am fitting this I am fitting this function approximation of course there will be an error here there will be an error here so u cap is my approximation u cap is my approximation theta1 into f1z theta2 into f2z and so on okay polynomial was one type of approximation I had chosen this to be one I had chosen this to be z I had chosen the second to be z2 z3 and so on that is one particular type of approximation I could have chosen first one to be sinz second to be cosz third to be 2 sinz third fourth to be 2 cosz and so on cos2z sorry cos2z sin2z and I could have chosen some other functions I could have chosen the general polynomial I could have chosen shifted the general polynomial so it is up to me what should I choose I could have chosen all kinds of different functions here I can apply the same theory which is very nice because I know this functions I have chosen this functions okay I can evaluate them at a particular point okay so let us take a scenario where you want to approximate this let us take instead of being abstract let me put it in a concrete form so theta1 say f1 is my sinz plus theta2 cosz plus theta3 sin2z plus theta4 cos2z plus error let us say this is my this is my this is my approximation function okay what do I do I do the same thing which I did earlier I just write u1 u2 these are the values which I know at n different points they are the values that I know at n different points I can say first one is sinz1 cosz1 sin2z1 cos2z1 second row is sinz2 and finally sinzn cos so I write this huge matrix how many parameters 4 parameters 4 parameters so this is theta1 theta2 theta3 theta4 plus I have this e1 to en same equation okay so this f here could be any complex function mind you this particular model is linear in parameter okay we have formally defined what is the linear function sometime back so you should just check when you call a function to be linear function f of alpha x plus beta y will be alpha times f of x plus beta times f of y that will exactly hold here so this is a linear in parameter function any linear in parameter model you can do this okay you can actually so what is what what do I get here this is my u vector okay this is my a matrix this is my a matrix this is my theta and this is my e how do I get least square estimate of theta a transpose a so least square estimate of theta is simply theta hat least square that is what we write theta hat y hat it is an estimate of theta there are different ways of getting theta if you were to define one norm instead of two norms we will get a different theta so I am calling this as theta which is obtained through least square of errors okay that is why theta hat least squares is nothing but a transpose a now we have shown that this is a positive definite symmetric matrix a positive definite matrix means no eigenvalue 0 it must be invertible so I can write inverse a transpose u in fact this matrix is called as 0 inverse of a why 0 inverse a is a non-square matrix a is a non-square matrix okay a is n cross m I cannot invert it by the normal sense of n cross n square matrix this matrix why it is 0 inverse what happens if you multiply post multiplied by a when you call something to be inverse you multiply the matrix and matrix inverse you should get identity matrix take this matrix post multiplied not pre-multiply post multiplied by a what will happen identity matrix so that is why this a transpose a inverse a transpose is called as 0 inverse of a matrix in matlab there is a function called p i n v 0 inverse i n v can be used for square matrices p i n v can be used for non-square matrices you just say p i n v doing this in matlab is just two minutes formulate a matrix p i n v a times u you get the theta the square theta okay fraction of a second you can do this should know the theory behind this that is very important okay so is this clear I do not have to have polynomials I can have any complex function okay I will give you an example from chemical engineering and sometimes you do not have to begin with you may not have a linear equation but you might be able to come to a linear in parameter equation once you do a transformation say I will give you an example I want to fit data I am carrying out some reaction and I want to estimate the kinetics of the reaction okay so I have this r a is equal to or minus r a is equal to k c a to power n okay or let us put it k 0 e by r t right now maybe I should write in the order should be k 0 e to the power e by r t into c a to power n this is my model okay actually I should write this model with an error here we do not write it because this will not be exact model we are proposing this model it is an approximate model so we should strictly speaking should write an error error here say epsilon because do not confuse with e here e here is exponential so this is my model and I want to get d square estimates what are the unknown parameters k 0 e r is known okay and n what is the data that you have c a and t c a and t okay is the data that you have I could do a log transformation of this model okay I can say log of minus r a is equal to log k 0 minus e e by r t plus n log c a right n log c a okay now I can write this as log k 0 plus or rather minus e by r into 1 by t plus n log n log c a I have collected data for concentration and at different concentrations at different temperature I have data for rate rate expression I want to get a least square estimate okay is this a linear in parameter model what are the parameters log k 0 log k 0 e by r or e whatever e if you want to take r on this side you can do that since you know r so e is unknown parameter and n okay so here in this matrix what you will get in this matrix what I will get is 1 1 here then minus 1 by t 1 minus 1 by t 2 minus 1 by t n this column this column is coming because of this variable 1 by t okay the third column what will be the third column log c a 1 log c a 2 actually log I should write ln natural log log k 0 e by r and n and what should be here what should be here r 1 minus log r 1 minus log not minus log log of minus r n that minus