Today, we're opening one of Yu-Gi-Oh's rarest products that you've probably never seen before. What's up, guys? We're back with another epic product opening. This one, I'm not sure if you guys have seen this one. If you've been around for over a year on the channel, you may have seen me open this one other time before, but it wasn't actually sealed. This time, we're opening a sealed version. But before we get into what it is, we have a giveaway. I'll be giving away these three cards. All you have to do is like the video, be subscribed, turn on notifications, let me know what you think about this product. Let's just go ahead and get into the opening. All right, guys, so the item that we are opening is an item that I've opened before, but this time it's sealed. We have a dimension of chaos special edition. So you might be like, wait, dimension of chaos? They had a special edition? In the U.S., they did not have a special edition, but in Europe, which as you can tell, it's the smaller size special edition box, they did have a special edition dimension of chaos. So I once opened this product, but it was an unsealed version. I also showed off this sealed version in the video and said, we're not gonna open that at the moment. A year later, actually over a year later, I decided it was time to open it up. We actually did not open this in the every special edition opening because I didn't even think it existed at first. I saw that where it said there was one of these and I could never find even a picture of one. So I ended up finding this and yeah, so I missed something on the every special edition opening. Unfortunately, if you've missed that video though, go watch it. It's a good one, long, lots of awesome openings, but let's open this up for a little redemption today. I also threw in a few extra packs because there's a weird thing about this special edition that I'm gonna talk about as we get into it, but let's go ahead and crack it open. So the reason that I added some extra packs in is because the way they do European special editions or at least these is they would put all three packs into one like cellophane pack and it was like a giant mega pack except for it didn't even have like a pack wrapper on it. It was just cellophane. So you basically get three packs in one. So there's basically only 10 packs inside of this versus having 30 in a regular like US special edition. So what you can see here is we get the 10 mini boxes here, you know, in the US we have the thicker, you know, thicker and taller ones. This one contains one cellophane pack and also has the superior variant cards. I don't remember where exactly those are. They might be outside the pack. Let's just, I don't know, let's just go into it. It's been a while since I've opened this. Kind of excited to do this again because, you know, I might never open this product again. We have, yeah, as you guys can see, look, it's literally everything in there including the promos, the packs, the foils. If you already get a foil, it's gonna be in here somewhere. It's the weirdest thing ever. So fried for a tiger, this would have been the promo. I mean, it's kind of in the pack. It's very strange the way they do it. I don't love it actually. I think it's kind of a bad way to do it I mean, everybody likes opening the pack, you know, in the mystery. This feels a little bit more like a, like a custom mystery pack or something. So it's a little bit weird. So there's our two promos right there. If you do get a foil, I think it's right in the middle. So if we get like a ghost rare, you know, Scarlight Red Dragon Archfiend, which we pulled four times on the channel. It's been a long time though. So I'd be loved to, I'd be love. I'd love to do it again. We got the contract change. I'll just see what we can do. I don't know what kind of value this thing's even worth because I haven't seen one in a while. Didn't check eBay to see if maybe one had popped up, but yeah, it's, it's a pretty hard one to find. I don't know how much it costs. I can't even remember what I paid for it. It was a, it was part of a larger deal. I believe in contract laundering. We have gradle slime. So there's a rare. I think you get your three rares in a row. So I think it goes rare, rare. There's a radiant and that's actually a pretty good card and rare. So manage spectra unicorns. So we just go over three. Oh no. I forgot you can get, you get rares and foil. So here's our foil. So you get three rares in a row. Foils are not guaranteed in this because this came out right before they started doing guaranteed foil. So gradle dragon. Oh, wait, what? Is it stuck together? And gradle legal. So it looks like we got one foil out of our three packs. It's the weirdest way to open packs. Plush fire. I think that's banned. Weirdest way to open packs because you open them up. You get all your foils at once. Like one, two, three. If you got three, it'd be insane. We actually pulled two band cards out of that one pack or three packs, I guess you could call them. That was an interesting opening right there. But I also threw in these other packs. So it wouldn't be too quick of an opening because as you just saw, we opened three packs at once. So that can really speed up your opening. Let's do two from the back. This is ghosts from the past too. I've thrown in some legendary collection, 25th packs. We've got some ghost packs, a lot of fun stuff. We have Despia and we have Vision Hero increase. All right, let's do a ghost from the past one. And also while we're doing this, I want to shout out Poker Rucks. Poker Rucks is the channel where I do like Pokemon, like Nuzlocke runs and stuff like that. I've been doing a lot of content on Twitch and on Poker Rucks. So go check that out. If you guys are interested in that stuff at all, I'd really appreciate it because we're 100 watch hours away from being monetized. We're at 3,900 out of 4,000. So we're really, really close.  Nope, didn't happen. It would be really helpful if you guys did that for the Poker Rucks channel. I know a lot of you guys are not into Pokemon and that is totally fine. I'm not forcing you guys to go over there or anything, but anybody who is interested, go check it out. I think my editor for the Poker Rucks channel has done some really good stuff. I think he's very interesting. And we're gonna be putting out a lot more content. I got plans for over there. So if you guys don't want to go check it out, that'd be really awesome. And I would appreciate it. Those are our two promos right there. And it would help out that channel. So here we go. We have Magspector Fox and being monetized would be pretty cool. We have Magspector Storm. We have the Savad Kepler. The Cosmol Wicked Witch. Very nice. The Contract Laundry. Deity Swirl Spine. We have the Contract Change where our rares, we have Soul Claw. We have Skilled Red Magician. For some reason, it's kind of hard to see these cards, like the names. I don't know why. Sphere Caribo was in here. I forgot about that. Dueling Staple. We have a Pendulum area. Give us a Ghostraer. Come on. Vector Pendulum, the Draco Lord. That is a super. We'll take it. And Great Olimpact. So no, nothing else. No more foils or so many cards in here because it's three full packs. Like, what is that? Like 27 cards total? All right, not bad. Not bad at all. Let's go to Dark Crisis 25th Anniversary. Open this up. Such a weird opening, man. Dimension of Chaos Special Editions. They're crazy. Little one guard. They almost feel like they're not a legit product with the way that you open them. I've never seen anything like it. KS, we have Fairy of the Spring. We have Contract of the Abyss and a Dark Scorpion. Manay the Thorn. Okay, Dimension of Chaos number three. So far we've gotten two supers. So I would like something above a super. In this set, you can get Ghoster, as I mentioned, Scarlet Red Dragon Archvene. There's four Ultimate Rear as I believe in the set. And then there's Secret Rear as well. Of course, Ultra Rear isn't supers. We've already seen some supers. Got a couple of supers right there. Contract Lawner, got Super Soldier Soul. Super Every Samurai Drone, got the Dark Contract. This is like a mega pack on the live streams except for it's a legit Konami product. Imagine if they made legit mega packs. That'd be cool. You'd just buy the foils. If we could win it, we have Great Ocobra, Psyche Blade, the Diddy Burfomet, Sphere Caribo again to Link's Staple. We have the Rank Up Magic Raid Force, and we have, oh we got no foils in this one, oh. All right, so we went over three on that special edition. Two Fluffle Wings though, pretty cool. All right, next up, Ghost from the Past, two. Let's go. We have the Diddy Lamia, the Agent of Mystery, Domain of the True Monarch, Crimson Knight Vampire and a Dark Magician, the Dragon Knight, a cool looking card, but I don't think it's too valuable now because it's been reprinted, you know, well really only once, but you know, it's easy to pull out of this set. Seven more special editions, Dimension of Chaos. Come on, give us a Ghost Share.  If I've had this just sitting in a sealed box, a Ghost Share.  