What's up everyone? It's your girl, Kenty here from Layton Sports Cards and I am ripping brand new release today of 2021. Penini, Don Russ, Optic Football, Hobbies, Six Box, Half Case Break, number seven. Pick your team. Got Andrew L. Bills, Andrew G. Bucks, Brennan R. Panthers, Chris H. Jets, Don C. J. Broncos, Ed F. Ravens, Harper V with the Bengals and Jags, Jake O. Eagles, Jeffrey H. Steelers, Jim J. Texans, Jim A. Browns, Johannes G. Lyons, Jose S. Rams, Joseph C. Seahawks, Justin F. Bears, Ken M. Dolphins, Kenny H. Falcons, Matthew G. Titans, Nicholas U. Saints, Peter G. Chiefs and Chargers, Raquel B. Patriots, Ryan A. with the Cardinals, Ryan P. Washington Colts and Vikings, Sean M. Niners, Sean T. Giants, Stephen I. Raiders, Stuart Z. Packers, and Wayne K. with the Cowboys. Alright, best of luck everyone. Thanks for the film. Here we go. We had two downtowns in the last half case, but as we've seen before, that doesn't mean some hot possibility of getting some more out of this half case. And just a few breaks up to the daytime. More breaks tonight with Forrests starting at five. Also be sure to check out the National Breaks tab up on the site for the breaks we're doing at the National. So we've got Pat Firm, we've got Black Pandora already, a DJ Shark Jr. to 25.  Got break scheduled through Wednesday. Again, every break spot purchased in the Nationals and one of the National Breaks to 179 Derek Barnett. We'll get you an entry into the grand giveaway that we've got going on and the grand prize is awesome. A lot of really nice prizes. Jamar Chase on the blue to 179. There you go, bagels. Not too many Jamar Chase colors coming out today. So very nice hit. 121 of 179. Bangles on that one. Go Harper. Orange, I don't feel it. I thought that was gold for a second. To 199 Vikings. 100 total prizes in that giveaway. We've got the 75 red Rated Rookie Auto Kellan Mon Vikings from Minnesota. Jamie Davis, hollow Jimmy G. Niners. Tante Smith rookie, John Slater. We've got Legendary Logos, Shrain Lance rookie for the Niners. That's a cool one there, San Fran. Miners.  Bears. Atwell Rated Rookie on the Silver Circles to 125 for Sean Slater. DUI Hilton, Heyton Turner rookie. Rondell Moore, we've got Diami Brown, the rookie's insert. Basham, James White Hollow. AJ Green, Elijah Mulden rookie. Bafae Owe, Dominators of Devante Adams. Got Kellan Mon rookie. Aqua to 299. Justin Herbert for the Chargers. Seeing some nice Herbie color coming out today for the gold earlier. Andre Sisko, Pink Velocity is 79, Derek Henry Titans. Michael Carter, Hollow Jamar Jefferson. Lyons, same Ellinger. Last pack, box one. Justin Fields and a My House, Patrick Maholes. Cheaps, box two. And at Gainwell, we've got Rising Suns of Cooper Cup. Black Pandora, it is. On the Black Pandora there, that's even harder to see on that car. Kind of see it on the bottom there. It is to 25. Rams, Kyle Trask, Red, Hines Worthen, 99, Steelers. Javon Holland, Blue to 179, Larry Johnson, Chiefs. Truba Hubbard, we've got a Trevor Lawrence Hollow. There you go, Jacksonville. Nice hit, Jacks. On the T-Law. Mag that. Nice, Tormy Trumbull. I think we've pulled a haul of about every rookie quarterback so far, I think. Silver circles to 125, down to Brown. Maybe not Fields. Oh, I believe every other one. Tyler Wallace, we've got Davis Mills. Lime Green to 35. Boo! Jim J. Love the Lime Green. Lime of 35 too, nice bookend. There you go. We'll mag that one, Mills Mafia. Miles Sanders Hollow. Cornell Powell, we've got Dan Marino on this short print mythical. Nice hit, Dolphins. Only second mythical of the day here. First one was, it was a cowboy. It was Emmett Smith. Emmett Smith, that's right. Dan Marino on this mythical. Dolphins, we'll mag that short print for you. Short print this year. Got Terrace Marshall Jr. gifted rookies. Panthers. Schrinco, we've got to 199. Kyler Murray Cardinals. Najee Harris, Rated Rookie. We've got Justin Fields Aqua to 299. Bears, boom! Chicago. Justin F. First Fields color of the day. 86 out of 