is a notation so it should be log minus r 1 log minus r 2 you know all these reaction rates this remember minus is a notation not so we are not taking log of a negative number so this is the equation that you get this is the u vector which you know this is the u vector because you know the rates at different temperature and concentration okay you have estimates of the rates this matrix is known to you a matrix temperatures are known to you concentrations are known to you so this is known matrix this is known matrix this is my theta which I want to estimate okay what is the least square solution a transpose a inverse a transpose u this remember this formula very very important a transpose a inverse a transpose this is called a pseudo inverse of a transpose a inverse a transpose a transpose a transpose a is always a square matrix and if columns of a are linearly independent it is always invertible matrix and then and what you get here from the least square sense is the minimum okay there cannot be any other value of theta which will give you smaller sum of the square of errors for a linear in parameter model you cannot get you cannot get a model which will give you smaller value than this optimum value which you get okay so this is my least square problem this least square problem is used in many ways in the assignment I will give you other problems from chemical engineering where you can you do least square fitting to estimate the parameters sometimes what happens is that sometimes a model is not transformable to a linear it cannot be linearized I will call this as a linearization step in the linearization step you can do some transformation and convert originally the model is not in not a linear in parameter e and n and k0 they are multiplying and they do not appear in you know the fundamental definition will not satisfy here that is f of alpha x plus beta y is same as alpha f of x plus beta f of that will not be satisfied for this function but it will be satisfied this transform function now this is not possible always to get this I will tell you one more model in chemical engineering where you can do this transformation okay and estimate the parameters this is how it is done one more classic model in chemical engineering is let me if I am wrong Nusselt number is equal to alpha 1 into Reynolds number raise to alpha 2 and Prandtl number raise to alpha 3 right Nusselt number is equal to then how do I this is not a linear in parameter model what are the known quantities here I would have I would have data for Nusselt number Reynolds number for different flows I have collected data for you know Prandtl number reset number and I want to fit I want to fit and I want to estimate alpha 1 alpha 2 alpha 3 okay this is not a linear in parameter model but simple log transformation so if I take log of Nu it will be log alpha 1 plus alpha 2 log Reynolds number plus alpha 3 log Prandtl number this transform model is linear in parameter okay I could use least square estimation technique to estimate log alpha 1 alpha 2 alpha 3 if I get log alpha 1 I can get alpha 1 not an issue right so this is this is simple transformation what is mass transfer correlation Schmidt number is equal to or Sherwood number sorry Sherwood number is equal to yeah so SH is equal to some beta 1 plus Reynolds number raise to alpha 1 beta 2 plus what Schmidt number well for me it is almost 20 years now so you are fresh so right this is this is some 0.63 you also you may have viscosity correction mu by mu s raise to something fourth parameter so you may have four parameters but once you do this transformation it is a linear in parameter model you can use least square parameter estimation these columns will be different this column will be different same idea works you get least square estimates of alpha 1 alpha 2 alpha 3 alpha 4 just by taking A transpose A inverse so polynomial fitting is not the only thing I am just now polynomial fitting we started with because we wanted to do something with discretizing a boundary value problem or partial differential equation but least square estimation goes much much much beyond all this was well discovered by Gauss the famous mathematician well in the realm of mathematics or in the realm of history of mathematics Gauss is called as prince of mathematics and the work he did actually is now major fields okay least square estimation Gaussian densities Gaussian quadrature in so there is so many things so many things I mean I do not know what we would be doing if Gauss had not discovered Gauss was a child prodigy he discovered many things at very very early age and the things that he started actually he started looking at least square estimation because he wanted to fit I think he was looking at the problem of fitting a orbit into the data for obtained from motion of planets around the sun that was the problem that was being discussed at that time so what is the best fit it does not happen to be a circle actually it is a ellipse and you have to fit because if you look at a data the data has some errors and then you have to do a best fit to get the model correct model so what is started about 150 or 200 years back is now just spans I mean it is all these tools are used in image reconstruction they are used in soft sensing they are used in just name it least square estimation forms the foundation okay or work by Gauss forms the foundation so we are here today because of the sprints of mathematics Gauss.


Still in reverse state, the governor, Simeon Ali Fubara, has signed into law the 2024 Appropriation Bill of 800 billion Naira. This is coming a day after he presented the budget estimates to the State House of Assembly led by Edison here. The signing ceremony was held on Thursday in the conference room of the governor's office at the government house. Fubara, during his presentation to the assembly, said the 800 billion Naira budget was aimed at promoting economic development through inclusive growth and addressing socioeconomic inequality in the state. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.