I don't know, Magispector Storm, Contract Chain, so I don't know. That could be a thing. I always think about that. Grattle Cobra, I don't know how you guys feel about your sealed product. Let me know. Do you guys ever think that if you have sealed product laying around? Shuffle Reborn, we have Super Rush Headlong, that's a Duel Link special as well. Grattle Split, they basically took docks and just made Duel Links. We have, what is this? Giant Pearfish? I don't remember that one. Super Soldier Ritual, that's not bad either. Here we go, a gateway to Chaos, all right. Super, can we get something better than that? Are they, is there anything better than Super in here? I feel like last time we pulled all Supers too. Interesting. It makes you wonder, do they actually go better than Super out of here? I can't remember. I can't remember if we ever got anything better. All right, Ghost from the Past one. Let's go. Give us the Dark Magician, please. Sunvine Healer would be insane. Time to fly back, nothing there. Okay, just an ultra rare, that's fine. Let's go on to our, this is our last special edition of the right side of the box. So this could be a game changer. All we've had so far is, I think three Supers out of four special editions. So this week would consider a dud, a special edition opening. Let's change it now. We have more promos. So I mean, technically we have a lot of super rare promos, but those are guaranteed. So it doesn't mean much. We have Super Soldier, Psychic Blade. Have we gotten more than one Super per pack? I think, I remember this. You were getting like one Super every time. Mags Spectre Storm, we have Simone Kepler, we have Cosmo, Wicked Witch, the Emerald Conductor, the Performal Pal, Splash, Mammoth, Dumbo, we have, ooh, Gamma Seal, the Sea Turtle Kaiji, that's a good one. DDD Wave King Caesar, it's also pretty good and a Mags Spectre Cat, Nekomata, and a Galilee. Man, more supers. Can we get something that's not a Super please? I mean, it were a rare common. I'm just going to clarify. Okay, 10 total packs left, including five special editions, which I'm counting as one pack, even though there's more than that. One, two, three for the Spell Ruler pack. Can we get Blue Eyes too? We got Crab Turtle, we got Slot Machine, Ceremonial Bell, Hamburger Recipe, Lavender Wall, Amoeba, and a painful choice. It's been painful having to choose. Well, it really hasn't been that painful. We didn't really make any choices here today, honestly, but it would have been painful in theory. All right, left side of the special edition box gotta be better, right? Gotta have some Ultra Secrets, Ultis, maybe even a Ghost, you know, I don't know. It's pretty hard to pull Ultis out of these because there are only four in the total set.  We have Performage, Mirror Conductor, that's two promos, Shuffle Reborn for our Monster Reborn, Cosmall, Kyubi, we got the Dark Contract Swamp King, the Despot 006, Mirror Conductor, Super Soldier Rebirth, Super Every Samurai Drone, we got Great Okobra, Super Every Samurai Soul Claw, Super Soldier Rebirth. We have Gamma Seal, again, that's a good one. Toon Barrel Dragon, also a pretty good rare. Giant Pearfish again, and an Ultra Rare Fright for Sabertubes, we finally got one. This is like a $20 card back when we were opening this set a lot, then it got a reprint, now it's like less than a dollar, I think, and then Great Illegal. So now I'm wondering, okay, you can actually really see on this card, this is like the Euro-looking Ultra, you can tell. I don't know if you guys can tell, but it's a little bit more Euro-y. I don't remember if you can get, can you get two foils, because if you can get two foils out of this, it's a little messed up, because it's like they combine three packs all with a potential of a foil into one, with a potential of only one foil, that's bad. I don't think that's all it works, but it's feeling like that so far. All right, IOC, here we go. I mean, I'll take that Ultra Rare, that was nice. One, two, three. Now we just need a secret Ulti and Ghost to end it off. We have Chaos, Necromancer, Primal Seed, O'Jama Black, DD Borderline, Inferno, Prickle Fairy, Compulsory Evacuation Device, and a Yellow Luster Shield, so IOC got nothing for you. Four Special Editions left. I still have hope for a Ghost Share. I don't care if it's only one foil if it's a Ghost Share. How about that? Let's make it happen. Or Airbox with all Ghost Shares, every card in this pack, so 27 Ghost Shares. If that happened, that would be maybe the craziest thing that's ever happened in a Yu-Gi-Oh opening. Can you imagine just be like Ghost, Ghost, Ghost, Contract Change, Shuffle Reborn, Death Spot 006, Raid Raptor Wild Vulture, Contract Change, Ignite Veteran, we have Kaiju Capture Mission, the Kaiyubi, Game of Seal, that's a third one. That's nice. We've got the Samurai Cavalry of Reptiair. I can't see it straight on. The name is just like, I don't know, it's not capturing it. Radiant, another Kaiju, and the Great Elfaricide Super. Come on, another foil. Let's go, come on, another foil. Let's go, come on, come on. We got a synchro back there. Oh, okay, maybe it doesn't mean anything then. Dang it, Death Spot Jack gave me hope. I thought we had something. Ah, synchros always look like they're gonna be a foil for some reason. All right, so six out of seven special editions have had one foil. The other one had zero, so, hmm, interesting. One, two, three, let's see. Come on, Pharaoh Servant, only tank rucks in 34. We're good to see it. We got Skyscout, aka Harpy's brother, Grotto, Solomon's Law Book, Reign of Mercy, Inspection, Prohibition, and Bombardment, Beetle. Still three more chances on special editions of Dimension of Chaos, aka Dox. Let's go. Can we get something nice? Dox, come on, come on, you can do this. We have Fright for Tiger. We have Destruction Sword Flash. Ooh, rucks in special. We have the Dark Contract with Swamp King. Pot of the Forbidden, I remember this is like a short print. DD Swirl Swime, we have the Storm, Syvon Kepler, Super Soldier Rebirth, DD Swirl Slime, we got Ignite Veteran, Grattle Split, Super River Samurai Thief, we got Syvon Kepler, we have a DDD Oblivion King, Abyss Ragnarok, Rare, Druone Barrel Dragon, also nice, Ragnar Magic Raid Force, Gateway to Chaos again, super, and come on, come on. Bro, it's not again another band card, Plush Fire, oh my goodness. Oh, another Plush Fire, Double Plush Fire in there, okay, but no double foils, unfortunately. All right, Blue Eyes, White Dragon, here we go, three, here we go. Let's pull something amazing, Thunder Beast, we got Wasteland, we got Petite Dragon, Two-Mouthed Dark Ruler, Dissolve Rock, Silver Fang, Silver Bow and Arrow, Fissure, and a mountain, very nice mountain card, but yeah, L.O.B, 25th Anniversary, letting us down again, who would've thought? All right, two special additions to go. Can we pull a Ghost Share? We have the Promos, all right, Engraver. We have Raid Raptor, Wild Vulture, Super Soldier Soul, we have Deity's Rosaline, God You Capture Mission, Contract Laundering, Samurai Thief, we have Samurai Soul Claw, Super Soldier Rebirth, our contract with the Swamp King, we have Super Soldier, Wicked Witch, Psyche Blade, Radiant again, not bad, we have a Rank Up Magic Rage Force, again, okay. We have Pendulum Area, I don't think we've pulled that one yet, and a Deity Rebel King, Leonidas, and will there be something else afterwards? No, there will not. Oh my goodness, Plush Fire, yet again, appearing. All right, one more pack of Metal Raiders, then one more special edition pack of Docks. This has been not a great opening, I would say, I mean, I don't think we've pulled, we've pulled what, Painful Choice, that's it, Electric Lizard, we got Potential of the Picanha Moth here, though, that could turn it around. We didn't pull an Oni Tank, rocks in 34, that's not bad. Rocco Grotto, Soul Release, Steel Scorpion, Elegant Egotist, and a Ryukishon, powered. All right, our final Dimension of Chaos, oh, this one got a little bent up, this will probably be the one with a Dented Ghost Dragon or something. Here we go, how's the pack look? Looks okay, I don't think anything got too beat up. We have Fright for Tiger, Destruction Sword Flash. We have Contract Laundering, DD Swirl Slime, can we get a Double Foil or something above an Ultra Air? Either way, I'll be happy. Veteran, Laundering, Contract Change, we got Kaiju Capture Mission, Shuffle Reborn, Psychic Blade, Magspector Storm, so many cards, Wave King Caesar, not bad. We got, oh, we got a little bit of a lower name, Assault Blackwing Kunai the Drizzle, that's cool. We've got another lower name, Abyss Ragnarok, and an Ultra Rare, Charging Gaia. The Fierce Knight, is there another Foil after this? Please, please, please, please, no. So we got nine Foils, which is not bad, but you know, no Double Foil, so it feels kinda weird, I don't know how those are set up, but all right, if you enjoyed the video, make sure to subscribe to the channel, if you enjoyed it, and don't forget to, what was I gonna say? And go to check out Poké Rocks, if you guys wanna see, you know, some Pokemon stuff, I'd appreciate it. Shout out to Toenfo Show, Daxer, JT Show, Puffins of Doom, Ernesto D'Anda, Dizzy, Missycle, America, Deutzer, Supreme Stage 21, and then a Thai show, Ian Moosa, Junior Barting, Mehmed Gekko, and Thomas Plain. Thank you guys for supporting the channel, and I'll see you guys in the next video, peace.