299. Beautiful. Mag that one. That's a great box. Uzrique Michael Vick Hollow. Cam Akers, we've got Ian Book, Rated Rookie. Saints. Eric Stokes, Aaron Rogers, My House Hollow. Mark Jefferson, Aqua Devante Adams of 299. Jalen Phillips, Silver Circles to 125. James Winston, Saints. Got Kaderius Tony, Rated Rookie. A Bateman out of 150 for the Ravens. Rashad Bateman. Char, Kritchie Grant, Slash Packbox too. Sry Smith, we've got Retro Series, Roger Stalback on the Black Pandora. Where is that just? Yeah, that's Pandora. That one's even harder to see. That's crazy. See a little bit on the bottom again. Again, 21 of 25. Nice Black Pandora there. Green. Mitchell, Aqua out of 299. George Kittle, Niners. Barley, we've got Jalen Waddle on the Pink Velocity to 79. Those Dolphins. Second one of those today. Got Jamar Chase, Hollow, Darren Waller. Metcalfs, even Collins, Rookie. Jacob Harris, we've got Ice, Rated Rookie. Anthony Schwartz to 15 for the Browns. He's a little numbered rookie there, Cleveland. Elvin Joseph, Chesterat on the Aqua to 299. Jalen Waddle, Rookie. We've got A Carson Wentz to 99 for the Colts. Leatherwood, Hollow, Richie Grant Falcons. Green Hunt, Trey Sermon, Rookie. Connor Long, Rising Suns, PS2. Broncos, Mark Jefferson. We've got Corey Davis, Silver Circles to 125 Jets. Phillips, Orange to 199, Rated Rookie. Kenneth Gainwell. I can't hear you. Cadarius, Tony, Alvin, Camara, Hollow. Rich in the building. Some nice cards coming out of them. Rich is not in the building. Oh, Rich is not in the building. Never mind. Richie Grant, Rated Rookie. Did not hear that. Shai Smith, we've got My House of Josh Allen for the bills. Jake Funk, we've got Blue to 179. George Kittle, Niners. Russo, we've got two of five. Why is this numbered out of five? I'm so confused. I don't know, but it is two of five, Greg Russo for the bills. We got Buffalo on the low numbered. Wonder if that was supposed to have a color on it. I am not sure. Buffalo, Andrew L. That's crazy. Two of five. Huh, all righty then. That's the first sticker auto we've seen on a base. Rated Rookie. Just looks like a whole error card to me. We've got Rated Rookie Kyle Pitts. Lowest numbered auto of the day. Jamie Darden, we've got Retro Series Hollow, Chad Johnson. Sammy Brown, and a Najihara Skifted Rookie. All right, box four. Everybody in Chad go. Y'all got really quiet. We're on back to work off their lunch break, I guess. Najiharis, we've got Red to 99. Tylen Wallace, Ravens. Ruzrique, Blumat Stafford to 179. Ramps got Ian Book Rookie. Hollow, LaViscushinal Jr. J. Eric Stokes Rookie. Got Kyle Schrauss. Hollow, Joe Thysman on the Retro Series. Tylen Wallace, Orange to 199. Devo, Ronnie Perkins. Aqua to 299. Devin Singletary. Cornel Powell, Jared Golf Hollow. Jared Patterson, we've got Mack Jones. Mythical Short Print. Boom! Wow! Hit Patriots! That's Raquel B. This is only the third Mythical of the day. What is this? Break seven? So out of three and a half cases. There you go. That is sick. It's nice to center, too, if I'd say so. Could be a little bit to the left. Not by much, though. Wow. Beautiful card there. We will mad that one. Geez, they've all been like old school players, too. Javante Williams, Gridiron Kings. Wow. First, I thought that was an auto. I was like, wait a second. What? Aqua to 299. Baker Mayfield Browns. There's zero. Truba Hubbard. We've got Mike Evans on the Silver Circles to 125. It's home to us every time you say that. Tommy Trumbull. Hollow. Sewel. Glyons. Joe Burrow. Kenneth Gainwell Rookie. Goddammit Brown on the Elite Series Rookies. Caleb Phillips. Blue to 179. Patrick Mahomes. Chiefs. It's Kaderius Tony. Orange. Saquon Barkley. She Grant Rated Rookie to 125. Elijah Moore. Oh, wow. Hold on. There's an error pack for you. How about back to back? Hollow Rated Rookie Autos. Got Elijah Moore, Jets, and Nasha. Boy, it's still a little bit ready. There you go, Steelers. Nice hit there to 125 on the Najee. Mad that one. And then Elijah Moore, Hollow. Also to 125. We will take