In today's video, I will share with you one of the simplest and yet very very effective trading strategy with this app of ours. These two technical analysis strategies are very simple to use even for complete beginners. And many traders have used these two technical analysis indicators to profit across different markets. Make sure you watch this video till the end because I will be using different charts to break down for you step by step how you can do it too. Hi everyone, my name is Chloe and welcome back to my channel. The only one place for you to learn our stocks investing as well as different ways to generate multiple strings from income. Let's start by first adding this indicator into the Octa Trading app. Under the indicator tab, look for store casting. Wait, before that, let me share with you a little bit more about Octa. A global broker that offers a wide range of trading options, whether you are into stocks, commodities or indices, they've got 230 choices for you. Octa Trading app can help you to get super low spreads and there are no sneaky commissions or swaps into your profits. But wait, there's more. If you're new to all these trading stuff, they've got a lot of educational materials in different languages, from live trading sessions, market analysis, and useful trading tips. Plus, they've got a demo account that you can test out with virtual money. Perfect for practicing without risking your hard-earned cash. They have solid customer service too. Need help at 3am? No problem. Their support team is there 24-7 to answer all your questions. Handling your money is a breeze at Octa. Deposit takes just a minute and withdrawal rolls are under 49 minutes even faster than your food delivery. So if you're ready to kickstart your trading journey safely, keep the link in the description or scan this QR code to download Octa Trading app. My promo code Aligato allows you to double your deposit for trading. Now let's get back to the video. Now let's delve into the first indicator in store casting. Exactly what is that and how you can use it. The store casting indicator is a short-term momentum indicator that compares the current close with the highest and the lowest close over a set period. Typically, the default period is 14, indicating the current candle's position in relation to the last 14 candles. The indicator consists of two lights, the blue K percentage line and the orange D percentage line. The blue line represents the actual value of the store casting, while the orange line is the three period moving average of the blue line. Later on, I will also share with you how we can use these two lines to enter and exit your positions. Beside these two lines, there's also a marked zone in the middle of the indicator, ranging from the 18 and 20 level. Similar to RSI, the store casting indicator identifies overbought and oversold region. If you are wondering what the RSI indicator is, I share about this in my previous video over here, so make sure you go and check it out too. So now let's use the author app to look into how you can use it to enter and exit your trade using store casting. The first thing to look out for is the overbought and oversold region. If the value is above 80, it suggests that currently it's in the overbought area, suggesting that the market could be too optimistic towards the underlying asset. Such scenario is usually followed by falling prices because when the market realize that the price is too high, they will start to sell. As you can see from the chart over here, the index subsequently fell by 7% after the store casting reaches the overbought area. On the other hand, when store casting reaches 20, it also means that it reaches the oversold region, hinting that right now the market could be too pessimistic, resulting in the asset price reaching the oversold region. As a result, value buyers will start to emerge and when they start buying, the prices will get pushed up. As you can see from the chart over here, once store casting reaches the oversold region, the prices start to go up. However, there are certain limitations in terms of just looking at store casting oversold and overbought. As you can see, there are situations that the prices continue to go up despite reaching the overbought region. So if you took profit at the first sign of overbought, you actually miss out another 5% gain as the market continues to trend upwards. Worse, if you decide to short the market when the market reaches the overbought region, your trades could end up losing money too. Vice versa, it will also be incomplete to enter your bullish trade just because the market reaches the oversold region. Because despite reaching the oversold, the prices could continue to go down just like what happened back in the 2020 March COVID-19 period, the stock price fell by another 8% despite reaching the oversold region. That's why apart from just looking at the oversold and overbought region, we should also look into the two lines using the store casting, which is the K and D line cross over. Now, before I share a little bit more about how you can use K and D line crossover, if you like this video so far, make sure you give it a thumbs up, subscribe and hit the notification button so that you will not miss out any future updates that I have in my channel. Also comment down below what kind of indicators are you currently using for your trades as well. Now let's take a look at how we can use this K and D line crossover to enter and exit our trade factor. Firstly, when the blue K% line crosses above the orange D% line, it generally indicates that the market is going to go up. For example, in this chart, once the blue line crosses above the orange line, the market went up 4% and 10% respectively. Vice versa, when we look at the other scenario, when the blue line crosses below the orange line, the market generally starts to fall. As with the chart over here, the index fell by 7% when the blue line starts to cross below orange line. But by now, you might be thinking, hmm Chloe, there are certain times that despite of the crossover, the market continues to trend further instead of reversing. What's happening? Does it mean that it's a false signal? You are absolutely right. By right, the stock price over here should be dropping after the blue line crossed below the orange line. However, instead of dropping, it actually went up. That's why we need to combine what we have learned so far in totality so that we can make a more accurate prediction of the stock price movement. So right now, let's combine. So what we truly want to look out for from stochastic is the crossover after it reaches the oversold or overbought region. Now let's take a look at some more examples. With this chart, instead of buying at the first side of oversold or overbought, or line crossover in late September, which was actually a false signal, we should only initiate our bullish trade in early October, when the blue line cross above the orange line inside the 2018 event. Because it represents a stronger indication that the upward momentum is going to continue. And right after, the price went up. Conversely, we should only enter our sell position when the crossover happens after the oversold region is reached. And in this case, the bearish trade can be entered in early August, when the blue line cross below orange line within the 2018 region. Of course, no indicators is foolproof. That's why it's always good to combine different indicators so that to increase the profitability of your trade. For myself, I always like to combine stochastic with MACD. Think of MACD as your market detective. It's like having a special tool that can help you to support the potential trend reversal. I talked in-depth about how to use MACD in my previous video over here. On top of that, I also shared two additional indicators in this video. So if you want to have a deeper understanding of different technical analysis indicators, then make sure you check out the video over here. So now let's add MACD into the October trading app, go to the indicator tab and select MACD. Now let's interpret MACD and stochastic all in one chart. What we want to look out for is, after the stochastic blue line cross above orange line within the 2018 region, for example in August over here, then we look at does MACD give us any sign of potential trend reversal. Indeed, at that time, MACD was showing light pink and it's also soaking up, showcasing that the bearish momentum is actually getting weaker and bullish momentum is on the way of coming back. So right after that, the stock price started to rebound. The same can be applied to spot bearish trends. For example, in this chart over here, the stochastic has reached the overbought region. At the same time, MACD started to show its first red bar, indicating that the bearish momentum is coming back. And then afterwards, the prices start to fall. In a nutshell, MACD helped you to see when the trend might be changing direction while stochastic helps you to see things that might be getting too extreme with buying and selling. So using the blue and orange line crossover, you can better enter and exit your trades with higher certainty. Remember though, all these indicators aren't foolproof. There's no tool that can guarantee you 100% accuracy. That's why it's so important to do position sizing. The key is to learn to use them effectively while managing your risk at the same time. On top of these two indicators, there are also many different indicators that you can use inside of the trading app, including Ichimoku Cloud, moving averages, RSI and more. So when you are entering your trade, it's good to look at different indicators to increase your chances of success. Also, do understand that forage trading carries risks as well, so make sure you learn how to do it effectively before embarking your journey. And the good thing is, OPPA starts providing demo accounts for you to practice first before you get started your real trades. So if you want to get started your trading journey, do consider signing up your account with OPPA and access all the free tools that they provide for you. All to do is to open your account via my link in the comment section below. You can also join my Telegram channel over here to get more additional stock investing updates. Until next time, happy trading and I will see you in the next video. Arigato!