What's going on everybody? Got Kyle and Shawn here with Layton Sports Guards and we are ripping 2023 Bowman's Best Hobby, 8 box case number 31, random team style. Did a randomizer for the break. Had John K with the Dodgers down to James W with the White Sox. Alrighty guys, we do have the Super Fractor bounty going right now. We have 11-25 if we hit a Super Fractor in this one for the team that has it, we'll get Layton break credit. We also have a $40 guest, the Super bounty and guesses will begin now. You guys can guess any player in the set. If we do hit that Super Fractor you will be getting $40 in break credit. Corbin Carroll, Shady, first one there. Alright guys, so we'll give about 30 seconds here. Keep getting those gases in and if we do hit that Super Fractor, like I said, we will get some Layton break credit in your account. Hmm? Yeah, that's not too bad. I'll probably get the best, yeah. Alright guys, about 10 more seconds. 10 more seconds. Alright, 3, 2, and 1. Guesses are now over. Guesses are now over. Yeah, that was yesterday. He guessed Cameron Brink in the basketball break. Cameron Brink. Very nice. Alrighty here guys, let's do it. Bowman's Best 8 box case number 31. Let's keep an eye out for some supers here. Good luck everybody. Thank you Todd for grabbing a spot in Almanac as well. Saturday night guys, Personal's Almanac. It is on the website already. It is down to about 15 to go. Down to about 15 to go. What a guess. What a guess. Alrighty guys, good luck. Come on Super. Spencer's officially lost it. Hey what's up DW? DW what up? Laying with the Tom Brady guess? Okay, okay. They might have snuck one in here. They didn't tell us about it. Super Fractor Tom Brady. Come on. They snuck one in. You had brawny as always? Nothing wrong with that Shady. We'll get one. We'll get a Super Brawny. Going for that, that 101. That uh, that Doolado. Yes sir, Doug. Yes sir, 1125 on the Bounty Man. I am trying to hit that for someone. Get someone some break credit. He's lost it. Michael Harris. Got a rookie Matt McLean on the projections. Correa Refractor. Come on, super early. Let's do it early. There's a taste the lotter. Insert Otto there for the Guardians. Otto for the Guardians. Thank you Masanori. Taking a personal. Taking a personal. Can't wait for those two clowns to make their next trip down to Florida. Yeah right. There's a rookie Davis Martin. And Marcelo Meyer for the Red Sox to 99. Green Mini Donna. Colson Montgomery. Probably won't do it too quickly though with the drive they had to do to get here. Probably won't turn around too quick. There's a Max Clark on the Wave Tigers. Max Clark. Spencer Jones. Come on, super. There's a base Otto. Myrocentric Martinez. The Dodgers. Young international signing for the Dodgers. Chalacta is going to be Francisco Alvarez and Liova Paguerra Refractor rookie. Spots real quick. So we are sold out all the way up to Bowman Chrome. Hobby and Delight, the second random team break. That one is at 10 to go. Sold out until then. There's a Masterpieces Corbin and Yuri Peretz on the projections rookie. Matt Shaw Refractor. Appreciate that guys. 10 to go on the second one. Seven box mixers. It's four Bowman Chrome basketball delight and then three hobby. There's a base Otto Roman Anthony. Nice one there for the Red Sox. Playing well for the Red Sox. There's Waldo. Go Dodgers. Go Dodgers. That's what Sean says. Emmanuel Bonilla real to real. And rookie Tyler Freeman. And Logan Ohapi Refractor rookie. Come on, super. Come on, super. Real to real Francisco and Seiya Suzuki a 250 purple. Vaughn Grissom. It's Gold Lava. That one's going to be a Gabriel Gonzalez for the Mariners on the Gold Lava Otto. That's one of their Mariners. It's a 75 and a hobby. Hobby bias. Niki Dusty taking a few definitive teams. Let's go Dusty. Appreciate you Dusty. Appreciate you Dusty. Rookie Mini Diamond. Matt Mervis. Matt Mervis and a shellact of Max Clark. Fred Freeman. Alrighty guys. One down. Box two. Come on, super. Come on, super. Top's chrome black coming up next guys. That one's also full. So we will get that going right after. And onto some basketball. Come on, super. There's Casey Schmidt. Rookie Projections. Tommy Troy. It's got to be today. Got to be. There's a Refractor of Niqua Pocoa Grego for the Phillies. Refractor Otto. There's a Noray Vera. Randy Johnson set and Guanipa Refractor. Thank you Mike. Taking two in the mixer and one in Bowman's Best Football. So that's down to single digits now. Eight and four in Bowman's Best Football. Our last random team breaks to the day. Pull on the Shimmer and Jordan Walker Refractor Rookie. So 150. Roderick Arias and a base out of Spencer Jones for the Yankees. Spencer Jones. Shohei Refractor. Jalen. More fancy with the Dome. Yeah. Esther Ruiz on the Mini Diamond. And a shellact is going to be Matt Shaw. Gray Rod Rookie. Yeah, Printing Plate 101's are possible for the bounty though. It's just for the Super Fractor 101. They do have 101 Printing Plates in this though, but we're only doing it for the Super Fractor bounty. Masterpieces, Masataka, George Valera, and a Mini Diamond Christian Vicarita 299. Oh, I got you. Yeah, yeah, there are certainly Printing Plate 101's in here. There's a Gold Otto. It's going to be Brock Jones. Go race. Gold to 50 there. True Gold. Bar the Cannons indeed. And a Masatake Yoshida Rookie. Cannons going to be a new offensive coordinator though. And I don't know if Mike Evans is staying. I don't have a lot of confidence in Mike Evans staying. What would you? Rookie Gabe Moreno. Matt McLean. Rookie. They did pretty good. 10 straight years with 1,000 yards in the bucks. And he's got one title, but I'm going to go to the Real. Pialonzo and Riley Green. You know everybody that takes it for your dog. Oh, anyone's going to take Mike Evans. Yeah, anybody. Anybody that can afford him. Your whole story is great. It's a Davidson Day Los Santos. 10 straight years with 1,000 yards.  Strong. He's a beast. Chalact is Jackson Churrio and a Green 299 James Altman. Rookie. Dodges. Trade for digs. Really. Really DW. I was thinking Chiefs. I've been thinking that since the beginning of the year basically. I thought he might get traded at the deadline honestly. We were playing a little bit better than expected though. So I was thinking Chiefs though. I don't know. They could definitely use a receiver. As a bill though, I could see that as well because I don't think they're keeping digs. That's been quite a rocky relationship between digs and Josh. I have to imagine they're going to move on. That drop would have made me drop them. Yeah. That was ridiculous. That was rough. I saw something like the last 10 weeks of the year Khalil Shakir had like almost double the yards of him or more yards than him. It's like, what are we doing? It's time to go. What are we doing? You can get something good for him. You can get herald with the bowman's best spot. And Fadzil with a Almanac spot. Almanac filling up quick. There's a Master Pieces Riley Green and a Hunter Brown Projections. Yuri Perez Refractor. Yeah, I don't want him to go to the Chiefs by any means but I just can see it happening. Jackson Holiday 250 and Otto is going to be Jacob Reimer. Base Otto for the Metz. Perez a Refractor. Yeah, no way do I want to see Mike Evans in Chiefs Red, but I could see it happening. Andrew Vaughn, Aaron Judge, shimmer of Gabe Gonzalez. Juan Soto. Yeah, same with Baker. I mean, like, it just wasn't expected much in general. So people didn't know who was going to throw to him. So it's fair. It's fair. But yeah, Baker knew what to do when you get Mike Evans in front of you. You throw to Mike Evans. That's the move. It's a 99. We got Ryan Clifford for the Strokes. It's a 99. Justin Crawford. Chalacta is going to be Langford for the Rangers and a Jacob Wilson. Masataka on the Projections. Luis Arias. Come on, Super. I'll make us wait the whole case. Come on. There's a Caden Wallace auto there for the Royals. Joey Vado. Rookie Matt Mervis, Randy Johnson set and a Blue Junior Caminero to 150. Go race. Cammie. Real to real judge. And Corbin on the Refractor Rookie. Corbin Carroll. Otto Daniel Montecino on the Refractor Auto for the Padres. Fathers out of the Ruchman Refractor. Justin taking a personal. I don't think that's going to go tonight, Justin. After you are watching, we have a lot of personals lined up. We'll probably go tomorrow on that personal. Chalacta is Phelan Selliston and Refractor Jay Ram. Alrighty, box number four. Good luck. Good luck.  And then we are on to Bowman basketball for the rest of the night. Or for a little bit of the night. And then we have football. Some Bowman's best football and then some absolute. Decided to keep chasing some more kabooms. Volpe on the Projections. Rookie Gabe Gonzalez. To 25 on the Mini Diamond Real to Real Auto is Peter Lanzo. For the Mets. Of course. There he is. Josh H. There we go. Very nice one there. The Polar Bear to 25 on the Real to Real. Mini Diamond Auto. It's ridiculous, man, on the Roderick Arias Refractor. I don't know what it is, man. I don't know what it is. I'm a Pete Magnet. I'm a Pete Lanzo Magnet. There's a Mini Diamond. Chalacta is going to be Jackson Holiday and Ezekiel Tovar. Rainey Johnson Rookie. Really nice one there, Mets. I was just laughing in case you were wondering because I always pull Peter Lanzo. It's like a running joke that I can always find a Peter Lanzo. I can always find a Peter Lanzo. There's a Acer Ruiz on the Prism. And an Ethan Salas. Nice one there. On the Aqua to 199. Aqua Lava. Brian Rochio Refractor. I don't want to be the Polar Bear, man. I don't like the cold. I don't want to be the Polar Bear. There's a Semibassio on the auto there for the Orioles. Nice international signing there. That's right, RPC. I am the Pete Magnet. Chalacta Skeens. No, I got you, Anthony. No worries. I was kind of confused, but yeah. We usually use 130 point for prices. I don't know if there's going to be an exact match of that, though, to kind of compare to. Masterpieces Max Clark and Justin Crawford Projections. I don't know if you'll find an exact comp, but there's plenty of, I'm sure there's plenty of Aaron Judge numbered to 10-5, exactly. Ezekiel Tovar and base auto Henry Bolt for the Ace. Tristan Casas Refractor. Peter Lanzo, man. Me and Pete. I need to meet that dude one day. There's a rookie, Caleb Killian. Chris Morrell Refractor. Real, real rookie Corbin Carroll. Yeah, maybe just throw it up, Anthony. Maybe someone will give a really good price for it. A red judge is definitely really nice. There's a 299 Felman Seliston, Mini Diamond, and Darnichi Valdez, base auto there. Cubs. Volpi Refractor rookie. And there's a Felman Seliston, Chalacta Ruiz. It's funny, RPC. I've actually pit a Peter Lanzo too, because in 2019 Bowman Cromby, he has Redemptions, and he's Peter Lanzo in those. So I've hit Peter Lanzos as well, Pete and Peter. Niki Bryce taking a team in Bowman's Best Football. Matthew taking a definitive spot, and Christopher taking a definitive spot. Appreciate you guys. Come on, super. Let's get some break credit going. Let's get some break credit going. Two to go in Bowman's Best Football, guys. Eight to go on our random team Bowman Crom Basketball. There is 22 total spots on the night. Appreciate that, guys. That's awesome. 