that. I was like, wait a second. Why does this pack feel thicker? It's not a patch auto. Back to back autos though. Shai Smith Rookie. Last patch, box four. Calvin Joseph and White Hot Rookie's Trace Sermon for the Niners. Box five. Frank Darby. Pink. Demian Harris on the Velocity of 79. Pay Blue to 175. Hunter Renfro. Got Mack Jones. We've got Desmond Patrick to 75 on the Rated Rookie Auto. Titans. Vera Tucker. Got Davis Mills. My House Hollow, Justin Herbert. Chargers. Kayla Farley, Red Rated Rookie, Ronnie Perkins. Jamar Chase Rated Rookie. We've got Gold up next. Gold of James Robinson for the Jags. Here you go, Jags. I love Gold. Five out of ten. It's Gold. Stephen Collins, Miles Garrett Hollow. No, Gold. We did pull up Reverend Jordan. Not like a top top rookie, but it's been the only Gold rookie we've pulled today so far. I think we can get one before the end of the day time. Chesa Rat. We've got Legendary Logos. Tom Brady on the Hollow. Bucks. Here we new some. Amon Rossi Brown Hollow. Rookie, Lyon. Tamara, Pete Warner. Ian Wangwu. We've got Kyle Trask, the Rookie's Insert. Bucks. Si Chenol Jr., Orange to 199. Jags. This is Patrick. Got Aqua to 299. Najee Harris. Rookie, Steelers. Ramon Dre, Blue to 179. Gross Matos. Panthers. Evans. Aqua, David Montgomery. Bears to 199. Little Harbert's. Got Danny Dymetallo. Giants. Joe Burrow. Terrace Marshall Jr. Last Pass. Boxed Pots. Nick Fulton and Rising Suns of Winfield Jr. All right. Last box here. We've got one more pick your team after this, and then we've got random divisions to end the day. Again, Force will be live starting at 5 p.m. everybody. The only breaks with spots open is baseball and basketball tonight. Jalen Phillips on the pink Velocity is 79. So let's get those filled up for him. He's got like five or six baseball breaks, and then a couple basketball and getting the more optic. Blue to 179. Elijah Moore. Jets. Also be sure to check out the Nationals Breaks tab on the website. DJ Moore, hollow. Got breaks listed through Wednesday, Tuesday and Wednesday National Breaks. Again, every spot you buy in to one of the National Breaks, you will get entered into the grand prize giveaway. Legendary logos. Justin Herbert for the Chargers. 100 total prizes going to be given away. Again, every spot in one of those National Breaks, we get chin entry. Hawkinson on the Blue to 179 Lions. We've got tier one baseball releasing next week. Scary Terry on the awkward 299 Eminence football. It's a really big one.  Tua on the hollow. Definitely some very nice breaks. We break it all day. We've got Dak Prescott. Black Pandora downtown. Breaks with black. That's crazy. Wayne Kay with the Cowboys on this one. Black Pandora. This one is three out of 25. Beautiful hit. Congrats again, Wayne. We will mag that one for you. Elijah Moore. We've got Tom Brady Dominators. Although there'll be plenty left, Bryce. Plenty. Micah Parsons. We've got Orange. Elijah Vera Tucker to 171.99. Jacks. Back-to-back breaks of them. Jack. We've got Shray Lance Rated Rookie. Aqua Kevin Byard Titans 299. Trevor Lawrence Rookie. We've got Hollow Rated Rookie. Zach Wilson for the Jets. Nice and their Jets. We'll mag that. Cooper Cups. Scritch. We've got PS2 and Gifted Rookies. Kellyn Mons. We've got Maury Rogers. Silver Circles to 125. Tommy Trembl for the Panthers. Yeah, there's going to be a downtown per case. Some of them we've pulled multiple downtowns. Rashad Bateman. We've got Black Pandora. Jim Kelly for the Bills to 25. Bill's Mafia there. Nice, Kelly. Archie Grant. We've got Rated Rookie to 50. Nice. Broncos. Givante Williams on the Pink Velocity Auto. Nice hit. Denver. Don C. Nice. 26 out of 50. That's 6 even. Which, which, oh, Herbie downtown. Wow. That's nice. We'll mag that. Williams for you. Couple packs left here. Leonard Rashad Bateman. Pack and then it recaps on Christian Barmore and a My House of Alvin Camara. For the Saints. Very nice last box there. All right, we'll do our numbered cards and autos here. First, Winfield Junior, PS2, Cooper