Welcome in everyone to the week for waiver wire Q&A with JJ Zachary and presented by fan dual week three is in the books and apparently the Jaguars and Lions are good now. We've got a lot of stuff that happened this weekend. Change the landscape of the waiver wire and we're going to be answering any and all questions you guys have as you're prepping for week four. Getting those fab budgets ready determining where you're going to spend that cash. I'm Simon Grunewald joined as always on these Tuesdays by JJ Zachary and JJ. What's up? What's up, man? I feel like this the waiver wire this week is one of those waiver wires where like these guys might be on your waiver wire, but they might not be like if Alexander Madison's out there. Great at Alexander, you know, if Jamal Williams is out there at Jamal Williams of Khalil Herbert's out there at Khalil Herbert. But you know, if you look at like the percent roster numbers they're like in that like 50 to 60 percent range, which you know is not the most reliable in the world. You know, we want to speak to the deeper leaguers as well and not just the shallow ones. Absolutely. We'll do our best to speak to some of those deeper leaguers, but you're right. If you look up, if you just Google week four waiver wire, all the names that pop up are going to be those guys that very well might be drafted in your league. I went and scoured my waiver wires a little bit earlier for some Jamal Williams, some Alexander Madison and some Khalil Herbert and did not find them anywhere. Everybody watching if you've got questions for us, whether you're on Facebook, YouTube, Twitch, wherever you're watching, throw them in the chat and we will gladly answer those for you. And then while you're there, go and hit that like button. If you're watching this on Facebook or on YouTube and subscribe to FanDuel on YouTube, follow them on Twitch and then find them on TikTok, Instagram, Twitter, at FanDuel across all of these platforms. And of course you can find JJ Zacharyson on Twitter at late round QB. So go and give him a follow over there. JJ, is that strategy working out for you so far this year? You're late round QB. I know you waffled a little bit in the off season on that. I did. Yeah. Look, I mean, at the end of the day, I, you know, the last few years, what we had seen from the quarterback position in fantasy football was that, you know, we'd seen better predictability at the position from a pre-draft from an ADP standpoint to how these guys finished. We saw some separation there. And so really what it came down to was I became more of like the last few years had become more of like a middle round quarterback guy as opposed to an early round one or a late round one. Do you think Josh Allen's going to pan out? But it does seem like, I mean, you probably agree with me, there's three quarterbacks that are just basically like lapping the field right now where it's Jalen Hertz, Josh Allen, Lamar Jackson. Lamar Jackson right now is averaging almost seven more fantasy points per game than he did during his MVP season, which is just wild. So yeah, I mean, I think that if you have one of those three quarterbacks, you're feeling really good.  No, it really seems that way. Jalen Hertz doing his best to make a case for League MVP, but Lamar Jackson standing back there going, watch this like, like you think you got it? Jalen, watch what I can do. We have a question in here from Dustin. Dustin said Cooper, London or Mike Williams as my wide receiver to Debo is wide receiver one. JJ, which of these three players would you be plugging in as your wide receiver to Amari Cooper, Drake London or Mike Williams? Yeah, I mean, I haven't looked at schedules in too much detail yet this week.  You know, no one's really talking about him in fantasy circles, but he's having a great couple of weeks, last couple of weeks. He's only him and CD lamb have had back to back weeks and weeks two and three of 35% target share better and Cooper is the one who's been really, really producing out of those two. You know, I think he's in a great spot. But I mean, from like a rest of season ranking standpoint, I think I like Drake London the most. I mean, he's just seeing such a massive target share in his offense. He's producing as well. If I'm looking at it this week, I don't know yet. I think they're probably all sort of clumped together. Mike Williams. I'm a little bit afraid of just because Keenan Allen is practicing. He's probably going to be back. I think there's a little bit more variance and variation with Mike Williams, but a decent spot. If I remember the schedule correctly, but right now I think my rest of season rank is a habit London Williams Cooper, but I do think that Cooper is sort of undervalued right now across the fantasy landscape because I don't think people are realizing how good he's actually been. Now, yeah, he's been great and he's the clear wide receiver one and when they're in that offense, so whenever I see questions like should I drop Cooper for this person or should I trade Cooper for this person? It's always with another team's wide receiver two or three on that team. One thing I will say Cooper in London in that Browns Falcons game. Surprisingly, at least to me, that's expected to be a high scoring game. The total for that game is set at 49 and a half on the Fandals Sports Book, one of the highest ones of the week. So you might just want pieces in that game. It's a very weird week from again. I only just started to look at like the week for stuff and ranking guys and stuff like that because I'm in waiver wire mode right now, but it's a very strange week in terms of the the totals in these games because you got like Seattle and Detroit. Detroit has the highest implied team total on the slate according to Fandals Sports Book. I mean, it's crazy. So we're going to see some teams that we don't usually see score some points this week. Yeah, absolutely. We are going to prioritize waiver wire questions. So if you guys have a waiver wire questions, throw them in the chat. We'll get to those first and then if we have time, we'll hit some of the other ones. But like JJ said, this is waiver wired time. That's where our focus has been the past couple days. So you might get some better answers for these start sit questions as the week goes on. We had a question in here from Linen said Trevor Lawrence worth a pickup in a 12 team league bad matchup this week, but looking long term, they had Lance so looking for that long term fill in. Yeah, you know, I did my rest of season rankings and I published them today over on my Patreon and Trevor Lawrence. I'm trying to look for him really quick Lawrence right now. I have a QB I want. Oh yeah, there it is QB 10 so rest of season. He's looking he's looking pretty good. You know where I've been impressed by what he's done.  The weapons are not nearly as bad as I think people thought Christian Kirk looks like a stud in the role that he's playing. I think that they're they're utilizing him very similarly to how Arizona used him this past year. You know, whenever he was able to play in the slot a little bit more. So yeah, I mean, and not only that, but Lawrence has like sneaky upside from a rushing perspective. So, you know, I think Lawrence is definitely a worth a pickup in the 12 team league. He should be rostered in pretty much every format. I think he's like a low end QB one from here on out. Yeah, I'm with you. He's not the kind of guy where I'm like just setting it and forgetting it week in week out. Know what I mean? I'd still be willing to maybe play some of those matchups, but he's approaching that territory. Yeah, like be open minded. You know, the way that we have to come up with a word for this, Simon, where like it's someone that you like plug in your lineup most weeks, but if there's a good streamer out there, you can play that streamer over him. Like I think Jared Goff over Trevor Lawrence this week makes sense. Goff going against the at all, you know, really good scoring environment. They're playing in a dome, all that kind of stuff. So like, you know, Goff is more of a streamer. I would rather have Trevor Lawrence rest of season, but if you want to bump him down and put put Jared Goff in for this one week, that's totally fine. So he's not a plug and play starter. He's sort of like a plug and play unless there's a really, really good streamer out there. Jill and I have started referring to players like that as probably starts like without your roster. He's a probably stuff like based on what's available. You're probably plugging them in week in week out. Chris in here had a question for us and said, please guys, I need help bad. I need it right now. We'll do our best to help you, Chris. Chris said, I just got offered a trade. I get Barkley, Deontay Johnson and Josh Jacobs for Echler, Debo and Damian Pierce. So a trade, take one Barkley, Deontay Johnson and Josh Jacobs sending away Echler, Debo and Pierce. JJ, what do you, what do you think about this trade? We don't have any info on league type scoring format, but just in a vacuum with the information we have. This is tough, honestly. You know, I think I usually I side with the team or with the side that's getting the best player in the deal. And I think by far the best player in this deal is Saquon Barkley. Barkley to me is like a top three or four guy rest of season. So, you know, I do think that Barkley is the best player in this trade, but Deontay Johnson, you know, he has a target share of course, but I'm worried about the offense in general. Josh Jacobs did see an uptick and looks through the air this past week, which was really good to see, but I don't know how sustainable that's going to be. Echler underperforming, Debo kind of underperforming. Damien Pierce, you know, worried about what could happen in negative game scripts and such, but I do think his role is going to grow as the season goes on.  Or to, sorry, to stay with the Echler side, but you know, I think it's a fair trade overall. I just, I call these kinds of trades musical chairs trades because you're really, you're not really like, like there's going to be a loser more than likely with a deal like this. I like to do more two for one. I like to do more, you know, a wide receiver for a running back to really help both teams, whereas right here, you know, yeah, you're taking a downgrade from Barkley to, or to, from Barkley to Echler and then Deontay to Debo's and a little bit of an upgrade or, you know, a definite upgrade and then Josh Jacobs, Damien Pierce. Yeah, like Damien Pierce, a little bit more rest of season, but it's not that dramatic. So there's just not that much going on here for me to be like, absolutely choose this side, absolutely choose this side. I think it's just a fair deal overall, just giving the fact that Barkley is pretty much by far the best player in this team. Yeah. And you hit on a point that I was going to say, JJ, I don't generally make trades like this in season because it does generally lead to like fostering like a negative output for at least one of these two teams and that makes it harder to trade with that person going forward. I want one where it's one position for a different position or two for one. Like you said, where someone needs depth, you need a starter, you can make something happen right there. David here wanted to know, is there any upside to Justice Hill? Is that someone that would be worth picking up right now? I don't think so. I mean, J.K. Dobbins is going to see more and more work in this offense as he gets healthier. And even still, I mean, you know, this offense is going to split the backfield in some way. And we've already seen this backfield not be very effective to start the year. I just don't think it's really worth it. You know, the target shares in Baltimore, you know, since since Lamar Jackson took over, they've been really low for running backs. They've seen the fewest targets in the NFL that that positional group since Lamar Jackson took over a few years ago. So I'm not really like super, super high on any Ravens running back. Although I will say, you know, I did my rest season rankings, like I said, and I had J.K. Dobbins ranked as like a low end RB two or something like that, just because of what we'll see later in the season, hopefully from him. And I don't think people are reacting enough to that. You know, a lot of times people just kind of look in the moment with these guys. Like no one's really thinking about Michael Gallup right now. Well, Michael Gallup is going to be back eventually and Dak Prescott is going to be back eventually. And, you know, it's not like CD lamb has been super, super consistent. Obviously he came through towards the end of last night's