22 spots on the night. Fair Harrison. I guess I'll be careful with that one. Masterpieces, Volpi, Zeke Otovar, and it's $2.99, Oscar Colas, or $1.99, sorry, Aqua Lava, Colas Lankford. Not wrong on that, Harrison. Goodness gracious. There's a gold again. Another goal is going to be Yvonne Grissom. Nice one there, Rookie Otto for the Braves. That's Vonn's new boy for the Red Sox. Nice Vonn there for the Braves. Gold to 50. Colin Hauke. Victor Maderos. Yo, Andrew Vargas. Oh, did you? I really like those, man. The on-card, very clean. There's a wave of Brian Rochio. Nolan Aronado. I really like those. The shellacked autos. There's a base auto. Davis and De La Sante. Second one for the D-backs. Shellacked Rookie of Adley and a blue Liova Paguerra to 150. Gunner Henderson refractor Rookie. Come on, Super. Got a Michael Harris. Peter Alonzo. Alonzo to the Cubs. I have heard a bit about Alonzo move, and I haven't heard specifics yet, but Neto there to $2.99. And reel-to-reel auto. That one's nice as well to $1.50. Brando Maella. This one Yankees had a nice two of these, reel-to-reels. Nice insert auto there. Top international prospect for the Yankees. Rookie Corbin. Sitting in the big glove. Oscar Coloss. Reel-to-reel Miguel. Mike Trot refractor. Come on, Super. Corbin Carroll. Got a base auto Braylor Guerrero. I got you, Harrison. Yeah, sorry about that. Sorry I've been getting good randoms recently. I feel you, my man. No worries. Got a shellactive camcorder. And a Rizzo. Rizzo refractor. Riding box number six. N.K. Larry taking a team in Bowman's Best Football. Leonie taking a couple of Phoenix release day spots tomorrow. Got PYT and random teams for Phoenix. You guys are interested in release day tomorrow. I think one to go Bowman's Best Football, guys. Ken May wants that last spot. It is a 10 case to light random teams. Just a few cases of that left. I think three or four. So that's been really fun. That is a pretty steep ask for just for Pete. I think they threw a little bit more in there, but that is pretty steep. Morel two prospects and two solid pitchers. Box number six. There's a rookie masterpieces Gunner and projections Coloss. Rikki Bradfield refractor. There's a junior Kimonero. Rikki prospectado for the race. That's one of their race. Yeah, a little. Nothing's not great. No. Working on it. Lissandro and 299 Oscar Coloss mini diamond. Yeah, that's happened to me plenty of times, Harrison. Get the right team, but the wrong, wrong break. For sure. It's a wave rookie of Outman, Jayrod. Auto Gabe Gonzalez refractor out of there. Mariners, Zack Neto, Rikki. Yeah, that's what I was thinking too. I was thinking they needed to sign Belly or trade him or do whatever they can do to get before they do everything else. Harris on the rookie shellat and Michael Harris base rookie refractor. Yeah, I would think they would have already locked him up by now, man. He had a great season. Really, really good season. Say projections, junior Kimonero. Go race. Tovar refractor rookie. Hey guys, there's a few spots left on Almanac. Just a few spots. Davidson Gutierrez. It is a personal's edition of Almanac coming on Saturday night. 200 mill is a decent hold up. It's a decent hold up. That would make you rethink for sure. Christian Yelly. Come on, super. Say Rio de Rio, Brooks Lee, and to 99 Lazaro Montes. Green Minidotten and Josh Young refractor rookie. So that's what Cody wants. 200 million. Really? Baseball players make some money, man. Yeah, dude. Baseball players make some money. They didn't get it. To 99, Eddie Beltrae. Eddie Beltrae for the Padres and Marcelo Mein. Yeah, he kind of took it into his own hands last year. He had to play good or else he wasn't going to get it. He did. Change teams and started playing real well. Shellat of Jackson Holiday and Sallison. All right. See here, guys. Two more. Two more. Bowman's Best. Get Top's Chrome Black going next. Full case of Black. Get Joel, taking some prism random team spots. And Brian's closing us out on Bowman's Best Football. Thank you, Mr. Brian. Mr. Brian C. Alrighty, guys. So close out on Bowman's Best Football. We have spots left in Bowman Chrome. Seven Box Mixer. It's four. Four Delight and three Hobby. And then we have 12 to go and PYT Bowman Chrome full case hobby. So just 20 spots on the night. 20 spots on the night. Omanio Bonilla on the projections. Junior Cami. Let's go, Truffle. Come on. Come on. Super. Say base auto. Daniel Guillarte. BrewCrew. And Rookie Coloss on the Randy Johnson set. Bryce Hoppe. Wave of Roderick Arias for the Yankees. And Rookie Nolan Gorman Refractor. And like I said, 20 total spots on the night and even less than that in Almanac for tomorrow or for Saturday night. It's a 99 Adley. Nice one there on the green. Nice one O's. Adley on the green. And blue auto to 150 is Jordan Beck for the Rockies. Blue auto to 150. Here's a Masterpieces Max Clark on the mini diamond. Not numbered there. Nice one there. Tigers. Third pick in the draft and a Junior Cami. Second half of this one. What's up Butternugget? What's up Cortes? How we doing? That's right. That is Thursday nights, man. We get it going. Get it going. Here's a Gold Lava to 75. Gabe Gonzalez, Mariners. Mariners having a nice break. And Bobby Miller Refractor Rookie. Rookie Otto on the Randy Johnson set to 250 is Victor Maderos. It'll be for the Angels. This one there, Angels. And a Casey Schmidt Refractor. What are you getting into tonight, Cortes? Besides trouble. Enki Min taking a spot in Phoenix for tomorrow. And Keith taking the Mets in a Bowman's Best Case. Reggie Crawford, Randy Johnson, and Francisco on the Refractor Rookie. Real to real Harper. You're done. Sean looks like he's slacking. Oh boy. Tighten up, Sean. No, no, no. Tighten up, Sean. I just thought of a verse though. Uh-oh. Is it Kenny Gomez Astros? He's right. He's songwriting right now. That's what he's getting into. Rookie Gunner Henderson and a Drew Jones at 299. Hey, we need it. We need it. Thank you. We could use it. Alrighty, guys. The last box here, Bowman's Best. Come on, Super Fractor. The bounty is at 11.25. Come on. Right here. Right here. Thank you, Joe Law taking four in Almanac. We are getting close, guys. We are getting close. We are getting close. Just a few spots. Single digits now, I believe in Almanac for Saturday night. Always a fun time. It'll be Sam and Jake are on Saturday. Let's go. Let's go. Come on, Super. Come on now. Francisco Alvarez projections and Brando Maillet to 250 on the purple. Paul Schienes or Fractor? Always, always time to think of a line though. Got to get it to the paper as quick as possible. I forget it. There's a Nicala Pocoa Grego on the base auto there for the Phillies. Oh, we're feeling the Super. Let's do it. Come on. Come on. Butter nugget. There's a rookie Logan Ohapi for the Angels. And Davidson. Butter nugget. Yeah, that's a good one. It's a good one. There's a Volpe nice one there on the Wave. Bichette. There's a lot of reasons, a lot of Fortnite right now. Yeah, I'd have to imagine. We don't hear nobody. I'll say those four didn't come back. Justin Henry Molloy only refractor. Deep in Ls. Tigers. Deep in Ls. There's a gold Tommy Troy. Nice one there. D-Bex. True gold. 250. Refractor Brett Beatty. Second half of the last box. Projections rookie James Altman. Chris Bryant. Leeover Pagaro to 299. On the 199 star on the Aqua. And a Leeover Pagaro auto. Rookie out of there for the Pirates. Gal Cabrera. Four packs. Come on. Come on. There's a real surreal Miguel Cabrera. Mini Diamond and a Max Muncie. Other Max Muncie. Two of them in the under. They're heavy. Oh, that one? Yep. Nice. We sold them one of those cards. Really? Yeah, the real Jackson Holley. That's pretty cool. Yeah, that's cool. Cody Sanger refractor rookie. Seems like a lot of guys now are kind of looking for their cards. That's pretty. That is cool. That's pretty cool, man. Got a blue auto on the back. It'll be Johnny Farmello. Nice one there for the Mariners. Top pick for the Mariners in the draft. And Shade Langlears. Last pack. Oh, super. Got a Shalacta of Colin Hauke. Lazaro Montets. Alrighty there, guys. That will do it. That will do it for Bowman's Best. Eight box case 31. No super in that one. I was hoping for that. All right, guys. We'll do a quick recap. And then we'll have Top's Crone Black next. Top's Crone Black. Can Joel take in a mixer spot? Let's go Joel. RJ taking a Almanac spot. RJ. And Andrew taking a mixer spot. We are close. I think that's six now. I think that's six now. Hey, appreciate you hanging out with us, Truffle. Appreciate that. Later. Six and 12, guys. From the Truffle shuffle. 18 spots on the night. 18. All right, man. We'll see you. Nuggets and tater tots. All right, I like it. I like it. Nothing wrong with that. We'll take some. Here's a base auto. Leovo Pagaro. Justin Henry Malloy. Grego. Kenny Gomez to 150. Jordan Beck. Base auto guillartate to 99. Eddie Beltry. Gutierrez. There's Gabe Benzala's refractor. Junior Caminero. Guerrero. De Los Santos. Valdez. Henry Bolts. Sammy Bassio. There's a refractor. Montecino. Base Caden Wallace. One is Jacob Reimer to 99. Clifford. And a base Davison De Los Santos. Hey, appreciate that, sir. We'll see you in a bit then. We're in a minute. Spencer Jones base. Refractor of Grego. There's an insert to 250. Victor Manderos from the Randy Johnson set. Otto Roman Anthony. Martinez. The Lauder. Farmello to 150. Got Maiaia to 150 on the insert. Otto Yankees to 75. Gabe Benzala to 50. Brock Jones to 50. Von Grissom and to 25 was Peter Lanzo. Mini diamond auto reel to reel. Always find my man Pete. Alrighty there, guys. That'll do it for Bowman's best hobby. 8 Box Case 31. Ray and a team style. We'll do tops chrome black here in just one moment.