Cup. This is a Black Pandora to 25 Rising Suns. Roger Stalback, also Black Pandora. Jim Kelly, Black Pandora Bills. DJ Shark, Black Pandora. Gold, James Robinson. Hello, Herbert. Vera Tucker. Kenneth Gainwell. Nashi Harris. Elijah Moore. Tommy Schrumble. Rashad Slater. Ronnie Perkins. Tyler Wallace. Jalen Phillips. Jalen Waddle. Anthony Schwartz. Our autos. Rashad Bateman. Ravens. Elijah Moore. Hollow Jets. Des Fitzpatrick. Titans. Kellan Mann. Vikings. Then we had the two of five. Greg Rousseau. Good of Bills. Two of five on that one. And our mag cards. Oh, I didn't realize there were so many mag cards. We had the Hollow Nashi Harris for the Steelers. Javante Williams. Pink Velocity Auto Broncos. The Mythical Dan Marino. Dak Prescott Black Pandora downtown 25 Cowboys. Zach Wilson Hollow Jets. We had a Trevor Lawrence Hollow Jags. Justin Fields Aqua to 299 Bears. Jamar Chase to 179. Bangles. We had the Lime Green to 35. Davis Mills. Texans. And then the Mythical Short Print Mac Jones Patriots. All right, that'll do it for this half case. We've got one more half case picker team coming right up.


Angelo, are you online? Hello, yes, I am. So I think it has enough lines.  Sorry. OK, so Angelo, can you share your slides? Yes. Can you see it? So we see you, not your slides yet? Uh-huh. OK. OK. So go on. Start. Yeah. OK. So hello, everyone. Good morning, good afternoon. I am Angelo Marco-Ramosa from the National Institute of Physics, UP, University of the Philippines, Wilhelmine, from the Philippines. So the talk I will give for 20 minutes is entitled First Passage Characteristics of Resetting Bias Diffusion with Mixed Absorbing and Reflecting Boundaries. So since it's only a 20-minute talk, we'll just cut some stuff. And we'll try to manage. Angelo, I'm sorry I'm interrupting you. It's a 50-minute talk, actually. Oh, 15 minutes. Uh-huh. Yeah. So after talk. OK. Go on. So from this title, since it's a diffusion, we know a diffusion has so many things to talk about. You have, it can be anything. So from the title, we'll narrate down to what I'm going to talk for 15 minutes. So this is the title. So from the title, first we have boundaries. So the boundaries, let's say, for this talk, it will be only a one-dimensional lattice. And then it's just limited from x equal to 0 to x equal to 1. And then we also have absorbing and reflecting boundaries. So here, we set x equal to 0 to be an absorbing boundary. While x equal to 1, the reflecting boundary. Also, in this talk, we also included, we're going to talk about the first class characteristics, such as the mean and the variance, since mean and variance can show the behavior of your distribution. So from here, the implications are, since we have an absorbing boundary at x equal to 0, the limit of our distribution at any time when the space approaches that boundary x equal to 0 should be 0. While the reflecting boundary at x equal to 1, the implication of this is the flux at x equal to 1 should be 0 at any time p. Also, since we included the setting, in this talk, our variable for setting is small r. And then our random walker will reset to a position, say, x0. Also, we included a bias. And then in here, the bias will be indicated by the variable v. So the plan to solve the first passage character 6 is, so first, how do we solve for the first passage or the mean first passage time? So in papers, we read that so that they can solve for this, their process is, first, they solve the probability distribution with the setting, and then compute the first passage time with the setting, and then get the mean first passage. But this, for me, it's not intuitive. And then I'm going to show a more, I say this, friendly approach. So for me, I will start with the distribution, and then solve for the last transform of it, our probability distribution, and then compute the first passage time without the setting. And then later on, we include the setting onto it, then solve for the mean first passage time so that we can see the