game. Thank God. But you know, he dropped that pass, etc. And so, you know, there's guys like that where you have to have a long term view with these with these with these players. So I do actually think that J.K. Dobbins might even be a buy just given the way that people are viewing him right now. But no, I don't think adding Justice Hill is really worth it. I'm with you. And especially after that performance last week, like people were disappointed in J.K. Dobbins, if they plugged him in their lineups, this could be the time to go out there and send out a trade offer and no, uh, no upside to Justice Hill for me. Um, that CD lamb touched down though, J.J. That was the first moment I I've convinced my girlfriend to play fantasy football with me the past couple of years, right? But it's been kind of very casual off to the side where she had a matchup against one of her coworkers. She got in a work league yesterday or this year and like with staring at her phone and she walks in on watching the game. She's like, I need one more point from CD lamb. Is it going to happen? Like is it going to happen? And then she walked in and five minutes later that touch and we were like, yeah, like it was the first time I watched her like feel that sweat. And it was awesome. It was awesome. Yeah. It was awesome. There we had another question in here. Ike Azar wants to know, should I keep stashing picket in non one quarterback league? So in our super flex two quarterback leagues is picket worth a stash? Yeah. I mean, it always, yeah, always depends on who you'd be, who you'd be picking up instead of picket, but I think pickets worth a stash. I mean, Mitch Trubisky's done nothing to show us that he's, he's going to be the long term starter there. I know that Mike Tomlin can be stubborn that Steelers front office the way they operate that coaching staff operates. They will, they will slow play it more than likely, but I think picket has an opportunity to be a starter halfway through the season and super flex, you know, as annoying as it is just hold that player. You know, what were you? I guess my question is like, what were you expecting when you drafted picket? Like this is, this is sort of what we thought was going to happen. Honestly, to the point of like Trubisky not playing well and now that he's not playing well, if anything, you would want to hold on to picket more than if Trubisky was actually playing decently. So I think he's still a hold. Yeah, he's got to be. And that's a great point. I've been saying it with rookie wide receivers this year as well. Like if you're thinking about dropping those guys, then you probably shouldn't have drafted them to begin with.  Dustin in here wants to know Mack Hollins worth a waiver wire pickup. If so, what percentage of fab should we spend? Mack Hollins had one heck of a week this week came down with what was at 158 receiving yards in the absence of Hunter Renfrow. Is this for real? He had 10 targets in this game, eight targets the week before. Is this someone that needs to be on our radar? Yeah, so I mean, I'm going to be selling and patting myself in the back here and I kind of am by saying this, but he I talked about Mack Hollins on my sleeper show this past week. He was one of my sleepers that was rostering fewer than 10% of Yahoo Leagues and I'm saying that because the reason I was on Mack Hollins was not just because Hunter Renfrow is out, but Tennessee has been really bad at guarding perimeter wide receivers and Mack Hollins is a permanent perimeter wide out opposite of Devonte Adams in that offense. So when Hunter Renfrow is back, a lot of looks are going to be funneled back towards Hunter Renfrow and not necessarily Mack Hollins.  I mean, he's a full time player on Vegas. They could see a lot of negative game scripts, you know, playing opposite Devonte Adams can't be a bad thing. But expecting what we saw this past week each week is definitely not something that I would do. Like, for instance, like if you're if you're debating between Mack Hollins or Romeo Dobbs or Zay Jones, I would take the other two over Mack Hollins because I think that there's a higher chance that a player like Zay Jones maintains his target share and Romeo Dobbs has such a high upside within that offense and just given the fact that he's a rookie in the ambiguity there. So, you know, it just depends on who you would be rostering instead, but I think in like a 12 deep league or a 14 plus team league, I think Mack Hollins is fine. Yeah, it's the uses that you mentioned that shocked me. Like I was going through and I missed that going through the first couple of weeks, then this massive week happened and I was like, well, like we got to look into this a little bit like what's going on and you're right. He was on the field week one, 88% of the snaps week to 87% of this snap saw a slight jump this week, but he's the wide receiver that's on the field next most after Devante Adams even when Hunter Remperos healthy out there. Yeah. So you got to look at his direction. You can't just completely ignore it right there. Joseph had a question for us. He wanted to know how do you feel about adding in joku or Tanya? I'm starting Everett right now. Yeah, look, I like Everett more than those two in general moving forward, you know, Justin Herbert was banged up. I think that he should be better moving forward. But David and joku, I mean, like we saw last week, obviously he blew up against Pittsburgh, but the week before that he had like an 18.5% target share week one. He had a 3.3%. I think there's a lot of anchoring bias going on where week one David and joku doesn't do anything. So everyone's like, oh, and joku is not going to be part of this offense, but he's been part of the offense the last two weeks and the Browns have been one of the most effective offenses in terms of EPA to start the season. They're they're really doing well offensively moving the chains. A lot of that has to do with their run game, but you could be percent really hasn't been that that bad at like at least, you know, sustaining and helping these these past catchers be relevant fantasy. So I think David and joku who has, you know, a fringe top 10 route participation rate to start the year at tight end. We know this offense is tight and centric. They run a lot of 12 personnel. I think in joku's a good fantasy asset. I think he's like a high end tight end to maybe even a low end tight end one from here on out, but I do like Gerald Everett. I have Gerald Everett one spot higher in my rest of season ranking. So I do think that that in this in this kind of instance, I don't think it's a bad idea to just roster both Everett and in joku and sort of flip flop based on matchup each week. And in joku will be having a quarterback change at one point this season. We see the Sean Watson come back to this Browns team. So he's the kind of quarterback of your gun or the kind of tight end. If you're going to roster a second tight end, there's something changing that can elevate him even up a notch at a later point this season. So I'm with you. I think in joku is definitely worth adding enough in joku and tonion. He's the guy that I want to add onto my team. Ike had a question for said if you roster David Montgomery, would you drop him for Herbert and just bet against Mon Monty rest of season? No, I wouldn't I wouldn't do that. I haven't seen any report. Have you seen any report today on Montgomery and how long he might be out? No, I haven't seen any up. It feels like it's just completely ambiguous with all of these running back. So like Daven Cook is going to be in a brace. Deontre Swift will play, but it's day to day. And then David Montgomery, we've heard nothing about yet. Yeah. The only thing I heard was was Eberfluss saying that that he was going to that he was day to day and he wasn't going to give us any information on it. I mean, the bottom line is Montgomery is seeing more work than little Herbert when both are healthy. You know, I personally I thought that's going into the season that there was a non zero chance that Herbert was just a better player than David Montgomery. I think we saw this past week that it's possible that Herbert's very, very good. But at the end of the day, these these things come down to coaching staff decisions. And if they think that David Montgomery should see the Rockmore, then David Montgomery is going to see the Rockmore. I would not be dropping David Montgomery pretty much in any format. But I would be adding Clule Herbert if I don't have him in every form. Yeah, don't drop David Montgomery. Do not drop David Montgomery. You can't drop to running back that has been the lead running back for their team. Just because the back I've got a hundred plus yards this week. That being said, I think Herbert's one of my favorite pickups if he's on the waiver wire not just this week but before the season. Like this is one of those guys where there aren't very many names that come along the waiver wire where they could realistically take over as the number one running back on their team without an injury. Right. Like we could see Herbert run away with this. Not that that's what I'm predicting, but it can happen. Yeah, David Montgomery on the last year of his contrast rookie contract. So it's not like this team and this team is not tied to Montgomery at all. They weren't the team that drafted them. The regime that drafted them. You know, there's a good chance that that you know, he's gone after this year. So they might play into that and just like Clule Herbert beat the guy. Yeah, my lot of question in here for us and how would you rank waiver priority over these receivers? Zay Jones, Tyler Boyd or Cadarius Tony. So I guess which one of these guys is your first and then if you had to rank him after that. Yeah. So I think that these kinds of questions just depend on like if you need a media production because I think like Boyd and Zay Jones sort of like get thrown into a bucket of these guys will at least give you some sort of target share. They're more reliable. They will produce. I think of those two I'd rather have Tyler Boyd than Zay Jones. But you know, Zay Jones is a good pickup I think this week. But if you're just looking for upside, if you just want sort of the combination of the two because you're just going to bench stash these guys. I think Romeo Dobbs is probably the ad. I mean, we saw him this past week without Christian Watson and Sammy Watkins now out for the season. You know, he saw a huge target share in the offense. He was very, very productive.  There's a lot of ambiguity there. You sort of lean into that ambiguity. So I think that if you're just looking for that upside, Dobbs is probably the play. But I like all four of these guys like I think that if you need like a random flex every once in a while or even this week, Zay and Tyler Boyd are fine enough. If you need stashes, Dobbs is great. Tony's great. And you know, if you guys want another stash another random stash on that Giants team with no Sterling Shepherd Wanda Robinson, he could end up once he's back from his knee injury. He could end up playing the slot for them, which is the role that I thought he was going to play entering the season. I definitely didn't think Sterling Shepherd was going to come back and look the way that he did off that Achilles. Now, obviously, unfortunately, Sterling Shepherd tears his ACL. So there's a lot up in the air within that Giants offense. Hopefully Tony can get healthy, but also don't see upon Wanda Robinson who is a really, really underrated prospect. Yeah, you said it exactly, right? I'm generally looking for upside with some of these receivers unless you need someone to fill in now. And that's going to be the rookie who we just saw with eight targets from Aaron Rodgers in this last game and could potentially be the wide receiver one in a Packers offense.  