of the Chief Justice for Administration and Management of Massachusetts, Robert Mulligan, Chief Justice of Connecticut, Chase Rogers, and the Chief Justice of Maine, Lee Softly. Very good. Wow. Thank you very, very much for being with us. And have you coin flipped or anything? We coin flipped. Here we go. You're organized. I'm up. I guess good afternoon now. My name is Chase Rogers, and I'm here to address you in my role as Chief Justice of the Connecticut Supreme Court. I first want to thank you for the honor of having the opportunity to testify before you today. I plan to limit my comments today to the critical issue of providing access to our courts, even when funding is severely limited. By way of background, Connecticut, we have a unified court system with 201 authorized judges and 4,200 employees. Our budget is about $500 million, which represents about 3% of Connecticut's state budget. In addition to our core-related functions of adjudicating cases, the judicial branch provides a host of other services, including adult and juvenile probation, victim services, child support enforcement, and operating the juvenile detention facilities. I highlight this because while funding for some of these non-adjudicative functions has increased over the past 10 years, they now represent one half of our budget. On the other hand, funding for our core-related functions have remained essentially flat during the same 10-year period. This stagnation was compounded by several cuts unilaterally imposed during the last fiscal year by our previous governor. To address this shortfall, we were forced to close one juvenile court, two law libraries, froze non-unionized employees' salaries, eliminated reimbursements for out-of-state travel, instituted a hiring freeze, and furloughed our employees and judges for seven days during the past two and a half years. We also currently have 17 judge vacancies. We face different financial challenges this year, as the state is facing its largest deficit ever. In response, the Connecticut General Assembly enacted a biennial budget that included savings of $2 billion in anticipated employee union concessions. Additionally, the governor made it very clear that if a deal was not reached, about 4,700 state employees would be laid off, which would mean more than 400 of these layoffs would occur in the judicial branch. While the governor and the coalition have since agreed to a union concession package, it still must be ratified by the unions and approved by the legislature. So the situation for us remains very fluid even today. To address these uncertainties, we have been working on various contingency plans. These include laying off branch employees throughout the system, closing more courthouses, eliminating special dockets, and closing additional law libraries. As you can imagine, any of these measures alone would dramatically impact the services that we can provide to our residents. Of course, we're not alone. This is a difficult time for state courts across the country. To respond to budget reductions, many of our state judicial branches have been forced to reduce or freeze salaries, impose layoffs, furlough, delay the filling of vacancies, reduce the hours of operation, and increase fines and fees. And I just wanna spend a second on the fines and fees and reducing hours. Unfortunately, the option of reducing the hours of operation and increasing fees and fines may have a serious negative impact on access to justice. How does a working single mom who's trying to pay a fine which is already gonna result in fewer groceries for the week take care of the problem if no business is conducted after 4 p.m. without losing more work time? And at what point do fees become simply too high for a low income individual to pursue his or her rights? It's not hard to imagine a scenario where the courts are really available only to the people with time and money. Fortunately, we haven't had to implement and I'm gonna fight it to the death, either one of those options, although both of them still need to be considered. The problem we face are compounded because in times of trouble, residents desperately seek help from the courts much more than in prosperous periods. In other words, the courts cannot simply say close for business due to lack of funding. Our statistics tell the story. Over the past four years, Connecticut has seen an increase in the number of civil cases added to our dockets by 37%, mostly attributable to the increase in foreclosure and contract collection cases. We are also seeing more people appearing before us who lack the funds to hire an attorney. In Connecticut, for example, in 2010, an astounding 84% of all family cases and 27% of all civil cases had at least one party who was self-represented. The numbers are close to 90% in housing matters. This is my biggest concern, the lack of legal representation because I believe that this is changing the system in ways that we cannot even imagine yet. What we do know is that the lack of attorney representation puts even more pressure on the court system to provide a level playing field in order to ensure that justice is done. It does not appear that the number of self-represented parties is going to go down. The situation is even of greater concern when you consider that legal aid organizations are able to meet only a small fraction of the legal needs of those who cannot afford an attorney. Another significant challenge, which was alluded to before, facing the system throughout the country is the growing number of limited English proficiency residents. Like other states, we have had to be creative because funding is not available to hire additional interpreters. To respond to this need, the Connecticut Judicial Branch is contracted with a language services company that provides over-the-telephone translations of more than 170 languages. And I know you had asked about cross-pollination between the states. I believe that at least two other states have come down to see how that's working in Connecticut and we try to, you know, when we find something, we try to share that information. In addition, we've enhanced our website to better serve both self-represented parties and the LAP population. We also now have many how-to publications that have been translated into Spanish and other languages, and we've developed videos to assist self-represented parties in navigating a particular court process so that they have the information they need before coming to court. We've also increased our use of video conferencing. For example, the appellate court, which is interesting, has begun using video conferencing equipment in matters involving incarcerated self-represented parties so that prisoners don't need to be transported to the court. Why do I mention some of the things we've been doing? I think it's important to know that we're not just resting on the status quo. And while all of these initiatives are important and necessary, there is only so much the creativity can accomplish. We are not a discretionary agency, and I would argue that our courts, particularly in these bad times, are more relevant and necessary than before. Unfortunately, I do fear that many, including some within government, view the courts as just another agency. That is why forums such as today are so important, and I appreciate the ABA's efforts to spotlight the critical role that our state courts play in our society and why it's paramount that the courts receive adequate funding. I and my colleagues in other states are ready to assist in these efforts in any way that you ask us to do so. Thank you again for the opportunity to address you today. Thank you, Chief. Thank you. Good afternoon. I wanna thank Dean Broderick and the University of New Hampshire School of Law for hosting this important event. I also wanna thank the ABA for having the energy and foresight to address the long-term effects on access to justice caused by these unprecedented budget restrictions on judicial branches throughout the country. You asked whether this was a crisis of the courts or the justice system. I wanna suggest to you that this is a crisis of democracy. I recently spent some time with a judge from Guatemala who was here to see how we did it and was astounded to find all of the cuts and all of the difficulties that we're suffering in the United States, whereas you've indicated earlier, our system of justice has been the envy of the world. He suggested in what I thought was a fairly eloquent phrase that the surest way for a democracy to commit suicide is to forget that an independent justice system is at the very core of the government's operations. We are not, as Chief Justice Chase has just said, we are not a discretionary agency. We are a core function of government and we have to be funded. I say that in the context of a state which for several decades has been funded at the lowest per capita levels of any court system in the nation. Adding to these difficulties, we haven't escaped the economic disaster that's befallen most state governments in recent years. The resulting budget cuts hitting a judicial branch that has been chronically underfunded have created additional impediments to our capacity to provide timely access for justice to all of the public. Even before the crisis of the last several years, the main public has historically done without many of the core components of a court system. For example, basic safety. In main courthouses, we've been very slow to institute entry screening. At this point, after 10 years of efforts, we are entry screening in our courthouses less than 20% of our court days. There are far too many days when anyone with a dangerous weapon can walk straight into a courtroom in the state of Maine. There are only 39 courthouses for a geographic expanse of 35 million square miles and only 53 trial judges for a population of 1.3 million people. Maine's judicial branch has no electronic filing capacity, court schedules are not available online and there is insufficient staff to provide central help lines. In contrast to many states, Maine does not have sufficient clerks to work in the courtrooms with our judges. In far too many courtrooms, the judge is alone on the bench having to deal with recording equipment by him or herself or even with the assistance of distracted court security. Several years ago, we were forced to lay off one third of our court reporter staff leaving only 10 court reporters for the entire state before we were able to create a quality system of electronic court recording. And the Maine judicial branch has very few administrators. For example, scheduling of trial judges in the state is done by the trial court chiefs with paper and pencil. If the notebook gets lost, we have no idea what we're doing. We've also had to eliminate all but the most critical of books for our judges and to rely entirely on online research to the, I hate to say it, youngsters at the law school that does not sound painful. But for a multi-generational group of judges, losing books has been a very difficult transition. So it's against that backdrop that the economic disasters of the last several years have taken an additional toll in the state of Maine. To respond to across-the-board budget cuts, the Maine judicial branch has had to leave between 35 and 45 of its 493 total general fund positions vacant. That 493 includes security, judges, clerks, the works. The rolling freeze has meant even fewer staff to respond to continuing flow of new cases and the results have been very troubling. In several areas of the state, courthouses are dark for pre-arranged hours each week. We have instituted a system of administrative weeks, now three a year, during which we don't schedule any ordinary dockets across the state, just to give the clerks' offices an opportunity to catch up with a flood of paper. We establish these administrative weeks well in advance. And for example, the administrative weeks for 2012 are already set. So we don't disrupt the public. We don't cancel dockets. And they have proved to be highly effective in assisting in the paperwork backlogs. Unfortunately, that takes three weeks out of the year that eliminates time to get the actual trials done. The Supreme Judicial Court has also established guidelines to assure that the highest priority case types are reached as quickly as possible. The priorities, not surprisingly, include any matters of personal violence, criminal cases, child protection cases, and family matters in which child-related disputes are present. Unfortunately, the results of setting these priorities has been substantial delays in civil, non-family matters. This of course creates delays for the business community, landlords, and small businesses at a time when the main economy can ill afford it. Our county law libraries found their funding and access to electronic research cut with the ultimate result that only two county libraries survived with any meaningful presence today. Judicial education's been cut to the bone. Our ability to bring the clerks together to train them on new laws, new forms, and new methods of calculating interest has been dramatically reduced. These basic responsibilities often result in increased strain in the clerk's offices with inevitable errors and omissions that make things even more difficult for the public. All of our substantial trial dockets, even difficult family matters, are handled through the, hated by the bar, trailing docket system, causing inevitable uncertainty and further difficulties for the public. In some regions, parties have to return to our courthouses six or seven times before their matter is reached. The technological promises of improved efficiency have remained out of our reach because of lack of resources and the ensuing mobius loop of new cases, fewer resources, and fewer tools to address the unremitting caseload has taken its toll. One of the oddest but increasingly alarming problems we have is the issue of record storage. Since all records are still on paper and we don't have resources for appropriate storage facilities, the boxes and boxes of files and files pile up in the clerk's offices, in hallways, in chambers, overflowing the storage rooms, creating fire hazards and serious traffic difficulties in our courtrooms. The mortgage foreclosure crisis has added to the strain with foreclosure filings more than doubling in the last four years. Unfortunately, we're now learning that court