characteristics of the first passage. So in this process, my plan, we have milestones. So first, we need to identify the evolution of the probability. So in here, we start with this. And then after we identify the evolution of our probability, we need to get the probability rate. After this, we will move on to the last transformative probability distribution. And then from here, we can get easily the last transform of the first passage. And then in this talk, the main idea in here, or my contribution, or such, is we include their setting from a non-resetting first passage. Later, I will show how it is related. And then after this, we can now get the moments, like mean and variance. So in here, in this process, in these milestones, it is much easier since we are going just to take the derivatives and not to take integrations. And we know it's easier to take integratives than integrations. So the mathematical methods for this is first, from our evolution of probability, we're going to use Taylor expansion to get the probability rate. And then after to get the, we will take the Laplace transform with the application of our conditions, boundary conditions, continuity conditions, and initial conditions. We will get the Laplace transform. After that, there's a definition of first passage that will connect the Laplace transform of probability distribution to the first passage time distribution. And then we will add the setting. Then there's a definition of moments from this. So can I interrupt you for a second? Can you just, I may have missed this, but what does resetting correspond to physically in X or S space? Sorry. So resetting means, so since we have a random walker, it means that while it traverses the region, there's a probability that our random walker will be teleported into a resetting position. In this talk, it will be X naught. Here, the setting means our random walker, the only probability will go to the X naught. I see. Okay. Yes, so it's a sudden jump. He says teleportation, but it's not the same. Okay, okay, I see. In this talk, we'll be teleportation. Well, some you can set actually a traversing time, the setting time, traversing the setting time to go to that position. So there are papers there, you can look for them and then you can read about them. So here, so let's start in the solving for this. So the evolution of the probability. So for example, at the bottom of the screen, you can see that there's a sample of a lattice and then the blue dot is our position X. So the evolution of probabilities means that from time T, what will happen to our random walker from T to time T plus DT? So in here, as you can see, all the P's are our probability at a position X and then T and for time T and then T plus DT, which is the reference for the next time step. So the things that are not common here are the case. So example, this K, K plus at location X minus HT is the probability of a random walker from X minus H, where H is the spacing size or spacing step, X minus H. So the K plus is the probability of it moving to the right to going to position X, while K minus X plus HT is the probability of a random walker at X plus H to move to position X at time T. So as you can see, at the position X, there's an increase of probability or increase of numbers of random walker going to there, since you can go from X minus H and X plus H to go to position X. Furthermore, the probability will decrease since the random walker can move from PXT, the position X, leaving it. So if the random walker, it can go from position X, it can go to the left given by the probability K minus or probability rate K minus and then probably K plus for moving to the right. So this is the, for me, this is more intuitive because they can look at a lattice and then think what you want to have or like a recipe or the ingredients you want so that if it can move two steps, you can add more terms in here. So from here, from our milestones, we tell you expand this. So we tell you expand this on DT and H and