And on that same note talking about Romeo, Ronnie Hotdog what's up Hotdog wants to know would you use your number one waiver wire pick on Mr. Romeo doves? I mean, it depends on the league size and more I think he's like a fringe a fringe player that you could do that with but if like Khalil Herbert's out there, I would rather get Khalil Herbert if Alexander Madison is even out there potentially maybe I'd get Madison but yeah, I mean, I think that he's probably the best wide receiver ad this week. Yeah, I'm with you right here. Larry in here was asking about holding and praying with Tony now that Sterling Shepard went down. It sounds like you don't think Tony is drop able based on your answer to that last question that he's someone you would prefer to stash? Yeah, I don't think so. I mean, when he plays he's been pretty effective. I know that earlier the season he wasn't but I mean, he had one of the best yards per route runs that we've seen of any rookie since 2011 last season in terms of targets per route run he was second among rookie wide receiver since 2011 behind only Tyreek Hill. So he's very good when he's active. The problem is he clearly can't stay healthy. I don't think he's won this coaching staff over yet either. So that's a problem as well. But I do think he's worth a hold because the Stirling Shepherd injury. Yeah, leaning in here wanted to know we got some more rookie questions. People are loving these rookie wide receivers this year. But once I know should I drop Dotson for a larvae? So we'll start with that one. Would you drop Dotson for a larvae right now? I mean, I like a larvae more than Dotson rest of season but I would do my best to try to hold on to both those guys. Yeah, you don't want to drop Dotson right now. Dude's on the field constantly and already producing this first three weeks. But I'm with you a larvae is the preference. If Dotson's your worst player then congratulations on your team. Maybe try to make some trades instead of dropping Dotson. The other one is drop Henderson for Herbert. So Daryl Henderson for Khalil Herbert. Are you making that move? I mean, again, I would want to see who like if there's anyone else in your roster. I'd rather like hold both those guys. I mean, obviously Henderson you know sort of on the downswing with what's going on with cam makers and the usage there cam makers had 12 carries to Henderson's four. But the good news is that Henderson still playing third downs. He out snapped and outproduced cam makers in the first half last week. So I do think that's likely a split backfield for LA. And I think they want cam makers to be a thing but cam makers just keeps telling them I don't want this job after you know calling a goal line all the time and stuff. So I you know, it's tough. I mean like if you if you're purely looking for upside I think Herbert's probably the guy because Henderson probably now needs an injury to acres in order for that upside to really hit. So I can understand it from that perspective but if you need running back help I try to just hold on to both those guys and maybe drop a wide receiver like like if you need running back help I would probably prefer just having Henderson and Herbert over Dotson for instance like in that case I know it's a 10 team league don't think that I'm like sitting here telling people to drop John Dotson because he's awesome but I'm just saying like in this particular instance it kind of makes some sense. Yeah that's that's where I was going to go. If you're running back needy the answer to your question is don't drop Henderson. He's a running back getting touches right now at worse than a committee potentially could be the leadback. We've seen him we've seen him do that so far this season. Rushman wants to know if you're streaming tight ends this week only in Joku Everett or Higby so looking for someone to pick up off the waiver wire this week we've talked a little bit about in Joku and Everett but adding Higby into the mix now. Yeah I mean I think they're all like I don't have a strong preference right now. I think rest of season I prefer Everett so if you want to just go that direction you know you could just pick up Everett but again like we talked about earlier just given like there's not many tight ends that are doing anything right now in fantasy football which is what we see every single season I wouldn't be against just having both in Joku and Everett and just kind of playing matchups each week Higby is fine I just I don't think he's the same kind of kind of sealing as in Joku No I know my friend Jay Jim and Jay on Twitter he is on team never Higby not going to start him he'd be mad at me if I said Higby here but I'm saying in Joku I like what I've seen from him so far and I like the matchup this week going up against the Atlanta Falcons so I'm expecting a decent game from him over there we had another question in here B3B wanted to know thoughts on Travis Fulgum should you be picking up Travis Fulgum in any formats JJ is that a player that you're looking into I would think not I would think not No we haven't seen him even play at all this year right we're not seeing too much from him I don't know what kind of Liger and maybe 18 Liger 18 Liger you put him in there Joseph wants to know how much should we trust rookies Drake London Olava and Garrett Wilson going forward so we've touched on Drake London Chris Olava a little bit already but Garrett Wilson not a great game after his unbelievable game the week before do you have trust and Garrett Wilson going forward for fantasy I mean you know trust is subjective I I think that both London and Olava are now sort of like staples and you're starting lineup Olava more of like a wide receiver three type London more of a wide receiver two type Garrett Wilson maybe more of like a wide receiver three to four type maybe closer to four the one thing that I'm really worried about the jets is number one Zach Wilson's coming back so tendencies might shift a little bit maybe Elijah Moore gets a little bit of love because Elijah Moore's very good at football too but number two the jets right now have a 73 percent pass rate which is by far the highest in the league since 2011 the highest pass rate that we've seen from any team is 67 percent from the 2013 Atlanta Falcons so that's going to drop and when that drops when that pass rate drops you're going to see the target totals for these pass catchers drop as well so target share matters a lot and Garrett Wilson seeing a decent of target share don't get me wrong but it's going to impact Garrett Wilson in some way so I still try like I trust Drake London and Chris a lot of a to be in my starting line up Garrett Wilson not necessarily plug-and-play guy but it depends on so many factors when we use the word trust and when we're talking about like you know like I don't really know what that means in terms of it being like applicable and being able to apply that that information but you know I have Drake London and Chris a lot of a ranked ahead of Garrett Wilson rest of season yeah am I willing to plug Garrett Wilson in my lineups absolutely do I trust that he's going to put up a wide receiver to a better week for me now not at all especially with Zach Wilson coming back like you recognize the range of outcomes that you're that you're potentially going to get whenever you plug a player like that into your line up another question in here from Chris Chris wants to know should I pick up Penny off the waivers for depth so for shot Penny sitting on the waiver wire are you picking them up I mean is it is it crazy that I don't think this is like an obvious yes like I think it's fine and something like was shot Penny yeah like like it depends on like how deep your league is and all this kind of stuff I think he's probably in store for a decent enough game this week but Kenneth Walker is only going to see more and more work as the season goes on for shot Penny last year only saw eight total targets all season long and he's only seen for to start this season so it you know he's just not used as a true workhorse not used as a three down back and in a bad offense it's just I don't want an early down back in a bad offense and so you know it depends on what you need what that's just that goes for a lot of these questions but I don't think that he's just like automatic pick them up kind of guy like I would rather have Khalil Herbert than Rashad Penny rest of season because I think little Herbert has a much much higher ceiling than Rashad Penny has yeah I I think he's worth picking up we've seen his upside right we've seen what he can do if he is the one back in that backfield Kenneth Walker or rookie already had some health issues at the beginning of this year I'm not picking up Rashad Penny to start them and if you're looking for that guy to start next week he's not that dude but if you can afford to put someone on your bench if you just need some some potential lottery tickets at RB Rashad pennies a guy that I'd be willing to pick up we got a question here from Cyclaw wants them to drop Elijah Moore Dotson or Josh Palmer for one of the running backs coming out this week he named four of them Jamal Williams Khalil Herbert Alexander Madison and Brian Robinson so would you be willing to drop one of those wide receivers for one of these running backs I think it's okay to drop Palmer there with Keenan Allen probably coming back it's not like Palmer's been this like must must have kind of player I mean he's been fine but you know Elijah Moore with with Zach Wilson returning hopefully he sees a little bit more work Johan Dotson already doing some work so I think Palmer is the odd man out here yeah it's got to be Palmer for me and then Khalil Herbert would be my preferred pickup out of those if Brian Robinson is sitting on waivers view what's your interest level and picking up Brian Robinson we saw him last Sunday before the game yeah I mean I think he's a decent dart throw right now but you know the chances are chances are like the most probable outcome is that we see a three-way committee then in Washington it could really be a mess so I'm gonna say I'm gonna say that of those guys I would definitely add the other three before Robinson but I do think that Robinson is fine as a stash right now yeah absolutely I think we got time to hit one more in here Swayvie in here was saying my message is coming through we see him Swayvie and Swayvie wants to know Jalen Hertz and James Connor for Russell Wilson and Nick Chubb so another one of those musical chairs trades that we were talking about earlier JJ a quarterback and a running back for a quarterback and a running back but it's quite a downgrade from Jalen Hertz to Russell Wilson in this one based on what we've seen so far you making this trade I have no strong preference here honestly I mean it depends on like what you have like if I'm taking on Jalen Hertz and James Connor I'm hoping that I have a really good running back that I can also sort of flip flop with James Connor like I don't have to necessarily rely on James Connor a whole lot I might lean that way because Jalen Hertz could break fantasy football a little bit this year and then I'll just take my chance on getting a guy off the waiver wire because I don't think you're going to get a quarterback off the waiver wire or you know from Russ that's going to come close to matching Jalen Hertz production this year like you're going to find an edge at Jalen Hertz Lamar Jackson and Josh Allen so I actually think that this is not a terrible terrible deal if you're getting the Hertz side and I can't believe that I'm saying this after years of late round quarterbacking and all that but I do think that it's probably the Hertz side I mean there's there's a lot of factors that would play into that but I might lean that way because I think that Hertz is giving you a positional edge that you just will have a very hard time finding a quarterback this year and as much as I want to say that Nick Chubb is just going to remain this unbelievably dominant best in the league for fantasy besides say one Barclay he's not receiving back and he's not going to be so there's a very real chance his value drops or his production drops as the season goes on JJ I've had an absolute blast answering questions with you here this Tuesday everybody watching thank you so much for tuning in and bringing your questions for us to answer JJ is here every Tuesday either with myself or John Luke Garofalo answering your waiver wire questions make sure to go and give him a follow on Twitter at late round QB we will be back next week at this same time same place doing the same thing until then though we're out of here thanks again everyone


But today we take another step forward to continue letting people know what they can do to prepare, to react and to rebuild from when Mother Earth shakes our city and our state and why we are here for the 10th anniversary of the great Shake Out Drill. If you just remember nothing else, drop, cover and hold on when the earth shakes, you're in a good place. It felt real, it felt scary, you don't know when it's coming. You have to think about what you have in your house, what can fly. I saw all the stuff that was falling off the wall, you know, and I have like knick-knacks and stuff, it's time to minimize. It's at 10.18 a.m. as millions of people across the city, state and country drop, cover and hold on. And other people see you doing this, they are seeing somebody get ready for earthquakes and human beings do what they see other people do it. The world, cause you can't tell everybody everywhere.