delays in our landlord tenant cases have affected a number of our small businesses and citizens whose income has been augmented by ownership of small apartment buildings, resulting to foreclosures now are adding to the economic misery in Maine. Maine trial judges always among the lowest paid in the country, although the best looking, I would like to have on the record. We have now officially dropped to the very least paid according, accounting for the cost of living, which may also mean we are absolutely at the top of the best looking judges around. Overall, the strain on the system is taking its toll, delays in the resolution of cases are substantial, judgments and rits are delayed, paper gets lost, safety is compromised, the inevitable oversights and mistakes that occur in a strained system have even affected liberty interests. There is, however, in Maine, a bright spot on the horizon. In this legislative session, notwithstanding the continually challenging economic circumstances of the state, Governor LePage presented a budget that allows the judicial branch to fill critical vacancies and to replace one of our most dangerous courthouses. In addition, a study will occur this summer to determine the costs and time necessary to bring electronic filing to Maine's courts. I'm pleased to report that with bipartisan support the governor's budget has been tentatively approved by the Appropriations Committee. If the budget passes as proposed, we will be able to eliminate dark hours in the clerk's offices, slightly improve entry screening capacity, and to begin to address the serious backlogs in civil business and landlord tenant cases. I've been gratified to work with both of the other branches of government and to hear them now reflecting back to us the critical importance of justice, not just for the economic health for the state of Maine, but also for democracy itself. The governor and I met immediately after his inauguration and we've been talking regularly since then. Legislators have accepted our invitations to visit busy courthouses, to wash the proceedings and to meet with judges. They invited me to speak to the committee on the court's jurisdiction and they followed up with questions and suggestions. The Maine Supreme Judicial Court sits every fall in local high schools to hear oral argument allowing thousands of students and parents to see an appellate court at work all at the invitation of the local legislators. Lawyer legislators have been very effective and have articulated the public's right to a working court system and explained the actual results of chronic underfunding. While there is no panacea, effective communication among the branches of government has been critical in Maine and I'm optimistic that the efforts underway really do represent a renewed understanding of the critical nature of justice in our society. Thank you very much for this opportunity. I'm happy to answer questions. Thank you, thank you. Dickens couldn't have written some of your testimonies about what's happening, it's really very tragic. Chief Justice Mulligan. I'm Bob Mulligan, the C-Jam of the Mass Trial Court. I'm here for Chief Justice Roderick Ireland, the Chief Justice of our Supreme Judicial Court who sends his regrets. First, I'd like to also thank you, Mr. Olson and Ms. Olson and Attorney David Boyce for your enormous investment of time and effort into this vitally important issue and to the August members of the ABA panel. I'd like to speak briefly about Massachusetts, our funding, our response to the lack of funding and what we see as the result of our response and frankly some very elementary solutions which I think would be important to us. I've filed written testimony, I'm not going to read it but I may refer to the charts on page 15, 16 and 17. First of all, the Massachusetts court system has 379 judges in the trial court. We operate at 103 courthouses across the state. We average more than 40,000 people excluding employees and jurors visiting our courthouses each day. Last year, for example, we issued, judges issued 38,000 restraining orders disposed of 243,000 criminal cases and 250,000 civil cases. We started fiscal year 09, FY09 at $605 million. That was our appropriation. Our appropriation for FY10 was $559 million. I think this is on page 15. Our appropriation, this fiscal year is $544 million. The fiscal year ends on June 30th and today we're in the budget process for FY12. The numbers in play from the House and Senate, the House number is 520.5. The Senate number is 519.7, 519.8, excuse me. So there's only $700,000 in play for us right now when it goes to conference. Those figures will represent from 605 and FY09 to 520 next fiscal year, FY12, an $85 million or 14% reduction in our funding. Well, what has been the response of the trial court to that reduction in funding? You've heard a lot of the things that have been done by the states. We've done the same things. We've had an absolute hiring freeze in place since October of 2008, very limited hiring before that, for the year before that. But since October of 2008, regardless who was retired from our system, he or she has not been replaced. Not one person has been hired in the organization. We've promoted limited within the organization to fill positions of leadership. The judges, the clerics and the managers all took five days, worked five days without pay our last fiscal year. We've closed courthouses.  It's been a personal goal of mine and a goal of the other trial court chiefs that we not lay off people, not even to lay off in one area, say in the area where they may be less core to hire in another area. So the result of this hiring freeze and some retirement incentives we've put in place, you'll see on page 16, we have a decrease of 1,091 employees from July 1st, 07 to last Wednesday. So 1,000 people, that's 14.3%. Since the hiring freeze, I think it's about 1,025. Of the 1,091 people, 220 of them are court officers, 220 of them are security force who provide front door security. We do have front door security at all of our courthouses and who provide security in the courtroom. So obviously we can tell stories about the anecdotes and stories about the effect of this reduction in personnel. One of the things we're very proud of, we did very good work. We established a green team and we have lowered our energy costs from 20 million a year in FY08 to less than 15 million a year through rewriting contracts and some other environmental initiatives. As a matter of fact, the green team has won three awards from the EPA. Various other cost-eating measures, I'm not gonna go through all of them. So what do we see as an impact from this reduction in personnel? We use the court tools from the advocates of the court tools. Mary McQueen will be happy to hear that. Those are the metrics-oriented measurement systems proposed by the National Son of a State Courts. If you look on page 17 of the, of the, my testimony, you'll see the bar graphs on the bottom showing that our time to this disposition has remained flat. Our clearance rate is now below 100%. It was 116% in 2006, 101% in 2007. It's now 96.9%. We can't keep up with the cases at what you're coming into the system. And unlike New York, our foreclosures have driven our increases, but basically our numbers are fairly static. They haven't increased that much in the last couple of years. The age of pending cases is increasing dramatically. As you can see in the blue bar graph at the center from 2007, we had 73,500 cases are laying about inventory. Those are the cases beyond time standards. And last year we had 92,000. So we can directly show through empirical numbers the effect of this reduction in 1,000 people is having on our ability to deliver timely justice. I'm almost embarrassed to say this, but you talk about solutions. I'm almost embarrassed to say this. They seem so paltry, but these are things I could use as CGM in Massachusetts. First of all, an appropriation without line items and without earmarks. An appropriation of which I would have full authority to use where I saw fit. Two, the ability to close courthouses. To close courthouses without political interference, if I could put it that way, and the ability to redraw jurisdictional lines. And a third, very simple thing, when I think these exist in many states, a judicial impact statement, including the requisite funding for any initiatives that are placed on the trial court or on the Massachusetts judiciary. Thank you very much for the opportunity to speak about Massachusetts. Thank you, Chief Justice Mulligan. And thank you particularly for those ideas at the end. We are working on a resolution to present to the House of Delegates, the American Bar Association in August. And we're preparing a lengthy report that is going to incorporate many of the things that we've been hearing today. Chief Justice. Yes, I just have two very brief questions. In my last year as Chief Justice, I've had an unscientific email survey to all the lawyers in New Hampshire. And I asked them to rate the court system on a one to 10, 10 being fabulous, one being you should go out of business. The average rating among the 800 lawyers who replied was 5.5 on a 10 point scale. And that was before the recent budget cuts. My question is this. I'm not asking to comment on the determination of the staff or the judges because I think I know that that's pretty high. How would you rate on a letter scale, A being fabulous, F being failing, the system that's on the ground today in Connecticut, Maine, and Massachusetts, and how much more money or what percentage increase in your budget would you need to have a court system that you could be proud of on the ground? Well, I wanna keep my job, so I'm not gonna say an F, but you know, as you know, we've tried to be very innovative. So I would say without patting myself on the back or the people that work with me, we're about a B right now, but what I fear is what's about to happen, particularly with the limiting inter-gloves proficiency and the lack of attorney representation. So I don't wanna give you a dollar figure, but what I would say to you and sort of following up on the solution idea where I think all the courts need money is for technology and that, we have been successful, we do have mandatory e-filing and civil matters now and that has reduced the number of civil clerks that we need for that function and we have them doing other things like helping people who come in and say, I don't have a lawyer and I don't know where to go. During our busiest times, we pull clerks out and have them literally as greeters at the front door. So any way that we can start getting some funding for technology that we can then share around the country, that would be a tremendous help to I think the states. Chief Justice, the Maine does not have lifetime tenure. Can you answer that question? Yeah. I would say that all the courts in Maine are above average. That's my story and I'm sticking to it, but your question leads me to actually reflect back a question to you. One of the things that we are learning when we talk to the bar is that fewer and fewer lawyers want to be involved in litigation of any type. We're finding the young lawyers coming out of law school are in fairly unprecedented numbers not staying in the kinds of practice that bring them to court. So when we ask lawyers how are we doing, we are asking a smaller and smaller group of people and in fact, the people we need to be asking are those who are unrepresented, who are in our courts so very often and asking them that question is very difficult. I think we are not doing well by the public right now, but I'm sticking with my above average ranking. Chief Justice Mason, Keeler, everyone. Very good. This may not sound reasonable, but I would say the courts are working at a B plus, frankly. I say that because the people take great pride in what they do. The type A's are gonna work harder and harder through lunch and work late. The others who may not be type A's are gonna work at the same level they always worked at. So the people have stepped up and responded tremendously. I have some very difficult problems we have, I had assigned a union contract in 2007. I was able to get the money for FY08 for that particular union, 3500 clerical employees. I couldn't pay them in nine and 10. So they went back to the money they were making in FY07. I got the money this year to pay them part of what I owe them. Negotiations with our probation officer and security officer union right now. They haven't had a contract since 2006. And I don't have the money to pay them, frankly. Yet, as I say, these people's soldiers are on through these difficult times because they committed to what they do. I think that the grades reflect enormous conscientious commitments by the members of the staff and the judges. But if you were to give a grade, and I'm not gonna ask you this, of what it should be, what it is compared to what it should be for our citizens. If the courts were properly funded, I suspect you'd give a different answer.  I have no question. I'd like to make an observation that I would ask all of you who are present here to note. And that is when we had our hearing in Atlanta and today by these outstanding six chiefs that we've heard from, with the exception of a question that was directly asked of Judge Lipham. Not one judge, not one chief, asked for any salary increases for the members of their court or their staffs. What they've asked for is an opportunity for them and their staff members and up-fellow judges and the state court trial judges that they also supervise to do their job. The reality of it is, is that very bright and talented law graduates coming right out of law school will go to work for any one of them and members of their court. And one year later with one or two years of legal experience compared to 20 or more years of legal experience that you have before, they will make more money than the chiefs that you've heard from today. If we were someplace else in another country and when I was president of the American Bar from 2003 to 2004, I will tell you I've gone to other countries. And I've interacted with members of the bench. What we've heard here today and what we heard in Atlanta is really a crisis that they can't carry this weight by themselves. They need everybody's assistance. Bravo. And one more hand for our panel. Thank you very much. We wish you had more time. I'll work it.