we'll have this. Well, I omitted the higher orders of DT squared and H cubed, okay? So from here, it's kind of not common. It's very uncommon. But in the next slide or next equation or there's a simpler notation such that this equation seven is the more and the equation eight are the more common equation we know, okay? So again, here, V is our variable that shows bias and D is our diffusion coefficient, okay? So we have a homogeneous media, yes? Anjalo, I'm sorry for the interruption. We are almost at the 10 minute mark. So you are five minutes flexible but leave some time for questions, thank you. Okay, so we have a homogeneous media. So V and D are just constants. Now, so our conditions I said earlier are boundary conditions which are given by nine and 10 which I said earlier, initial condition equation 11 we said that say the random variable start at the resetting position. We can put it anywhere else but for here, let's set it at the resetting position and then we have a continued condition. So since we have two different mid boundary it's wise to cut your probability distribution into two so that we're here it's P less than and P greater than so that you can apply a boundary condition on one say, which is the P at X equal to zero and then another function P greater than where you apply boundary condition at X equal to one, okay? So when you use less transfer we will get this equation, okay? So in here, we have a some, constant of, so this is a constant of X, this some value C. Next, after that we solve for the first passage. So first passage is just the flux wherein we can think of the first time the run of Walker Beach at position X. Here, we want to see at X equal to zero and we'll get this equation. Now, to get the first passage probability with the setting with this paper by Pal we obtain this equation 18 where the relationship of first passage time without the setting and first passage time with the setting we obtain this equation such that we will be able to get our the characteristics of the first passage. So the end moment is given by this one. So equation 20 is the definition and the equation 21 is using the our previous equation. So from this we will be able to get the first passage characteristics mean the first moment. It is given by this equation. So it is actually very long. So we use equation 23 to simplify our equation, okay? And then this is the second moment, the variance. We will able to have this equation. So we have three more large functions of capital C, capital gamma and capital lambda where they scale as equation 25. So example of our first passage of the mean is given by this. So where the y-axis is the first moment the mean first passage time and then the x-axis are resetting rate R, okay? So in here we can see that the difference of the colors are the different V and then the D we just set equal to one. So in here we can see that the bias increases when you increase or rather the first moment increases as to increase the bias, which makes sense because the bias when it's positive it goes to the right. So if the random worker wants to move to the right going away from our absorbing boundary it will take more time. And also in this plot it shows that the points the huge points in the plot are the minimum point at this region. We can see that it is different for a different V and also as you can see in the shape of the plot there are some resetting part, example here. So Joel we have less than one minute you have to wrap it up, okay, go on. So in here it takes more time to go to the absorbing boundary than if you increase the resetting rate it will take less time and then if you go further it will take again more time. So there's an optimal resetting rate on this such. So that's all of my talk. So thank you for listening. Lots of love from the fieldings. Thank you. Well, thank you very much. It's nice we have such a diverse range of topics for today afternoon. We don't have time for questions again but if you have a question please.