Hello everyone, I am Mr. Sachin Rathod working as assistant professor in mechanical engineering department from Wall Street Institute of Technology, Swalapur. Today we are dealing with a reverted gear train. So, in this session the learning outcome is at the end of this session student will be able to calculate the speed ratio of So, the simple diagram is there for the reverted gear train. So, in this diagram, so reverted gear train is nothing but if the input axis and output axis of the shaft on which the gears are mounted are coaxial then it is called as a reverted gear train. So, in this gear, gear number one is a driver, consider gear number one is a driver and gear number four is a driven gear. So, we are getting the motion from one gear is connected to the second gear and on the second gear and the third gears are mounted on the same shaft. So, it is a kind of the compound gear train. So, second gear and third gear are mounted on the same gear, same shaft. So, from the gear number two to shaft and gear number three are rotated with the same speed. So, from the three it is transmitted to the gear number four which is the driven gear. So, we can transmit the motion from first gear to the second, second to the third and third to the fourth. And here this the shaft for the driver or all them it is called as the input shaft is having the coaxial with the output shaft. So, it is called as a reverted gear train. So, this kind of the reverted gear train we have to find out the speed ratio. Already we are knowing what is in my speed ratio. The speed ratio is nothing but speed ratio. The speed ratio is nothing but speed ratio is nothing but it is the ratio of speed of driver divided by speed of driver. So, this is a we can call driver gear divided by speed of driven gear. So, it is called as a speed ratio. So, the speed of the driver gear divided by speed of the driven gear. It is nothing but the speed of the driver is nothing but the one and driven is nothing but the four. It is equal to the N1 by N4. So, it is also kind of the compound reverted gear train. So, we can find out the speed ratio in terms of the number of the teeth is nothing but number of teeth. We can calculate it is equal to product of number of teeth on driven gear divided by product of number of teeth on driver gear. So, if you observe this mechanism. This is the driver gear for this is driven gear and this is a driven gear. So, this is a driver gear for this driven gear. So, one and three are the driver gear for 2 and four driven gear. So, we can call product of number of teeth on the driven gear. So, 2 and four are the driven gears. here. So, we can call T2 into T4 divided by the number of teeth on the driver here. So, 1 and 3 T1 into T3. So, it is nothing but N1 by N4. So, we can formula for finding the speed ratio. And second thing is that, if you observe this mechanism, the distance between the two shafts, these two shafts, suppose we can call the distance between the two shafts is x. So, we are getting, so this is the radius, suppose the gear number 1 is having the p series this much. So, the radius we are getting this much. So, this we can call for the gear number 1, this is r1, gear number 2, it is r2 that is the pitch circle radius, gear number 3, it is r3, gear number 4, it is r4. So, x is the distance between the two shafts is equal to r1 plus r2 is equal to r3 plus r4. So, just we require these two formula. By using these two formula, we can easily find out the speed ratio or any geometry from this reverted gear train. So, you can think about what are the applications of reverted gear train. So, this is the question for you. So, generally if you observe the lathe machine at the back gear box of the lathe machine, we are using the reverted gear train. So, the application main application in case of the back gear of lathe machine. So, consider this numerical. So, we have to solve this numerical. So, in this question, the speed ratio of the reverted gear train as shown in the figure is 12. So, speed ratio is nothing, but we are knowing speed of the driver divided by speed of the driven. So, here the NA and ND is the driver by driven. So, we are getting NA by ND is equal to 12. The module of the pitch of the gear A and B is 3.125. Therefore, MA is equal to MB is equal to 3.125 and C and D that is MC is equal to MD is equal to 2.5. So, calculate the suitable number of the tith on the gears. So, you have to calculate the number of the tith that is the TA, TB, TC, TD that you have to calculate. So, in this question, so the speed ratio they are given us. So, we can simplify this. So, the speed ratio is nothing, but NA by ND and in case of the reverted gear train we are knowing that the speed ratio that is the speed of the driver by speed of the driven is calculated by the product of number of the tith on the driven gear divided by product of number of tith on the driver gear. So, we are getting TB into TD divided by TA into TC. So, by using this formula we can calculate the speed ratio. So, here they are given as a speed ratio is equal to 12. So, we can simplify this we are getting TB by TA is equal to square root of 12 and TD by TC is equal to square root of 12. Because in these two gears the transmitted power should be the same that is why we are getting TB by TA is equal to if we make the product of this we are getting the speed ratio is equal to 12. So, we can easily calculate TB is equal to square root of 12 and TD is equal to square root of 12 TC. So, we are getting the relation between A and B. So, this is the first equation and the second equation. Next expression we are knowing the distance between a two shaft that is a x that given as 200 mm. Therefore, x is equal to RA plus RB is equal to RC plus RD. Therefore, we are getting x is equal to 200, 200 is equal to RA. We are knowing the relation between R and M. Here the R is equal to MT by 2. So, therefore, we are getting MA TA by 2 plus MB TB by 2 is equal to MC TC by 2 plus MD TD by 2. So, we are getting MA TB by 2. So, we are getting TA plus MB TB is equal to 400 and MC TC plus MD TD is equal to 400. Just we have taken a common 1 by 2 it will get 400, 200 into 2 we are getting the 400. So, we are getting the 2 equation. So, here the MA MB are the same 3.125 therefore, we are getting TA plus TB is equal to 400 divided by 3.125 and TC plus TD is equal to 400 divided by here the MC and MD are the same 2.5 it is coming to 2.5. Therefore, TA plus TB is equal to 400 by this TC plus TD is equal to 400 by this. So, we have to solve this. This is the equation number 3 equation number 4. So, by comparing the equation number 1, 2, 3 and 4 we have to calculate the value of TA TB, TC TD. So, for making the calculation we are getting here TA plus TB is equal to. So, for the calculation purpose 400 divided by 3.125 we are getting 128, 128 and TC plus TD is equal to 400 divided by 3.125 and TD is equal to 400 divided by 2.5 we are getting 160. So, this is equation number 5 equation number 6. So, here we are getting TB is equal to square root of 12, square root of 12, 3.464 3.464 TA and TD is equal to 3.464 TA and TD is equal to 3.464 TA and TD is equal to 3.464 TC. Therefore, by putting the value TB is equal to 3.464 we are getting TA plus 3.464 TA is equal to 128. Therefore, TA is equal to 128 divided by 4.35. So, we are getting 28.67. Similarly, TC and TD if you put TD is equal to 3.4 where therefore, we are getting TC plus 3.464 TD is equal to 160. Therefore, TC is equal to 160 divided by 4.464 is equal to 35.85. Therefore, if you consider is equal to 28 TA is equal to and TC is equal to 36. Therefore, if you put this value in this equation number 5 we are getting TB is equal to 128 minus 28 is equal to 100 and TD is equal to 160 minus 36. So, these are our answers. So, we are getting TA is equal to 28, TB is equal to 100, TC is equal to 36 and TD is equal to 30. So, like this we have to solve the equations. So, here are the calculation for this TD and TB calculation. So, these are my references. Thank you.