So in the last lecture we were looking at the iterative methods for solving linear algebraic equations. In particular we looked at two different methods one was Gauss-Seidel method another was Jacobi method. I want to solve linear algebraic equation Ax equal to b we looked at two methods one was Jacobi method other was Gauss-Seidel method and I want to look at one more variation of these two methods in fact there are many variations I am just going to indicate few of them but this is over relaxation or relaxation method is slightly conceptually different from these two in the sense that you are trying to introduce a tuning parameter which will accelerate conversions. So what we are really going to look at is well what I told you that in general Jacobi method is slower than the Gauss-Seidel method Gauss-Seidel method we the difference is that as and when a new iterate is formed we use that in the next calculations that is the difference between Gauss-Seidel and Jacobi method. So Gauss-Seidel method actually tends to converge much faster than Jacobi method now I want to see whether I can do still better and I still further enhance the convergence okay. So this relaxation method this is a variant of these iterative schemes basic idea is like this suppose you know suppose I am at this point y let us call this point y and I want to reach y star I want to reach this point y star I am currently at this point y okay I am currently at this point y and to reach from here to here I apply some method okay I apply some method so let us say my method takes me from here to this point which is y cap okay so I will denote this point as plus okay I am at initial point y I have some method by which I am going to reach y star y star is where I want to go okay but when I have a method of going from here to here okay when I apply this method okay I go from y to y cap. Now if going from y to y cap is taking me closer to y star okay I could move more in this direction okay I could move more in this direction and then go closer even closer try to go in closer okay. So what I can do is I can go to a point y tilde which is y plus omega times y minus y cap so y cap is where my first method takes me y tilde is where if I enhance movement in this direction will take me so let us say this is my this is my y tilde so I am going to move further in the same direction I am going to move further in the same direction so I am going to enhance movement in that direction by moving in so my next iterate is not going to be y cap but I am going to have my next iterate as y tilde which is obtained by moving further in the direction. So the idea here is like this that if I start using Gauss-Siedl method okay I will get let us say I am at y through Gauss-Siedl I reached y cap okay so instead of taking y cap as my next iterate what I could do is I can look at this direction y minus y cap and then you know multiply that and add that to y so I will reach a point which is even further even probably closer to y star this is the basic idea in this relaxation business there are two kinds of relaxations one relaxation is over relaxation so we are going further in some cases it is under relaxation sometimes you know this direction in which you are going might be too far away from y star you may have to contract you may have to come back okay so there are two possibilities one is one is omega is less than one so this is well there should be some limit in this case it turns out to be for linear systems it turns out to be 2 so this is over relaxation okay so basically what I am going to do here is something like this well I am not going to use in the present case under relaxation I am going to use over relaxation I am going to have omega which is greater than one okay omega greater than one so see I am starting from initial guess xk and applying Gauss-Siedl method let us say we get okay see xik xik I am now talking about the ith element of the vector okay from xik if I apply Gauss-Siedl method let us say I get zik plus one I am not calling this x again okay this is my intermediate variable because this is not going to be my next iterate okay what I am going to do is I am going to come up with the next iterate xk plus one okay by enhancing the movement in this direction so my xik plus one okay this is going to be xik plus omega times zik k plus one minus xik where omega is omega is greater than one if omega is equal to one we are not interested in that case because we will reduce to Gauss-Siedl method okay I want to enhance I want to go further than what Gauss-Siedl method is giving me just try to understand this what I am going to do is I am going to start applying Gauss-Siedl method to find a new point but the new point I am going to take it as an intermediate point this new point which I get through Gauss-Siedl I am going to take an intermediate point okay and the next iteration is to be calculated using old guess plus this correction now this correction is developed by enhancing or moving further in the direction of the Gauss-Siedl this is Gauss-Siedl step okay this is the original point so difference between this will give you direction in which you have to move and omega times that okay so this is how I am going to generate the new iterate okay what happens if I put omega equal to one it will be Gauss-Siedl if omega is equal to one it is just Gauss-Siedl method if omega is greater than one it is over relaxation you are moving further than then and hope is that if I do this I will reach my solution faster okay so in general you can even make it you know move faster to the solution if you choose this omega between 1 and 2 so now the question that naturally comes is well how and how to choose this omega and when will it converge and so on so we will of course in a due course I will answer all those questions but is the idea clear we just want to enhance the direction in which we are moving that is Gauss-Siedl direction and move a little further so that maybe we will reach the target faster yeah but when you are reaching towards the solution this will be also small no so you are yeah so there might be some oscillations it depends upon now what whether it will cause oscillations or whether it will cause a smooth decay will depend upon eigenvalues and I am going to talk about that okay so yeah that is a good guess that you may have a problem when you we are close to the solution you might overshoot yeah so that may happen so we have to now relate and we have to understand how the convergence occurs and that is where okay so the actual details you can see here the algorithm I have given here how to implement but if you are the idea is clear algorithm will not be difficult to understand now let us start getting into analysis implementation part you know will be covered when you do programming and I am not worried about implementation part or the algorithm how will you efficiently implement this is given in the tables in the nodes and you can have a look at that when you the critical part is convergence analysis okay so what I am going to do now is rearrange my equations in a matrix vector form okay now this will give me a way to analyze the system of equations or the convergence behavior that is what I want to analyze the vector matrix rotation which I am going to develop here and going to use maybe for next 2 or 3 lectures is not meant for programming programming will be done you know row by row you put a for loop and each row you do calculations that is how you do the programming for this the analysis which I am going to do is going to be using matrices and vectors and that is mainly because analyzing convergence becomes very easy using vector matrix notations okay so do not confuse the 2 things whatever we did till now was meant for actually programming okay now what I am going to do is for analysis okay because getting insights into the analysis of this method using summations becomes very very difficult instead of that if you do everything using matrix notation it is very easy okay so let us get on to the let us say Gauss-Seidel method so what is my Gauss-Seidel method my first equation in the Gauss-Seidel method I can write as a11 x1 k plus 1 is equal to b1 minus summation i going from 2 to n right i going from 2 to n or j going from 2 to n a1 j or let us write it more explicitly let us write this instead of summations it will be better to write this explicitly so this will be a12 x2 k minus a13 x3 k a1 n xn k this is my first equation in the Gauss-Seidel method I have just earlier when I wrote the algorithm I had divided by a11 okay now my intention is different I want to get some convenient vector matrix notation so I have multiplied by a11 so this is the equation which I have to solve right my second equation here is my second equation is actually a22 x2 k plus 1 is equal to b2 minus a21 x1 k plus 1 minus a23 is this fine this is my second equation the iteration in Gauss-Seidel method okay this is Gauss-Seidel method okay this is Gauss-Seidel method the first iterate that was formed is used here the first iterate that was formed is immediately used here okay so I am going to rearrange this I am going to take this on this side okay I am going to take it on this side so I will get a21 x1 k plus 1 plus a22 x2 k plus 1 is equal to b2 minus a23 x3 k everyone with me on this I have taken k plus 1 on one side I have left k on one side okay I have left all xk on one side I am taking k plus 1 on one side not clear I have just taken this which was substituted on right hand side to left hand side okay likewise I can go on doing this so what will be the for the third one can you guess a31 x1 k plus 1 plus a32 x2 k plus 1 plus a33 x3 k plus 1 is equal to v3 minus a34 x4 k up to a4n xn k right I am taking all xk plus 1 on the left hand side I am leaving everything that is xk on the right hand side okay now I want to use I want to put this into a vector and matrix notation it is going to be a long equation okay so this here is a11 a21 a22 do you see this on the left hand side is the lower triangular part of a matrix okay the lower triangular part of a matrix is equal to lower triangular part and the diagonal part okay lower triangular part and the diagonal part what will I get here I will get 0 a12 up to a1n 0 0 a23 a2n right this will be last element here will be 0 and this will be a n minus 1n this into x1 k x2 k xn k plus what will be on this side well I have made a mistake one mistake it should be minus here this should be minus all this is minus minus signs will appear here okay because we have all minus signs coming there right and here will be b vector if you see it is b1 b2 b3 b4 okay the b vector will appear here okay this matrix appears here this matrix appears here okay what is the relationship of these matrices what is the relationship of these matrices to original matrix A LU no what is LU decomposition LU decomposition is completely different don't don't mistake LU decomposition or LDU you transpose that is not this this is this is physically the lower triangular lower triangular and the diagonal part of the matrix this is physically the upper triangular part minus of upper triangular part pardon me you add it so this is if I write this matrix if I decide to write A matrix as sum of three matrices okay see if I decide to write A matrix as sum of three matrices L plus D plus U don't confuse this with LDU transpose LU decomposition is different from this I am just using the notation L and U here this is not LU decomposition this is I mean if I draw a picture this is splitting a matrix into three parts this is diagonal this is strictly upper triangular part of this matrix and this is strictly lower triangular part of the matrix this is diagonal elements this is all elements that are in the okay so this is my U this is my L and this is my D okay so writing this matrix as if I just do pictorially I am just writing this matrix as addition of three matrices strictly lower triangular part the diagonal part and strictly upper triangular part I am just using the same notation as LU decomposition this is not same as this is not same as A is equal to LU that is multiplication that comes through Gaussian elimination this is just simply separating three physically separate parts okay so this and this do not confuse I am just using same notation that is all or also you might see in some books or in one in strang you also have this sometimes you write A as LDU transpose so do not confuse that and this okay only notations are same okay so I have written it like this so this makes me or this particular way of writing this matrix A allows me to do express this method Gaussian method in a vector matrix notation okay so this equation which I have written in matrix form I am going to rewrite this as L plus D into xk plus 1 is equal to minus u xk plus B is everyone with me on this just look at the matrices okay this is L plus D on the left hand side multiplying xk plus 1 okay here it is u strictly upper triangular part of A matrix A is written as L plus D plus u and then I can write this method next iterate is obtained by solving this matrix equation is equivalent to solving this matrix equation actually we are going to do line by line as I told you algorithmically we are not going to write this matrix equation ever we are going to do line by line calculations okay but what you are doing line by line is actually equivalent to this calculation is that okay okay so which means my next iterate is obtained as xk plus 1 is equal to minus L plus D inverse u xk plus conceptually what you are doing is obtaining a new iterate by this method okay sometime back I talked about inverting the matrix or approximately inverting the matrix and so on if you look here if you look here we are trying to say well I cannot invert the full matrix easily but I can invert the lower triangular part it has a nice structure I can exploit that and invert that okay to come up with a new iterate if I do a similar rearrangement of equations in the case of Jacobi method then what will I get if I do this is for Gauss-Seidel method for Jacobi method for Jacobi method what you can show is that doing the iterations is equivalent to D times xk plus 1 is equal to minus L plus u xk plus B xk plus 1 is equal to minus D inverse L plus u xk plus D inverse times B for Jacobi method if you do rearrangement of the calculations you can show actually doing one Jacobi step is equivalent to solving this equation what is nice about Jacobi method inverting the diagonal matrix is very easy just write 1 upon the diagonal elements right that is why we choose to do this so this is very very easy as compared to inverting the whole matrix if all the diagonal elements are nonzero if you arrange the matrix in such a way that all the diagonal elements are nonzero then doing this is very very easy it is okay so Jacobi method is equivalent to doing this okay now what about relaxation method okay relaxation method you can show that you have to do a little more algebra to come up with these matrices for the relaxation method but nevertheless finally you get this equation D plus omega L for relaxation method it turns out it turns out that it is this matrix it is this matrix right hand side is this and it solving this equation iteratively at each point okay so likewise there are other variations what I have taught you is called as actually forward Gauss-Siedl method there is also reverse Gauss-Siedl method okay then there is a reverse or backward Gauss-Siedl method then there is a symmetric Gauss-Siedl method in which you first do forward Gauss-Siedl then you backward Gauss-Siedl so there are all kinds of variations which make conversions faster okay so all of them for all of them you can actually express you can express iterations in terms of these fundamental three components L, D, U okay and so I have listed some of these variations here now let me generalize this let me generalize this so in general if I look at these equation I can have a pattern here what is this pattern this pattern is like this I am every time constructing a new iteration by following formula S inverse T xk plus S inverse B okay what is S matrix what is T matrix changes from method to method but essentially my equation looks like this whichever iteration method I take I take Gauss-Siedl what is S in Gauss-Siedl L plus D what is T here minus U T here is minus U okay so I can actually list this okay so my basic fundamental iteration equation is xk plus 1 is equal to S inverse T xk plus S inverse B now Jacobi method S corresponds to D and T corresponds to minus L plus U okay Gauss-Siedl method S corresponds to L plus D T corresponds to minus U can you guess this is forward back forward can you guess what will be backward Gauss-Siedl see here it is L plus D what will be backward Gauss-Siedl U plus D okay and here it will be minus L backward Gauss-Siedl will be S corresponds to U plus D and T corresponds to minus L in this case relaxation method what what is S this will be S matrix okay this will be T matrix actually you will have to probably divide by omega and then then get that to divide everything by omega then you will get S and T matrices okay to divide everything by omega you will get S matrix T matrix and then same idea okay the fundamental equation fundamental equation is this my fundamental equation is this okay so so basically what I need to do is I need to analyze behavior of this equation right how does this equation behave what is what is this equation have you seen this kind of equations new value is equal to a matrix into old value have you seen this kind of equations these are called as linear difference equations new iterate is equal to matrix into old iterate this is linear difference equation except you might have seen this in time okay here this equation is with respect to the iteration index of iteration okay so if I put it in some standard form okay which I am going to do soon then things will fall in place but you should be able to connect things what you have done some abstract form and when it is going to be applied somewhere okay now now let us say this iterations converge okay we still have not analyzed whether they converge or not but let us say they converge and say x star is the solution okay let us say my x star is the solution so where what will be the final equation what do we might converge what will happen if I what will happen if this converges it will give itself right the final value should give itself so x star is equal to S inverse T x star plus S inverse B is this fine so finally this is where I want to reach okay let me call this as equation 1 let me call this as equation 2 I am going to subtract this equation from this equation can I do that what will cancel this term will be 0 so if I subtract 2 from 1 you know I get this equation x k plus 1 minus x star is equal to S inverse T x k minus x star let me call this as error is this fine this is new error what is error error is the distance from the solution okay distance from the true solution x star is the true solution well I will show you that x star actually indeed is the true solution when you do this method okay we have to show that we should reach finally the point which is solution of A x equal to B that is that also has to be shown okay we will do that of course is everyone with me on this this is a linear difference equation okay and then finally I want to reach the solution of A x equal to B okay so far so good so now let us start analyzing this equation so we started from those complex row summations okay now we have come to a very compact nice form everything looks like this you know one simple equation x e k plus 1 is equal to okay how does this equation behave okay let us say I start with some initial guess say x naught is my initial guess okay what is the error at time x naught it is x star minus e 0 is equal to x 0 minus x star what is this error I do not know if I knew then I would know x star no I do not know what is this error nevertheless I can do analysis without requiring to know the error I am going to analyze the behavior of this equation the beauty of this analysis is that you can analyze without requiring to know what is e naught or what is even okay I am just going to look at properties of S inverse t okay if S inverse t has certain property okay I am guaranteed that this sequence of errors generated by this difference equation will go to 0 if error goes to 0 I am reaching the solution what is the meaning of error going to 0 difference between the iteration and a true is reducing that is what I want to happen right okay so let us start applying this equation so what is even S inverse t e 0 right what is e 2 S inverse t even which is S inverse t square e 0 this is okay I am just substituting for even I am just substituting for even okay what can you say about the error at instant k no at e k at e k can I write this is S inverse t raise to k can I write this well while denoting vectors this e is a vector by the way e is a vector x is a vector x star is a vector okay so x naught minus x star is a vector e is a vector this notation of superscript in the brackets is intentional you should not confuse it with you know raise to something this is not e raise to 0 this is 0th vector okay so in the iterations in the iteration at any point k in the iterations I have to now analyze what happens to this matrix when it is multiplied with itself multiple times okay so what should happen now is do you agree with me what I want to happen is this limit as k tends to infinity if I do more and more iterations I go closer and closer to the solution that is what should happen okay so which means limit as k tends to infinity S inverse t raise to k e naught should be 0 vector is e 0 a 0 vector no it is not a 0 vector so what I want to happen actually is S inverse t raise to k should tend to 0 to null matrix as k tends to infinity what should happen is S inverse t so I should choose S inverse t in such a way that this condition holds okay this condition holds looks quite formidable how do I choose a splitting of a matrix in such a way that this condition holds okay well not that bad as it looks like we will look at the theoretical basis then it will be clear that it is not that difficult to do this let me first show that we are indeed going to go to the solution okay by doing this error is going to go to 0 if error goes to 0 where will you reach okay you will reach the solution actually if I apply the difference equation again and again okay I can show I can start with this difference equation X k is equal to S inverse t or X k plus 1 is equal to S inverse t X k plus S inverse t S inverse b I can start with this difference equation apply it from 0 1 2 3 4 and I can show that actually X k is equal to S inverse t X naught X naught is my initial guess okay I am not deriving this you can derive this very easily what the expression that I am writing finally just recursively write the equations and you will get what I am writing plus S inverse t k minus 1 plus S inverse t less to k minus 2 up to S inverse t plus I into S inverse b okay if you use this difference equation again and again starting from X 0 you will be able to derive this expression okay now this expression has two components if you look here this expression has two components what are the two components one component is this S inverse t sorry S inverse t rest to k I forgot to put k here that is important S inverse t rest to k so this has S inverse t rest to k into X naught okay now what we wanted to happen was S inverse t rest to k should go to null matrix okay S inverse t should go to null matrix so which means if this goes to null matrix this part will be nullified this part will be nullified if I choose S and t intelligently such that this condition holds okay then this part will be nullified where will the iterations go right iterations will go to this now whatever I am writing here is this same as solving AX equal to b we have to prove that are you getting what I am saying see here I started with the argument that well my look at look look here I started with this argument here I said that error should be error should be defined like this then there is a difference equation that governs the error if I apply the difference equation actually I will get that error at time k will be S inverse t rest to k error at time 0 okay error will go to 0 provided this matrix this matrix goes close and close to null matrix okay this matrix that is my next argument this matrix should go close and close to null matrix then I looked at my original equation this is my original equation iteration equation I applied it again and again again and again and then I could derive this it is very easy to derive this expression okay you start with X0 X1 is equal to something X0 this then X1 is equal to or X2 is equal to S inverse t X1 and instead of X1 you substitute for okay you can eliminate and get everything in terms of X0 and then right hand side okay it just repeated application of this equation starting from 0 1 2 3 4 you will get this expression not very difficult to derive now if this part goes to 0 what it means is that as you progress in the iterations okay the effect of initial guess goes to 0 even if your initial guess is wrong if you have chosen S inverse t correctly this part will become 0 and whatever is your initial guess the solution will start going towards this vector on the right hand side so now what I have to show is that this vector on the right hand side is indeed the solution that is first what I am going to show second what I want to do is to give you insights into how do you choose S and t such that convergence is guaranteed okay how to choose S and t such that convergence is guaranteed that is my next mission okay so my claim is that if this condition happens that is S inverse t raise to k if this goes to 0 0 null matrix if this is tending to null matrix the solution that is xk tends to okay if this happens then iterations tend to this vector okay I want to use one matrix identity I suppose you have studied this in your first year or in your 12th standard i minus a inverse i minus a inverse can be written as a series right so this is actually a series where k is increasing so actually I can replace this I can replace this by this okay so which means which means if I use this particular series expansion okay I can say that actually xk is tending to i minus S inverse t inverse S inverse b right see this S inverse b is going to be there I am just replacing this square bracket I am replacing the square bracket by its limit as k tends to infinity this is the limit right this equation is as k tends to infinity as k tends to infinity I can replace I can replace this thing in the bracket okay by i minus S inverse t whole to the inverse is everyone with me yeah so what is this equal to what is this equal to can you expand this further this can be very easily shown to be S minus t inverse just expand this you will get S minus t you take S inverse common you will get S see this thing in the bracket can be written as S inverse into S minus t whole thing inverse right what is S inverse inverse S multiplied by S inverse will give you i okay what remains is S inverse t inverse but what is S minus t S minus t is nothing but a okay so this is nothing but just go back and see this is nothing but okay this is nothing but a so this sequence is going to converge to the true solution that is a inverse b this method of constructing sequence of iterates is actually equivalent to inverting a matrix and solving getting the solution provided you choose S and t correctly what do you mean by S and t correctly S and t should be such that S inverse t rest to k should go to null matrix okay so now the next part of the puzzle is that well under what conditions this will happen under what conditions how do you choose S and t such that you know you will go to under what kind of matrices we will look at class of matrices that will guarantee convergence then we will look at we will come to the point where we will be able to tweak these matrices using relaxation method basically what you may not expect right now but what is going to come is Eigen value analysis now what I am going to do is relate convergence to Eigen values of this matrix S inverse t and what I am going to show is that if Eigen values of S inverse t are strictly less than 1 okay then convergence will occur then the problem is transferred to how to choose S and t such that Eigen values of S inverse t are strictly less than 1 okay the problem is transferred to how do I choose S and t such that again so we are going to relate this to Eigen values okay we are going to relate this to Eigen values very very fundamental and actually analyzing difference equations of this type is where the Eigen value problem arises that is what I want to also highlight when we are taught in the linear algebra course Eigen value problem well the teacher comes and write lambda a v is equal to lambda v I mean why a v is equal to lambda v so you must have seen that Eigen value problem pops out when you are trying to solve linear differential equations I am going to show that it pops out when you try to solve linear difference equations okay same thing happens when you are trying to solve linear partial differential equations you get Eigen function problems okay Eigen functions and Eigen values here you will get Eigen vectors and Eigen values same idea used in different domains okay to understand how matrices behave without actually requiring to solve it so the beauty of that analysis is that we will be able to talk about conversions without actually solving for it we can just look at Eigen values and say whether this will converge or not converge okay that is what we are going to go towards okay. So we will continue that with the next class I will start with analyzing linear difference equations and their behavior and then correlate that to analysis of these equations.