A candle in the night, a peaceful word to write A reassuring light, a story to be told A legend of the bold, a fire when you The feeling of creation is like an invitation A beautiful sensation, one step after another There's so much to discover, let yourself be bothered Treasure for the eye is hiding in the sky You can see if you try, a surprise for the ear Is ready to appear, if you give out your fear Problems are not serious, the world is more mysterious Let your joy grow among us, one step after another There's so much to discover, don't let yourself be bothered


No, J.K. Dobbins ain't about to leave the Ravens to go there. Right? Ain't no way. Well, maybe it is.  With Justin Herbert, cool. With Hayden Hurst, cool. With Jim Harbaugh, cool. With Gus Edwards, cool. With Bradley Bozeman, cool. It ain't even about none of them, though. With Greg Roman. Is it still cool? Take it before we get into the video. Make sure you subscribe to the channel, turn notifications on, and run them likes up. J.K. Dobbins. I don't really like this one for your big dog. Because J.K. Dobbins, with him visiting with the Chargers, not saying that it's the end all be all that, OK, since he took this visit, then he's absolutely going to sign with the Chargers. But that does increase his chances of with signing with the Chargers, especially his familiarity with some people over there. But this is the same J.K. Dobbins that was frustrated when the Baltimore Ravens, when the specific office of coordinator, Greg Roman, did not give him the ball on the goal line and instead decided to call the QB Sneak with Tyler Huntley. This is the same J.K. Dobbins that had moments, different moments of frustration in that offense under Greg Roman, but to possibly go right back to it. Hey, what? Who knows? Who knows what could possibly happen? But I guess maybe J.K. Dobbins, maybe he didn't got a problem with it like he said he did.  Let bygones be bygones and so on and so on. I done worked under one hardball for a while. I done worked under the other one. I done been with Greg Roman pretty much my entire career. Why not keep it up?  I could really do some things in this offense. I could really kind of show out in this offense. Maybe not come playoff time, but during the regular season, oh, yeah, yeah, we're going to be all right. And maybe J.K. Dobbins was thinking, you know what? Chargers don't be making a playoff anyway, so I'm not even going to be in that situation. But no, I'm just playing though. But with J.K. Dobbins, I just thought it was very, I thought it was funny almost. It's almost comical that he visited with the Chargers. But again, I get this NFL and you're running back and J.K. Dobbins is in a tough, tough, tough situation because he, like we've continued to talk about, all the qualities of an RB one in the NFL, every single quality. He can run, he can cut, he can get you a stiff arm, he can catch, he break tech. He can do everything as an RB one, running back one. But the only thing that's just killed his career has been the injuries. And you feel for him because with J.K. Dobbins, we know what Gus Edwards, we've seen the flashes, we've seen the potential, but Raven's never really said, Gus, you're going to be the guy. We want you to be our true RB one. They never did that. With Justice Hill, they never viewed him as an RB one, but he also, of course, never got the opportunity. So Keaton Mitchell, it was looking like, it was looking like we were getting something. But then he unfortunately got hurt and got lost for the season. And I'm worried for Keaton Mitchell because I just hope that that doesn't have any long-term impact on just his opportunity. I know that it'll obviously have a short-term impact on his opportunity, because we don't even know when he's coming back, but I hope it doesn't have a long-term impact on his opportunity. But anyway, with J.K. Dobbins, which is different from a lot of other running backs besides Mark Ingham, because they signed Mark Ingham to be the guy. But there had been a long stretch, a long period of time for the Baltimore Ravens where they were getting all these different running backs. Like we had Justin Forset, that was clearly our RB one back in those days. Because after Ray Rice, it was just the only true RB ones that the Baltimore Ravens had after Ray Rice was Justin Forset and Mark Ingham. And that's it. Let me know if I'm forgetting somebody, because I might be, but I don't think I am because all the other running backs that the Baltimore Ravens have had have been running back by committee. They've had guys that have started, but who has been the true RB one? Like, oh yeah, that's Ravens guy. Alex Collins, he was kind of RB one kind of, but not like clear cut, like straight up RB one. But he did take the majority of the carries, but it was still running back by committee. And enough teams do running back by committee nowadays, but it was seeming like with JK Dobbins, like the Ravens, they wanted him to be the guy. They wanted him to take over. They wanted him to really take the bulk of the carries for the Baltimore Ravens and really be, seemed like they wanted to go back to that RB one style. And right when they were giving him the keys, right when they said, JK, it's all yours. Take it. He got hurt. And that was when he got hurt in that pre-season game. And yeah, that just messed up everything. And you know what's crazy? You know what's crazy? He's actually, well, he got to sign with it them first. He ain't signed with them as of yet. But if he goes back there, it's like a lot of stuff that he would possibly be going back to is stuff that kind of messed him up. Like we already talked about the situation in the playoff game against the Bengals and he was frustrated after that game. Say, hey, that should have been me. It should have been me getting the carries and whatnot. But in that pre-season game, I'm like 99% sure. It was actually Bradley Boseman that missed the block. And we know mistakes happen. Mistakes happen. We all make mistakes on the job all the time. It's life. It is what it is. It ain't a big deal. But Bradley Boseman would be blocking for him once again. And again, one mistake, just because somebody made one mistake and it ended up costing J.K. Dobbins, his, not his career, but his season. It doesn't mean that that person's a bad player because Bradley Boseman is by no means a bad player at all. But he would be behind him again. So with that being said, I just, I really wonder if this visit is just to sort of put his name back out there. I wonder if it's a hardball doing a favor because that's something to think about too. Because, and John Hardball came out and said it before, but he talked about, like I remember when they had, I think it was Crockett Gilmore. And he said that they do this before, they do this sometimes where they will bring in players for visits just so they can get their names circulating in the league again. Just so they can start to get them some buzz again. So I wonder, I wonder if this is one of those scenarios where Jim Hardball, the brother, the younger brother of John Hardball, the younger brother. That's crazy that Jim Hardball is a younger brother. Anyway, I wonder if this is Jim Hardball doing John Hardball and J.K. Dobbins a little favor. Because, and they already got to say it was two. So imagine that, like imagine, that's why this is a whole thing is so funny. And if this actually happens, if this goes down, it's gonna be like, whoa, like, these are the Los Angeles Ravens. That's what they are, the Los Angeles Ravens. Cause if he signs there, he will be, it'll be J.K. Dobbins and Gus Edwards all over again. Not a bad tandem there. Not a bad tandem at all. Cause both of those boys can run the ball, both of those boys can play. They can play like crazy. But again, with J.K. Dobbins, he just, he gotta stay healthy. So is he gonna really leave the Baltimore Ravens to go to the LA Ravens? Well, it is a real possibility.


Harley, Dana, what is this? This is the desombification of the EasyLink Blue Fruit. Originally, I did this with the CSR chipset. Now we're trying to rebuild this board with an ESP32, which has Bluetooth classic support. I have it wired up here to an Arduino Uno. The DTR line is connected to a capacitor. You can see data being transmitted. Blue means it's connected to Bluetooth. And I just uploaded a NeoPixel sketch. So what's interesting about this code is it does the baud rate selection correctly. So whatever baud rate you open up, the COM port over here on the computer at, it does that. And also it passes through the DTR, DSR, RTS, and CTS lines. So it's actually kind of like a transparent serial port over a Bluetooth classic. So far it's working pretty well. So I'm excited to get this design wrapped up and into the Adafruit shop.


Thanks everybody for making it out today. Today we have Clifford Smith from the University of North Carolina at Greensboro, and today we'll be talking about the non-crossing bond post sets. So take us away. And in case this does make it to the internet, my name is Smite, but that's okay. Oh, I'm so sorry. I was not sure. No, no, no, no. It's, if you're from Ireland, I think you're supposed to say Smith. We just like think ourselves are, I guess my grandfather thought he was fancy. Or something and was going to call himself Smith. So thank you for letting me know. So, yeah, we're going to, I'm going to talk to you today about the non-crossing bond post set. This is joint work with Joshua Hallam, myself and Matt Farmer. It was begun when Josh was a postdoc at Wake Forest University nearby where UNCG and Matt was his master's student now, Matt is a PhD student of mine at UNCG. And Joshua is tenure track at Loyola Maramount University in California. All right, so we're going to start our story with four partially ordered sets, three of them lattices. The first lattice that we're going to talk about is the partition lattice. That's capital Pi N. So you collect all the set partitions of the standard and elements set one through N. And you put a partial order on this by setting Pi 1 to be a less than or equal to Pi 2 if every part in Pi 1 is a subset of part in Pi, a part of Pi 2. So another way to think of this is you obtain Pi 2 from joining parts in Pi 1 until you reach Pi 2. So this partial order turns out to be a lattice if you can form a meat of two partitions. The smallest partition that is less than or equal to Pi 1 and Pi 2 and that turns out to be just a kind of shattering of Pi 1 and Pi 2. You take apart from Pi 1 and apart from Pi 2 and if they're non-empty you take their intersection and these are the parts of the meat. So joining is just the meat of the elements that lie above both Pi 1 and Pi 2. Here we see an example of Pi 4. There's the partition where all the elements are in singleton classes. There's the next level of the lattice where I've taken two elements and joined them together to form a part one two or a part one three. In this example you can see that I've joined one, two and three to make one, two, three. And so we have partitions with two parts. There's two different types, one with three elements and one element set and then there's some other ones with two element subsets and then at the top is the, the maximal element of the lattice, the partition of just one part one, two, three, four. The partition lattice is ranked. The rank is the n minus one number minus the number of parts of Pi and this is because the covering relations are obtained by taking exactly two parts and one partition and joining them. And that gives you the element that covers an element that covers that partition. And so, you know there's an n minus one steps of these joins you're you're at the top of the lattice and all the chains between any two elements all the maximal chains between any two elements are the same length. You just join two parts together at a time until you reach the top element. So here we see the same lattice Pi four with the levels, the ranks so you'll notice that it's exactly n minus n minus one minus the number of components. So we're going to be talking about the characteristic polynomial of these postsets and lattices so there's the Mobius function which is defined to be one for the zero element. And then you define the Mobius function of every other elements so that all the intervals. If you look at any x, and you look at all the wise in the interval between zero and x, the Mobius values for those elements should sum to zero. Another way to put it is that new effects is negative the sum of the Mobius values of all the elements strictly less than x. So if he happens to be a rank post that as many of our postsets will be, you can form the characteristic polynomial, where you sum up over all the elements the Mobius value of the elements, weighted with the power of T, and the power of T rather than being the rank of the element is the rank of the post that minus the rank of the element. So, for example, here is our Pi four, the Mobius value of the zero element is always given one. Here's an interval, the Mobius values have to sum to zero. So this one has to be a negative one. Let's see. This one has to be negative one. This one has to be negative one here is another element. It's above these two so there's an interval. The Mobius values have to sum up to one so this Mobius value is a one. If you look at this one, it's got three elements below it, and this one, and so on this interval, the Mobius values have to sum to zero so you get one minus one minus one minus one and then this one has to be two, and so on. And the characteristic polynomial is just to collect the sum of the Mobius values for each rank. It's run a little bit backwards so T cubed gets the Mobius values at this rank, T squared gets the Mobius values summed at this rank so that's a negative six. So Mobius values summed at this rank, and so that's two plus two plus two plus three, and that gets you 11 and then there's one Mobius value at the top and that's the constant coefficient and that's a Mobius value of negative six. So the non crossing partition lattice is a restriction of the partition lattice where we forbid parts to cross. So that means you can't have members of one part a and a prime interleave with members of another part B and B prime. So you can't have parts that have elements that do this with one another. And so a partition is called a non crossing if no two parts of it's none two of its parts cross. And so we're going to denote that with NCM. And it's a sub lattice of pie and it's closed undertaking meets being non crossing is that is so it's definitely going to be a sub lattice. And it's going to be ranked as it's lattice. Sorry, it's ranked. And here we see the characteristic polynomial of it, and there's not a whole lot of difference between NC for and pie for there's really only one partition that you have to throw out you have to throw out 1324. So the partition with parts 1324 because they interleave all they cross one another, all the other partitions are okay. So that changes Mobius values a little bit, because it's such a small lattice this element of course disappears, and it's Mobius value of one disappears with it so this negative six gets reduced to a negative five. So in distinction, the coefficients and instead of being one minus six 11 minus six there one minus six 10 minus five. The bond lattice of a graph is another lattice it's based on the partitions, the partition lattice, but you only take certain partitions, you take those set partitions. These parts induce connected components in your graph. All right, so it's all the set partitions but you only take parts that induce connected components in your graph. Another way to look at it is as a set of sub graphs of G sub graphs that span and whose components are induced. There's just a one to one correspondence between these. And if you look at it in terms of graphs. One bond is less than or equal to another if the graphs are contained. And so the meat of two bonds is just the intersection of the two graphs. So this is a ranked post set, and you can see its rank function there. Just to remind you here is the characteristic polynomial for pi for, and I'm sorry this should be an NC. This should be right so if it's pie for and if it's if the graph is K for there's no restriction right. Any part. That's a subset of KN is going to induce a connected component because all the edges are there. Sorry, that's the point I wanted to make with that slide. If you want to pick any partition one for is one part to three is another part. Those parts will induce connected components because all the edges are there. The story gets interesting if you have a graph that's not the complete graph for instance this twisted for cycle. The partition one for two three has to be thrown out look at this part one for it doesn't induce a connected sub graph so this thing gets tossed. These get tossed for the same reason one for does not induce a connected sub graph and neither does two three. But that turns out to be all of them. And so some movies values disappear and the movies values adjust to give you a characteristic polynomial that you see here. And here's another example where a lot more things get thrown out. So that's the graph underlying it and very little survives of the original five for. So what we did or what Josh's idea was to kind of complete the picture you've got the partition lattice. You've got the non crossing partition lattice behind it. Then you can introduce graphs and you've got the bond lattice of a graph. How about the non crossing bond. I guess it turns out to not be a lattice but it's the non crossing bond post set so it's the it's the missing fourth corner of the quadrilateral. So, let's start again with a graph on the vertices one through and again the non the members of the non crossing bond post set are those non crossing set partitions. Whose induce connected components and we furthermore require that these components don't cross one another. So if you look at it from the graph perspective you're looking at sub graphs, such that the components of HR induced and don't cross. The non crossing post set is not necessarily the non crossing bond post set is not necessarily a lattice and might not even be ranked but the non crossing bond post set on K for again is the same thing as the non cross the bond post set. Or for restrictions but here's an example where things are different. Here's pie four and the characteristic polynomial. And you'll see that 1324. While it's a element of the bond post set. It's actually a crossing bond, it's components cross one another. Now, we are fixing a cyclic ordering of the vertices so all this crossing is with respect to a cyclic ordering of the vertices so you see now the graphs are are arranged like this so my four is there. And NC four just has that one thing thrown out and the two blow it thrown out and the various function and characteristic polynomial adjust. So, the non crossing bond post set. That's not be a lattice. Here's an example. If you just look at the graph that just consists of the edge one for so that's one part that contains one for and the rest are single tens. And you look at the other bond three five that just consists of the edge three five and all other points are signal tens. These are bonds in the non crossing post set. And one for you join three five should be the unique minimal sub graph that contains both one four and three five. So here is a minimal bond that contains one four and three five, but you can go around the other edge of the cycle and get another minimal bond containing one four and three five. And they're not. They're not comparable. So, the join of these two elements does not exist in the non crossing bond post set. So, early on we were able to characterize when the non crossing bond post that is a lattice, and in some sense the obstruction, the potential obstruction that I just showed you on the last slide is the only obstruction. If you have very simple bonds just an edge E and just an edge F and they cross. If the joint of those two bombs always exists for crossing edges, enough, then NC, the non crossing bond post that is a lattice. And another way to look at that is that for all crossing E and F, there's got to be a join and it turns out the join is the unique minimal induced connected sub graph containing E and F. So this join of E and F the unique minimal component and EF is what we're going to call it. Sorry. Right, so if G has two components that cross you can take an edge from one and an edge from other that will cross and this unique minimal induced connected sub graph on exist there will be no way to get a connected sub graph going from one component to another to both contain E and F. So we're just going to assume that G has no crossing components from now on so that, at least our non crossing bond post that will have a maximal element the graph G itself. We're able to characterize when the non crossing bonds that post that was ranked when it has no crossing components, the non crossing bond post that is going to be ranked. If and only if well unsurprisingly if you take one bond, and it's covered by another. You get from one to the other by joining two components of age. There's a proof here and I think I'll just skip it. Here's an example where the non crossing bond post it is not ranked. So, this is actually a cover relation, H is covered by G, but you can clearly see you did not join two components to get from H to G. And the reason is, if you just try joining components. Just, you just can't do it. Let's say I tried to join two six with three five. Well there's no edges connecting them. So, if I try to make a part out of two six three five it's not a connected component. So I can't do that. If I try to join one and if I tried to join one and three five, I can do that because there's an edge connecting one five and that'll give me a connected component but then that edge is going to cross this component. So you can just go through all the, all the possibilities and this, there's just no way to go directly by joining two components you have to join them all at once. So you have to jump ranks. So, I want to talk about an interesting combinatorial formula for the characteristic polynomial of the bond lattice, because we're going to be trying to repurpose that combinatorial formula to get a combinatorial formula for the characteristic polynomial of the non crossing bond post site. So we're going to start with the combinatorial formula for the bond lattice first. So we're going to put a total order on the edges in G. And we'll say a non broken circuit with respect to this order is a spanning forest such that if he is not an edge in the forest and, well, when you add the edge you'll create a unique cycle, a path in the forest together with. Similarly, if you join an edge that's that's within a component of the forest you'll create a new cycle. What you don't want is you don't want this e to be the minimal element of that cycle with respect to that partially in order. I guess you could say a broken cycle is you take a cycle and you remove its smallest element. So that's what you would consider a broken cycle so a non broken circuit is something that is maximal and doesn't have a broken doesn't have a broken cycle in it. So for instance it's going to be a forest right if it has a cycle in it, then it has a broken cycle in it just remove the smallest weight edge. So let's let NBC K count the number of K edge non broken circuits. So the idea is every time you add an edge. If you create a cycle. There will be an edge less than that on the cycle. So let's do some counts. We're going to put 12 less than 13 less than 24 less than 34 as our total order. How many K edge forests are there, there's just one one forest with no edges. How many forests are there with one edge. There's four of them. And I don't have to worry about creating any broken cycles because there's no cycles to create. And the two edge non broken circuits there's six of them there's the two edge forests. Now we can get into trouble if we have a non broken circuit of three edges. There's one spanning forest of three edges that we have to throw out we have to throw out this one, because here's an edge that I could add, and it's going to be the minimal element on its cycle, because one to just happens to be the minimal and these turn out to be exactly the coefficients of the characteristic polynomial of the partition lattice in this reverse order, where the number of edges and the degree of T add to three. So the relationship that this comes from is the reason this comes about is Whitney's theorem of the characteristic polynomial so the chromatic polynomial of the graph is the polynomial that such that when you plug in T you get the number of property colorings of G. So, if Whitney's theorem was that if G is any graph on and vertices and you have any total ordering on the edge set whatsoever. Then the number of non broken circuits of K edges is invariant with respect to the order you can pick any order and you'll still get the same number of non broken circuits on K edges. And the characteristic polynomial has as its coefficients, these non broken circuit counts in reverse order. Okay, so with a little bit of argument, we can use this to get a non broken circuit formula for the characteristic polynomial of the partition lattice. First of all, let's remember what the characteristic polynomial is you look over all the bond lattice, excuse me, you look at over all bonds. You take the mu of the bond and then the appropriate T polynomial with it. I'm grouping them according to the degree of T that they get. Right here I'm substituting in the actual ranks of the bond lattices it's n minus the number of connected components of G. Moving on to the next page. It's a not hard argument to show that the characteristic polynomial the chromatic polynomial and the characteristic polynomial of the bond post that are related in this way. And then it's just a straight substitution, and you get a formula for the coefficients of the characteristic polynomial of the bond post the bond lattice. So there we go. A formula for the coefficients of the characteristic polynomial of the bond lattice in terms of non broken circuits. And there they are the one minus four or six minus three that we saw from that previous example are on the previous page. For the same graph. If you look at the non crossing bond post that the characteristic polynomial for that is this one T cubed minus four T squared plus five T minus two. What you saw in many examples was the phenomenon that the absolute value of the coefficient for the non crossing bond post that was just less than or equal to the absolute value of the same coefficient for the bond post that characteristic polynomial. I was thinking that maybe since there was a combinatorial count for the coefficients of the bond post that polynomial maybe there would also be a combinatorial count for the coefficients of the characteristic polynomial of the non crossing bond post that. And in fact that's what we found. We slightly modified, or slightly generalized the notion of a non broken circuit to a non crossing non broken circuit. So the non crossing non broken circuits with K edges are the non broken circuits with respect to the total order on the edges that also have non crossing edges that also have no crossing edges. And it turned out in many cases that these were precisely the counts that you needed to get you the polynomial, the coefficients of the characteristic polynomial for the non crossing bond post set. So, for example, six goes down to five look at that T coefficient that corresponds to non crossing that corresponds to broken circuits non broken circuits of two edges. And there are six two edge forests that are non broken circuits. And one of them is crossing and has crossing edges so we got to throw that out. So the six goes down to a five. Exactly what it should be. So for the constant coefficient, the three is supposed to go down to the two. Now what was the three. It was the three edge non broken non broken circuits. So, not including this one. This is non broken. This is not a non broken circuit because of this edge. There's one more that we have to throw out this one because it's got crossing edges in it. So, the three goes down to a two, as it should. And we get the polynomial. So, this is what we found the characteristic polynomial for the non crossing bond post set can in some cases be given as a formula where the coefficients are common editorial counts. of objects specifically non broken circuits that are also non crossing. But only in certain circumstances. Or the ones that we found there's there's examples where we couldn't make this work, but we were able to make this work if the non crossing bond post that was the lattice and had what we called a NC NBC ordering or non crossing non broken set ordering. Or if G was a perfectly labeled graph. I'll say a little bit about what both of those things mean. So in particular, you know, unlike the situation with Whitney's theorem, the number of non broken circuits with K edges did not depend on the total ordering you put on the edges. Unfortunately, when you're looking at non crossing non broken circuits, the counts do depend on the ordering. So, which is part of the reason that you can't have a universal statement here. But if you happen to have an NC NBC ordering. So what is that you look at the joint of E and F any to crossing edges. The minimal connected induced sub graph containing edges in F, if you require that that always have an edge G less than E and F in your ordering. And in fact, you do get these combinatorial counts. And in case that seems obscure. I will. I will try to make it sound a little better in that if you're given a graph we have a very efficient algorithm that will either find the ordering that will make this a true theorem, or will prove that such an ordering can't exist. So at least, you know, it's not like it's a collection of graphs that we have no idea about that satisfy this theorem we know if you're given a graph we can tell you if it'll satisfy this theorem. The other situation in which we have this theorem is if he is perfectly labeled. So that's when you can put an order in on the edges of the, on the vertices of the graph and all the back neighborhoods of a vertex format cleats. So, there's more results in the paper that we wrote that got published in electronic journal combinatorics. And a number of families of graphs and tabulated some properties that the non crossing bond post that had some of the properties we considered where ones that have these joins ones that have this NC NBC ordering ones that are too connected or perfectly labeled. And the non crossing bond post that properties, we examined where the property that it was graded or lattice or had this combinatorial theorem for the coefficients of the characteristic of the characteristic polynomial. We also considered shell ability of the chain complex. So the, as we mentioned, you have this combinatorial interpretation, when you have an NBC ordering. It turns out you'll always have this particular ordering when the graphs are too connected. So, if the graph is too connected, you also have that combinatorial theorem so it's not a non negligible class of graphs for which you have this combinatorial theorem to connected ones will work. There's some deletion contraction results known for the chromatic polynomial and, and hence for the characteristic polynomial of the bond lattice. We were able to produce some deletion contraption results for the non crossing bond post that although they're not, they're not really that pretty, further directions that we were working on at the time that we were looking at this we're trying to guarantee trying to find conditions under which the non crossing bond post that is ranked. It would be nice to know that, at least so that we would know what are the situations in which we can even discuss characteristic polynomials, but a good criteria for this eluded us. One thing we noticed was that, if you have a perfectly labeled graph, the coefficients of the non crossing both on non crossing bond post that appeared to be log concave and every example that we've tried. This is a major recent theorem that the coefficients of the bond lattice are log concave so it might be interesting to at least show that the coefficients of the non crossing bond post that characteristic polynomial are log concave. But we didn't. We didn't do a whole lot on that. It seemed like a hard problem as well. Right. Well, I think that's what I had to say about it. So thanks for your attention. Thank you. Everybody could thank you. Thank you. And are there any questions for Clifford. I don't know if it's a question or thought but this yeah this the result of what is it other proceed to and Oh, right, right. Yeah. And cats is so hard. Yeah, yeah, yeah, exactly. You can tell why we didn't want to spend a lot of time on On the other hand, it's on the other hand, it's perfectly labeled so, you know, maybe, you know, so maybe it's not that hard, but right. Yeah, I mean I was just thinking, you know, there's this closely related conjecture due to, I think the unimodal version was due to Rota and then the log concave version was due to Welsh at the sterling numbers of the second kind are I wonder if you have you looked at those rank sizes. In this case for No, no, we did not actually. That's, that is interesting. Yeah. Well, it's something to add to further. It might be even harder, but. Yeah, yeah, maybe. Yeah. That's always my favorite of the two questions. Yeah, no. Yeah, they're great questions. Yeah, thank you. Any other questions for Clifford. There was stuff in the chat. I don't know, maybe. Just thank you. Okay. Well, thank you. Thank you so much. Thank you. I'd like to invite everyone to thank our speaker again and, you know, thank you for a very wonderful talk. I actually, you know, I wasn't sure if I should ask, because I don't know that this is a well formed question. Oh yeah, sure. Maybe maybe this was a little bit delayed, but there was one slide where you had, you were talking about this condition for the non crossing postsets do not be a lattice or to be a lattice and you know you have this condition. That's right. Yeah. So every, every pair of edges are searching that there has to exist a unique way to find an induced sub graph. Yeah, right. Yeah. Yeah, and they, and they look, they look, they look very interesting actually they you have a crossing edge, you know, you have an edge and then you, the, the MEFs those those joins of, of ENF, they're like a path, there's ENF, and there might be, there might be just one inch. Okay, so there's a path between them, right. There's a path between them and then the very last vertex of the path might connect to one endpoint of E or both. So it's like either like, like it just the path ends and eat, or it's like a little dumbbell at the end, and the same thing with F so it's like a dumbbell graph and. And so you can actually test for this pretty easily looking for such structures is not hard I mean you can, you can write a terribly inefficient algorithm to do this, in other words. There's probably a better way to do it, but yeah. Yeah, I was trying to think of what that might look like and you just, you sort of answered my question. Yeah, no that's exactly what they look like. You know that's why it's. So that's why that one example didn't work. Let's see where was it. Oh there. That's it. So you can see there's, there's kind of like another way to go around. Yeah, I think there's the, there's like a minimal. There's like a minimal in connected sub graph but you can sort of go around the cycle in two ways, and that's that that's the problem. Right. Okay. Thank you. Yeah, sure. So. Thanks again, Cliff. And I think, you know, thanks everyone for coming out for our street seminar this week. And I think, go ahead and end there and I'll see everybody next week. See you. Thanks.